Find link

language: af: Afrikaans als: Alemannisch [Alemannic] am: አማርኛ [Amharic] an: aragonés [Aragonese] ar: العربية [Arabic] arz: مصرى [Egyptian Arabic] as: অসমীয়া [Assamese] ast: asturianu [Asturian] az: azərbaycanca [Azerbaijani] azb: تۆرکجه [Southern Azerbaijani] ba: башҡортса [Bashkir] bar: Boarisch [Bavarian] bat-smg: žemaitėška [Samogitian] be: беларуская [Belarusian] be-tarask: беларуская (тарашкевіца) [Belarusian (Taraškievica)] bg: български [Bulgarian] bn: বাংলা [Bengali] bpy: বিষ্ণুপ্রিয়া মণিপুরী [Bishnupriya Manipuri] br: brezhoneg [Breton] bs: bosanski [Bosnian] bug: ᨅᨔ ᨕᨘᨁᨗ [Buginese] ca: català [Catalan] ce: нохчийн [Chechen] ceb: Cebuano ckb: کوردیی ناوەندی [Kurdish (Sorani)] cs: čeština [Czech] cv: Чӑвашла [Chuvash] cy: Cymraeg [Welsh] da: dansk [Danish] de: Deutsch [German] el: Ελληνικά [Greek] en: English eo: Esperanto es: español [Spanish] et: eesti [Estonian] eu: euskara [Basque] fa: فارسی [Persian] fi: suomi [Finnish] fo: føroyskt [Faroese] fr: français [French] fy: Frysk [West Frisian] ga: Gaeilge [Irish] gd: Gàidhlig [Scottish Gaelic] gl: galego [Galician] gu: ગુજરાતી [Gujarati] he: עברית [Hebrew] hi: हिन्दी [Hindi] hr: hrvatski [Croatian] hsb: hornjoserbsce [Upper Sorbian] ht: Kreyòl ayisyen [Haitian] hu: magyar [Hungarian] hy: Հայերեն [Armenian] ia: interlingua [Interlingua] id: Bahasa Indonesia [Indonesian] io: Ido is: íslenska [Icelandic] it: italiano [Italian] ja: 日本語 [Japanese] jv: Basa Jawa [Javanese] ka: ქართული [Georgian] kk: қазақша [Kazakh] kn: ಕನ್ನಡ [Kannada] ko: 한국어 [Korean] ku: Kurdî [Kurdish (Kurmanji)] ky: Кыргызча [Kirghiz] la: Latina [Latin] lb: Lëtzebuergesch [Luxembourgish] li: Limburgs [Limburgish] lmo: lumbaart [Lombard] lt: lietuvių [Lithuanian] lv: latviešu [Latvian] map-bms: Basa Banyumasan [Banyumasan] mg: Malagasy min: Baso Minangkabau [Minangkabau] mk: македонски [Macedonian] ml: മലയാളം [Malayalam] mn: монгол [Mongolian] mr: मराठी [Marathi] mrj: кырык мары [Hill Mari] ms: Bahasa Melayu [Malay] my: မြန်မာဘာသာ [Burmese] mzn: مازِرونی [Mazandarani] nah: Nāhuatl [Nahuatl] nap: Napulitano [Neapolitan] nds: Plattdüütsch [Low Saxon] ne: नेपाली [Nepali] new: नेपाल भाषा [Newar] nl: Nederlands [Dutch] nn: norsk nynorsk [Norwegian (Nynorsk)] no: norsk bokmål [Norwegian (Bokmål)] oc: occitan [Occitan] or: ଓଡ଼ିଆ [Oriya] os: Ирон [Ossetian] pa: ਪੰਜਾਬੀ [Eastern Punjabi] pl: polski [Polish] pms: Piemontèis [Piedmontese] pnb: پنجابی [Western Punjabi] pt: português [Portuguese] qu: Runa Simi [Quechua] ro: română [Romanian] ru: русский [Russian] sa: संस्कृतम् [Sanskrit] sah: саха тыла [Sakha] scn: sicilianu [Sicilian] sco: Scots sh: srpskohrvatski / српскохрватски [Serbo-Croatian] si: සිංහල [Sinhalese] simple: Simple English sk: slovenčina [Slovak] sl: slovenščina [Slovenian] sq: shqip [Albanian] sr: српски / srpski [Serbian] su: Basa Sunda [Sundanese] sv: svenska [Swedish] sw: Kiswahili [Swahili] ta: தமிழ் [Tamil] te: తెలుగు [Telugu] tg: тоҷикӣ [Tajik] th: ไทย [Thai] tl: Tagalog tr: Türkçe [Turkish] tt: татарча/tatarça [Tatar] uk: українська [Ukrainian] ur: اردو [Urdu] uz: oʻzbekcha/ўзбекча [Uzbek] vec: vèneto [Venetian] vi: Tiếng Việt [Vietnamese] vo: Volapük wa: walon [Walloon] war: Winaray [Waray] yi: ייִדיש [Yiddish] yo: Yorùbá [Yoruba] zh: 中文 [Chinese] zh-min-nan: Bân-lâm-gú [Min Nan] zh-yue: 粵語 [Cantonese]

