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Find link is a tool written by Edward Betts.searching for N+1 549 found (58784 total)

alternate case: n+1

Fibonacci sequence
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n + 1 − F m + 1 F n = ( − 1 ) n F m − n {\displaystyle F_{m}F_{n+1}-F_{m+1}F_{n}=(-1)^{n}F_{m-n}} F 2 n = F n + 1 2 − F n − 1 2 = F n ( F n + 1 + F nStandard deviation (7,607 words) [view diff] no match in snippet view article find links to article

replacing N − 1 with N − 1.5, yielding: σ ^ = 1 N − 1.5 ∑ i = 1 N ( x i − x ¯ ) 2 , {\displaystyle {\hat {\sigma }}={\sqrt {{\frac {1}{N-1.5}}\sumPi (17,500 words) [view diff] no match in snippet view article find links to article

∑ n = 1 ∞ 1 n k ( a q n − 1 + b q 2 n − 1 + c q 4 n − 1 ) , {\displaystyle \pi ^{k}=\sum _{n=1}^{\infty }{\frac {1}{n^{k}}}\left({\frac {a}{q^{n}-1}}+{\fracTaylor series (8,236 words) [view diff] no match in snippet view article find links to article

x n + 1 n ! = 1 + ∑ n = 1 ∞ x n n ! + ∑ n = 0 ∞ x n + 1 n ! = 1 + ∑ n = 1 ∞ x n n ! + ∑ n = 1 ∞ x n ( n − 1 ) ! = 1 + ∑ n = 1 ∞ ( 1 n ! + 1 ( n − 1 )Variance (10,005 words) [view diff] no match in snippet view article find links to article

the denominator are n, n − 1, n + 1, and n − 1.5: n is the simplest (the variance of the sample), n − 1 eliminates bias, n + 1 minimizes mean squaredBinomial distribution (7,339 words) [view diff] no match in snippet view article find links to article

n + 1 ) p ⌋ if ( n + 1 ) p is 0 or a noninteger , ( n + 1 ) p and ( n + 1 ) p − 1 if ( n + 1 ) p ∈ { 1 , … , n } , n if ( n + 1 ) p = n + 1Normal distribution (22,254 words) [view diff] no match in snippet view article find links to article

distribution with (n − 1) degrees of freedom: s 2 ∼ σ 2 n − 1 ⋅ χ n − 1 2 , σ ^ 2 ∼ σ 2 n ⋅ χ n − 1 2 . {\displaystyle s^{2}\sim {\frac {\sigma ^{2}}{n-1}}\cdot \chiPrime number (14,098 words) [view diff] no match in snippet view article find links to article

factors divides both n and ( n − 1 ) ! {\displaystyle (n-1)!} , and so ( n − 1 ) ! ≡ − 1 ( mod n ) {\displaystyle (n-1)!\equiv -1{\pmod {n}}} is impossibleRound-robin tournament (3,305 words) [view diff] no match in snippet view article find links to article

( n − 1 ) {\displaystyle (n-1)} , then subtract ( n − 1 ) {\displaystyle (n-1)} from the sum. This schedule can also be represented as a (n-1, n-1) tableGolden ratio (12,981 words) [view diff] no match in snippet view article find links to article

n = φ n − 1 + φ n − 3 + ⋯ + φ n − 1 − 2 m + φ n − 2 − 2 m φ n − φ n − 1 = φ n − 2 . {\displaystyle {\begin{aligned}\varphi ^{n}&=\varphi ^{n-1}+\varphiRational number (3,516 words) [view diff] no match in snippet view article find links to article

( m 1 , n 1 ) + ( m 2 , n 2 ) ≡ ( m 1 n 2 + n 1 m 2 , n 1 n 2 ) , {\displaystyle (m_{1},n_{1})+(m_{2},n_{2})\equiv (m_{1}n_{2}+n_{1}m_{2},n_{1}n_{2}),}E (mathematical constant) (6,151 words) [view diff] no match in snippet view article

series e = ∑ n = 0 ∞ 1 n ! = 1 + 1 1 + 1 1 ⋅ 2 + 1 1 ⋅ 2 ⋅ 3 + ⋯ . {\displaystyle e=\sum \limits _{n=0}^{\infty }{\frac {1}{n!}}=1+{\frac {1}{1}}+{\fracPolynomial (8,042 words) [view diff] no match in snippet view article find links to article

polynomial n a n x n − 1 + ( n − 1 ) a n − 1 x n − 2 + ⋯ + 2 a 2 x + a 1 = ∑ i = 1 n i a i x i − 1 . {\displaystyle na_{n}x^{n-1}+(n-1)a_{n-1}x^{n-2}+\dotsList of trigonometric identities (12,067 words) [view diff] no match in snippet view article find links to article

n − 1 ) x ) sin x {\displaystyle {\begin{aligned}\cos((n-1)x+x)&=\cos((n-1)x)\cos x-\sin((n-1)x)\sin x\\\cos((n-1)x-x)&=\cos((n-1)x)\cos x+\sin((n-1)x)\sin5 (12,152 words) [view diff] no match in snippet view article find links to article

form 2 2 n + 1 {\displaystyle 2^{2^{n}}+1} , and more generally the second Sierpiński number of the first kind, n n + 1 {\displaystyle n^{n}+1} . ThereWeighted arithmetic mean (8,987 words) [view diff] no match in snippet view article find links to article

^ pwr ) = 1 n 1 n − 1 ∑ i = 1 n ( y i p i − Y ^ p w r ) 2 = 1 n 1 n − 1 ∑ i = 1 n ( n n y i p i − n n ∑ i = 1 n w i y i ) 2 = 1 n 1 n − 1 ∑ i = 1 n (Gamma function (13,243 words) [view diff] no match in snippet view article find links to article

non-positive integers. For every positive integer n, Γ ( n ) = ( n − 1 ) ! . {\displaystyle \Gamma (n)=(n-1)!\,.} Derived by Daniel Bernoulli, for complex numbersFactorial (8,400 words) [view diff] no match in snippet view article find links to article

factorial: n ! = n × ( n − 1 ) × ( n − 2 ) × ( n − 3 ) × ⋯ × 3 × 2 × 1 = n × ( n − 1 ) ! {\displaystyle {\begin{aligned}n!&=n\times (n-1)\times (n-2)\timesRefractive index (8,486 words) [view diff] no match in snippet view article find links to article

normal incidence reduces to: 44 R 0 = | n 1 − n 2 n 1 + n 2 | 2 . {\displaystyle R_{0}=\left|{\frac {n_{1}-n_{2}}{n_{1}+n_{2}}}\right|^{2}\!.} For common glassTrigonometric functions (8,994 words) [view diff] no match in snippet view article find links to article

tan x = ∑ n = 0 ∞ U 2 n + 1 ( 2 n + 1 ) ! x 2 n + 1 = ∑ n = 1 ∞ ( − 1 ) n − 1 2 2 n ( 2 2 n − 1 ) B 2 n ( 2 n ) ! x 2 n − 1 = x + 1 3 x 3 + 2 15 x 5Summation (4,491 words) [view diff] no match in snippet view article find links to article

progression) ∑ i = 0 n − 1 ( b + i d ) a i = b ∑ i = 0 n − 1 a i + d ∑ i = 0 n − 1 i a i = b ( 1 − a n 1 − a ) + d ( a − n a n + ( n − 1 ) a n + 1 ( 1 − a ) 2Recursion (3,664 words) [view diff] exact match in snippet view article find links to article

{\displaystyle G(0)=a} F ( n + 1 ) = f ( F ( n ) ) {\displaystyle F(n+1)=f(F(n))} G ( n + 1 ) = f ( G ( n ) ) {\displaystyle G(n+1)=f(G(n))} where a is anMedian (7,621 words) [view diff] exact match in snippet view article find links to article

\beta } equal to n + 1 {\displaystyle n+1} allows the last expression to be written as F ( v ) n ( 1 − F ( v ) ) n B ( n + 1 , n + 1 ) d F ( v ) {\displaystyleGini coefficient (10,528 words) [view diff] exact match in snippet view article find links to article

1 n − 1 ( n + 1 − 2 ( ∑ i = 1 n ( n + 1 − i ) y i ∑ i = 1 n y i ) ) {\displaystyle G(S)={\frac {1}{n-1}}\left(n+1-2\left({\frac {\sum _{i=1}^{n}(n+1-i)y_{i}}{\sum2 (3,077 words) [view diff] no match in snippet view article find links to article

In symbols, ∑ n = 0 ∞ 1 2 n = 1 + 1 2 + 1 4 + 1 8 + 1 16 + ⋯ = 2. {\displaystyle \sum _{n=0}^{\infty }{\frac {1}{2^{n}}}=1+{\frac {1}{2}}+{\frac {1}{4}}+{\fracPolygon (4,287 words) [view diff] no match in snippet view article find links to article

y 0 ) , ( x 1 , y 1 ) , … , ( x n − 1 , y n − 1 ) {\displaystyle (x_{0},y_{0}),(x_{1},y_{1}),\ldots ,(x_{n-1},y_{n-1})} in order. For convenience in someFast Fourier transform (7,331 words) [view diff] no match in snippet view article find links to article

Let x 0 , … , x n − 1 {\displaystyle x_{0},\ldots ,x_{n-1}} be complex numbers. The DFT is defined by the formula X k = ∑ m = 0 n − 1 x m e − i 2 π kPearson correlation coefficient (8,207 words) [view diff] no match in snippet view article find links to article

( n − 2 ) Γ ( n − 1 ) ( 1 − ρ 2 ) n − 1 2 ( 1 − r 2 ) n − 4 2 2 π Γ ( n − 1 2 ) ( 1 − ρ r ) n − 3 2 2 F 1 ( 1 2 , 1 2 ; 1 2 ( 2 n − 1 ) ; 1 2 ( ρ r1 (3,551 words) [view diff] no match in snippet view article find links to article

{\displaystyle n} multiplied or divided by 1 remains unchanged ( n × 1 = n / 1 = n {\displaystyle n\times 1=n/1=n} ). This makes it a mathematical unit, and for this10 (3,204 words) [view diff] exact match in snippet view article find links to article

Retrieved 2022-12-08. Sloane, N. J. A. (ed.). "Sequence A108100 ((2*n-1)^2+(2*n+1)^2.)". The On-Line Encyclopedia of Integer Sequences. OEIS FoundationBinomial coefficient (10,483 words) [view diff] no match in snippet view article find links to article

formula ( n k ) = n × ( n − 1 ) × ⋯ × ( n − k + 1 ) k × ( k − 1 ) × ⋯ × 1 , {\displaystyle {\binom {n}{k}}={\frac {n\times (n-1)\times \cdots \times (n-k+1)}{k\timesSine and cosine (6,000 words) [view diff] no match in snippet view article find links to article

complex analysis, one can find that the infinite series ∑ n = − ∞ ∞ ( − 1 ) n z − n = 1 z − 2 z ∑ n = 1 ∞ ( − 1 ) n n 2 − z 2 {\displaystyle \sum _{n=-\inftyRecursion (computer science) (6,890 words) [view diff] no match in snippet view article

hanoi ( n ) = { 1 if n = 1 2 ⋅ hanoi ( n − 1 ) + 1 if n > 1 {\displaystyle \operatorname {hanoi} (n)={\begin{cases}1&{\mbox{if }}n=1\\2\cdot \operatornameExponential distribution (6,543 words) [view diff] exact match in snippet view article find links to article

n + 1 ∣ x 1 , … , x n ) = n n + 1 ( x ¯ ) n ( n x ¯ + x n + 1 ) n + 1 , {\displaystyle p_{\rm {CNML}}(x_{n+1}\mid x_{1},\ldots ,x_{n})={\frac {n^{n+1}\left({\overlineNatural logarithm (6,072 words) [view diff] exact match in snippet view article find links to article

= n + 1 n {\displaystyle x={\tfrac {n+1}{n}}} for positive integers n, we get: ln ( n + 1 n ) = ∑ k = 1 ∞ 1 k ( n + 1 ) k = 1 n + 1 + 1 2 ( n + 1 )Newton's method (7,140 words) [view diff] exact match in snippet view article find links to article

initial guess, x0. The process is repeated as x n + 1 = x n − f ( x n ) f ′ ( x n ) {\displaystyle x_{n+1}=x_{n}-{\frac {f(x_{n})}{f'(x_{n})}}} until aStudent's t-test (6,651 words) [view diff] no match in snippet view article find links to article

Z i 2 n − 1 ∼ χ n − 1 2 n − 1 × ( σ 1 2 m + σ 2 2 n ) {\displaystyle {\frac {\sum _{i=2}^{n}Z_{i}^{2}}{n-1}}\sim {\frac {\chi _{n-1}^{2}}{n-1}}\timesBinomial theorem (6,250 words) [view diff] exact match in snippet view article find links to article

Thus ( x + y ) n + 1 = ∑ k = 0 n + 1 ( n + 1 k ) x n + 1 − k y k , {\displaystyle (x+y)^{n+1}=\sum _{k=0}^{n+1}{\binom {n+1}{k}}x^{n+1-k}y^{k},} which isMarkov chain (13,167 words) [view diff] exact match in snippet view article find links to article

( X t n + 1 = i n + 1 ∣ X t 0 = i 0 , X t 1 = i 1 , … , X t n = i n ) = p i n i n + 1 ( t n + 1 − t n ) {\displaystyle \Pr(X_{t_{n+1}}=i_{n+1}\mid X_{t_{0}}=i_{0}Sequence (6,094 words) [view diff] no match in snippet view article find links to article

2 = 2 nd element a 3 = 3 rd element ⋮ a n − 1 = ( n − 1 ) th element a n = n th element a n + 1 = ( n + 1 ) th element ⋮ {\displaystyleLens (6,308 words) [view diff] no match in snippet view article find links to article

and image is given by n 2 v + n 1 u = n 2 − n 1 R {\displaystyle {\frac {n_{2}}{v}}+{\frac {n_{1}}{u}}={\frac {n_{2}-n_{1}}{R}}} where R is the radiusDiscrete cosine transform (12,046 words) [view diff] no match in snippet view article find links to article

k 2 = ∑ n 1 = 0 N 1 − 1 ( ∑ n 2 = 0 N 2 − 1 x n 1 , n 2 cos [ π N 2 ( n 2 + 1 2 ) k 2 ] ) cos [ π N 1 ( n 1 + 1 2 ) k 1 ] = ∑ n 1 = 0 N 1 − 1 ∑ nFourier transform (21,136 words) [view diff] no match in snippet view article find links to article

\mathbb {Z} ,} whose amplitude and phase are given by the analysis formula: c n = 1 P ∫ − P / 2 P / 2 f ( x ) e − i 2 π n P x d x . {\displaystyle c_{n}={\tfracRiemann zeta function (10,186 words) [view diff] no match in snippet view article find links to article

complex variable defined as ζ ( s ) = ∑ n = 1 ∞ 1 n s = 1 1 s + 1 2 s + 1 3 s + ⋯ {\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}={\fracRefraction (2,570 words) [view diff] no match in snippet view article find links to article

the refractive indices n 2 n 1 {\displaystyle {\frac {n_{2}}{n_{1}}}} of the two media: sin θ 1 sin θ 2 = v 1 v 2 = n 2 n 1 {\displaystyle {\frac {\sinPercentile (2,587 words) [view diff] exact match in snippet view article find links to article

than 1 N + 1 {\displaystyle {\frac {1}{N+1}}} is also excluded and would cause an error.) x = f ( p , N ) = { 1 , p ∈ [ 0 , 1 N + 1 ] p ( N + 1 ) , pM1 motorway (4,242 words) [view diff] no match in snippet view article find links to article

53°06′05″N 1°19′26″W / 53.1013°N 1.3240°W / 53.1013; -1.3240 (M1, Junction 28) Tibshelf 138.3 222.5 Tibshelf services 53°08′19″N 1°19′51″W / 53.1385°N 1Cross product (11,439 words) [view diff] no match in snippet view article find links to article

( 1 , n − 1 ) {\displaystyle (1,n-1)} -tensor, which takes as input n − 1 {\displaystyle n-1} vectors, and gives as output 1 vector – an ( n − 1 ) {\displaystyleMoving average (2,876 words) [view diff] exact match in snippet view article find links to article

1 {\displaystyle {\textit {CA}}_{n+1}} results in CA n + 1 = x n + 1 + n ⋅ CA n n + 1 = x n + 1 + ( n + 1 − 1 ) ⋅ CA n n + 1 = ( n + 1 ) ⋅ CA n + x nTriangular number (3,159 words) [view diff] exact match in snippet view article find links to article

= n ( n + 1 ) 2 = n 2 + n 2 = ( n + 1 2 ) , {\displaystyle T_{n}=\sum _{k=1}^{n}k=1+2+3+\dotsb +n={\frac {n(n+1)}{2}}={\frac {n^{2}+n}{2}}={n+1 \chooseDirac delta function (13,810 words) [view diff] no match in snippet view article find links to article

decomposition is: δ ( x ) = { ( n − 1 ) ! ( 2 π i ) n ∫ S n − 1 ( x ⋅ ξ ) − n d ω ξ n even 1 2 ( 2 π i ) n − 1 ∫ S n − 1 δ ( n − 1 ) ( x ⋅ ξ ) d ω ξ n oddMoving average (2,876 words) [view diff] exact match in snippet view article find links to article

1 {\displaystyle {\textit {CA}}_{n+1}} results in CA n + 1 = x n + 1 + n ⋅ CA n n + 1 = x n + 1 + ( n + 1 − 1 ) ⋅ CA n n + 1 = ( n + 1 ) ⋅ CA n + x nFinance (5,997 words) [view diff] no match in snippet view article find links to article

∑ t = 1 n F C F F t ( 1 + W A C C t ) t + [ F C F F n + 1 ( W A C C n + 1 − g n + 1 ) ] ( 1 + W A C C n ) n {\displaystyle \sum _{t=1}^{n}{\frac3 (3,091 words) [view diff] no match in snippet view article find links to article

known number n {\displaystyle n} such that n {\displaystyle n} ! − 1 and n {\displaystyle n} ! + 1 are prime, as well as the only prime number p {\displaystyleGeometric series (11,779 words) [view diff] no match in snippet view article find links to article

∏ n = 1 ∞ ( 1 − w 2 n ) ( 1 + w 2 n − 1 ) 2 {\displaystyle \vartheta _{00}(w)=\prod _{n=1}^{\infty }(1-w^{2n})(1+w^{2n-1})^{2}} ψ H ( w ) = ∏ n = 1 ∞Ideal gas law (4,482 words) [view diff] no match in snippet view article find links to article

5 N T = C 5 or N 1 T 1 = N 2 T 2 {\displaystyle NT=C_{5}\quad {\text{or}}\quad N_{1}T_{1}=N_{2}T_{2}} Equation 6 P N = C 6 or P 1 N 1 = P 2 N 2 {\displaystyleContinuous uniform distribution (4,150 words) [view diff] exact match in snippet view article find links to article

b − a = b n + 1 − a n + 1 ( n + 1 ) ( b − a ) . {\displaystyle E(X^{n})=\int _{a}^{b}x^{n}{\frac {dx}{b-a}}={\frac {b^{n+1}-a^{n+1}}{(n+1)(b-a)}}.} TheSeries (mathematics) (9,676 words) [view diff] exact match in snippet view article

alternating series ∑ n = 1 ∞ ( − 1 ) n + 1 n = 1 − 1 2 + 1 3 − 1 4 + 1 5 − ⋯ , {\displaystyle \sum \limits _{n=1}^{\infty }{(-1)^{n+1} \over n}=1-{1 \over 2}+{1Uncertainty principle (19,094 words) [view diff] exact match in snippet view article find links to article

n + 1 | n + 1 ⟩ {\displaystyle a^{\dagger }|n\rangle ={\sqrt {n+1}}|n+1\rangle } a | n ⟩ = n | n − 1 ⟩ , {\displaystyle a|n\rangle ={\sqrt {n}}|n-1\rangle1000 (number) (25,170 words) [view diff] no match in snippet view article

3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A080040 (2*a(n-1) + 2*a(n-2) for n >Determinant (14,070 words) [view diff] no match in snippet view article find links to article

M_{i,j}} is defined to be the determinant of the ( n − 1 ) × ( n − 1 ) {\displaystyle (n-1)\times (n-1)} -matrix that results from A {\displaystyle A} byEntropy (information theory) (9,695 words) [view diff] no match in snippet view article

increase with the number of outcomes i.e. H n ( 1 n , … , 1 n ⏟ n ) < H n + 1 ( 1 n + 1 , … , 1 n + 1 ⏟ n + 1 ) . {\displaystyle \mathrm {H} _{n}{\biggSimplex (7,560 words) [view diff] exact match in snippet view article find links to article

x / n + 1 {\displaystyle dx/{\sqrt {n+1}}} of the increment, ( d x / ( n + 1 ) , … , d x / ( n + 1 ) ) {\displaystyle (dx/(n+1),\ldots ,dx/(n+1))} ,Quicksort (9,995 words) [view diff] no match in snippet view article find links to article

n − 1 ) C ( n − 1 ) = n ( n − 1 ) − ( n − 1 ) ( n − 2 ) + 2 C ( n − 1 ) {\displaystyle nC(n)-(n-1)C(n-1)=n(n-1)-(n-1)(n-2)+2C(n-1)} n C ( n ) = ( n +Recurrence relation (4,158 words) [view diff] no match in snippet view article find links to article