jump to random article

searching for Positive real numbers 174 found (228 total)

alternate case: positive real numbers

Lehmer mean (837 words) [view diff] exact match in snippet view article find links to article

mathematics, the Lehmer mean of a tuple x {\displaystyle x} of positive real numbers, named after Derrick Henry Lehmer, is defined as: L p ( x ) = ∑

{\displaystyle x_{i}} and coefficients c k {\displaystyle c_{k}} are positive real numbers, and the exponents a i k {\displaystyle a_{ik}} are real numbers

1 , u 2 , … , u n {\displaystyle u_{1},u_{2},\dots ,u_{n}} and positive real numbers v 1 , v 2 , … , v n {\displaystyle v_{1},v_{2},\dots ,v_{n}} : (

one can take exponents from any strictly increasing sequence of positive real numbers, and the same result holds. Szász showed that for complex number

or negative. Such a polynomial must have coefficients that are positive real numbers. The term is sometimes restricted to polynomials whose roots have

In mathematics, a sequence of positive real numbers ( s 1 , s 2 , . . . ) {\displaystyle (s_{1},s_{2},...)} is called superincreasing if every element

David Silverman. It is played by two players on a given set S of positive real numbers. Before play starts, a threshold T and penalty ν are chosen with

The identric mean of two positive real numbers x, y is defined as: I ( x , y ) = 1 e ⋅ lim ( ξ , η ) → ( x , y ) ξ ξ η η ξ − η = lim ( ξ , η ) → ( x

mathematics". The functions f ( x ) = b x {\displaystyle f(x)=b^{x}} for positive real numbers b {\displaystyle b} are also known as exponential functions, and

example of a topology on the set S := R+ \ Z+, i.e. the set of all positive real numbers that are not positive whole numbers. To give the set S a topology

In mathematics, the geometric–harmonic mean M(x, y) of two positive real numbers x and y is defined as follows: we form the geometric mean of g0 = x and

the number of digits right of the decimal point. Truncation of positive real numbers can be done using the floor function. Given a number x ∈ R + {\displaystyle

write down arbitrary (not necessarily in X {\displaystyle X} ) positive real numbers x 0 , x 1 , x 2 , … {\displaystyle x_{0},x_{1},x_{2},\ldots } such

x_{1},\dots ,x_{n}} are positive real numbers, then the generalized mean or power mean with exponent p of these positive real numbers is M p ( x 1 , … , x

homomorphism from the set of invertible operators to the set of positive real numbers. The Fuglede−Kadison determinant of an operator A {\displaystyle

Nesbitt's inequality, named after Alfred Nesbitt, states that for positive real numbers a, b and c, a b + c + b a + c + c a + b ≥ 3 2 . {\displaystyle {\frac

in honour of Franz Mertens. This definition can be extended to positive real numbers as follows: M ( x ) = M ( ⌊ x ⌋ ) . {\displaystyle M(x)=M(\lfloor

1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} are positive real numbers. Then 0 < n 1 x 1 + 1 x 2 + ⋯ + 1 x n ≤ x 1 x 2 ⋯ x n n ≤ x 1 +

states that if the quadratic form defines a homomorphism into the positive real numbers on the non-zero part of the algebra, then the algebra must be isomorphic

called a rate parameter. In each of these forms, both parameters are positive real numbers. The distribution has significant applications across various fields

[X]^{2}/\operatorname {E} [Y].} Example 1. Nesbitt's inequality. For positive real numbers a , b , c : {\displaystyle a,b,c:} a b + c + b a + c + c a + b ≥

→ R is a surjective and even bijective (mapping from the set of positive real numbers to the set of all real numbers). Its inverse, the exponential function

can be generalized to positive real numbers (not necessarily irrational) and negative integers as well: if positive real numbers r {\displaystyle r} and

function of a metric space, but instead of taking values in the positive real numbers, it takes values in a group of reflections, called the Weyl group

are typically large positive integers, or more generally, large positive real numbers, but may also be other numbers in other contexts. Googology is the

real exponential function and hence satisfies eln x = x for all positive real numbers x. Complex logarithm functions can be constructed by explicit formulas

{\displaystyle f} is said to be continuous if there is a function of all positive real numbers ε {\displaystyle \varepsilon } and x ∈ X {\displaystyle x\in X}

real values (like the determinant or matrix trace). Working with positive real-numbers brings several advantages: If the estimator of a single parameter

^{2}}{2}}+2\zeta (3)\right)z^{2}+O(z^{3}).} When restricted to the positive real numbers, the gamma function is a strictly logarithmically convex function

{ωn} clearly tends toward zero, by well-known properties of the positive real numbers. This fact can be used to prove, rigorously, that the convergents

original on 2019-08-10. Retrieved 2019-08-09. The parallel sum of two positive real numbers x:y = [(1/x) + (1/y)]−1 arises in electrical circuit theory as the

{\displaystyle \lambda =(\lambda _{1},\dots ,\lambda _{n})} of positive real numbers (the widths of the subintervals), satisfying ∑ i = 1 n λ i = 1.

square roots of negative numbers. For example, if x and y are both positive real numbers, the following chain of equalities appears reasonable at first glance:

Then, given c {\displaystyle c} and α {\displaystyle \alpha } two positive real numbers, if f ∼ G G ( a , d , p ) {\displaystyle f\sim GG(a,d,p)} , then

mean. It was introduced by Kenneth B. Stolarsky in 1975. For two positive real numbers x, y the Stolarsky Mean is defined as: S p ( x , y ) = lim ( ξ

integrals have value π/2 whenever the numbers 3, 5, 7… are replaced by positive real numbers such that the sum of their reciprocals is less than 1. In the example

measured in grams is a function from this collection of weight to positive real numbers. The term "weight function", an allusion to this example, is used

convergence. Specifically, Abel's test states that if a sequence of positive real numbers ( a n ) {\displaystyle (a_{n})} is decreasing monotonically (or

inequality to a power n > 0 (equiv., −n < 0), when a and b are positive real numbers: 0 ≤ a ≤ b ⇔ 0 ≤ an ≤ bn. 0 ≤ a ≤ b ⇔ a−n ≥ b−n ≥ 0. Taking the

real values (like the determinant or matrix trace). Working with positive real numbers brings several advantages: If the estimator of a single parameter

function is strictly logarithmically convex when restricted to the positive real numbers. In fact, by the Bohr–Mollerup theorem, this property can be used