= ( n − 1 k − 1 ) + ( n − 1 k ) , {\displaystyle {\binom {n}{k}}={\binom {n-1}{k-1}}+{\binom {n-1}{k}},} with the base cases ( n 0 ) = ( n n ) = 1 {\displaystyleMathematical induction (6,840 words) [view diff] exact match in snippet view article find links to article

among all n + 1 {\displaystyle n+1} horses. The base case n = 1 {\displaystyle n=1} is trivial, and the induction step is correct in all cases n > 1 {\displaystyleMann–Whitney U test (5,778 words) [view diff] no match in snippet view article find links to article

of: U 1 = n 1 n 2 + n 1 ( n 1 + 1 ) 2 − R 1 , U 2 = n 1 n 2 + n 2 ( n 2 + 1 ) 2 − R 2 {\displaystyle U_{1}=n_{1}n_{2}+{\tfrac {n_{1}(n_{1}+1)}{2}}-R_{1}Hash function (7,840 words) [view diff] no match in snippet view article find links to article

key K = ( k n − 1 . . . k 1 k 0 ) 2 {\displaystyle K=(k_{n-1}...k_{1}k_{0})_{2}} can be regarded as the polynomial K ( x ) = k n − 1 x n − 1 + . . . + kAtomic orbital (10,600 words) [view diff] no match in snippet view article find links to article

n , 1 , + 1 real = R n , 1 3 4 π ⋅ x r ψ n , 1 , − 1 real = R n , 1 3 4 π ⋅ y r {\displaystyle {\begin{aligned}\psi _{n,1,+1}^{\text{real}}=&R_{n,1}{\sqrtFourier series (10,850 words) [view diff] exact match in snippet view article find links to article

) = 2 ∑ n = 1 ∞ ( − 1 ) n + 1 n sin ( n x ) sinh ( n y ) sinh ( n π ) . {\displaystyle T(x,y)=2\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}\sin(nx){\sinh(ny)Expected value (7,633 words) [view diff] exact match in snippet view article find links to article

= X 1 {\displaystyle Y_{0}=X_{1}} and Y n = X n + 1 − X n {\displaystyle Y_{n}=X_{n+1}-X_{n}} for n ≥ 1 , {\displaystyle n\geq 1,} where X n {\displaystyleFloor and ceiling functions (5,868 words) [view diff] no match in snippet view article find links to article

= 1 n − 1 ⌈ k m n ⌉ = 1 2 ( m + 1 ) ( n − 1 ) , {\displaystyle \sum _{k=1}^{n-1}\left\lceil {\frac {km}{n}}\right\rceil ={\tfrac {1}{2}}(m+1)(n-1),} ∑Mandelbrot set (7,513 words) [view diff] exact match in snippet view article find links to article

those of the real logistic family, x n + 1 = r x n ( 1 − x n ) , r ∈ [ 1 , 4 ] . {\displaystyle x_{n+1}=rx_{n}(1-x_{n}),\quad r\in [1,4].} The correspondenceBig O notation (8,017 words) [view diff] no match in snippet view article find links to article

following are true for n → ∞ {\displaystyle n\to \infty } : ( n + 1 ) 2 = n 2 + O ( n ) , ( n + O ( n 1 / 2 ) ) ⋅ ( n + O ( log n ) ) 2 = n 3 + O ( n 5 / 2Exponentiation (13,585 words) [view diff] no match in snippet view article find links to article

sides by b n {\displaystyle b^{n}} gives b 0 = b n / b n = 1 {\displaystyle b^{0}=b^{n}/b^{n}=1} . The fact that b 1 = b {\displaystyle b^{1}=b} can similarlyDiscrete Fourier transform (10,475 words) [view diff] no match in snippet view article find links to article

⋅ 1 ⋯ ω N 0 ⋅ ( N − 1 ) ω N 1 ⋅ 0 ω N 1 ⋅ 1 ⋯ ω N 1 ⋅ ( N − 1 ) ⋮ ⋮ ⋱ ⋮ ω N ( N − 1 ) ⋅ 0 ω N ( N − 1 ) ⋅ 1 ⋯ ω N ( N − 1 ) ⋅ ( N − 1 ) ] {\displaystyleLp space (12,891 words) [view diff] exact match in snippet view article find links to article

t n + 1 = 0 {\displaystyle t_{n+1}=0} and ( t n + 1 < f ≤ t n ) = ∅ {\displaystyle (t_{n+1}<f\leq t_{n})=\varnothing } so that f n = 1 r n f 1 ( t n +Kurtosis (5,201 words) [view diff] no match in snippet view article find links to article

n + 1 ) m 4 − 3 ( n − 1 ) m 2 2 ] ( n − 1 ) ( n − 2 ) ( n − 3 ) ( n − 1 ) 2 n 2 m 2 2 = n − 1 ( n − 2 ) ( n − 3 ) [ ( n + 1 ) m 4 m 2 2 − 3 ( n − 1 )Binary search algorithm (9,602 words) [view diff] no match in snippet view article find links to article

T(n)} : T ( n ) = 1 + ( n + 1 ) ⌊ log 2 ( n + 1 ) ⌋ − 2 ⌊ log 2 ( n + 1 ) ⌋ + 1 + 2 n = ⌊ log 2 ( n ) ⌋ + 1 − ( 2 ⌊ log 2 ( n ) ⌋ + 1 − ⌊ log 2Invertible matrix (7,017 words) [view diff] no match in snippet view article find links to article

the linear Diophantine equation s + ∑ l = 1 n − 1 l k l = n − 1. {\displaystyle s+\sum _{l=1}^{n-1}lk_{l}=n-1.} The formula can be rewritten in terms ofHyperbolic functions (4,822 words) [view diff] no match in snippet view article find links to article

n = 1 ∞ 2 2 n ( 2 2 n − 1 ) B 2 n x 2 n − 1 ( 2 n ) ! , | x | < π 2 coth x = x − 1 + x 3 − x 3 45 + 2 x 5 945 + ⋯ = ∑ n = 0 ∞ 2 2 n B 2 n x 2 n − 120 (number) (2,562 words) [view diff] exact match in snippet view article

form ( 2 P n P n + 1 , P n + 1 2 − P n 2 , P n + 1 2 + P n 2 = P 2 n + 1 ) {\displaystyle \left(2P_{n}P_{n+1},P_{n+1}^{2}-P_{n}^{2},P_{n+1}^{2}+P_{n}^{2}=P_{2n+1}\right)}N-sphere (5,824 words) [view diff] case mismatch in snippet view article find links to article

s_{n-2}s_{n-1})(s_{n-1}|J_{n-1}|)\\&\qquad {}+(-1)^{n+n}(rs_{1}\dotsm s_{n-2}c_{n-1})(c_{n-1}|J_{n-1}|)\\&=(rs_{1}\dotsm s_{n-2}|J_{n-1}|(s_{n-1}^{2}+c_{n-1Diffusion (8,402 words) [view diff] no match in snippet view article find links to article

expression: C 1 − C 2 = − n 2 n 1 n 2 D 12 { ∇ ( n 1 n ) + n 1 n 2 ( m 2 − m 1 ) P n ( m 1 n 1 + m 2 n 2 ) ∇ P − m 1 n 1 m 2 n 2 P ( m 1 n 1 + m 2 n 2 ) ( F 1 −Bézier curve (6,966 words) [view diff] no match in snippet view article find links to article

n + 1 b i , n + 1 ( t ) P i + ∑ i = 0 n i + 1 n + 1 b i + 1 , n + 1 ( t ) P i = ∑ i = 0 n + 1 ( i n + 1 P i − 1 + n + 1 − i n + 1 P i ) b i , n + 1 (Central limit theorem (8,929 words) [view diff] no match in snippet view article find links to article

since the asymptotic normality fails for X n = Y n − Y n − 1 {\textstyle X_{n}=Y_{n}-Y_{n-1}} where Y n {\textstyle Y_{n}} are another stationary sequenceEffect size (8,124 words) [view diff] no match in snippet view article find links to article

n 1 + n 2 n 1 n 2 + ( g ∗ ) 2 2 ( n 1 + n 2 ) . {\displaystyle {\hat {\sigma }}^{2}(g^{*})={\frac {n_{1}+n_{2}}{n_{1}n_{2}}}+{\frac {(g^{*})^{2}}{2(n_{1}+n_{2})}}Bessel function (10,584 words) [view diff] exact match in snippet view article find links to article

− n − 1 ( x ) y n ( x ) = ( − 1 ) n + 1 j − n − 1 ( x ) {\displaystyle {\begin{aligned}j_{n}(x)&=(-1)^{n}y_{-n-1}(x)\\y_{n}(x)&=(-1)^{n+1}j_{-n-1}(x)\end{aligned}}}Histogram (3,135 words) [view diff] no match in snippet view article find links to article

cross validation: a r g m i n h J ^ ( h ) = a r g m i n h ( 2 ( n − 1 ) h − n + 1 n 2 ( n − 1 ) h ∑ k N k 2 ) {\displaystyle {\underset {h}{\operatornameNorth Sea (11,989 words) [view diff] no match in snippet view article find links to article

Walde (Walde Lighthouse, in France, 50°59'37"N, 1°54'53"E) and Leathercoat Point (England, 51°10'01.4"N 1°24'07.8"). northeast of Dover. On the NorthwestSnell's law (3,817 words) [view diff] no match in snippet view article find links to article

is equal to the ratio of the refractive indices ( n 2 n 1 {\displaystyle {\tfrac {n_{2}}{n_{1}}}} ) of the two media, or equivalently, to the ratio ofOxfordshire (2,326 words) [view diff] no match in snippet view article find links to article

and the D’Arcy Dalton Way. Northernmost point: 52°10′6.58″N 1°19′54.92″W / 52.1684944°N 1.3319222°W / 52.1684944; -1.3319222, near Claydon Hay FarmBirthday problem (6,897 words) [view diff] no match in snippet view article find links to article

p ¯ ( n ) ≈ 1 ⋅ e − 1 / 365 ⋅ e − 2 / 365 ⋯ e − ( n − 1 ) / 365 = e − ( 1 + 2 + ⋯ + ( n − 1 ) ) / 365 = e − n ( n − 1 ) / 2 365 = e − n ( n − 1 ) 730Support vector machine (8,802 words) [view diff] exact match in snippet view article find links to article

y n + 1 {\displaystyle y_{n+1}} given X n + 1 {\displaystyle X_{n+1}} . To do so one forms a hypothesis, f {\displaystyle f} , such that f ( X n + 1 )Graham's number (3,272 words) [view diff] no match in snippet view article find links to article

3 , n = 1 3 ↑ g n − 1 3 , n ≥ 2 , n ∈ N {\displaystyle g_{n}=\left\{{\begin{matrix}3\uparrow \uparrow \uparrow \uparrow 3,&n=1\\3\uparrow ^{g_{n-1}}3,&n\geqEuclidean vector (9,030 words) [view diff] no match in snippet view article find links to article

\end{aligned}}} Distributing the dot-multiplication gives u = p e 1 ⋅ n 1 + q e 2 ⋅ n 1 + r e 3 ⋅ n 1 , v = p e 1 ⋅ n 2 + q e 2 ⋅ n 2 + r e 3 ⋅ n 2 , w = p e 1 ⋅Spiral (4,431 words) [view diff] no match in snippet view article find links to article

gets A = 1 2 ∫ φ 1 φ 2 a 2 φ 2 n d φ = a 2 2 ( 2 n + 1 ) ( φ 2 2 n + 1 − φ 1 2 n + 1 ) , if n ≠ − 1 2 , {\displaystyle A={\frac {1}{2}}\int _{\varphiAntiderivative (3,294 words) [view diff] exact match in snippet view article find links to article

x n + 1 n + 1 + c {\displaystyle F(x)={\tfrac {x^{n+1}}{n+1}}+c} if n ≠ −1, and F ( x ) = log | x | + c {\displaystyle F(x)=\log |x|+c} if n = −1. InPower series (3,366 words) [view diff] no match in snippet view article find links to article

n = 1 ∞ a n n ( x − c ) n − 1 = ∑ n = 0 ∞ a n + 1 ( n + 1 ) ( x − c ) n , ∫ f ( x ) d x = ∑ n = 0 ∞ a n ( x − c ) n + 1 n + 1 + k = ∑ n = 1 ∞ a n − 1Logistic regression (20,426 words) [view diff] exact match in snippet view article find links to article

explanatory variables (including x0) and N + 1 {\displaystyle N+1} categories, we will need N + 1 {\displaystyle N+1} separate probabilities, one for eachLogistic regression (20,426 words) [view diff] exact match in snippet view article find links to article

explanatory variables (including x0) and N + 1 {\displaystyle N+1} categories, we will need N + 1 {\displaystyle N+1} separate probabilities, one for eachTuple (2,178 words) [view diff] no match in snippet view article find links to article

pairs; indeed, a n-tuple can be identified with the ordered pair of its (n − 1) first elements and its nth element. Tuples are usually written by listingChi-squared distribution (6,364 words) [view diff] no match in snippet view article find links to article

logarithm of the characteristic function: κ n = 2 n − 1 ( n − 1 ) ! k {\displaystyle \kappa _{n}=2^{n-1}(n-1)!\,k} The chi-squared distribution exhibits strongPower series (3,366 words) [view diff] no match in snippet view article find links to article

n = 1 ∞ a n n ( x − c ) n − 1 = ∑ n = 0 ∞ a n + 1 ( n + 1 ) ( x − c ) n , ∫ f ( x ) d x = ∑ n = 0 ∞ a n ( x − c ) n + 1 n + 1 + k = ∑ n = 1 ∞ a n − 1Continued fraction (9,525 words) [view diff] no match in snippet view article find links to article

h n − 1 − k n − 1 h n = ( − 1 ) n , {\displaystyle k_{n}\ h_{n-1}-k_{n-1}\ h_{n}=(-1)^{n}\ ,} or equivalently h n k n − h n − 1 k n − 1 =Limit (mathematics) (5,698 words) [view diff] no match in snippet view article

the Basel problem, where a n = 1 / n 2 {\displaystyle a_{n}=1/n^{2}} . Then ∑ n = 1 ∞ 1 n 2 = π 2 6 . {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\fracCompressor (7,010 words) [view diff] no match in snippet view article find links to article

− T 1 ) n − 1 = n R T 1 n − 1 [ ( P 2 P 1 ) ( n − 1 ) / n − 1 ] {\displaystyle W_{comp,in}={\frac {nR(T_{2}-T_{1})}{n-1}}={\frac {nRT_{1}}{n-1}}\left[\left({\fracStirling's approximation (4,688 words) [view diff] no match in snippet view article find links to article

∑ n = 1 N − 1 B 2 n 2 n ( 2 n − 1 ) z 2 n − 1 , {\displaystyle \ln \Gamma (z)\sim z\ln z-z+{\tfrac {1}{2}}\ln {\frac {2\pi }{z}}+\sum _{n=1}^{N-1}{\fracIsambard Kingdom Brunel (7,788 words) [view diff] no match in snippet view article find links to article

-2.399764 (Charfield station) ST7233192265 Charlbury 51°52′19″N 1°29′24″W / 51.872°N 1.49°W / 51.872; -1.49 (Charlbury station) SP3510819441 ChippenhamFactorization (7,734 words) [view diff] no match in snippet view article find links to article

E n − 1 + E n − 2 F + E n − 3 F 2 + ⋯ + E F n − 2 + F n − 1 ) {\displaystyle E^{n}-F^{n}=(E-F)(E^{n-1}+E^{n-2}F+E^{n-3}F^{2}+\cdots +EF^{n-2}+F^{n-1})}Arithmetic progression (2,003 words) [view diff] no match in snippet view article find links to article

n {\displaystyle a_{n}} ) is given by: a n = a 1 + ( n − 1 ) d {\displaystyle a_{n}=a_{1}+(n-1)d} A finite portion of an arithmetic progression is calledDecimal (5,010 words) [view diff] no match in snippet view article find links to article

[x]n−1. This way one has [x]n = [x]0.d1d2...dn−1dn, and the difference of [x]n−1 and [x]n amounts to | [ x ] n − [ x ] n − 1 | = d n ⋅ 10 − n < 10 − n +Mean squared error (3,827 words) [view diff] no match in snippet view article find links to article

1 2 − σ 2 ) 2 ] = E [ ( n − 1 ) 2 a 2 S n − 1 4 − 2 ( n − 1 a S n − 1 2 ) σ 2 + σ 4 ] = ( n − 1 ) 2 a 2 E [ S n − 1 4 ] − 2 ( n − 1 a ) E [ S nDiophantine equation (4,788 words) [view diff] no match in snippet view article find links to article

x n − 1 = r n − 1 + t n − 1 ( x 1 − r 1 ) . {\displaystyle {\begin{aligned}x_{2}&=r_{2}+t_{2}(x_{1}-r_{1})\\&\;\;\vdots \\x_{n-1}&=r_{n-1}+t_{n-1}(x_{1}-r_{1})Euler's totient function (6,440 words) [view diff] no match in snippet view article find links to article

gcd(9, 9) = 9. Therefore, φ(9) = 6. As another example, φ(1) = 1 since for n = 1 the only integer in the range from 1 to n is 1 itself, and gcd(1, 1) = 1Wilcoxon signed-rank test (7,161 words) [view diff] exact match in snippet view article find links to article

+ n = n ( n + 1 ) / 2 {\displaystyle 1+2+\dots +n=n(n+1)/2} , these three statistics are related by: T + = n ( n + 1 ) 2 − T − = n ( n + 1 ) 4 + T 2Queueing theory (4,854 words) [view diff] exact match in snippet view article find links to article

_{1}+\mu _{1})P_{1}} λ n − 1 P n − 1 + μ n + 1 P n + 1 = ( λ n + μ n ) P n {\displaystyle \lambda _{n-1}P_{n-1}+\mu _{n+1}P_{n+1}=(\lambda _{n}+\mu _{n})P_{n}}Natural number (5,462 words) [view diff] no match in snippet view article find links to article

3 = 2 ∪ {2} = {0, 1, 2} = {{ }, {{ }}, {{ }, {{ }}}}, n = n−1 ∪ {n−1} = {0, 1, ..., n−1} = {{ }, {{ }}, ..., {{ }, {{ }}, ...}}, etc. It can be checkedPerfect number (4,913 words) [view diff] no match in snippet view article find links to article

perfect number is of the form 2 n − 1 ( 2 n − 1 ) {\displaystyle 2^{n-1}(2^{n}-1)} where 2 n − 1 {\displaystyle 2^{n}-1} is prime. He seems to be unawareMultivariate normal distribution (9,474 words) [view diff] no match in snippet view article find links to article

1 n − 1 ∑ i = 1 n ( x i − x ¯ ) ( x i − x ¯ ) T = 1 n − 1 [ X ′ ( I − 1 n ⋅ J ) X ] {\displaystyle {\widehat {\boldsymbol {\Sigma }}}={\frac {1}{n-1}}\sumM62 motorway (4,828 words) [view diff] no match in snippet view article find links to article

of M62) 53°39′36″N 1°51′41″W / 53.6601°N 1.8613°W / 53.6601; -1.8613 (Junction 23 of M62) 53°40′18″N 1°50′00″W / 53.6717°N 1.8332°W / 53.6717;Tree (graph theory) (3,282 words) [view diff] no match in snippet view article

also equivalent to any of the following conditions: G is connected and has n − 1 edges. G is connected, and every subgraph of G includes at least one vertexQuantum logic gate (10,122 words) [view diff] no match in snippet view article find links to article

n − 1 ( H | 0 ⟩ ) = 1 2 n [ 1 1 ⋮ 1 ] = 1 2 n ( | 0 ⟩ + | 1 ⟩ + ⋯ + | 2 n − 1 ⟩ ) = 1 2 n ∑ i = 0 2 n − 1 | i ⟩ {\displaystyle \bigotimes _{0}^{n-1}(H|0\rangleRotation matrix (15,019 words) [view diff] no match in snippet view article find links to article

matrix will have (n − 1) + (n − 2) + ⋯ + 2 + 1, or ∑ k = 1 n − 1 k = 1 2 n ( n − 1 ) {\displaystyle \sum _{k=1}^{n-1}k={\frac {1}{2}}n(n-1)} entries belowDynamic programming (9,215 words) [view diff] no match in snippet view article find links to article

obtained in state y at the last time n. The values Vi at earlier times i = n −1, n − 2, ..., 2, 1 can be found by working backwards, using a recursive relationshipStainless steel (10,037 words) [view diff] no match in snippet view article find links to article

+ ∑ n = 1 N OC ( 1 + i ) n + ∑ n = 1 N LP ( 1 + i ) n + ∑ n = 1 N RC ( 1 + i ) n {\displaystyle {\text{LCC}}={\text{AC}}+{\text{IC}}+\sum _{n=1}^{N}{\fracHarmonic series (mathematics) (6,143 words) [view diff] no match in snippet view article

positive unit fractions: ∑ n = 1 ∞ 1 n = 1 + 1 2 + 1 3 + 1 4 + 1 5 + ⋯ . {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n}}=1+{\frac {1}{2}}+{\frac {1}{3}}+{\fracAvogadro constant (2,229 words) [view diff] no match in snippet view article find links to article

Avogadro constant is the reciprocal of amount of substance, N − 1 {\displaystyle {\mathsf {N}}^{-1}} . The Avogadro number, sometimes denoted N0, is the numericN1 (rocket) (7,881 words) [view diff] no match in snippet view article

N-1: For the Moon and Mars A Guide to the Soviet Superbooster. ARA Press; First edition. ISBN 9780989991407. Wikimedia Commons has media related to N-1Bias of an estimator (5,350 words) [view diff] no match in snippet view article find links to article