sometimes a branch cut is used; in this case removing the non-positive real numbers from the domain of the function and eliminating π {\displaystyle

n ) n ∈ N {\displaystyle (\lambda _{n})_{n\in \mathbb {N} }} of positive real numbers λ n > 0 {\displaystyle \lambda _{n}>0} such that x ¯ = lim n → ∞

problems with the extension of these definitions to bases that are not positive real numbers. For example, a negative real number has a real nth root, which

particular, with multiplication. This means that, if a and b are positive real numbers such that a = sup x ∈ A x {\displaystyle a=\sup _{x\in A}x} and

{\displaystyle X} and r > 0 {\displaystyle r>0} ranges over the positive real numbers, forms a basis for a topology on X {\displaystyle X} that is called

coordinates for a point of the Teichmüller space of S consist of 3g − 3 positive real numbers called the lengths and 3g − 3 real numbers called the twists. A

{x}{y}}+{\sqrt {\frac {y}{z}}}+{\sqrt[{3}]{\frac {z}{x}}}} for all positive real numbers x, y and z. Suppose we wish to find the minimal value of this function

\{M_{i}\}} in H converges to M in H if there are a sequence of positive real numbers ϵ i {\displaystyle \epsilon _{i}} converging to 0, and a sequence

norm topology of continuous functions on a closed interval in the positive real numbers. This is a generalization of the Stone–Weierstrass theorem. Paul

{\displaystyle f(z)={\sqrt {z}}\,} be the usual square root function on positive real numbers. One may extend its domain to a neighbourhood of z = 1 {\displaystyle

logarithmic integral has an integral representation defined for all positive real numbers x ≠ 1 by the definite integral li ⁡ ( x ) = ∫ 0 x d t ln ⁡ t . {\displaystyle

{\displaystyle {\sqrt {a}}{\sqrt {b}}={\sqrt {ab}},} which is valid for positive real numbers a and b, and was also used in complex number calculations with one

used of these uses the gamma function, which can be defined for positive real numbers as the integral Γ ( z ) = ∫ 0 ∞ x z − 1 e − x d x . {\displaystyle

\infty }x_{n}.} Let ( x n ) {\displaystyle (x_{n})} be a sequence of positive real numbers converging to l {\displaystyle l} and define a n := log ⁡ ( x 1

(PM)^{2}}={(MY)^{2}\cdot (PM)^{2}},} hence MX = MY, since MX, MY, and PM are all positive, real numbers. Thus, M is the midpoint of XY. Other proofs exist, including one

c=f_{n}(c^{n})=f_{n}(b^{n})=b} holds, as the root function on the positive real numbers is an inverse function to the function z ↦ z n {\displaystyle z\mapsto

multiplicative group action of the scaling transformations on the positive real numbers. Another class of simple examples comes from statistical estimation

1 , r 2 , r 3 , … {\displaystyle r_{1},r_{2},r_{3},\ldots } of positive real numbers such that B i ⊆ r i B {\displaystyle B_{i}\subseteq r_{i}B} for

Gallagher. Let x {\displaystyle x} and Q {\displaystyle Q} be any two positive real numbers with x 1 / 2 log − A ⁡ x ≤ Q ≤ x 1 / 2 . {\displaystyle x^{1/2}\log

abundant numbers is given by the following monotonic mapping from the positive real numbers. Let e p ( ε ) = ⌊ ln ⁡ ( 1 + p − 1 p 1 + ε − p ) ln ⁡ p ⌋ {\displaystyle

multiplicative characters. Consider the multiplicative group of positive real numbers (R+,·). Then functions fu : (R+,·) → C such that fu(a) = au, where

x = e. (See figure at right) x−x Unique global maximum over the positive real numbers at x = 1/e. x3/3 − x First derivative x2 − 1 and second derivative

{\displaystyle {\mathcal {P}}} and r {\displaystyle r} ranges over the positive real numbers is a subbasis at the origin for the topology induced by P {\displaystyle

composite numbers is given by the following monotonic mapping from the positive real numbers. Let e p ( x ) = ⌊ 1 p x − 1 ⌋ {\displaystyle e_{p}(x)=\left\lfloor

x\in X.} Suppose a {\displaystyle a} and b {\displaystyle b} are positive real numbers and q , p 1 , … , p n {\displaystyle q,p_{1},\ldots ,p_{n}} are

poisson-gamma or Tweedie distribution is continuous over the strictly positive real numbers, with a mass at zero. For any set of independent random variables

distribution resembles a normal distribution. More specifically, for large positive real numbers κ {\displaystyle \kappa } , f ( x ∣ μ , κ ) ≈ 1 σ 2 π exp ⁡ [ −

n = [ a , n ] {\displaystyle I_{n}=[a,n]} a bounded interval of positive real numbers. For x, y belonging to I, define x ⋆ n y {\displaystyle x\star _{n}y}

\left(y_{i}\right)_{i=1}^{\infty }} in H {\displaystyle H} and positive real numbers ( λ i ) i = 1 ∞ {\displaystyle \left(\lambda _{i}\right)_{i=1}^{\infty

numbers and r 1 , … , r n {\displaystyle r_{1},\dots ,r_{n}} are positive real numbers. Seminormed spaces and topological groups In a seminormed space

Let both functions be defined on some unbounded subset of the positive real numbers, and g ( x ) {\displaystyle g(x)} be strictly positive for all large

points of branches of the curve as the parameter φ ranges over the positive real numbers. For any (x, y) generated in this way, dividing x by y cancels the

{\displaystyle \{x\in \mathbb {R} \mid x>0\}} is the set of all strictly positive real numbers, which can be written in interval notation as ( 0 , ∞ ) {\displaystyle

given by: The nonzero complex numbers for a complex place p The positive real numbers for a real place p in S, and all nonzero real numbers for p not

onto (surjective). However, if the codomain is restricted to the positive real numbers R + ≡ ( 0 , ∞ ) {\displaystyle \mathbb {R} ^{+}\equiv \left(0,\infty

number fields. Main source: An infinite set of trivial solutions in positive real numbers is given by x = y . {\displaystyle x=y.} Nontrivial solutions can

{\displaystyle a=(a_{1},\dots ,a_{n})} define the "a-mean" [a] of positive real numbers x1, ..., xn by [ a ] = 1 n ! ∑ σ x σ 1 a 1 ⋯ x σ n a n , {\displaystyle

and b 1 , b 2 ⋯ b n {\displaystyle b_{1},b_{2}\cdots b_{n}} are positive real numbers with a 1 + a 2 ⋯ + a n = a {\displaystyle a_{1}+a_{2}\cdots +a_{n}=a}

{\displaystyle f} is R + {\displaystyle \mathbb {R} ^{+}} (the set of all positive real numbers and zero). The preimage of { 4 , 9 } {\displaystyle \{4,9\}} under

{ a j } j ∈ N {\displaystyle \{a_{j}\}_{j\in \mathbb {N} }} be positive real numbers with ∑ j a j < ∞ {\displaystyle \sum _{j}a_{j}<\infty } . Define

{X}}} , let { a N } {\displaystyle \{a_{N}\}} be a sequence of positive real numbers such that lim N a N = ∞ {\displaystyle \lim _{N}a_{N}=\infty }

spaces, though they lack some of the properties that logarithms of positive real numbers possess. The continuum hypothesis (CH) states that there are no

product is at least K {\displaystyle K} . When defined over the positive real numbers, S {\displaystyle S} has infinitely many minimal elements of the

generalization of Schur's inequality is the following: Suppose a,b,c are positive real numbers. If the triples (a,b,c) and (x,y,z) are similarly sorted, then the