[nS^{2}]=(n-1)\sigma ^{2}{\text{ and }}\operatorname {Var} (nS^{2})=2(n-1)\sigma ^{4}.} and so MSE = ( c ( n − 1 ) − 1 ) 2 σ 4 + 2 c 2 ( n − 1 ) σ 4 {\displaystyleMatrix multiplication (6,025 words) [view diff] no match in snippet view article find links to article

C = ( a 11 b 11 + ⋯ + a 1 n b n 1 a 11 b 12 + ⋯ + a 1 n b n 2 ⋯ a 11 b 1 p + ⋯ + a 1 n b n p a 21 b 11 + ⋯ + a 2 n b n 1 a 21 b 12 + ⋯ + a 2 n b n 2 ⋯M6 motorway (3,736 words) [view diff] no match in snippet view article find links to article

extension: 2008 Major junctions South end Catthorpe 52°24′01″N 1°10′31″W / 52.4004°N 1.1752°W / 52.4004; -1.1752 (M6, southern terminus) Major intersectionsReal number (7,562 words) [view diff] no match in snippet view article find links to article

that D n − 1 + a n / 10 n ≤ a , {\displaystyle D_{n-1}+a_{n}/10^{n}\leq a,} and one sets D n = D n − 1 + a n / 10 n . {\displaystyle D_{n}=D_{n-1}+a_{n}/10^{n}Logarithm (11,492 words) [view diff] exact match in snippet view article find links to article

integers. Putting z = n + 1 n {\displaystyle \textstyle z={\frac {n+1}{n}}} in the above series, it follows that: ln ( n + 1 ) = ln ( n ) + 2 ∑ kGeometric mean (4,878 words) [view diff] exact match in snippet view article find links to article

are defined: a n + 1 = a n + h n 2 , a 0 = x {\displaystyle a_{n+1}={\frac {a_{n}+h_{n}}{2}},\quad a_{0}=x} and h n + 1 = 2 1 a n + 1 h n , h 0 = y {\displaystyleCollatz conjecture (7,014 words) [view diff] no match in snippet view article find links to article

the function f as follows: f ( n ) = { n / 2 if n ≡ 0 ( mod 2 ) , 3 n + 1 if n ≡ 1 ( mod 2 ) . {\displaystyle f(n)={\begin{cases}n/2&{\text{if }}n\equivLaplace transform (8,154 words) [view diff] no match in snippet view article find links to article

− s n − 1 f ( 0 − ) − ⋯ − f ( n − 1 ) ( 0 − ) , {\displaystyle {\mathcal {L}}\left\{f^{(n)}(t)\right\}=s^{n}\cdot {\mathcal {L}}\{f(t)\}-s^{n-1}f(0^{-})-\cdotsCapacitance (4,182 words) [view diff] no match in snippet view article find links to article

N = 1 {\displaystyle \Delta N=1} and Δ Q = e . {\displaystyle \Delta Q=e.} The "quantum capacitance" of the device is then C Q ( N ) = e 2 μ ( N + 1 )Europe 1 (2,399 words) [view diff] no match in snippet view article find links to article

Europe 1, (Europe un) formerly known as Europe n° 1, is a privately owned radio station created in 1955. It was owned and operated by Lagardère ActiveNewton (unit) (958 words) [view diff] no match in snippet view article

kilogram-force, kilopond pound-force poundal 1 N ≡ 1 kg⋅m/s2 = 105 dyn ≈ 0.10197 kp ≈ 0.22481 lbf ≈ 7.2330 pdl 1 dyn = 10–5 N ≡ 1 g⋅cm/s2 ≈ 1.0197×10−6 kp ≈ 2.2481×10−6 lbfSquare number (2,534 words) [view diff] no match in snippet view article find links to article

= (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1). Alternatively, the nth square number can be calculated from the previous two by doubling the (n − 1)thCapacitor (14,954 words) [view diff] exact match in snippet view article find links to article

1 n + 1 ) (volts) B 1..n = A n ( 1 − 1 n + 1 ) A − B = 0 {\displaystyle {\begin{aligned}{\text{(volts)}}A_{\mathrm {eq} }&=A\left(1-{\frac {1}{n+1Combination (3,936 words) [view diff] no match in snippet view article find links to article

n − 1 k − 1 ) + ( n − 1 k ) , {\displaystyle {\binom {n}{k}}={\binom {n-1}{k-1}}+{\binom {n-1}{k}},} for 0 < k < n, which follows from (1 + X)n = (1 +Skewness (3,957 words) [view diff] exact match in snippet view article find links to article

var ( G 1 ) = 6 n ( n − 1 ) ( n − 2 ) ( n + 1 ) ( n + 3 ) . {\displaystyle \operatorname {var} (G_{1})={\frac {6n(n-1)}{(n-2)(n+1)(n+3)}}.} In normalTime complexity (4,846 words) [view diff] no match in snippet view article find links to article

{\tilde {O}}(n)} . Quasilinear time algorithms are also O ( n 1 + ε ) {\displaystyle O(n^{1+\varepsilon })} for every constant ε > 0 {\displaystyle \varepsilonIntegration by parts (6,846 words) [view diff] no match in snippet view article find links to article

product for π {\displaystyle \pi } π 2 = ∏ n = 1 ∞ 4 n 2 4 n 2 − 1 = ∏ n = 1 ∞ ( 2 n 2 n − 1 ⋅ 2 n 2 n + 1 ) = ( 2 1 ⋅ 2 3 ) ⋅ ( 4 3 ⋅ 4 5 ) ⋅ ( 6 5 ⋅Riemann hypothesis (16,487 words) [view diff] no match in snippet view article find links to article

s ) = ∑ n = 1 ∞ ( − 1 ) n + 1 n s = 1 1 s − 1 2 s + 1 3 s − ⋯ , {\displaystyle \left(1-{\frac {2}{2^{s}}}\right)\zeta (s)=\eta (s)=\sum _{n=1}^{\inftyKruskal–Wallis test (2,415 words) [view diff] exact match in snippet view article find links to article

exactly ( N − 1 ) N ( N + 1 ) / 12 {\displaystyle (N-1)N(N+1)/12} and r ¯ = N + 1 2 {\displaystyle {\bar {r}}={\tfrac {N+1}{2}}} . Thus H = 12 N ( N + 1 ) ∑Focal length (2,340 words) [view diff] no match in snippet view article find links to article

( n − 1 ) ( 1 R 1 − 1 R 2 + ( n − 1 ) d n R 1 R 2 ) , {\displaystyle {\frac {1}{f}}=(n-1)\left({\frac {1}{R_{1}}}-{\frac {1}{R_{2}}}+{\frac {(n-1Shetland (13,102 words) [view diff] no match in snippet view article find links to article

Brindister: 60°06′52″N 1°12′57″W / 60.114475°N 1.215874°W / 60.114475; -1.215874 Scord: 60°08′32″N 1°15′42″W / 60.142287°N 1.261629°W / 60.142287;Analysis of algorithms (3,680 words) [view diff] no match in snippet view article find links to article

3 T 5 + 4 T 5 + ⋯ + ( n − 1 ) T 5 + n T 5 + ( n + 1 ) T 5 = T 5 + 2 T 5 + 3 T 5 + 4 T 5 + ⋯ + ( n − 1 ) T 5 + n T 5 + ( n + 1 ) T 5 − T 5 {\displaystyleBernoulli number (13,189 words) [view diff] exact match in snippet view article find links to article

for n ≥ 1 B n = n 2 n + 1 − 2 ∑ k = 0 n − 1 ( − 2 ) − k W n − 1 , k . {\displaystyle B_{n}={\frac {n}{2^{n+1}-2}}\sum _{k=0}^{n-1}(-2)^{-k}\,W_{n-1,k}Elliptic curve (8,223 words) [view diff] no match in snippet view article find links to article

= exp ( ∑ n = 1 ∞ ( 1 − α n − α ¯ n + q n ) T n n ) = exp ( ∑ n = 1 ∞ T n n − ∑ n = 1 ∞ α n T n n − ∑ n = 1 ∞ α ¯ n T n n + ∑ n = 1 ∞ q n T n n )Convolution (8,308 words) [view diff] no match in snippet view article find links to article

∗ g N ) [ n ] ≡ ∑ m = 0 N − 1 ( ∑ k = − ∞ ∞ f [ m + k N ] ) g N [ n − m ] . {\displaystyle (f*g_{N})[n]\equiv \sum _{m=0}^{N-1}\left(\sum _{k=-\infty }^{\inftyDegrees of freedom (statistics) (4,493 words) [view diff] no match in snippet view article

steps (one, namely, the sample mean) and is therefore equal to N − 1 {\textstyle N-1} . Mathematically, degrees of freedom is the number of dimensionsEuler's formula (3,641 words) [view diff] no match in snippet view article find links to article

x ) = Re ( e i ( n − 1 ) x ⋅ e i x ) = Re ( e i ( n − 1 ) x ⋅ ( e i x + e − i x ⏟ 2 cos x − e − i x ) ) = Re ( e i ( n − 1 ) x ⋅ 2 cos x − eMersenne prime (6,327 words) [view diff] no match in snippet view article find links to article

for which n the number (1 + i)n − 1 is a Gaussian prime which will then be called a Gaussian Mersenne prime. (1 + i)n − 1 is a Gaussian prime for the followingRussian roulette (2,914 words) [view diff] no match in snippet view article find links to article

{\displaystyle k} 's all-game loss probability is ( n − 1 n ) k ⋅ 1 n {\displaystyle ({\tfrac {n-1}{n}})^{k}\cdot {\tfrac {1}{n}}} . The probability ofBenford's law (7,247 words) [view diff] no match in snippet view article find links to article

encountered as the n-th (n > 1) digit is ∑ k = 10 n − 2 10 n − 1 − 1 log 10 ( 1 + 1 10 k + d ) . {\displaystyle \sum _{k=10^{n-2}}^{10^{n-1}-1}\log _{10}\left(1+{\fracCoefficient of variation (4,018 words) [view diff] no match in snippet view article find links to article

1 / 2 Γ ( n − 1 2 ) e − n 2 ( σ μ ) 2 c v 2 1 + c v 2 c v n − 2 ( 1 + c v 2 ) n / 2 ∑ ∑ ′ i = 0 n − 1 ( n − 1 ) ! Γ ( n − i 2 ) ( n − 1 − i ) ! iCatalan number (5,838 words) [view diff] exact match in snippet view article find links to article

therefore: ( n − 1 + n + 1 n − 1 ) = ( 2 n n − 1 ) = ( 2 n n + 1 ) {\displaystyle {n-1+n+1 \choose n-1}={2n \choose n-1}={2n \choose n+1}} and the numberBootstrapping (statistics) (8,256 words) [view diff] no match in snippet view article

there are a total of ( 2 n − 1 n ) = ( 2 n − 1 ) ! n ! ( n − 1 ) ! {\displaystyle {\binom {2n-1}{n}}={\frac {(2n-1)!}{n!(n-1)!}}} different resamplesOrdinary differential equation (4,751 words) [view diff] no match in snippet view article find links to article

equation of the form F ( x , y , y ′ , … , y ( n − 1 ) ) = y ( n ) {\displaystyle F\left(x,y,y',\ldots ,y^{(n-1)}\right)=y^{(n)}} is called an explicit ordinaryISO 216 (3,350 words) [view diff] no match in snippet view article find links to article

as An = S × L, where (measuring in metres) A n = { S = ( 1 2 ) n + 1 2 L = ( 1 2 ) n − 1 2 {\displaystyle {\text{A}}_{n}={\begin{cases}S=\left({\sqrt {\fracThames Estuary (2,658 words) [view diff] no match in snippet view article find links to article

490′N 1°07.750′E / 51.541500°N 1.129167°E / 51.541500; 1.129167 (Knock John No. 5) Knock John № 4 Port buoy Group flashing (3) red 10s 51°32.323′N 1°07Hypercube (2,045 words) [view diff] no match in snippet view article find links to article

linear recurrence relation E m , n = 2 E m , n − 1 + E m − 1 , n − 1 {\displaystyle E_{m,n}=2E_{m,n-1}+E_{m-1,n-1}\!} , with E 0 , 0 = 1 {\displaystyleCase study (4,805 words) [view diff] no match in snippet view article find links to article

or action. A case study does not necessarily have to be one observation (N=1), but may include many observations (one or multiple individuals and entitiesGenerating function (14,532 words) [view diff] exact match in snippet view article find links to article

_{n=0}^{\infty }n(n-1)s_{n}z^{n}+(1-3z)^{3}\sum _{n=0}^{\infty }n(n-1)(n-2)s_{n}z^{n}\right)\\[4px]&=(n+1)(n+2)(n+3)s_{n}-9n(n+1)(n+2)s_{n-1}+27(n-1)n(n+11,000,000,000 (3,232 words) [view diff] no match in snippet view article find links to article

OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A080040 (2*a(n-1) + 2*a(n-2) for n > 1)". The On-Line Encyclopedia of Integer Sequences. OEIS FoundationLight (6,073 words) [view diff] no match in snippet view article find links to article

material and another. It is described by Snell's Law: n 1 sin θ 1 = n 2 sin θ 2 . {\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}\ .} whereGlossary of mathematical symbols (9,607 words) [view diff] no match in snippet view article find links to article

is important and readers might assume either definition, N 1 {\displaystyle \mathbb {N} _{1}} and N 0 {\displaystyle \mathbb {N} _{0}} are used, respectivelyDivergence theorem (7,505 words) [view diff] no match in snippet view article find links to article

dx'=\int _{\mathbb {R} ^{n-1}}u(x',g(x'))\,dx'.} Now fix i ∈ { 1 , … , n − 1 } {\displaystyle i\in \{1,\dots ,n-1\}} . Note that ∫ R n − 1 ∫ − ∞ g ( x ′ ) uOrthogonal matrix (4,802 words) [view diff] exact match in snippet view article find links to article

orthogonal matrix quadratically: Q n + 1 = 2 M ( Q n − 1 M + M T Q n ) − 1 {\displaystyle Q_{n+1}=2M\left(Q_{n}^{-1}M+M^{\mathrm {T} }Q_{n}\right)^{-1}}Gradient descent (5,311 words) [view diff] no match in snippet view article find links to article

include the sequence γ n = | ( x n − x n − 1 ) T [ ∇ F ( x n ) − ∇ F ( x n − 1 ) ] | ‖ ∇ F ( x n ) − ∇ F ( x n − 1 ) ‖ 2 {\displaystyle \gamma _{n}={\fracNumber (7,755 words) [view diff] no match in snippet view article find links to article

} , and sometimes N 0 {\displaystyle \mathbb {N} _{0}} or N 1 {\displaystyle \mathbb {N} _{1}} when it is necessary to indicate whether the set shouldEutectic system (3,459 words) [view diff] no match in snippet view article find links to article

T 2 − 1 1 − ∑ i = 1 n − 1 x i − 1 1 − ∑ i = 1 n − 1 x i − 1 1 − ∑ i = 1 n − 1 x i − 1 1 − ∑ i = 1 n − 1 x i − 1 1 − ∑ i = 1 n − 1 x i − H n ∘ R T 2 ]Quantum mechanics (11,698 words) [view diff] case mismatch in snippet view article find links to article

the corresponding energy levels are E n = ℏ ω ( n + 1 2 ) . {\displaystyle E_{n}=\hbar \omega \left(n+{1 \over 2}\right).} This is another example illustratingRunge–Kutta methods (6,696 words) [view diff] exact match in snippet view article find links to article

n + 1 {\displaystyle y_{n+1}} is the RK4 approximation of y ( t n + 1 ) {\displaystyle y(t_{n+1})} , and the next value ( y n + 1 {\displaystyle y_{n+1}}Homology (mathematics) (6,435 words) [view diff] exact match in snippet view article

∂ n + 1 = 0 n + 1 , n − 1 , {\displaystyle \partial _{n}\circ \partial _{n+1}=0_{n+1,n-1},} i.e., the constant map sending every element of C n + 1 {\displaystyleStudent's t-distribution (5,734 words) [view diff] no match in snippet view article find links to article

t ( 0 , τ 2 = n / ( n − 1 ) , n − 1 ) . {\displaystyle t_{\mathsf {ML}}\sim {\mathcal {lst}}(0,\ \tau ^{2}=n/(n-1),\ n-1)~.} The location-scaleVelocity (3,414 words) [view diff] no match in snippet view article find links to article

given by the harmonic mean of the speeds v ¯ = n ( 1 v 1 + 1 v 2 + 1 v 3 + ⋯ + 1 v n ) − 1 = n ( ∑ i = 1 n 1 v i ) − 1 . {\displaystyle {\bar {v}}=n\left({1Manifold (9,476 words) [view diff] no match in snippet view article find links to article

sphere and hyperspheres, are n ( n − 1 ) / 2 {\displaystyle n(n-1)/2} dimensional manifolds, where n − 1 {\displaystyle n-1} is the dimension of the sphereMaxwell–Boltzmann distribution (5,695 words) [view diff] no match in snippet view article find links to article

{mv}{kT}}v^{n-1}+(n-1)v^{n-2}{\biggr ]}=0} This yields the most probable speed (mode) v p = ( n − 1 ) k T m . {\textstyle v_{\rm {p}}={\sqrt {\frac {(n-1)kT}{m}}}Low-pass filter (4,293 words) [view diff] no match in snippet view article find links to article

o u t ( ( n − 1 ) T ) = V i ( 1 − e − ω 0 n T ) − V i ( 1 − e − ω 0 ( ( n − 1 ) T ) ) {\displaystyle v_{\rm {out}}(nT)-v_{\rm {out}}((n-1)T)=V_{i}(1-e^{-\omegaPound (force) (1,178 words) [view diff] no match in snippet view article

avoirdupois pound (lb) result in a pound-force equal to 4.4482216152605 N. 1 lbf = 1 lb × g n = 1 lb × 9.80665 m s 2 / 0.3048 m ft ≈ 1 lb × 32.174049 f t s 2 ≈Orthogonal group (7,813 words) [view diff] no match in snippet view article find links to article

2 q n ( n − 1 ) ( q n − 1 ) ∏ i = 1 n − 1 ( q 2 i − 1 ) , {\displaystyle \left|\operatorname {O} ^{+}(2n,q)\right|=2q^{n(n-1)}\left(q^{n}-1\right)\prodFermat number (4,487 words) [view diff] no match in snippet view article find links to article

F n − 1 − 1 ) 2 + 1 {\displaystyle F_{n}=(F_{n-1}-1)^{2}+1} F n = F 0 ⋯ F n − 1 + 2 {\displaystyle F_{n}=F_{0}\cdots F_{n-1}+2} for n ≥ 1, F n = F n −Loan (2,048 words) [view diff] no match in snippet view article find links to article

interest rate c is: P = L ⋅ c ( 1 + c ) n ( 1 + c ) n − 1 {\displaystyle P=L\cdot {\frac {c\,(1+c)^{n}}{(1+c)^{n}-1}}} For more information, see monthlyBeta distribution (43,410 words) [view diff] no match in snippet view article find links to article

sample excess kurtosis = G 2 = N ( N + 1 ) ( N − 1 ) ( N − 2 ) ( N − 3 ) ∑ i = 1 N ( Y i − y ¯ ) 4 v ¯ Y 2 − 3 ( N − 1 ) 2 ( N − 2 ) ( N − 3 ) {\displaystyleEuler's constant (6,627 words) [view diff] no match in snippet view article find links to article

the pair of series γ = ∑ n = 1 ∞ N 1 ( n ) + N 0 ( n ) 2 n ( 2 n + 1 ) log 4 π = ∑ n = 1 ∞ N 1 ( n ) − N 0 ( n ) 2 n ( 2 n + 1 ) , {\displaystyle {\begin{aligned}\gammaArea (5,316 words) [view diff] no match in snippet view article find links to article

y_{i})} (i=0, 1, ..., n-1) of whose n vertices are known, the area is given by the surveyor's formula: A = 1 2 | ∑ i = 0 n − 1 ( x i y i + 1 − x i + 1Block cipher (6,542 words) [view diff] exact match in snippet view article find links to article

n + 1 , R n + 1 ) = ( L n + 1 ′ , R n + 1 ′ ) {\displaystyle (L_{n+1},R_{n+1})=(L_{n+1}',R_{n+1}')} . The decryption of a ciphertext ( L n + 1 , R n +11 (number) (3,183 words) [view diff] no match in snippet view article

numbers n {\displaystyle n} and m {\displaystyle m} where n ! + 1 = m 2 {\displaystyle n!+1=m^{2}} are known; the largest pair (7, 71) satisfies 5041List of churches preserved by the Churches Conservation Trust in Northern England (2,511 words) [view diff] no match in snippet view article find links to article

or year Notes Grade St Andrew, Bywell Northumberland 54°56′53″N 1°55′34″W / 54.9481°N 1.9260°W / 54.9481; -1.9260 (St Andrew, Bywell) c. 850 The towerPeriodic table (27,127 words) [view diff] exact match in snippet view article find links to article

{\displaystyle v} satisfies the condition v = v N = 1 4 R 2 N ( N + 1 ) {\displaystyle v=v_{N}={\frac {1}{4}}R^{2}N(N+1)} , where N = n + l {\displaystyle N=n+l}Permutation (10,321 words) [view diff] no match in snippet view article find links to article

formula: P ( n , k ) = n ⋅ ( n − 1 ) ⋅ ( n − 2 ) ⋯ ( n − k + 1 ) ⏟ k f a c t o r s {\displaystyle P(n,k)=\underbrace {n\cdot (n-1)\cdot (n-2)\cdots (n-k+1)}Chinese remainder theorem (7,179 words) [view diff] no match in snippet view article find links to article

+ a 2 m 1 n 1 . {\displaystyle x=a_{1}m_{2}n_{2}+a_{2}m_{1}n_{1}.} Indeed, x = a 1 m 2 n 2 + a 2 m 1 n 1 = a 1 ( 1 − m 1 n 1 ) + a 2 m 1 n 1 = a 1 + (Complete graph (1,218 words) [view diff] no match in snippet view article find links to article

Kuratowski to graph theory. Kn has n(n – 1)/2 edges (a triangular number), and is a regular graph of degree n – 1. All complete graphs are their own maximalRoulette (7,550 words) [view diff] no match in snippet view article find links to article

they employ: ∑ n = 1 ∞ M [ ξ n ] = − 1 37 ∑ n = 1 ∞ r n → − ∞ . {\displaystyle \sum _{n=1}^{\infty }M[\xi _{n}]=-{\frac {1}{37}}\sum _{n=1}^{\infty }r_{n}\toPhonon (6,669 words) [view diff] exact match in snippet view article find links to article

the nth atom is − 2 C u n + C ( u n + 1 + u n − 1 ) = m d 2 u n d t 2 . {\displaystyle -2Cu_{n}+C\left(u_{n+1}+u_{n-1}\right)=m{\frac {d^{2}u_{n}}{dt^{2}}}Shor's algorithm (5,687 words) [view diff] exact match in snippet view article find links to article

2 2 n + 1 {\displaystyle k/2^{2{n}+1}} is accurate to j / r {\displaystyle j/r} by 2 n + 1 {\displaystyle 2n+1} bits. Thus, | j r − k 2 2 n + 1 | ≤ 1Definite matrix (8,431 words) [view diff] no match in snippet view article find links to article

c} a real constant. In the n = 1 {\displaystyle n=1} case, this is a parabola, and just like in the n = 1 {\displaystyle n=1} case, we have Theorem: ThisComplete graph (1,218 words) [view diff] no match in snippet view article find links to article

Kuratowski to graph theory. Kn has n(n – 1)/2 edges (a triangular number), and is a regular graph of degree n – 1. All complete graphs are their own maximalErgodic theory (3,727 words) [view diff] no match in snippet view article find links to article

have: lim N → ∞ 1 N ∑ n = 0 N − 1 U n ( I − U ) = lim N → ∞ 1 N ( I − U N ) = 0 {\displaystyle \lim _{N\to \infty }{1 \over N}\sum _{n=0}^{N-1}U^{n}(I-U)=\limSet (mathematics) (4,654 words) [view diff] no match in snippet view article

+ … | A n | ) − ( | A 1 ∩ A 2 | + | A 1 ∩ A 3 | + … | A n − 1 ∩ A n | ) + … + ( − 1 ) n − 1 ( | A 1 ∩ A 2 ∩ A 3 ∩ … ∩ A n | ) . {\displaystylePremier League (18,480 words) [view diff] no match in snippet view article find links to article

2013. The total number of matches can be calculated using the formula n*(n-1) where n is the total number of teams. "Why is there a Saturday footballCoxeter group (3,561 words) [view diff] exact match in snippet view article find links to article

Sn+1; the generators correspond to the transpositions (1 2), (2 3), ... , (n n+1). Any two non-consecutive transpositions commute, while multiplying two consecutivePower of a test (4,215 words) [view diff] no match in snippet view article find links to article

is B ( θ ) = Pr ( T n > 1.64 | μ D = θ ) = Pr ( D ¯ n − 0 σ ^ D / n > 1.64 | μ D = θ ) = Pr ( D ¯ n − θ + θ σ ^ D / n > 1.64 | μ D = θ ) =Hamiltonian (quantum mechanics) (4,901 words) [view diff] no match in snippet view article

-particle case: H ^ = ∑ n = 1 N T ^ n + V ^ = ∑ n = 1 N p ^ n ⋅ p ^ n 2 m n + V ( r 1 , r 2 , … , r N , t ) = − ℏ 2 2 ∑ n = 1 N 1 m n ∇ n 2 + V ( r 1 ,Spearman's rank correlation coefficient (4,159 words) [view diff] exact match in snippet view article find links to article

thus V a r ( U ) = ( n + 1 ) ( 2 n + 1 ) 6 − ( ( n + 1 ) 2 ) 2 = n 2 − 1 12 {\displaystyle \mathrm {Var} (U)=\textstyle {\frac {(n+1)(2n+1)}{6}}-\left(\textstyleLambda calculus (11,331 words) [view diff] no match in snippet view article find links to article

Consider the factorial function F(n) recursively defined by F(n) = 1, if n = 0; else n × F(n − 1). In the lambda expression which is to represent this functionHarmonic mean (5,959 words) [view diff] no match in snippet view article find links to article

x_{n}} is defined to be H ( x 1 , x 2 , … , x n ) = n 1 x 1 + 1 x 2 + ⋯ + 1 x n = n ∑ i = 1 n 1 x i . {\displaystyle H(x_{1},x_{2},\ldots ,x_{n})={\fracHydrogen atom (5,791 words) [view diff] no match in snippet view article find links to article

number: it can run only up to n − 1 {\displaystyle n-1} , i.e., ℓ = 0 , 1 , … , n − 1 {\displaystyle \ell =0,1,\ldots ,n-1} . Due to angular momentum conservationAkaike information criterion (5,504 words) [view diff] no match in snippet view article find links to article

! m 1 ! ( m − m 1 ) ! p m 1 ( 1 − p ) m − m 1 ⋅ n ! n 1 ! ( n − n 1 ) ! q n 1 ( 1 − q ) n − n 1 {\displaystyle {\mathcal {L}}(p,q)\,=\,{\frac {m!}{m_{1}Hydrocarbon (2,580 words) [view diff] exact match in snippet view article find links to article

3 n + 1 2 ) O 2 ⟶ n CO 2 + ( n + 1 ) H 2 O {\displaystyle {\ce {C}}_{n}{\ce {H}}_{2n+2}+\left({{3n+1} \over 2}\right){\ce {O2->}}n{\ce {CO2}}+(n+1){\ceQuantum field theory (14,854 words) [view diff] no match in snippet view article find links to article

the above example, O(N) has N(N − 1)/2 continuous symmetries (the dimension of its Lie algebra), while O(N − 1) has (N − 1)(N − 2)/2. The number of brokenTime value of money (3,978 words) [view diff] no match in snippet view article find links to article

Where i = g : F V ( A ) = A ⋅ n ( 1 + i ) n − 1 {\displaystyle FV(A)\,=\,A\cdot n(1+i)^{n-1}} The following table summarizes the different formulas4 (9,309 words) [view diff] no match in snippet view article find links to article

\\\end{aligned}}} They are defined as locally trivial fibrations that map f : S 2 n − 1 → S n {\displaystyle f:S^{2n-1}\rightarrow S^{n}} for values of n = 2 ,Andorra (12,663 words) [view diff] no match in snippet view article find links to article

The New York Times Geographic data related to Andorra at OpenStreetMap Wikimedia Atlas of Andorra 42°33′N 1°35′E / 42.550°N 1.583°E / 42.550; 1.583Cooperativity (1,951 words) [view diff] no match in snippet view article find links to article

estimations of each cascade's layer, n ≤ n 1 . n 2 {\displaystyle n\leq n_{1}.n_{2}} , where n 1 {\displaystyle n_{1}} and n 2 {\displaystyle n_{2}} are theLaplace operator (4,056 words) [view diff] no match in snippet view article find links to article

rewritten as: 1 r N − 1 ∂ ∂ r ( r N − 1 ∂ f ∂ r ) . {\displaystyle {\frac {1}{r^{N-1}}}{\frac {\partial }{\partial r}}\left(r^{N-1}{\frac {\partial f}{\partialList of rivers of Yorkshire (1,006 words) [view diff] no match in snippet view article find links to article

54°2′27″N 1°56′35″W / 54.04083°N 1.94306°W / 54.04083; -1.94306 (Mouth of River Dibb) 143 m 469 ft Grimwith Reservoir 54°4′48″N 1°54′41″W / 54.08000°N 1Modulo (3,348 words) [view diff] no match in snippet view article find links to article

operands. The range of values for an integer modulo operation of n is 0 to n − 1 (a mod 1 is always 0; a mod 0 is undefined, being a division by zero). WhenGraph (discrete mathematics) (3,693 words) [view diff] no match in snippet view article

vertex is n − 1 (or n + 1 if loops are allowed, because a loop contributes 2 to the degree), and the maximum number of edges is n(n − 1)/2 (or n(n + 1)/2 ifPrediction interval (2,847 words) [view diff] exact match in snippet view article find links to article

with n – 1 degrees of freedom: X n + 1 s ∼ T n − 1 . {\displaystyle {\frac {X_{n+1}}{s}}\sim T^{n-1}.} Solving for X n + 1 {\displaystyle X_{n+1}} givesStandard RAID levels (4,427 words) [view diff] no match in snippet view article find links to article

_{2}\;\oplus \;...\;\oplus \;\mathbf {D} _{n-1}} Q = ⨁ i g i D i = g 0 D 0 ⊕ g 1 D 1 ⊕ g 2 D 2 ⊕ . . . ⊕ g n − 1 D n − 1 {\displaystyle \mathbf {Q} =\bigoplusΣ-algebra (5,312 words) [view diff] no match in snippet view article find links to article

lim sup n → ∞ A n = ⋂ n = 1 ∞ ⋃ m = n ∞ A m = ⋂ n = 1 ∞ A n ∪ A n + 1 ∪ ⋯ . {\displaystyle \limsup _{n\to \infty }A_{n}=\bigcap _{n=1}^{\infty }\bigcup _{m=n}^{\inftyMutualism (biology) (4,977 words) [view diff] no match in snippet view article

mutualists are quantified as: d N 1 d t = r 1 N 1 − α 11 N 1 2 + β 12 N 1 N 2 d N 2 d t = r 2 N 2 − α 22 N 2 2 + β 21 N 1 N 2 {\displaystyle {\begin{aligned}{\fracGhana (14,593 words) [view diff] no match in snippet view article find links to article

conference. Key Development Forecasts for Ghana from International Futures Ghana 2012 Summary Trade Statistics 8°02′N 1°05′W / 8.03°N 1.08°W / 8.03; -1.08600 (number) (3,861 words) [view diff] exact match in snippet view article

Pentagram number of the form 5 n 2 − 5 n + 1 {\displaystyle 5n^{2}-5n+1} . Hexagram number of the form 6 n 2 − 6 n + 1 {\displaystyle 6n^{2}-6n+1} i.e. aQuantum harmonic oscillator (6,794 words) [view diff] no match in snippet view article find links to article

] + a † a ) | n ⟩ = ⟨ n | ( N + 1 ) | n ⟩ = n + 1 ⇒ a † | n ⟩ = n + 1 | n + 1 ⟩ ⇒ | n ⟩ = 1 n a † | n − 1 ⟩ = 1 n ( n − 1 ) ( a † ) 2 | n − 2 ⟩ = ⋯ =Chebyshev polynomials (11,111 words) [view diff] no match in snippet view article find links to article

n 2 − 1 T n + 1 − 1 n − 1 T 1 T n = n n 2 − 1 T n + 1 − 1 2 ( n − 1 ) ( T n + 1 + T n − 1 ) = 1 2 ( n + 1 ) T n + 1 − 1 2 ( n − 1 ) T n − 1 . {\displaystyleMean anomaly (1,324 words) [view diff] no match in snippet view article find links to article

as a series expansion: M = f + 2 ∑ n = 1 ∞ ( − 1 ) n [ 1 n + 1 − e 2 ] β n sin n f {\displaystyle M=f+2\sum _{n=1}^{\infty }(-1)^{n}\left[{\frac {1}{n}}+{\sqrtInductance (8,469 words) [view diff] no match in snippet view article find links to article

m , n = 1 K i m L m , n d i n = ! ∑ n = 1 K ∂ W ( i ) ∂ i n d i n . {\displaystyle \sum \limits _{m}^{K}i_{m}v_{m}{\text{d}}t=\sum \limits _{m,n=1}^{K}i_{m}L_{mRadius (1,188 words) [view diff] no match in snippet view article find links to article

n sides of length s is given by r = Rn s, where R n = 1 / ( 2 sin π n ) . {\displaystyle R_{n}=1\left/\left(2\sin {\frac {\pi }{n}}\right)\right..}Lucas number (2,593 words) [view diff] exact match in snippet view article find links to article

following: L n = F n − 1 + F n + 1 = 2 F n + 1 − F n {\displaystyle L_{n}=F_{n-1}+F_{n+1}=2F_{n+1}-F_{n}} L m + n = L m + 1 F n + L m F n − 1 {\displaystyleCube (algebra) (2,982 words) [view diff] no match in snippet view article

consecutive integers can be expressed as follows: n3 − (n − 1)3 = 3(n − 1)n + 1. or (n + 1)3 − n3 = 3(n + 1)n + 1. There is no minimum perfect cube, since the cubeCovariance matrix (5,410 words) [view diff] no match in snippet view article find links to article

x n − 1 ] [ 1 − ρ x 1 , x 2 ∣ x 3 . . . ⋯ − ρ x 1 , x n ∣ x 2 . . . x n − 1 − ρ x 2 , x 1 ∣ x 3 . . . 1 ⋯ − ρ x 2 , x n ∣ x 1 , x 3 . . . x n − 1 ⋮ ⋮Arqiva (2,485 words) [view diff] no match in snippet view article find links to article

(51°18′28.5″N 1°14′41″W / 51.307917°N 1.24472°W / 51.307917; -1.24472) Haverfordwest Heathfield Holme Moss (53°32′00″N 1°51′29″W / 53.53333°N 1.85806°WL'Hôpital's rule (6,962 words) [view diff] no match in snippet view article find links to article

interest rates: lim r → 0 P r ( 1 + r ) n ( 1 + r ) n − 1 = P lim r → 0 ( 1 + r ) n + r n ( 1 + r ) n − 1 n ( 1 + r ) n − 1 = P n . {\displaystyle {\begin{aligned}\limFermi–Dirac statistics (4,821 words) [view diff] no match in snippet view article find links to article

¯ i = ∑ n 1 , n 2 , … n i P n 1 , n 2 , … = ∑ n 1 , n 2 , … n i e − β ( n 1 ε 1 + n 2 ε 2 + ⋯ + n i ε i + ⋯ ) ∑ n 1 , n 2 , … e − β ( n 1 ε 1 + nAtrazine (5,303 words) [view diff] no match in snippet view article find links to article

6-triazine 2-Chloro-4-ethylamino-6-isopropylamino-s-triazine 6-Chloro-N-ethyl-N'-(1-methylethyl)-1,3,5-triazine-2,4-diamine Identifiers CAS Number 1912-24-9 YEuclidean algorithm (15,008 words) [view diff] no match in snippet view article find links to article

integer r n − 1 {\displaystyle r_{n-1}} will then be the GCD and we can state gcd ( a , b ) = r n − 1 {\displaystyle {\text{gcd}}(a,b)=r_{n-1}} . The algorithmTogo (6,986 words) [view diff] no match in snippet view article find links to article

Wikimedia Atlas of Togo Key Development Forecasts for Togo from International Futures Trade Togo 2012 Summary Trade Statistics 8°N 1°E / 8°N 1°E / 8; 1Normal (geometry) (2,452 words) [view diff] no match in snippet view article

representation r ( t 1 , … , t n − 1 ) = p 0 + t 1 p 1 + ⋯ + t n − 1 p n − 1 , {\displaystyle \mathbf {r} \left(t_{1},\ldots ,t_{n-1}\right)=\mathbf {p} _{0}+t_{1}\mathbfPerturbation theory (quantum mechanics) (15,886 words) [view diff] no match in snippet view article

+\lambda \left|n^{(1)}\right\rangle \right)=1} ⟨ n ( 0 ) | n ( 0 ) ⟩ + λ ⟨ n ( 0 ) | n ( 1 ) ⟩ + λ ⟨ n ( 1 ) | n ( 0 ) ⟩ + λ 2 ⟨ n ( 1 ) | n ( 1 ) ⟩ = 1 {\displaystyleConsistency (2,791 words) [view diff] no match in snippet view article find links to article

R T Φ t 0 ¯ … t n − 1 ¯ {\displaystyle R^{{\mathfrak {T}}_{\Phi }}{\overline {t_{0}}}\ldots {\overline {t_{n-1}}}} if R t 0 … t n − 1 ∈ Φ ; {\displaystyle9 (4,607 words) [view diff] no match in snippet view article find links to article

sum will be nine. In base- N {\displaystyle N} , the divisors of N − 1 {\displaystyle N-1} have this property. There are other interesting patterns involvingMean motion (1,900 words) [view diff] no match in snippet view article find links to article

simply one revolution divided by this time, or, n = 2 π P , n = 360 ∘ P , or n = 1 P , {\displaystyle n={\frac {2\pi }{P}},\qquad n={\frac {360^{\circ }}{P}}Euler method (4,906 words) [view diff] exact match in snippet view article find links to article

is the backward Euler method: y n + 1 = y n + h f ( t n + 1 , y n + 1 ) . {\displaystyle y_{n+1}=y_{n}+hf(t_{n+1},y_{n+1}).} This differs from the (standardAlkane (5,904 words) [view diff] no match in snippet view article find links to article

alkanes range in complexity from the simplest case of methane (CH4), where n = 1 (sometimes called the parent molecule), to arbitrarily large and complexAvro Lancaster (15,106 words) [view diff] no match in snippet view article find links to article

53°52′29″N 1°39′36″W / 53.874647°N 1.660124°W / 53.874647; -1.660124 695 Armstrong Whitworth Whitley 52°22′59″N 1°29′26″W / 52.382954°N 1.490615°WFinite difference method (3,581 words) [view diff] exact match in snippet view article find links to article

) = f ( n + 1 ) ( ξ ) ( n + 1 ) ! ( h ) n + 1 , x 0 < ξ < x 0 + h , {\displaystyle R_{n}(x_{0}+h)={\frac {f^{(n+1)}(\xi )}{(n+1)!}}(h)^{n+1}\,,\quadTotal internal reflection (13,483 words) [view diff] no match in snippet view article find links to article

as n 1 = c / v 1 , {\displaystyle n_{1\!}=c/v_{1}\,,} where c is the speed of light in vacuum. Hence v 1 = c / n 1 . {\displaystyle v_{1\!}=c/n_{1}\Normal subgroup (3,163 words) [view diff] no match in snippet view article find links to article

and therefore there is n 1 ′ ∈ N {\displaystyle n_{1}'\in N} such that n 1 a 2 = a 2 n 1 ′ . {\displaystyle n_{1}a_{2}=a_{2}n_{1}'.} This proves that thisComposite number (848 words) [view diff] no match in snippet view article find links to article

number of distinct prime factors. For the latter μ ( n ) = ( − 1 ) 2 x = 1 {\displaystyle \mu (n)=(-1)^{2x}=1} (where μ is the Möbius function and x is halfPerturbation theory (quantum mechanics) (15,886 words) [view diff] no match in snippet view article

+\lambda \left|n^{(1)}\right\rangle \right)=1} ⟨ n ( 0 ) | n ( 0 ) ⟩ + λ ⟨ n ( 0 ) | n ( 1 ) ⟩ + λ ⟨ n ( 1 ) | n ( 0 ) ⟩ + λ 2 ⟨ n ( 1 ) | n ( 1 ) ⟩ = 1 {\displaystyleFace (geometry) (1,100 words) [view diff] no match in snippet view article

An n-dimensional simplex (line segment (n = 1), triangle (n = 2), tetrahedron (n = 3), etc.), defined by n + 1 vertices, has a face for each subset ofEllipsis (5,042 words) [view diff] no match in snippet view article find links to article

+ 100 = ∑ n = 1 100 n = 100 ? {\displaystyle 1+2+3+\cdots +100\ =\sum _{n=1}^{100}n=100?} (see termial) 1 × 2 × 3 × ⋯ × 100 = ∏ n = 1 100 n = 100River Wharfe (3,332 words) [view diff] no match in snippet view article find links to article

21″N 1°57′5.02″W / 54.0508917°N 1.9513944°W / 54.0508917; -1.9513944 Barden Bridge, River Wharfe 54°0′45.32″N 1°55′19.15″W / 54.0125889°N 1.9219861°WTemperature (12,974 words) [view diff] no match in snippet view article find links to article

number of microstates in the combined system 1 + system 2 is N 1 ⋅ N 2 {\displaystyle N_{1}\cdot N_{2}} , the logarithm of which (times the Boltzmann constant)Quantum superposition (5,263 words) [view diff] exact match in snippet view article find links to article

differential equation: i d ψ n d t = c ∗ ψ n + 1 + c ψ n − 1 {\displaystyle i{d\psi _{n} \over dt}=c^{*}\psi _{n+1}+c\psi _{n-1}} In the case in which left and rightSufficient statistic (6,668 words) [view diff] no match in snippet view article find links to article

1 n ( x 1 n ) = ∏ i = 1 n ( 1 β − α ) 1 { α ≤ x i ≤ β } = ( 1 β − α ) n 1 { α ≤ x i ≤ β , ∀ i = 1 , … , n } = ( 1 β − α ) n 1 { α ≤ min 1 ≤ i ≤ n X iCantor set (6,916 words) [view diff] no match in snippet view article find links to article

n − 1 3 ∪ ( 2 3 + C n − 1 3 ) = 1 3 ( C n − 1 ∪ ( 2 + C n − 1 ) ) {\displaystyle C_{n}:={\frac {C_{n-1}}{3}}\cup \left({\frac {2}{3}}+{\frac {C_{n-1}}{3}}\right)={\fracAnnuity (2,481 words) [view diff] no match in snippet view article find links to article

value is given by: s n ¯ | i = ( 1 + i ) n − 1 i , {\displaystyle s_{{\overline {n}}|i}={\frac {(1+i)^{n}-1}{i}},} where n {\displaystyle n} is the numberLondon Symphony Orchestra (8,954 words) [view diff] no match in snippet view article find links to article