_{n=1}^{\infty }\left({\frac {4n^{2}}{4n^{2}-1}}\right).} The product of positive real numbers ∏ n = 1 ∞ a n {\displaystyle \prod _{n=1}^{\infty }a_{n}} converges

∞ {\displaystyle M=\{M_{k}\}_{k=0}^{\infty }} be a sequence of positive real numbers. Then the Denjoy-Carleman class of functions CM([a,b]) is defined

{\displaystyle pX+qY\leq m} and graphically by a budget line in the positive real numbers. Assuming strongly monotonic preferences, only bundles that are

two points are sometimes called the foci. Let d1, d2 be non-equal positive real numbers. Let C be the internal division point of AB in the ratio d1 : d2

is strictly larger as the Legendre transform is only defined for positive real numbers. See this article for example. Let F denote a cumulative distribution

in the n-body problem of celestial mechanics, for any choice of positive real numbers m1, ..., mn as the masses? Partially resolved. Proved for almost

induce the same topology, which happens if and only if there exist positive real numbers C {\displaystyle C} and D {\displaystyle D} such that for all x

(1/2+it)|^{2k}\,dt=O(T^{\varepsilon })} for all positive integers k and all positive real numbers ε. This has been proved for k = 1 or 2, but the case k = 3 seems

graphs that admit a positive labeling (labeling of the nodes by positive real numbers) with the following property: Twice any label is the sum of the

numbers count the (0,1) matrices for which all eigenvalues are positive real numbers. The proof is bijective: a matrix A is an adjacency matrix of a

\left|x\right|^{r}+\left|y\right|^{s}+\left|z\right|^{t}=1} where r, s, and t are positive real numbers that determine the main features of the superquadric. Namely: less

root function is holomorphic everywhere except on the set of non-positive real numbers (on strictly negative reals it is not even continuous). The above

highly structured. For any such packing, there must exist three positive real numbers a {\displaystyle a} , b {\displaystyle b} , and c = b a {\displaystyle

elements of an infinite continued fraction consist entirely of positive real numbers, the determinant formula can easily be applied to demonstrate when

asymptotically positive. (the domain of logarithms is the set of all positive real numbers.) Although L'Hôpital's rule applies to both 0 / 0 {\displaystyle

For example, the real numbers form a group for addition, and the positive real numbers form a group for multiplication. The exponential function x ↦ e

non-decreasing function δ ( ε ) {\displaystyle \delta (\varepsilon )} of positive real numbers ε {\displaystyle \varepsilon } such that Δ t < δ ( ε ) {\displaystyle

{\displaystyle H_{\rm {v}}^{px}=1/H_{\rm {s}}^{xp}} and that, both being positive real numbers, ln ⁡ H s x p = − ln ⁡ ( 1 / H s x p ) = − ln ⁡ H v p x {\displaystyle

{\displaystyle \lambda _{i}} , representing a diverging sequence of positive real numbers. The first eigenvalue is zero for closed domains or when using the

|v_{k}\rangle ),} where p k > 0 {\displaystyle {\sqrt {p_{k}}}>0} are positive real numbers, r ψ {\displaystyle r_{\psi }} is the Schmidt rank of | ψ ⟩ {\displaystyle

set = R + n   . {\displaystyle \mathbb {R} _{+}^{n}\ .} (a set of positive real numbers, the consumer cannot preference negative amount of commodities)

{1}{4}}+{\frac {1}{4}}}}={\frac {3}{1.5}}=2\,.} The harmonic mean H of the positive real numbers x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} is

)/{\sqrt {2}}} . Where α , β {\displaystyle \alpha ,\beta } are positive real numbers to be chosen later with α 2 + β 2 = 1 {\displaystyle \alpha ^{2}+\beta

These different conventions differ by elementary terms that are positive real numbers. Kramer, K.; Tunnell, J. (1982). "Elliptic curves and local ϵ-factors"