The London Symphony Orchestra (LSO) is a British symphony orchestra based in London. Founded in 1904, the LSO is the oldest of London's symphony orchestrasNth root (4,896 words) [view diff] no match in snippet view article find links to article

n + y n = x + y n x n − 1 + ( n − 1 ) y 2 x + ( n + 1 ) y 3 n x n − 1 + ( 2 n − 1 ) y 2 x + ( 2 n + 1 ) y 5 n x n − 1 + ( 3 n − 1 ) y 2 x + ⋱ . {\displaystyleFinite difference (5,764 words) [view diff] no match in snippet view article find links to article

h n [ f ] ( x ) = ∑ i = 0 n ( − 1 ) n − i ( n i ) f ( x + i h ) , {\displaystyle \Delta _{h}^{n}[f](x)=\sum _{i=0}^{n}(-1)^{n-i}{\binom {n}{i}}f{\biglRainbow (9,298 words) [view diff] no match in snippet view article find links to article

(wavelength 750nm, n = 1.330 based on the dispersion relation of water), the radius angle is 42.5°; for blue light (wavelength 350nm, n = 1.343), the radiusTaylor's theorem (9,587 words) [view diff] no match in snippet view article find links to article

n − 1 ) ( a ) ( a − a ) n − 1 ( n − 1 ) ! = 0 G ( a ) = ( a − a ) n = 0 {\displaystyle {\begin{aligned}F(a)&=f(a)-f(a)-f'(a)(a-a)-...-{\frac {f^{(n-1Fundamental theorem of calculus (5,063 words) [view diff] no match in snippet view article find links to article

) + [ − F ( x n − 1 ) + F ( x n − 1 ) ] + ⋯ + [ − F ( x 1 ) + F ( x 1 ) ] − F ( x 0 ) = [ F ( x n ) − F ( x n − 1 ) ] + [ F ( x n − 1 ) − F ( x n − 2List of unsolved problems in mathematics (19,482 words) [view diff] no match in snippet view article find links to article

of the shortest addition chain producing 2 n − 1 {\displaystyle 2^{n}-1} is at most n − 1 {\displaystyle n-1} plus the length of the shortest additionWilliams Grand Prix Engineering (14,911 words) [view diff] no match in snippet view article find links to article

51°37′5″N 1°24′46″W / 51.61806°N 1.41278°W / 51.61806; -1.41278 Formula One portal Williams Grand Prix Engineering Limited, currently racing in FormulaSymmetric group (6,031 words) [view diff] no match in snippet view article find links to article

transpositions: }}} ( n n − 1 ) ( n − 1 n − 2 ) ⋯ ( 2 1 ) ( n − 1 n − 2 ) ( n − 2 n − 3 ) ⋯ , {\displaystyle (n\,n-1)(n-1\,n-2)\cdots (2\,1)(n-1\,n-2)(n-2\,n-3)\cdotsTetration (6,860 words) [view diff] no match in snippet view article find links to article

n := { 1 if n = 0 , a a ↑↑ ( n − 1 ) if n > 0 , {\displaystyle {a\uparrow \uparrow n}:={\begin{cases}1&{\text{if }}n=0,\\a^{a\uparrow \uparrow (n-1)}&{\text{ifMathematical proof (4,616 words) [view diff] exact match in snippet view article find links to article

an odd number. But (2n − 1) + 2 = 2n + 1 = 2(n+1) − 1, so 2(n+1) − 1 is odd (P(n+1)). So P(n) implies P(n+1). Thus 2n − 1 is odd, for all positive integersEllipse (15,658 words) [view diff] no match in snippet view article find links to article

π a [ 1 − ∑ n = 1 ∞ ( ( 2 n − 1 ) ! ! ( 2 n ) ! ! ) 2 e 2 n 2 n − 1 ] = − 2 π a ∑ n = 0 ∞ ( ( 2 n − 1 ) ! ! ( 2 n ) ! ! ) 2 e 2 n 2 n − 1 , {\displaystyleHypergeometric distribution (3,974 words) [view diff] no match in snippet view article find links to article

K n − k ) ( N n ) = 1 , {\displaystyle \sum _{0\leq k\leq {\textrm {min}}(n,K)}{{K \choose k}{N-K \choose n-k} \over {N \choose n}}=1,} which essentiallyRange (statistics) (1,233 words) [view diff] no match in snippet view article

g ( x ) [ G ( x + t ) − G ( x ) ] n − 1 d x . {\displaystyle F(t)=n\int _{-\infty }^{\infty }g(x)[G(x+t)-G(x)]^{n-1}\,{\text{d}}x.} Gumbel notes thatJackknife resampling (2,104 words) [view diff] no match in snippet view article find links to article

aggregating the parameter estimates from each subsample of size ( n − 1 ) {\displaystyle (n-1)} obtained by omitting one observation. The jackknife techniqueOrder statistic (4,485 words) [view diff] exact match in snippet view article find links to article

= 1 ( N + 1 ) g ( 0 ) + 1 ( N + 1 ) ( N + 2 ) ∫ 0 1 Q ″ ( z ) δ N + 1 ( z ) d z {\displaystyle E(Y_{(1)})={\frac {1}{(N+1)g(0)}}+{\frac {1}{(N+1)(N+2)}}\intTensor (9,329 words) [view diff] exact match in snippet view article find links to article

, v n , v n + 1 , … , v n + m ) = S ( v 1 , … , v n ) T ( v n + 1 , … , v n + m ) , {\displaystyle (S\otimes T)(v_{1},\ldots ,v_{n},v_{n+1},\ldots ,v_{n+m})=S(v_{1}England (21,899 words) [view diff] no match in snippet view article find links to article

UK – official website of the British Government Geographic data related to England at OpenStreetMap 53°08′N 1°23′W / 53.13°N 1.38°W / 53.13; -1.38Error function (7,242 words) [view diff] no match in snippet view article find links to article

x = e − x 2 x π ( 1 + ∑ n = 1 ∞ ( − 1 ) n 1 ⋅ 3 ⋅ 5 ⋯ ( 2 n − 1 ) ( 2 x 2 ) n ) = e − x 2 x π ∑ n = 0 ∞ ( − 1 ) n ( 2 n − 1 ) ! ! ( 2 x 2 ) n , {\displaystyleLists of integrals (5,617 words) [view diff] exact match in snippet view article find links to article

non-integrable singularity at 0 for n ≤ −1: ∫ x n d x = x n + 1 n + 1 + C (for n ≠ − 1 ) {\displaystyle \int x^{n}\,dx={\frac {x^{n+1}}{n+1}}+C\qquad {\text{(for }}n\neqJPEG (13,261 words) [view diff] no match in snippet view article find links to article

divided into N 8×8 blocks B 0 , B 1 , B 2 , . . . , B n − 1 {\displaystyle B_{0},B_{1},B_{2},...,B_{n-1}} , then a 3-scan progressive encoding encodes DCList of tallest structures in the United Kingdom (1,076 words) [view diff] no match in snippet view article find links to article

52°22′26.89″N 1°11′17.35″W / 52.3741361°N 1.1881528°W / 52.3741361; -1.1881528 (Rugby VLF Mast); 52°22′16.24″N 1°11′5.63″W / 52.3711778°N 1.1848972°WMoment (mathematics) (3,099 words) [view diff] no match in snippet view article

said not to exist. If the n-th moment about any point exists, so does the (n − 1)-th moment (and thus, all lower-order moments) about every point. The zerothBlaise Pascal (6,606 words) [view diff] no match in snippet view article find links to article

3, ... and n = 1, 2, 3, ... The generator t00 = 1. Pascal concluded with the proof, t m n = ( m + n ) ( m + n − 1 ) ⋯ ( m + 1 ) n ( n − 1 ) ⋯ 1 . {\displaystyleExponential function (5,859 words) [view diff] no match in snippet view article find links to article

valid for all complex values of x {\displaystyle x} : exp x = lim n → ∞ ( 1 + x n ) n . {\displaystyle \exp x=\lim _{n\to \infty }\left(1+{\frac {x}{n}}\right)^{n}Transition metal (4,504 words) [view diff] no match in snippet view article find links to article

radium. The f-block elements La–Yb and Ac–No have chemical activity of the (n−1)d shell, but importantly also have chemical activity of the (n−2)f shellMagic square (22,234 words) [view diff] exact match in snippet view article find links to article

( n + 1 − i ) {\displaystyle (n+1-i)} and ( n + 1 − j ) {\displaystyle (n+1-j)} are exchanged where i < j < n + 1 2 {\displaystyle i<j<{\frac {n+1}{2}}}Quantifier (logic) (4,529 words) [view diff] no match in snippet view article

x n − 1 , y ) ∧ A ( x 1 , … , x n − 1 , z ) ⟹ y = z ) . {\displaystyle \forall y,z{\big (}A(x_{1},\ldots ,x_{n-1},y)\wedge A(x_{1},\ldots ,x_{n-1},z)\impliesPageRank (9,082 words) [view diff] no match in snippet view article find links to article

where R is the solution of the equation R = [ ( 1 − d ) / N ( 1 − d ) / N ⋮ ( 1 − d ) / N ] + d [ ℓ ( p 1 , p 1 ) ℓ ( p 1 , p 2 ) ⋯ ℓ ( p 1 , pChain rule (7,085 words) [view diff] no match in snippet view article find links to article

the composite function f 1 ∘ ( f 2 ∘ ⋯ ( f n − 1 ∘ f n ) ) {\displaystyle f_{1}\circ (f_{2}\circ \cdots (f_{n-1}\circ f_{n}))\!} , if each function f i {\displaystyleSimple Lie group (2,247 words) [view diff] no match in snippet view article find links to article

SL(n) of n by n matrices with determinant equal to 1 is simple for all n > 1. The first classification of simple Lie groups was by Wilhelm Killing, andCao Cao (30,343 words) [view diff] no match in snippet view article find links to article

Cited in Chen and Pei 429, 1.46 n. 1 (second n. 1). Pei Songzhi in Chen and Pei 429, 1.46 n. 1 (second n. 1): "臣松之以為今之虛封蓋自此始。" Book of Wei: "始置奉常宗正官。"Moons of Neptune (4,348 words) [view diff] no match in snippet view article find links to article

current position when Triton was captured. Neptune's outermost moon S/2021 N 1, which has an orbital period of about 27 Earth years, orbits farther fromPythagorean triple (11,390 words) [view diff] no match in snippet view article find links to article

n − 1 − a n − 2 + 2 {\displaystyle a_{n}=6a_{n-1}-a_{n-2}+2} with a 1 = 3 {\displaystyle a_{1}=3} and a 2 = 20 {\displaystyle a_{2}=20} b n = 6 b n −Real analysis (7,673 words) [view diff] no match in snippet view article find links to article

non-absolutely is ∑ n = 1 ∞ ( − 1 ) n − 1 n = 1 − 1 2 + 1 3 − 1 4 + ⋯ = ln 2. {\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{n-1}}{n}}=1-{\frac {1}{2}}+{\fracPoisson distribution (10,943 words) [view diff] no match in snippet view article find links to article

(\lambda _{n})} where λ 1 + λ 2 + ⋯ + λ n = 1 , {\displaystyle \lambda _{1}+\lambda _{2}+\dots +\lambda _{n}=1,} then ( X 1 , X 2 , … , X n ) {\displaystyleSrinivasa Ramanujan (11,059 words) [view diff] no match in snippet view article find links to article

previously unknown identities, such as ( 1 + 2 ∑ n = 1 ∞ cos ( n θ ) cosh ( n π ) ) − 2 + ( 1 + 2 ∑ n = 1 ∞ cosh ( n θ ) cosh ( n π ) ) − 2 = 2 Γ 4Mortgage (7,195 words) [view diff] no match in snippet view article find links to article

following formula: A = P ⋅ r ( 1 + r ) n ( 1 + r ) n − 1 {\displaystyle A=P\cdot {\frac {r(1+r)^{n}}{(1+r)^{n}-1}}} where: A {\displaystyle A} is the periodicMoons of Neptune (4,348 words) [view diff] no match in snippet view article find links to article

current position when Triton was captured. Neptune's outermost moon S/2021 N 1, which has an orbital period of about 27 Earth years, orbits farther fromReal analysis (7,673 words) [view diff] no match in snippet view article find links to article

non-absolutely is ∑ n = 1 ∞ ( − 1 ) n − 1 n = 1 − 1 2 + 1 3 − 1 4 + ⋯ = ln 2. {\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{n-1}}{n}}=1-{\frac {1}{2}}+{\fracIrrational number (5,420 words) [view diff] no match in snippet view article find links to article

polynomial equations p ( x ) = a n x n + a n − 1 x n − 1 + ⋯ + a 1 x + a 0 = 0 , {\displaystyle p(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{1}x+a_{0}=0\;,} whereVector space (11,557 words) [view diff] no match in snippet view article find links to article

} but ‖ x n ‖ 1 = ∑ i = 1 2 n 2 − n = 2 n ⋅ 2 − n = 1. {\displaystyle \|\mathbf {x} _{n}\|_{1}=\sum _{i=1}^{2^{n}}2^{-n}=2^{n}\cdot 2^{-n}=1.} More generallySpithead (243 words) [view diff] no match in snippet view article find links to article

50°45′05″N 1°08′12″W / 50.75140°N 1.13667°W / 50.75140; -1.13667 Spithead is an area of the Solent and a roadstead off Gilkicker Point in HampshireList of Star Wars starfighters (6,317 words) [view diff] no match in snippet view article find links to article

accidentally steals a Naboo N-1 starfighter and pilots it into the Droid Control Ship's docking bay, destroying the vessel from the inside. N-1 starfighters alsoLeonhard Euler (10,214 words) [view diff] no match in snippet view article find links to article

elaborate argument in 1741): ∑ n = 1 ∞ 1 n 2 = lim n → ∞ ( 1 1 2 + 1 2 2 + 1 3 2 + ⋯ + 1 n 2 ) = π 2 6 . {\displaystyle \sum _{n=1}^{\infty }{1 \over n^{2}}=\limCorrelation (5,122 words) [view diff] no match in snippet view article find links to article

Γ ( N − 1 2 ) ⋅ ( 1 − r 2 ) N − 2 2 ⋅ ( 1 − ρ 2 ) N − 3 2 ⋅ ( 1 − r ρ ) − N + 3 2 ⋅ F H y p ( 3 2 , − 1 2 ; N − 1 2Linear differential equation (4,757 words) [view diff] no match in snippet view article find links to article

n y ( n ) ( x ) + a n − 1 x n − 1 y ( n − 1 ) ( x ) + ⋯ + a 0 y ( x ) = 0 , {\displaystyle x^{n}y^{(n)}(x)+a_{n-1}x^{n-1}y^{(n-1)}(x)+\cdots +a_{0}y(x)=0Monoid (4,447 words) [view diff] no match in snippet view article find links to article

1, 2, ..., n−1} given by [ 0 1 2 ⋯ n − 2 n − 1 1 2 3 ⋯ n − 1 k ] {\displaystyle {\begin{bmatrix}0&1&2&\cdots &n-2&n-1\\1&2&3&\cdots &n-1&k\end{bmatrix}}}Oxford (9,841 words) [view diff] no match in snippet view article find links to article

university town of the past. Oxford's latitude and longitude are 51°45′N 1°15′W / 51.750°N 1.250°W / 51.750; -1.250, with Ordnance Survey grid reference SP513061Formetorex (280 words) [view diff] no match in snippet view article find links to article

Formetorex Names Preferred IUPAC name N-(1-Phenylpropan-2-yl)formamide Other names Formetorex N-Formylamphetamine N-(alpha-Methylphenethyl)formamide IdentifiersTwo's complement (5,379 words) [view diff] no match in snippet view article find links to article

N-bit integer a N − 1 a N − 2 … a 0 {\displaystyle a_{N-1}a_{N-2}\dots a_{0}} is given by the following formula: w = − a N − 1 2 N − 1 + ∑ i = 0 N − 2Norm (mathematics) (5,666 words) [view diff] exact match in snippet view article

{\displaystyle \ell ^{2}} distance. The set of vectors in R n + 1 {\displaystyle \mathbb {R} ^{n+1}} whose Euclidean norm is a given positive constant formsChannel Tunnel (15,935 words) [view diff] no match in snippet view article find links to article

51°00′45″N 1°30′15″E / 51.0125°N 1.5041°E / 51.0125; 1.5041 Status Active Start Folkestone, Kent, England, (51°05′50″N 1°09′21″E / 51.0971°N 1.1558°ESpherical harmonics (12,442 words) [view diff] no match in snippet view article find links to article

n − 1 ∂ ∂ r + r − 2 Δ S n − 1 = ∂ 2 ∂ r 2 + n − 1 r ∂ ∂ r + r − 2 Δ S n − 1 {\displaystyle \nabla ^{2}=r^{1-n}{\frac {\partial }{\partial r}}r^{n-1}{\fracRao–Blackwell theorem (2,164 words) [view diff] no match in snippet view article find links to article

θ ^ B A Y E S = n + 1 n [ 1 − ( X ( 1 ) 1 − k ) ( X ( n ) 1 + k ) − 1 [ ( X ( 1 ) 1 − k ) ( X ( n ) 1 + k ) ] n + 1 − 1 ] X ( n ) 1 + k {\displaystyleFunction (mathematics) (10,612 words) [view diff] exact match in snippet view article

{\displaystyle f} can be defined by the formula f ( n ) = n + 1 {\displaystyle f(n)=n+1} , for n ∈ { 1 , 2 , 3 } {\displaystyle n\in \{1,2,3\}} . When a functionCollusion (3,738 words) [view diff] no match in snippet view article find links to article

≥ n ( 1 − δ ) {\displaystyle 1\geq n(1-\delta )} 1 ≥ n − n δ {\displaystyle 1\geq n-n\delta } n δ ≥ n − 1 {\displaystyle n\delta \geq n-1} δ ≥ n − 1 nEstimation theory (2,557 words) [view diff] no match in snippet view article find links to article

\left[x[0]\right]=A} and E [ A ^ 2 ] = E [ 1 N ∑ n = 0 N − 1 x [ n ] ] = 1 N [ ∑ n = 0 N − 1 E [ x [ n ] ] ] = 1 N [ N A ] = A {\displaystyle \mathrm {E} \left[{\hatElectrostatics (2,558 words) [view diff] no match in snippet view article find links to article

× 10 − 12 C 2 ⋅ N − 1 ⋅ m − 2 . {\displaystyle \varepsilon _{0}\approx \mathrm {8.854\ 187\ 817\times 10^{-12}~C^{2}{\cdot }N^{-1}{\cdot }m^{-2}} .}Elliptic Curve Digital Signature Algorithm (2,831 words) [view diff] no match in snippet view article find links to article

{\displaystyle d_{A}} , randomly selected in the interval [ 1 , n − 1 ] {\displaystyle [1,n-1]} ; and a public key curve point Q A = d A × G {\displaystyleEmpirical distribution function (1,934 words) [view diff] no match in snippet view article find links to article

is defined as F ^ n ( t ) = number of elements in the sample ≤ t n = 1 n ∑ i = 1 n 1 X i ≤ t , {\displaystyle {\widehat {F}}_{n}(t)={\frac {{\mbox{numberOrientability (3,514 words) [view diff] no match in snippet view article find links to article

the above homology group is isomorphic to H n − 1 ( S n − 1 ; Z ) ≅ Z {\displaystyle H_{n-1}\left(S^{n-1};\mathbf {Z} \right)\cong \mathbf {Z} } . A choiceList of tallest buildings and structures (4,047 words) [view diff] no match in snippet view article find links to article

Clock Tower United Kingdom Birmingham 100 328 1908 52°27′00″N 1°55′51″W / 52.4499°N 1.9307°W / 52.4499; -1.9307 Wooden building Ascent MKE UnitedToulouse FC (1,411 words) [view diff] no match in snippet view article find links to article

Ground Stadium de Toulouse Capacity 33,150 Coordinates 43°34′59″N 1°26′3″E / 43.58306°N 1.43417°E / 43.58306; 1.43417 Owner RedBird Capital Partners (85%)List of Sites of Special Scientific Interest in Suffolk (9,704 words) [view diff] no match in snippet view article find links to article

52°10′N 1°0′E / 52.167°N 1.000°E / 52.167; 1.000 (Suffolk) Suffolk is a county in East Anglia. It is bounded by Norfolk to the north, CambridgeshireConfidence interval (4,617 words) [view diff] no match in snippet view article find links to article

{X}}={\frac {X_{1}+\cdots +X_{n}}{n}},} S 2 = 1 n − 1 ∑ i = 1 n ( X i − X ¯ ) 2 . {\displaystyle S^{2}={\frac {1}{n-1}}\sum _{i=1}^{n}(X_{i}-{\bar {X}})^{2}.}Burkina Faso (16,510 words) [view diff] no match in snippet view article find links to article

Futures. Burkina Faso Business Facts from Bizpages World Bank 2011 Trade Summary for Burkiana Faso 12°20′N 1°50′W / 12.333°N 1.833°W / 12.333; -1.833Uninterruptible power supply (6,163 words) [view diff] no match in snippet view article find links to article

equivalent to one very large UPS. "N + 1" means that if the load can be supplied by N modules, the installation will contain N + 1 modules. In this way, failureDerivative (7,187 words) [view diff] no match in snippet view article find links to article

{\displaystyle n} -th derivative as the derivative of the ( n − 1 ) {\displaystyle (n-1)} -th derivative or the derivative of order n {\displaystyleQ Sharp (1,751 words) [view diff] no match in snippet view article find links to article

$V_j$ when controlled by n-qubit number state $\ket{j}$. /// /// $U = \sum^{N-1}_{j=0}\ket{j}\bra{j}\otimes V_j$. /// /// # Input /// ## unitaryGeneratorConvergent series (2,028 words) [view diff] no match in snippet view article find links to article

powers of any n>1 produce a convergent series: 1 1 + 1 n + 1 n 2 + 1 n 3 + 1 n 4 + 1 n 5 + ⋯ = n n − 1 . {\displaystyle {1 \over 1}+{1 \over n}+{1 \over n^{2}}+{1OSI model (5,432 words) [view diff] no match in snippet view article find links to article

N−1, where it is known as the service data unit (SDU). At layer N−1 the SDU is concatenated with a header, a footer, or both, producing a layer N−1 PDURoot of unity (5,939 words) [view diff] no match in snippet view article find links to article

a positive integer, is a number z satisfying the equation z n = 1. {\displaystyle z^{n}=1.} Unless otherwise specified, the roots of unity may be takenNottingham (11,841 words) [view diff] no match in snippet view article find links to article

Location in Europe Show map of Europe Coordinates: 52°57′22″N 1°09′04″W / 52.9561°N 1.1512°W / 52.9561; -1.1512 OS grid reference SK 5711 4020 SovereignValence electron (2,333 words) [view diff] no match in snippet view article find links to article

the orbitals of the incomplete (n−1)d subshell are included, and for lanthanides and actinides incomplete (n−2)f and (n−1)d subshells. The orbitals involvedCentroid (4,177 words) [view diff] no match in snippet view article find links to article

x n − 1 , y n − 1 ) , {\displaystyle (x_{n-1},y_{n-1}),} is the point ( C x , C y ) , {\displaystyle (C_{x},C_{y}),} where C x = 1 6 A ∑ i = 0 n − 1 (Graph theory (6,394 words) [view diff] no match in snippet view article find links to article

of order n, the maximum degree of each vertex is n − 1 and the maximum size of the graph is n(n − 1)/2. The edges of an undirected simple graph permittingScientific notation (5,323 words) [view diff] no match in snippet view article find links to article

10^{n_{0}}} and x 1 = m 1 × 10 n 1 {\displaystyle x_{1}=m_{1}\times 10^{n_{1}}} with n 0 = n 1 {\displaystyle n_{0}=n_{1}} Next, add or subtract the significands:Inverse trigonometric functions (10,715 words) [view diff] no match in snippet view article find links to article

z 7 7 + ⋯ = ∑ n = 0 ∞ ( 2 n − 1 ) ! ! ( 2 n ) ! ! z 2 n + 1 2 n + 1 = ∑ n = 0 ∞ ( 2 n ) ! ( 2 n n ! ) 2 z 2 n + 1 2 n + 1 ; | z | ≤ 1 {\displaystyleStochastic approximation (4,147 words) [view diff] exact match in snippet view article find links to article

the following structure: θ n + 1 − θ n = a n ( α − N ( θ n ) ) , θ ¯ n = 1 n ∑ i = 0 n − 1 θ i {\displaystyle \theta _{n+1}-\theta _{n}=a_{n}(\alpha -N(\thetaLeeds United F.C. (10,873 words) [view diff] no match in snippet view article find links to article

1919) Ground Elland Road Capacity 37,608 Coordinates 53°46′40″N 1°34′20″W / 53.77778°N 1.57222°W / 53.77778; -1.57222 Owner 49ers Enterprises ChairmanStanding wave (6,571 words) [view diff] no match in snippet view article find links to article

the boundary condition restricts the wavelength of the standing waves to n = 1 , 2 , 3 , … {\displaystyle n=1,2,3,\ldots } Waves can only form standingMartingale (probability theory) (2,839 words) [view diff] no match in snippet view article

Yn : n = 1, 2, 3, ... } is a martingale with respect to { Xn : n = 1, 2, 3, ... }. To show this E [ Y n + 1 ∣ X 1 , … , X n ] = p ( q / p ) X n + 1 + qRoot mean square (2,662 words) [view diff] no match in snippet view article find links to article

{\displaystyle T} is the sampling period, ∑ n = 1 N x 2 [ n ] = 1 N ∑ m = 1 N | X [ m ] | 2 , {\displaystyle \sum _{n=1}^{N}{x^{2}[n]}={\frac {1}{N}}\sumCountable set (4,437 words) [view diff] exact match in snippet view article find links to article

numbers. This can be achieved using the assignments n ↔ n + 1 {\displaystyle n\leftrightarrow n+1} and n ↔ 2 n {\displaystyle n\leftrightarrow 2n} , soTangent (4,078 words) [view diff] no match in snippet view article find links to article

the curve is then g = u n + u n − 1 z + ⋯ + u 1 z n − 1 + u 0 z n = 0. {\displaystyle g=u_{n}+u_{n-1}z+\dots +u_{1}z^{n-1}+u_{0}z^{n}=0.\,} Applying theRoot mean square (2,662 words) [view diff] no match in snippet view article find links to article

{\displaystyle T} is the sampling period, ∑ n = 1 N x 2 [ n ] = 1 N ∑ m = 1 N | X [ m ] | 2 , {\displaystyle \sum _{n=1}^{N}{x^{2}[n]}={\frac {1}{N}}\sumCentroid (4,177 words) [view diff] no match in snippet view article find links to article

x n − 1 , y n − 1 ) , {\displaystyle (x_{n-1},y_{n-1}),} is the point ( C x , C y ) , {\displaystyle (C_{x},C_{y}),} where C x = 1 6 A ∑ i = 0 n − 1 (Force India (7,110 words) [view diff] no match in snippet view article find links to article

52°04′33″N 1°01′46″W / 52.07583°N 1.02944°W / 52.07583; -1.02944 Force India Formula One Team Limited, commonly known as Force India and later SaharaCircle (5,861 words) [view diff] no match in snippet view article find links to article

the form | x a | n + | y b | n = 1 {\displaystyle \left|{\frac {x}{a}}\right|^{n}\!+\left|{\frac {y}{b}}\right|^{n}\!=1} for positive a, b, and n. A supercircleCountable set (4,437 words) [view diff] exact match in snippet view article find links to article

numbers. This can be achieved using the assignments n ↔ n + 1 {\displaystyle n\leftrightarrow n+1} and n ↔ 2 n {\displaystyle n\leftrightarrow 2n} , soWave interference (4,612 words) [view diff] no match in snippet view article find links to article

= N − 1 {\displaystyle n=N-1} , where φ n − φ n − 1 = 2 π N . {\displaystyle \varphi _{n}-\varphi _{n-1}={\frac {2\pi }{N}}.} To show that ∑ n = 0 N −Standard error (2,690 words) [view diff] no match in snippet view article find links to article

: FPC): FPC = N − n N − 1 {\displaystyle \operatorname {FPC} ={\sqrt {\frac {N-n}{N-1}}}} which, for large N: FPC ≈ 1 − n N = 1 − f {\displaystyle \operatornameStochastic approximation (4,147 words) [view diff] exact match in snippet view article find links to article

the following structure: θ n + 1 − θ n = a n ( α − N ( θ n ) ) , θ ¯ n = 1 n ∑ i = 0 n − 1 θ i {\displaystyle \theta _{n+1}-\theta _{n}=a_{n}(\alpha -N(\thetaFermat's Last Theorem (11,703 words) [view diff] no match in snippet view article find links to article

equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutionsZipf's law (4,688 words) [view diff] no match in snippet view article find links to article

to the element of rank k (counting from 1) the probability f ( k ; N ) = 1 H N 1 k {\displaystyle f(k;N)={\frac {1}{H_{N}}}\,{\frac {1}{k}}} where HNKronecker delta (4,056 words) [view diff] no match in snippet view article find links to article

n = 1 2 π i ∮ | z | = 1 z x − n − 1 d z = 1 2 π ∫ 0 2 π e i ( x − n ) φ d φ {\displaystyle \delta _{x,n}={\frac {1}{2\pi i}}\oint _{|z|=1}z^{x-n-1}\Tagus (353 words) [view diff] no match in snippet view article find links to article

Station: Texas A&M University Press. p. 87, 97, 100. ISBN 9781585443901. OCLC 56517607. 40°19′11″N 1°41′51″W / 40.31972°N 1.69750°W / 40.31972; -1.69750On-Line Encyclopedia of Integer Sequences (5,561 words) [view diff] exact match in snippet view article find links to article

-3480, -576 OFFSET 1,2 COMMENTS B(n+2) = -B(n)*((n+2)*(n+1)/(4*Pi^2))*z(n+2)/z(n) = -B(n)*((n+2)*(n+1)/(4*Pi^2)) * Sum_{j>=1} a(j)/j^(n+2). Apart from signsGloucestershire Warwickshire Railway (2,227 words) [view diff] no match in snippet view article find links to article

Railway Cotswold Steam Preservation Ltd. - Owners of No. 2807 Warwickshire Railways 51°59′21″N 1°55′41″W / 51.98910°N 1.92813°W / 51.98910; -1.92813Grade II* listed buildings in Nottinghamshire (182 words) [view diff] no match in snippet view article find links to article

Annesley Statue 1832 12 October 1988 SK5109953620 53°04′39″N 1°14′19″W / 53.077371°N 1.238687°W / 53.077371; -1.238687 (Church of All Saints) 1275939Divisor function (3,734 words) [view diff] no match in snippet view article find links to article

n = 1 ∞ q n σ a ( n ) = ∑ n = 1 ∞ ∑ j = 1 ∞ n a q j n = ∑ n = 1 ∞ n a q n 1 − q n {\displaystyle \sum _{n=1}^{\infty }q^{n}\sigma _{a}(n)=\sum _{n=1}^{\inftyA27 road (3,053 words) [view diff] no match in snippet view article find links to article

list 51°00′44″N 1°40′51″W / 51.0123°N 1.6809°W / 51.0123; -1.6809 (Junction between A27 and A36) 50°59′00″N 1°30′22″W / 50.9834°N 1.5060°W / 50Trapezoidal rule (3,449 words) [view diff] no match in snippet view article find links to article

{\displaystyle [a,b]} such that a = x 0 < x 1 < ⋯ < x N − 1 < x N = b {\displaystyle a=x_{0}<x_{1}<\cdots <x_{N-1}<x_{N}=b} and Δ x k {\displaystyle \Delta x_{k}}Vector calculus (2,122 words) [view diff] no match in snippet view article find links to article

defined (generalizations in other dimensionalities either require n − 1 {\displaystyle n-1} vectors to yield 1 vector, or are alternative Lie algebras, whichQ–Q plot (2,496 words) [view diff] no match in snippet view article find links to article

(n + 1 − 2a) for some value of a in the range from 0 to 1, which gives a range between k / (n + 1) and (k − 1) / (n − 1). Expressions include: k / (n +Discrete uniform distribution (672 words) [view diff] exact match in snippet view article find links to article

variance of 1 k ( N − k ) ( N + 1 ) ( k + 2 ) ≈ N 2 k 2 for small samples k ≪ N {\displaystyle {\frac {1}{k}}{\frac {(N-k)(N+1)}{(k+2)}}\approx {\fracIndian mathematics (13,473 words) [view diff] exact match in snippet view article find links to article

n + 1 ) {\displaystyle f_{i}(n+1)} , (for n odd, and i = 1, 2, 3) for the series: π 4 ≈ 1 − 1 3 + 1 5 − ⋯ + ( − 1 ) ( n − 1 ) / 2 1 n + ( − 1 ) ( n +Block matrix (3,464 words) [view diff] no match in snippet view article find links to article

form A = [ B 1 C 1 ⋯ 0 A 2 B 2 C 2 ⋱ ⋱ ⋱ ⋮ A k B k C k ⋮ ⋱ ⋱ ⋱ A n − 1 B n − 1 C n − 1 0 ⋯ A n B n ] {\displaystyle \mathbf {A} ={\begin{bmatrix}\mathbf1 + 2 + 3 + 4 + ⋯ (4,231 words) [view diff] exact match in snippet view article find links to article

series is the triangular number ∑ k = 1 n k = n ( n + 1 ) 2 , {\displaystyle \sum _{k=1}^{n}k={\frac {n(n+1)}{2}},} which increases without bound as n goesCleveland, Yorkshire (519 words) [view diff] no match in snippet view article find links to article

54°30′00″N 1°08′02″W / 54.500°N 1.134°W / 54.500; -1.134 Cleveland /ˈkliːvlənd/ is a land of hills and dales from the River Tees to Vale of PickeringPartition of a set (1,882 words) [view diff] exact match in snippet view article find links to article

partitions of an n-element set is the Catalan number C n = 1 n + 1 ( 2 n n ) . {\displaystyle C_{n}={1 \over n+1}{2n \choose n}.} Wikimedia Commons has media related0.999... (12,910 words) [view diff] no match in snippet view article find links to article

numbers implies 0. ( 9 ) n + 1 / 10 n = 1 , 0. ( 9 ) n < 1 , {\displaystyle {\begin{aligned}0.(9)_{n}+1/10^{n}&=1,\\0.(9)_{n}&<1,\end{aligned}}} for everyProteus (moon) (1,822 words) [view diff] no match in snippet view article

discovery, Proteus received the temporary provisional designation S/1989 N 1. Stephen P. Synnott and Bradford A. Smith announced its discovery on JulyCauchy stress tensor (8,309 words) [view diff] no match in snippet view article find links to article

non-symmetric. This also is the case when the Knudsen number is close to one, K n → 1 {\displaystyle K_{n}\rightarrow 1} , or the continuum is a non-NewtonianGamma distribution (8,535 words) [view diff] no match in snippet view article find links to article

least two samples: N ≥ 2 {\displaystyle N\geq 2} , because for N = 1 {\displaystyle N=1} , the function ℓ ( k ) {\displaystyle \ell (k)} increases withoutCoefficient of determination (6,308 words) [view diff] no match in snippet view article find links to article

e. dftot = n − 1. Inserting the degrees of freedom and using the definition of R2, it can be rewritten as: R ¯ 2 = 1 − ( 1 − R 2 ) n − 1 n − p − 1 {\displaystyleOrthogonal frequency-division multiplexing (11,276 words) [view diff] no match in snippet view article find links to article

{\displaystyle M} , 0 ≤ n ≤ N − 1 {\displaystyle 0\leq n\leq N-1} . One takes the N {\displaystyle N} -point IFFT of X n , 0 ≤ n ≤ N − 1 {\displaystyle {\bf {X}}_{n}Pigeonhole principle (4,044 words) [view diff] no match in snippet view article find links to article

to n − 1, there are n possible holes. On the other hand, either the "0" hole, the "n − 1" hole, or both must be empty, for it is impossible (if n > 1) forField (mathematics) (10,362 words) [view diff] no match in snippet view article

the elements of E(x) have the form ∑ k = 0 n − 1 a k x k , a k ∈ E . {\displaystyle \sum _{k=0}^{n-1}a_{k}x^{k},\ \ a_{k}\in E.} For example, theAsymptote (4,505 words) [view diff] exact match in snippet view article find links to article

{-(\cos({\tfrac {1}{x}})+1)}{x^{2}}}} . For the sequence of points x n = ( − 1 ) n ( 2 n + 1 ) π , {\displaystyle x_{n}={\frac {(-1)^{n}}{(2n+1)\pi }},\quadDiagonal (1,900 words) [view diff] exact match in snippet view article find links to article

by ( n 4 ) + ( n − 1 2 ) = ( n − 1 ) ( n − 2 ) ( n 2 − 3 n + 12 ) 24 . {\displaystyle {\binom {n}{4}}+{\binom {n-1}{2}}={\frac {(n-1)(n-2)(n^{2}-3n+12)}{24}}Separable space (2,071 words) [view diff] no match in snippet view article find links to article

dense subset; that is, there exists a sequence { x n } n = 1 ∞ {\displaystyle \{x_{n}\}_{n=1}^{\infty }} of elements of the space such that every nonemptyMatrix (mathematics) (13,140 words) [view diff] no match in snippet view article

≤ i ≤ m − 1 {\displaystyle 0\leq i\leq m-1} and 0 ≤ j ≤ n − 1 {\displaystyle 0\leq j\leq n-1} . This article follows the more common convention in mathematical23 (number) (4,002 words) [view diff] no match in snippet view article

an Eisenstein prime with no imaginary part and real part of the form 3 n − 1. {\displaystyle 3n-1.} It is also the fifth Sophie Germain prime and theRank correlation (2,523 words) [view diff] exact match in snippet view article find links to article

{E} [U^{2}]=\textstyle {\frac {(n+1)(2n+1)}{6}}} and thus V a r ( U ) = ( n + 1 ) ( 2 n + 1 ) 6 − ( n + 1 ) ( n + 1 ) 4 = n 2 − 1 12 {\displaystyle \mathrmNumeral system (2,845 words) [view diff] no match in snippet view article find links to article

of the form: ( a n a n − 1 ⋯ a 1 a 0 . c 1 c 2 c 3 ⋯ ) b = ∑ k = 0 n a k b k + ∑ k = 1 ∞ c k b − k . {\displaystyle (a_{n}a_{n-1}\cdots a_{1}a_{0}.c_{1}c_{2}c_{3}\cdotsList of Sites of Special Scientific Interest in Dorset (930 words) [view diff] no match in snippet view article find links to article

1991 AONB, SAC Map River Avon System Y 475.9 1,176.1 51°01′34″N 1°45′36″W / 51.026°N 1.76°W / 51.026; -1.76 (River Avon System) SU169252 1996 NCRBinary tree (5,125 words) [view diff] no match in snippet view article find links to article

{\displaystyle C_{0}=1} , and C n = ∑ i = 0 n − 1 C i C n − 1 − i {\displaystyle \textstyle C_{n}=\sum _{i=0}^{n-1}C_{i}C_{n-1-i}} for any positive integer n. ItBayes estimator (3,819 words) [view diff] exact match in snippet view article find links to article

_{i})} , one is interested in estimating θ n + 1 {\displaystyle \theta _{n+1}} based on x n + 1 {\displaystyle x_{n+1}} . Assume that the θ i {\displaystylePentagonal number (923 words) [view diff] no match in snippet view article find links to article

number: p n = T n − 1 + n 2 = T n + 2 T n − 1 = T 2 n − 1 − T n − 1 {\displaystyle p_{n}=T_{n-1}+n^{2}=T_{n}+2T_{n-1}=T_{2n-1}-T_{n-1}} Generalized pentagonalNewcastle United F.C. (10,881 words) [view diff] no match in snippet view article find links to article

1892) Ground St James' Park Capacity 52,305 Coordinates 54°58′32″N 1°37′17″W / 54.9756°N 1.6215°W / 54.9756; -1.6215 Owners Public Investment Fund (80%)63 (number) (2,273 words) [view diff] no match in snippet view article

, except for when n = 1 {\displaystyle n=1} , a − b = 1 ; {\displaystyle a-b=1;\;} with a n − b n = 1 {\displaystyle a^{n}-b^{n}=1} having no prime divisorsPartial autocorrelation function (1,129 words) [view diff] no match in snippet view article find links to article

= 1 n − 1 ϕ n − 1 , k ρ ( n − k ) 1 − ∑ k = 1 n − 1 ϕ n − 1 , k ρ ( k ) {\displaystyle \phi _{n,n}={\frac {\rho (n)-\sum _{k=1}^{n-1}\phi _{n-1,k}\rhoRatio test (5,508 words) [view diff] no match in snippet view article find links to article

test (or "criterion") for the convergence of a series ∑ n = 1 ∞ a n , {\displaystyle \sum _{n=1}^{\infty }a_{n},} where each term is a real or complexCoxeter–Dynkin diagram (2,810 words) [view diff] no match in snippet view article find links to article

rank are: det(A1n = [2n−1]) = 2n (Finite for all n) det(An = [3n−1]) = n + 1 (finite for all n) det(Bn = [4,3n−2]) = 2 (finite for all n) det(Dn = [3n−3Dimension (3,894 words) [view diff] no match in snippet view article find links to article

element in the first cover) such that no point is included in more than n + 1 elements. In this case dim X = n. For X a manifold, this coincides withCommitment scheme (7,696 words) [view diff] no match in snippet view article find links to article

, . . . , p n − 1 {\displaystyle p_{0},p_{1},...,p_{n-1}} be the coefficients of p {\displaystyle p} , such that p ( x ) = ∑ i = 0 n − 1 p i x i {\textstyleLegendre polynomials (5,182 words) [view diff] exact match in snippet view article find links to article

recursion formula ( n + 1 ) P n + 1 ( x ) = ( 2 n + 1 ) x P n ( x ) − n P n − 1 ( x ) . {\displaystyle (n+1)P_{n+1}(x)=(2n+1)xP_{n}(x)-nP_{n-1}(x)\,.} This relationJulius Caesar (15,967 words) [view diff] no match in snippet view article find links to article

Iul., 81–82. Tempest 2017, p. 3–4, 261 n. 1; Meier 1995, p. 486 (reporting 23 wounds). Tempest 2017, p. 261 n. 1 cites all ancient accounts: Nic. Dam.Hilbert space (17,519 words) [view diff] no match in snippet view article find links to article

converges: ∑ n = 1 ∞ | z n | 2 {\displaystyle \sum _{n=1}^{\infty }|z_{n}|^{2}} The inner product on l2 is defined by: ⟨ z , w ⟩ = ∑ n = 1 ∞ z n w n ¯63 (number) (2,273 words) [view diff] no match in snippet view article

, except for when n = 1 {\displaystyle n=1} , a − b = 1 ; {\displaystyle a-b=1;\;} with a n − b n = 1 {\displaystyle a^{n}-b^{n}=1} having no prime divisorsMultinomial distribution (4,303 words) [view diff] no match in snippet view article find links to article

distribution is the set { ( n 1 , … , n k ) ∈ N k ∣ n 1 + ⋯ + n k = n } . {\displaystyle \{(n_{1},\dots ,n_{k})\in \mathbb {N} ^{k}\mid n_{1}+\cdots +n_{k}=n\}Algebraic equation (2,162 words) [view diff] no match in snippet view article find links to article

unknown x ( E ) a n x n + a n − 1 x n − 1 + ⋯ + a 1 x + a 0 = 0 {\displaystyle (\mathrm {E} )\qquad a_{n}x^{n}+a_{n-1}x^{n-1}+\dots +a_{1}x+a_{0}=0} , withRatio test (5,508 words) [view diff] no match in snippet view article find links to article

test (or "criterion") for the convergence of a series ∑ n = 1 ∞ a n , {\displaystyle \sum _{n=1}^{\infty }a_{n},} where each term is a real or complexVon Neumann–Bernays–Gödel set theory (15,521 words) [view diff] exact match in snippet view article find links to article

n + 1 [ x n + 1 ∧ … ] {\displaystyle \exists x_{n+1}[x_{n+1}\land \dots ]} become ∃ x n + 1 [ x n + 1 ∈ V ∧ … ] , {\displaystyle \exists x_{n+1}[x_{n+1}\inHyperbolic space (1,510 words) [view diff] exact match in snippet view article find links to article

2 + ⋯ + x n 2 − x n + 1 2 {\displaystyle q(x)=x_{1}^{2}+\cdots +x_{n}^{2}-x_{n+1}^{2}} on R n + 1 {\displaystyle \mathbb {R} ^{n+1}} , its restrictionHarmonic (2,206 words) [view diff] no match in snippet view article find links to article

these frequencies is periodic at 50 Hz. An nth characteristic mode, for n > 1, will have nodes that are not vibrating. For example, the 3rd characteristicQR code (8,649 words) [view diff] no match in snippet view article find links to article

that these polynomials are all on the form ∏ i = 0 n − 1 ( x − α i ) {\textstyle \prod _{i=0}^{n-1}(x-\alpha ^{i})} , however the rules for selectingArithmetic function (7,508 words) [view diff] no match in snippet view article find links to article

second product gives τ ( n ) = d ( n ) = ( 1 + a 1 ) ( 1 + a 2 ) ⋯ ( 1 + a ω ( n ) ) . {\displaystyle \tau (n)=d(n)=(1+a_{1})(1+a_{2})\cdots (1+a_{\omega1998 FIFA World Cup (7,663 words) [view diff] no match in snippet view article find links to article

Capacity: 41,300 Nantes Stade de la Beaujoire 47°15′20.27″N 1°31′31.35″W / 47.2556306°N 1.5253750°W / 47.2556306; -1.5253750 (Stade de la Beaujoire)Orbital mechanics (5,820 words) [view diff] no match in snippet view article find links to article

= { ∑ n = 1 ∞ M n 3 n ! lim θ → 0 ( d n − 1 d θ n − 1 [ ( θ θ − sin ( θ ) 3 ) n ] ) , ϵ = 1 ∑ n = 1 ∞ M n n ! lim θ → 0 ( d n − 1 d θ n − 1 [ ( θ θRandom variable (6,396 words) [view diff] no match in snippet view article find links to article

function that maps the pair to the sum: X ( ( n 1 , n 2 ) ) = n 1 + n 2 {\displaystyle X((n_{1},n_{2}))=n_{1}+n_{2}} and (if the dice are fair) has a probabilityOrdinal number (6,709 words) [view diff] no match in snippet view article find links to article

If n is finite, the n-th number class has cardinality ℵ n − 1 {\displaystyle \aleph _{n-1}} . If α ≥ ω, the α-th number class has cardinality ℵ α {\displaystyleRiemann integral (5,354 words) [view diff] no match in snippet view article find links to article

is, max ( x i + 1 − x i ) , i ∈ [ 0 , n − 1 ] . {\displaystyle \max \left(x_{i+1}-x_{i}\right),\quad i\in [0,n-1].} A tagged partition P(x, t) of an intervalCauchy sequence (3,218 words) [view diff] exact match in snippet view article find links to article

differences a n + 1 − a n = n + 1 − n = 1 n + 1 + n < 1 2 n {\displaystyle a_{n+1}-a_{n}={\sqrt {n+1}}-{\sqrt {n}}={\frac {1}{{\sqrt {n+1}}+{\sqrt {n}}}}<{\fracNegative binomial distribution (8,221 words) [view diff] no match in snippet view article find links to article

0.4 ) 5 0.4 n − 5 = ( n − 1 n − 5 ) 3 5 2 n − 5 5 n . {\displaystyle f(n)={(n-5)+5-1 \choose n-5}\;(1-0.4)^{5}\;0.4^{n-5}={n-1 \choose n-5}\;3^{5}\;{\fracExpression (mathematics) (956 words) [view diff] no match in snippet view article

to the complex: f ( a ) + ∑ k = 1 n 1 k ! d k d t k | t = 0 f ( u ( t ) ) + ∫ 0 1 ( 1 − t ) n n ! d n + 1 d t n + 1 f ( u ( t ) ) d t . {\displaystyleSpline (mathematics) (4,679 words) [view diff] no match in snippet view article

Si(x) for i = 0, …, n – 1. These must satisfy: S i ( x i ) = y i = S i − 1 ( x i ) , i = 1 , … , n − 1 , S 0 ( x 0 ) = y 0 , S n − 1 ( x n ) = y n , STwin prime (2,628 words) [view diff] exact match in snippet view article find links to article

that p n + 1 − p n = m {\displaystyle p_{n+1}-p_{n}=m} for all m < N and so for n large enough we have p n + 1 − p n > N , {\displaystyle p_{n+1}-p_{n}>NHyperplane (1,336 words) [view diff] exact match in snippet view article find links to article

translation b ~ ∈ R n + 1 {\displaystyle {\tilde {b}}\in \mathbb {R} ^{n+1}} as the set of all x ∈ R n + 1 {\displaystyle x\in \mathbb {R} ^{n+1}} such that nRandom number generation (4,433 words) [view diff] exact match in snippet view article find links to article

n + 1 = ( a X n + b ) mod m {\displaystyle X_{n+1}=(aX_{n}+b)\,{\textrm {mod}}\,m} to generate numbers, where a, b and m are large integers, and X n +Pyramid (geometry) (1,422 words) [view diff] no match in snippet view article

regular pyramid. For the pyramid with an n-sided regular base, it has n + 1 vertices, n + 1 faces, and 2n edges. Such pyramid has isosceles triangles as itsEnergy level (2,831 words) [view diff] no match in snippet view article find links to article

the nucleus. The shells correspond with the principal quantum numbers (n = 1, 2, 3, 4 ...) or are labeled alphabetically with letters used in the X-rayList of Sites of Special Scientific Interest in Norfolk (11,471 words) [view diff] no match in snippet view article find links to article

from the original on 16 March 2018. Retrieved 24 June 2018. 52°40′N 1°00′E / 52.667°N 1.000°E / 52.667; 1.000 Ratcliffe, Derek, ed. (1977). A Nature ConservationR (programming language) (7,947 words) [view diff] no match in snippet view article

data points. s = ∑ ( x i − x ¯ ) 2 n − 1 {\displaystyle s={\sqrt {\frac {\sum \left(x_{i}-{\bar {x}}\right)^{2}}{n-1}}}} Suppose a sample of four observationsPython (programming language) (13,245 words) [view diff] no match in snippet view article

ValueError('You must enter a non-negative integer') factorial = 1 for i in range(2, n + 1): factorial *= i print(factorial) Python's large standard library providesM40 motorway (3,452 words) [view diff] no match in snippet view article find links to article

51°43′29″N 1°03′27″W / 51.7246°N 1.0575°W / 51.7246; -1.0575 (M40, J7) 48.0 48.4 77.3 77.9 No Exit J8 Oxford, Cheltenham A40 51°43′56″N 1°04′36″WCredit default swap (15,043 words) [view diff] no match in snippet view article find links to article

has a default event, in which case it ends with a payment of N ( 1 − R ) {\displaystyle N(1-R)} shown in red, where R {\displaystyle R} is the recoveryLinear equation (2,137 words) [view diff] no match in snippet view article find links to article

linear equation in n variables form a hyperplane (a subspace of dimension n − 1) in the Euclidean space of dimension n. Linear equations occur frequentlyRiver Avon, Hampshire (1,559 words) [view diff] no match in snippet view article find links to article

51°20′56″N 1°56′53″W / 51.349°N 1.948°W / 51.349; -1.948 The River Avon (/ˈeɪvən/) is in the south of England, rising in Wiltshire, flowing throughBose–Einstein condensate (9,796 words) [view diff] no match in snippet view article find links to article

{\displaystyle f} the fugacity and g α ( f ) = ∑ n = 1 ∞ f n n α {\displaystyle g_{\alpha }(f)=\sum \limits _{n=1}^{\infty }{\frac {f^{n}}{n^{\alpha }}}} ItGrade I listed buildings in Derbyshire (196 words) [view diff] no match in snippet view article find links to article

Mill Earlier than 1803 3 February 1966 SK3454248081 53°01′44″N 1°29′11″W / 53.028907°N 1.486415°W / 53.028907; -1.486415 (North Mill) Built by William0 (7,839 words) [view diff] no match in snippet view article find links to article

that for an array of n items the sequence of array indices runs from 0 to n−1.[citation needed] There can be confusion between 0- and 1-based indexing;Geometric distribution (3,608 words) [view diff] no match in snippet view article find links to article

k^{n}\\&{}=p\operatorname {Li} _{-n}(1-p)&({\text{for }}n\neq 0)\end{aligned}}} where Li − n ( 1 − p ) {\displaystyle \operatorname {Li} _{-n}(1-p)} is the polylogarithmHomological algebra (3,857 words) [view diff] exact match in snippet view article find links to article

C n + 1 ⟶ d n + 1 C n ⟶ d n C n − 1 ⟶ d n − 1 ⋯ , d n ∘ d n + 1 = 0. {\displaystyle C_{\bullet }:\cdots \longrightarrow C_{n+1}{\stackrel {d_{n+1}}{\longrightarrowContinuous function (9,400 words) [view diff] no match in snippet view article find links to article

neighborhood N 1 ( f ( c ) ) {\displaystyle N_{1}(f(c))} there is a neighborhood N 2 ( c ) {\displaystyle N_{2}(c)} in its domain such that f ( x ) ∈ N 1 ( f (List of tallest buildings and structures in the Birmingham Metropolitan Area, West Midlands (10,702 words) [view diff] no match in snippet view article find links to article

Telecommunication Jewellery Quarter Post Office Tower GPO Tower 52°29′01″N 1°54′15″W / 52.483547°N 1.904303°W / 52.483547; -1.904303 2 Birmingham 2 The MercianZhuge Liang (25,943 words) [view diff] no match in snippet view article find links to article

52.1232 n. 1, biography of Zhuge Jin. Ying, Fengsu Tongyi: "葛嬰為陳涉將軍，有功而誅，孝文帝追錄，封其孫諸縣侯，因幷氏焉。此與吳書所說不同。" Cited in Chen and Pei 429, 52.1232 n. 1, biographyLehmann–Scheffé theorem (984 words) [view diff] no match in snippet view article find links to article

estimator: θ ^ BAYES = n + 1 n [ 1 − X ( 1 ) ( 1 + k ) X ( n ) ( 1 − k ) − 1 ( X ( 1 ) ( 1 + k ) X ( n ) ( 1 − k ) ) n + 1 − 1 ] X ( n ) 1 + k {\displaystyleHydrolysis (2,267 words) [view diff] no match in snippet view article find links to article

M ( H 2 O ) n − 1 ( OH ) ( m − 1 ) + + H 3 O + {\displaystyle {\ce {M(H2O)_{\mathit {n}}^{{\mathit {m}}+}{}+H2O<=>M(H2O)_{{\mathit {n}}-1}(OH)^{({\mathitGravitational constant (5,177 words) [view diff] no match in snippet view article find links to article

G c 4 ≈ 2.0766 × 10 − 43 N − 1 . {\displaystyle \kappa ={\frac {8\pi G}{c^{4}}}\approx 2.0766\times 10^{-43}\mathrm {\,N^{-1}} .} The gravitational constantTower of Hanoi (6,998 words) [view diff] no match in snippet view article find links to article

Since n is odd (n = 1), it is one peg to the left, i.e. on the left peg. Disk four is 1, so it is on another peg. Since n is odd (n = 1), it is one pegSchrödinger equation (10,112 words) [view diff] no match in snippet view article find links to article

take the values n = 1 , 2 , 3 , … , {\displaystyle n=1,2,3,\dots ,} ℓ = 0 , 1 , 2 , … , n − 1 , {\displaystyle \ell =0,1,2,\dots ,n-1,} m = − ℓ , … ,Discriminant (6,196 words) [view diff] no match in snippet view article find links to article

derivative, A ′ ( x ) = n a n x n − 1 + ( n − 1 ) a n − 1 x n − 2 + ⋯ + a 1 , {\displaystyle A'(x)=na_{n}x^{n-1}+(n-1)a_{n-1}x^{n-2}+\cdots +a_{1},} is aDiscriminant (6,196 words) [view diff] no match in snippet view article find links to article

derivative, A ′ ( x ) = n a n x n − 1 + ( n − 1 ) a n − 1 x n − 2 + ⋯ + a 1 , {\displaystyle A'(x)=na_{n}x^{n-1}+(n-1)a_{n-1}x^{n-2}+\cdots +a_{1},} is aAffine space (7,220 words) [view diff] no match in snippet view article find links to article

space of dimension 2 is an affine plane. An affine subspace of dimension n – 1 in an affine space or a vector space of dimension n is an affine hyperplaneList of Sites of Special Scientific Interest in Hampshire (6,009 words) [view diff] no match in snippet view article find links to article

Conservation Review. Vol. 2. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-21403-2. 51°03′28″N 1°18′29″W / 51.0577°N 1.3081°W / 51.0577; -1.3081River Swale (2,883 words) [view diff] no match in snippet view article find links to article

54°22′50.16″N 1°59′15.05″W / 54.3806000°N 1.9875139°W / 54.3806000; -1.9875139 Barney Beck 54°22′53.87″N 1°58′37.77″W / 54.3816306°N 1.9771583°WBinomial regression (2,055 words) [view diff] no match in snippet view article find links to article

binary regression can be considered a binomial regression with n = 1 {\displaystyle n=1} , or a regression on ungrouped binary data, while a binomial regressionCompact space (5,645 words) [view diff] no match in snippet view article find links to article

interval (0, 1) is not compact: the open cover ( 1 n , 1 − 1 n ) {\textstyle \left({\frac {1}{n}},1-{\frac {1}{n}}\right)} for n = 3, 4, ... does notEuropean Community number (637 words) [view diff] no match in snippet view article find links to article

is the following sum modulo 11: R = ( N 1 + 2 N 2 + 3 N 3 + 4 N 4 + 5 N 5 + 6 N 6 ) mod 1 1 {\displaystyle R=(N_{1}+2N_{2}+3N_{3}+4N_{4}+5N_{5}+6N_{6}){\bmodLehmann–Scheffé theorem (984 words) [view diff] no match in snippet view article find links to article

estimator: θ ^ BAYES = n + 1 n [ 1 − X ( 1 ) ( 1 + k ) X ( n ) ( 1 − k ) − 1 ( X ( 1 ) ( 1 + k ) X ( n ) ( 1 − k ) ) n + 1 − 1 ] X ( n ) 1 + k {\displaystyleAverage (3,241 words) [view diff] no match in snippet view article find links to article

n 1 x 1 + 1 x 2 + ⋯ + 1 x n {\displaystyle {\frac {n}{{\frac {1}{x_{1}}}+{\frac {1}{x_{2}}}+\cdots +{\frac {1}{x_{n}}}}}} argmin x ∈ R ≠ 0 ∑ i = 1 n (Pythagorean theorem (12,742 words) [view diff] no match in snippet view article find links to article

simplex, the square of the (n − 1)-content of the facet opposing the right vertex will equal the sum of the squares of the (n − 1)-contents of the remainingEurope (21,821 words) [view diff] no match in snippet view article find links to article

25.5 E −9.6 16.5 2.7 Arkhangelsk 64.5 N 40.5 E −12.7 16.3 1.3 Lerwick 60 N 1 W 3.5 12.4 7.4 Stockholm 59.5 N 19 E −1.7 18.4 7.4 Helsinki 60 N 25 E −4Uniform convergence (5,084 words) [view diff] exact match in snippet view article find links to article

can be found such that each of the functions f N , f N + 1 , f N + 2 , … {\displaystyle f_{N},f_{N+1},f_{N+2},\ldots } differs from f {\displaystyle f}History of calculus (5,929 words) [view diff] no match in snippet view article find links to article

n − 1 ( 1 − x ) n − 1 d x {\displaystyle \int _{0}^{1}x^{n-1}(1-x)^{n-1}\,dx} ∫ 0 ∞ e − x x n − 1 d x {\displaystyle \int _{0}^{\infty }e^{-x}x^{n-1}\Free fall (2,500 words) [view diff] no match in snippet view article find links to article

) = ∑ n = 1 ∞ [ lim r → 0 ( x n n ! d n − 1 d r n − 1 [ r n ( 7 2 ( arcsin ( r ) − r − r 2 ) ) − 2 3 n ] ) ] . {\displaystyle y(t)=\sum _{n=1}^{\inftyChromadorea (447 words) [view diff] no match in snippet view article find links to article

molecular markers are found in essential proteins such as tRNA (guanine-N(1))-methyltransferase and can serve as a reliable molecular method of distinguishingHaskell (4,530 words) [view diff] exact match in snippet view article find links to article

and widely used. So-called n+k patterns (definitions of the form fact (n+1) = (n+1) * fact n) were no longer allowed. This syntactic sugar had misleadingDrugs controlled by the German Betäubungsmittelgesetz (315 words) [view diff] no match in snippet view article find links to article

(6-Dimethylamino-4,4-diphenyl-heptan-3-yl)acetat α-Methylacetylfentanyl N-Phenyl-N-[1-(1-phenyl-propan-2-yl)-4-piperidyl]acetamid Allylescaline 4-Allyloxy-3Git (6,882 words) [view diff] no match in snippet view article find links to article

N − 1 is its default ancestor. However, when there is no like-named file in revision N − 1, Git searches for a file that existed only in revision N − 1Product rule (4,116 words) [view diff] no match in snippet view article find links to article

value, n + 1, we have d d x x n + 1 = d d x ( x n ⋅ x ) = x d d x x n + x n d d x x (the product rule is used here) = x ( n x n − 1 ) + x n ⋅ 1 (the inductionChanel (7,024 words) [view diff] no match in snippet view article find links to article

Blanc Le Lift Sublimage Blue Serum La Solution 10 de Chanel Vamp Nail Polish N°1 line (skincare and makeup products based on holistic beauty and eco-friendlyCar (8,923 words) [view diff] no match in snippet view article find links to article

University. 28 June 2003. Archived from the original on 28 June 2003. "car, n.1". OED Online. Oxford University Press. September 2014. Archived from theGas (6,356 words) [view diff] no match in snippet view article find links to article

4 dm3/mol (liters per mole). The relation is given by V 1 n 1 = V 2 n 2 , {\displaystyle {\frac {V_{1}}{n_{1}}}={\frac {V_{2}}{n_{2}}},} where n is the amountAlnwick Infirmary (621 words) [view diff] no match in snippet view article find links to article

55°24′32″N 1°49′39″W / 55.408827°N 1.827563°W / 55.408827; -1.827563 John Lambert was a local solicitor. Alnwick Infirmary 1819 building - 55°24′51″N 1°42′37″WSinc function (2,956 words) [view diff] no match in snippet view article find links to article

product-to-sum identity ∏ n = 1 k cos ( x 2 n ) = 1 2 k − 1 ∑ n = 1 2 k − 1 cos ( n − 1 / 2 2 k − 1 x ) , ∀ k ≥ 1 , {\displaystyle \prod _{n=1}^{k}\cos \left({\fracEast Anglia (3,012 words) [view diff] no match in snippet view article find links to article

and Lowestoft Enterprise Zone Alconbury Enterprise Campus. Archived 16 January 2016 at the Wayback Machine. 52°30′N 1°00′E / 52.5°N 1°E / 52.5; 1Dihedral group (3,439 words) [view diff] no match in snippet view article find links to article

∣ s 2 = 1 , t 2 = 1 , ( s t ) n = 1 ⟩ . {\displaystyle \mathrm {D} _{n}=\left\langle s,t\mid s^{2}=1,t^{2}=1,(st)^{n}=1\right\rangle .} In particularPlanck constant (7,635 words) [view diff] no match in snippet view article find links to article

and n ∈ { 1 , 2 , 3 , . . . } {\displaystyle n\in \{1,2,3,...\}} . Once the electron reached the lowest energy level ( n = 1 {\displaystyle n=1} ), itM42 motorway (1,023 words) [view diff] no match in snippet view article find links to article

coordinates) 52°20′56″N 1°48′35″W / 52.3488°N 1.8097°W / 52.3488; -1.8097 (Junction 3a) Termination point M40 52°28′39″N 1°42′39″W / 52.4774°N 1.7109°W / 52Bose–Einstein statistics (6,020 words) [view diff] exact match in snippet view article find links to article

sublevel, therefore w ( n , 1 ) = 1 {\displaystyle w(n,1)=1} . It is easy to see that there are ( n + 1 ) {\displaystyle (n+1)} ways of distributing nAutomobiles Alpine (4,677 words) [view diff] no match in snippet view article find links to article

49°54′44″N 1°05′06″E / 49.9121346°N 1.0849268°E / 49.9121346; 1.0849268 The Société des Automobiles Alpine SAS, commonly known as Alpine (French pronunciation:Cross-correlation (4,084 words) [view diff] no match in snippet view article find links to article

f ⋆ g ) [ n ] ≜ ∑ m = 0 N − 1 f [ m ] ¯ g [ ( m + n ) mod N ] {\displaystyle (f\star g)[n]\ \triangleq \sum _{m=0}^{N-1}{\overline {f[m]}}g[(m+n)_{{\text{mod}}~N}]}Grade II* listed buildings in South Yorkshire (114 words) [view diff] no match in snippet view article find links to article

Barnsley House c. 1670 18 April 1985 SE4103609639 53°34′54″N 1°22′54″W / 53.581744°N 1.381653°W / 53.581744; -1.381653 (Grimethorpe Hall) 1151202Wishart distribution (4,094 words) [view diff] no match in snippet view article find links to article

1 − 1 X ) / 2 2 n 1 p 1 / 2 | V 1 | n 1 / 2 Γ p 1 ( n 1 2 ) ] = n 1 p 1 2 log 2 + n 1 2 log | V 1 | + log Γ p 1 ( n 1 2 ) − n 1 − p 1 − 1 2 E pWashington Double Star Catalog (312 words) [view diff] no match in snippet view article find links to article

star with n components will be represented by entries in the catalog for n-1 pairs of stars. The database used to construct the WDS originated at LickNetwork topology (5,208 words) [view diff] no match in snippet view article find links to article

grows quadratically with the number of nodes: c = n ( n − 1 ) 2 . {\displaystyle c={\frac {n(n-1)}{2}}.\,} This makes it impractical for large networks55 (number) (951 words) [view diff] no match in snippet view article

and fifth, where the first two Fermat primes of the form 2 2 n + 1 {\displaystyle 2^{2^{n}}+1} are 3 {\displaystyle 3} and 5 {\displaystyle 5} (11 is alsoFigurate number (1,340 words) [view diff] case mismatch in snippet view article find links to article

) = n 1 = ( n + 0 1 ) = ( n 1 ) {\displaystyle P_{1}(n)={\frac {n}{1}}={\binom {n+0}{1}}={\binom {n}{1}}} (linear numbers), P 2 ( n ) = n ( n + 1 ) 2Butterfly effect (4,874 words) [view diff] exact match in snippet view article find links to article

parametrization of the logistic map: x n + 1 = 4 x n ( 1 − x n ) , 0 ≤ x 0 ≤ 1 , {\displaystyle x_{n+1}=4x_{n}(1-x_{n}),\quad 0\leq x_{0}\leq 1,} whichHomotopy group (3,417 words) [view diff] no match in snippet view article find links to article

fibration S O ( n − 1 ) → S O ( n ) → S O ( n ) / S O ( n − 1 ) ≅ S n − 1 {\displaystyle SO(n-1)\to SO(n)\to SO(n)/SO(n-1)\cong S^{n-1}} giving the longSorting algorithm (6,396 words) [view diff] no match in snippet view article find links to article

Other notes In-place merge sort — — n log 2 n {\displaystyle n\log ^{2}n} 1 Yes Merging Can be implemented as a stable sort based on stable in-placeExterior derivative (3,088 words) [view diff] no match in snippet view article find links to article

(n − 1)-form ω V = v 1 ( d x 2 ∧ ⋯ ∧ d x n ) − v 2 ( d x 1 ∧ d x 3 ∧ ⋯ ∧ d x n ) + ⋯ + ( − 1 ) n − 1 v n ( d x 1 ∧ ⋯ ∧ d x n − 1 ) = ∑ i = 1 n ( − 1 )Group (mathematics) (13,114 words) [view diff] no match in snippet view article

theory of groups, as depending on the symbolic equation θ n = 1 {\displaystyle \theta ^{n}=1} (1854) gives the first abstract definition of a finite groupZ-transform (4,524 words) [view diff] no match in snippet view article find links to article

origin "punched out". Let x [ n ] = − ( .5 ) n u [ − n − 1 ] {\displaystyle x[n]=-(.5)^{n}\,u[-n-1]} (where u {\displaystyle u} is the Heaviside step function)Italy (35,637 words) [view diff] no match in snippet view article find links to article

5, Statuto speciale per il Trentino-Alto Adige L. cost. 31 gennaio 1963, n. 1, Statuto speciale della Regione Friuli-Venezia Giulia "Ready for Ratification"Alternating series (1,655 words) [view diff] exact match in snippet view article find links to article

the natural logarithm: ∑ n = 1 ∞ ( − 1 ) n + 1 n x n = ln ( 1 + x ) . {\displaystyle \sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}x^{n}\;=\;\ln(1+x).}Stirling numbers of the second kind (4,007 words) [view diff] exact match in snippet view article find links to article

that a partition of the n + 1 {\displaystyle n+1} objects into k nonempty subsets either contains the ( n + 1 ) {\displaystyle (n+1)} -th object as a singletonRandom matrix (5,660 words) [view diff] exact match in snippet view article find links to article

λ n < λ n + 1 < … {\displaystyle \lambda _{1}<\ldots <\lambda _{n}<\lambda _{n+1}<\ldots } , one defines the normalized spacings s = ( λ n + 1 − λ n )Silkworm (missile) (970 words) [view diff] no match in snippet view article

SY-1 License produced version of the P-15 Termit. NATO reporting name CSS-N-1 Scrubbrush. SY-2 HY-1 NATO reporting names CSS-N-2 Safflower(ship-based)Phased array (5,021 words) [view diff] no match in snippet view article find links to article

accordingly[page needed]: A F = ∑ n = 1 N I n 1 [ ∑ m = 1 M I m 1 e j ( m − 1 ) ( k d x sin θ cos ϕ + β x ) ] e j ( n − 1 ) ( k d y sin θ sin ϕ + β79 (number) (535 words) [view diff] exact match in snippet view article

1 79 = ∑ n = 1 ∞ P ( n ) × 10 − ( n + 1 ) = 0.0126582278 … . {\displaystyle {\frac {1}{79}}=\sum _{n=1}^{\infty }{P(n)\times 10^{-(n+1)}}=0.0126582278\dotsRydberg formula (1,892 words) [view diff] no match in snippet view article find links to article

atomic electron transition. Note: Here, n 2 > n 1 {\displaystyle n_{2}>n_{1}} By setting n 1 {\displaystyle n_{1}} to 1 and letting n 2 {\displaystyle n_{2}}79 (number) (535 words) [view diff] exact match in snippet view article

1 79 = ∑ n = 1 ∞ P ( n ) × 10 − ( n + 1 ) = 0.0126582278 … . {\displaystyle {\frac {1}{79}}=\sum _{n=1}^{\infty }{P(n)\times 10^{-(n+1)}}=0.0126582278\dotsUnited States congressional apportionment (4,720 words) [view diff] exact match in snippet view article find links to article

A_{m+1}={\sqrt {\frac {m}{m+2}}}\ A_{m}} A n = n − 1 n + 1 A n − 1 {\displaystyle A_{n}={\sqrt {\frac {n-1}{n+1}}}\ A_{n-1}} where n is still the number of seatsPhased array (5,021 words) [view diff] no match in snippet view article find links to article

accordingly[page needed]: A F = ∑ n = 1 N I n 1 [ ∑ m = 1 M I m 1 e j ( m − 1 ) ( k d x sin θ cos ϕ + β x ) ] e j ( n − 1 ) ( k d y sin θ sin ϕ + βJensen's inequality (4,475 words) [view diff] no match in snippet view article find links to article

( 1 − λ n + 1 ) ∑ i = 1 n λ i 1 − λ n + 1 x i + λ n + 1 x n + 1 ) ≤ ( 1 − λ n + 1 ) φ ( ∑ i = 1 n λ i 1 − λ n + 1 x i ) + λ n + 1 φ ( x n + 1 ) . {\displaystylePound sterling (14,537 words) [view diff] no match in snippet view article find links to article

from the original on 25 June 2015. Retrieved 28 February 2012. sterling, n.1 and adj. "Easterling theory". Sterling Judaica. Archived from the originalMarcus Aurelius (16,718 words) [view diff] no match in snippet view article find links to article

Press, 1995), 21 n. 1. Mark, Joshua. 'Marcus Aurelius: Plato's Philosopher King'. World History Encyclopedia. 8 May 2018. Francis, p. 21 n.1, citing JustinWinchester (6,495 words) [view diff] no match in snippet view article find links to article

2005 and 2012 at the behest of Winchester City Council.(51°03′43″N 1°18′55″W / 51.062°N 1.31525°W / 51.062; -1.31525 (The Square)) Winchester has a varietyFresnel equations (8,291 words) [view diff] no match in snippet view article find links to article

| n 1 cos θ i − n 2 cos θ t n 1 cos θ i + n 2 cos θ t | 2 = | n 1 cos θ i − n 2 1 − ( n 1 n 2 sin θ i ) 2 n 1 cos θ i + n 2 1 − ( n 1 nMathematical fallacy (3,127 words) [view diff] no match in snippet view article find links to article

N + 1 horses of the same colour. Thus if any N horses are all the same colour, any N + 1 horses are the same colour. This is clearly true for N = 1 (iPolygonal number (1,109 words) [view diff] exact match in snippet view article find links to article

{\begin{aligned}P(s,n+1)-P(s,n)&=(s-2)n+1\,,\\P(s+1,n)-P(s,n)&=T_{n-1}={\frac {n(n-1)}{2}}\,,\\P(s+k,n)-P(s,n)&=kT_{n-1}=k{\frac {n(n-1)}{2}}\,.\end{aligned}}}President of Russia (4,998 words) [view diff] no match in snippet view article find links to article

Retrieved 22 July 2017. "Закон РФ о поправке к Конституции РФ от 14.03.2020 N 1-ФКЗ "О совершенствовании регулирования отдельных вопросов организации и функционированияFundamental theorem of algebra (7,720 words) [view diff] no match in snippet view article find links to article

combined; in other words, | z n | > | a n − 1 z n − 1 + ⋯ + a 0 | . {\displaystyle \left|z^{n}\right|>\left|a_{n-1}z^{n-1}+\cdots +a_{0}\right|.} When z traversesTyne and Wear (2,322 words) [view diff] no match in snippet view article find links to article

Wear at the English Heritage Archive Tyne and Wear at Curlie Portal: North East England 54°58′26″N 1°36′48″W / 54.974°N 1.6132°W / 54.974; -1.6132Oxford City F.C. (1,675 words) [view diff] no match in snippet view article find links to article

(51°44′38″N 1°15′28″W / 51.7438°N 1.2578°W / 51.7438; -1.2578), which was used from 1900 to 1988; and Cutteslowe Park (51°47′28″N 1°15′47″W / 51.7911°N 1.2631°WAffine transformation (3,570 words) [view diff] exact match in snippet view article find links to article

M = [ y 1 ⋯ y n + 1 1 ⋯ 1 ] [ x 1 ⋯ x n + 1 1 ⋯ 1 ] − 1 . {\displaystyle M={\begin{bmatrix}\mathbf {y} _{1}&\cdots &\mathbf {y} _{n+1}\\1&\cdotsCompound interest (2,547 words) [view diff] no match in snippet view article find links to article

compounding basis, so that ( 1 + r 1 n 1 ) n 1 = ( 1 + r 2 n 2 ) n 2 {\displaystyle \left(1+{\frac {r_{1}}{n_{1}}}\right)^{n_{1}}=\left(1+{\frac {r_{2}}{n_{2}}}\right)^{n_{2}}}A* search algorithm (4,743 words) [view diff] no match in snippet view article find links to article

function f ( n ) = g ( n ) + ( 1 + ε w ( n ) ) h ( n ) {\displaystyle f(n)=g(n)+(1+\varepsilon w(n))h(n)} , where w ( n ) = { 1 − d ( n ) N d ( n ) ≤ NLarge numbers (7,081 words) [view diff] exact match in snippet view article find links to article

value of k n + 1 {\displaystyle {k_{n+1}}} is increased by 1 and everything to the right of ( n + 1 ) k n + 1 {\displaystyle ({n+1})^{k_{n+1}}} is rewritten8 (8,076 words) [view diff] exact match in snippet view article find links to article

"Sequence A000217 (Triangular numbers: a(n) is the binomial(n+1,2) equal to n*(n+1)/2 and 0 + 1 + 2 + ... + n)". The On-Line Encyclopedia of Integer SequencesPolynomial ring (8,165 words) [view diff] no match in snippet view article find links to article

X n α n = ∑ i ( ∑ ( α 1 , … , α n − 1 ) ∣ ( α 1 , … , α n − 1 , i ) ∈ I c α 1 , … , α n − 1 X 1 α 1 ⋯ X n − 1 α n − 1 ) X n i , {\displaystyle \sum _{(\alphaGrade I listed buildings in West Yorkshire (148 words) [view diff] no match in snippet view article find links to article

Ilkley House 1906–08 12 December 2014 SE1085747608 53°55′28″N 1°50′10″W / 53.924495°N 1.83616°W / 53.924495; -1.83616 (Heathcote) 1133518 More imagesTensor product (8,642 words) [view diff] no match in snippet view article find links to article

K^{n}\to K^{n},} and thus linear maps ψ : P n − 1 → P n − 1 {\displaystyle \psi :\mathbb {P} ^{n-1}\to \mathbb {P} ^{n-1}} of projective spaces over K . {\displaystyleInteger partition (3,398 words) [view diff] no match in snippet view article find links to article

p(n)} by the convergent series. p ( n ) = 1 π 2 ∑ k = 1 ∞ A k ( n ) k ⋅ d d n ( 1 n − 1 24 sinh [ π k 2 3 ( n − 1 24 ) ] ) {\displaystyle p(n)={\fracPseudorandom number generator (3,312 words) [view diff] no match in snippet view article find links to article

function f : N 1 → R {\displaystyle f:\mathbb {N} _{1}\rightarrow \mathbb {R} } (where N 1 = { 1 , 2 , 3 , … } {\displaystyle \mathbb {N} _{1}=\left\{1,2Repunit (3,371 words) [view diff] no match in snippet view article find links to article

+ b + b 2 + ⋯ + b n − 1 = b n − 1 b − 1 for | b | ≥ 2 , n ≥ 1. {\displaystyle R_{n}^{(b)}\equiv 1+b+b^{2}+\cdots +b^{n-1}={b^{n}-1 \over {b-1}}\qquadFinite field (6,162 words) [view diff] no match in snippet view article find links to article

denote by n ⋅ x the sum of n copies of x. The least positive n such that n ⋅ 1 = 0 is the characteristic p of the field. This allows defining a multiplicationList of tallest structures in France (81 words) [view diff] no match in snippet view article find links to article

transmitter, central mast 350 m 1970 Guyed Mast Rosnay 46°42′47.49″N 1°14′42.22″E / 46.7131917°N 1.2450611°E / 46.7131917; 1.2450611 (HWU transmitter, centralAndorra la Vella (1,969 words) [view diff] no match in snippet view article find links to article

Andorra la Vella is located in the south west of Andorra, at 42°30′N 1°30′E / 42.500°N 1.500°E / 42.500; 1.500, at the confluence of two mountain streamsNuclear fusion (9,987 words) [view diff] no match in snippet view article find links to article

times the product of the reactant number densities: f = n 1 n 2 ⟨ σ v ⟩ . {\displaystyle f=n_{1}n_{2}\langle \sigma v\rangle .} If a species of nucleiDiscrete space (2,287 words) [view diff] no match in snippet view article find links to article

satisfies this inequality: 2 − ( n + 1 ) < r 1 < 2 n + 1 r r − 1 < 2 n + 1 log 2 ( r − 1 ) < n + 1 − log 2 ( r ) < n + 1 − 1 − log 2 ( r ) < n {\displaystyleGrade II* listed buildings in the West Midlands (142 words) [view diff] no match in snippet view article find links to article

Anglican Church 1907-1909 26 August 1976 SP1091698740 52°35′11″N 1°50′25″W / 52.586358°N 1.840316°W / 52.586358; -1.840316 (All Saints Church) 1343304APICA (synthetic cannabinoid drug) (601 words) [view diff] no match in snippet view article

APICA (2NE1, SDB-001, N-(1-adamantyl)-1-pentyl-1H-indole-3-carboxamide) is an indole based drug that acts as a potent agonist for the cannabinoid receptorsComplex number (13,683 words) [view diff] no match in snippet view article find links to article

contrary to the case of positive real numbers, one has ( z n ) 1 / n ≠ z , {\displaystyle (z^{n})^{1/n}\neq z,} since the left-hand side consists of n valuesSheffield (20,666 words) [view diff] no match in snippet view article find links to article

first time in its history. Sheffield is located at 53°22′59″N 1°27′57″W / 53.38297°N 1.4659°W / 53.38297; -1.4659. It lies directly beside RotherhamAdjugate matrix (4,805 words) [view diff] no match in snippet view article find links to article

R. The (i, j)-minor of A, denoted Mij, is the determinant of the (n − 1) × (n − 1) matrix that results from deleting row i and column j of A. The cofactorLindisfarne (8,986 words) [view diff] no match in snippet view article find links to article

Lighthouse Location Old Law, Middleton, United Kingdom Coordinates 55°42′N 1°48′W / 55.7°N 1.8°W / 55.7; -1.8 Tower Constructed 1859 Designed by John DobsonAbelian group (5,288 words) [view diff] no match in snippet view article find links to article

Aut ( P ) | = ( p n − 1 ) ⋯ ( p n − p n − 1 ) . {\displaystyle \left|\operatorname {Aut} (P)\right|=(p^{n}-1)\cdots (p^{n}-p^{n-1}).} In the most generalMid Suffolk (982 words) [view diff] no match in snippet view article find links to article

52°09′22″N 1°02′56″E / 52.1560°N 1.0489°E / 52.1560; 1.0489 Mid Suffolk is a local government district in Suffolk, England. The district is primarilyGrade I listed buildings in Nottinghamshire (153 words) [view diff] no match in snippet view article find links to article

Parish Church 12th century 13 October 1966 SK5034952363 53°03′58″N 1°15′00″W / 53.066144°N 1.250077°W / 53.066144; -1.250077 (Ruins of Church of All Saints)List of Sites of Special Scientific Interest in Oxfordshire (5,116 words) [view diff] no match in snippet view article find links to article

Nature Conservation Review. Vol. 2. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-21403-2. 51°45′N 1°17′W / 51.75°N 1.28°W / 51.75; -1.28Honeycomb (geometry) (1,319 words) [view diff] no match in snippet view article

A ~ n − 1 {\displaystyle {\tilde {A}}_{n-1}} C ~ n − 1 {\displaystyle {\tilde {C}}_{n-1}} B ~ n − 1 {\displaystyle {\tilde {B}}_{n-1}} D ~ n − 1 {\displaystyleList of Sites of Special Scientific Interest in Berkshire (4,124 words) [view diff] no match in snippet view article find links to article

51°25′N 1°00′W / 51.417°N 1.000°W / 51.417; -1.000 In England, Sites of Special Scientific Interest (SSSIs) are designated by Natural England, whichCotswold Way (935 words) [view diff] no match in snippet view article find links to article

Castle 51°56′49″N 1°57′22″W / 51.947°N 1.956°W / 51.947; -1.956 (Sudeley Castle) SP031276 Sudeley Castle 51°57′25″N 1°58′08″W / 51.957°N 1.969°W / 51Degree (graph theory) (1,274 words) [view diff] no match in snippet view article

regular graph where all vertices have the maximum possible degree, n − 1 {\displaystyle n-1} . In a signed graph, the number of positive edges connected toSimulated annealing (4,573 words) [view diff] no match in snippet view article find links to article

neighbors of each vertex is ∑ k = 1 n − 1 k = n ( n − 1 ) 2 = 190 {\displaystyle \sum _{k=1}^{n-1}k={\frac {n(n-1)}{2}}=190} edges (coming from n chooseErrors and residuals (2,168 words) [view diff] no match in snippet view article find links to article

only n − 1 degrees of freedom: 1 σ 2 ∑ i = 1 n r i 2 ∼ χ n − 1 2 . {\displaystyle {\frac {1}{\sigma ^{2}}}\sum _{i=1}^{n}r_{i}^{2}\sim \chi _{n-1}^{2}Ionization energy (5,892 words) [view diff] no match in snippet view article find links to article

most loosely bound electron from the species having a positive charge of (n − 1). For example, the first three ionization energies are defined as follows:M27 motorway (1,297 words) [view diff] no match in snippet view article find links to article

Constructed 1972–83 Major junctions West end Cadnam 50°55′06″N 1°35′35″W / 50.9182°N 1.5930°W / 50.9182; -1.5930 (M27 motorway (western end)) Major