_{i}(x_{i}^{2}+y_{i}^{2}),} where α , β {\displaystyle \alpha ,\beta } are positive real numbers which are independent of which atom we are looking at but depend

(n+1)}{\varphi (n)}},\;\;n=1,2,\ldots \right\}} is dense in the positive real numbers. They also proved that the set { φ ( n ) n , n = 1 , 2 , … } {\displaystyle

{\displaystyle f:S\to \mathbb {R} } be any map. If there exist positive real numbers a {\displaystyle a} and b {\displaystyle b} such that 0 ≥ inf s

numbers, to infinite dimension (Hilbert spaces, for example) and positive real numbers (in fractal geometry). In algebraic geometry, the dimension of an

) ≥ f ( a ) + f ( b ) {\displaystyle f(a+b)\geq f(a)+f(b)} for positive real numbers a {\displaystyle a} and b {\displaystyle b} . Proof Since f {\displaystyle

generalized from the domain N {\displaystyle \mathbb {N} } uniquely to positive real numbers only due to their recurrence relation and one given function-value

\sigma _{Y}(n-1)^{1/2}.} It has been shown that for a sample {yi} of positive real numbers, σ y 2 ≤ 2 y max ( A − H ) , {\displaystyle \sigma _{y}^{2}\leq

convergent to 0 {\displaystyle 0} if there exists a sequence of positive real numbers r ∙ = ( r i ) i = 1 ∞ {\displaystyle r_{\bullet }=(r_{i})_{i=1}^{\infty

r 2 , … {\displaystyle r_{1},r_{2},\ldots } is a sequence in of positive real numbers that converges to 0 {\displaystyle 0} in R {\displaystyle \mathbb

center)? Answer this question for all positive integers n and all positive real numbers r. (Certain special cases can be easy to compute.) Andrews, D. and

\delta (t)={\frac {1}{a}}\ \delta \!\left({\frac {t}{a}}\right)} for positive real numbers a {\displaystyle a} , it follows that: Ш   T ⁡ ( t ) = 1 T Ш ( t

w=(w_{n})_{n=1}^{\infty }\in c_{0}\setminus \ell _{1}} be a sequence of positive real numbers satisfying 1 = w 1 ≥ w 2 ≥ w 3 ≥ ⋯ {\displaystyle 1=w_{1}\geq w_{2}\geq

the angle between sides a and b is a right angle. For any three positive real numbers a, b, and c such that a2 + b2 = c2, there exists a triangle with

\mathbb {C} } and let M n {\displaystyle M_{n}} be a sequence of positive real numbers such that | f n ( x ) | ≤ M n {\displaystyle |f_{n}(x)|\leq M_{n}}

y. If a {\displaystyle a} and b {\displaystyle b} are distinct positive real numbers then 1 2 min ( a , b ) < | a ∥ b | < min ( a , b ) . {\displaystyle

{\displaystyle x\in X} is a vector and a , c > 0 {\displaystyle a,c>0} are positive real numbers such that p ( x ) + a c   <   inf k ∈ K p ( x + a k ) {\displaystyle

this arg {\displaystyle \arg } is 0 (i.e. all three products are positive real numbers), and by which Ptolemy's theorem A B ¯ ⋅ C D ¯ + A D ¯ ⋅ B C ¯ =

{\displaystyle \mathbb {C} } contains a subset P (namely the set of positive real numbers) of nonzero elements satisfying the following three conditions:

However, there are extensions to other situations. If x and y are positive real numbers, then the convexity of ψ {\displaystyle \psi } leads to the inequality:

foam faces (and hence the spin network edges) were labelled by positive real numbers as opposed to the half-integer labels of SU(2) spin networks. These

impedance is a quantity measured in ohms which represents resistance as positive real numbers in the usual manner, and also represents reactance as positive and

X} is the set of possible outcomes. E.g., it may be the set of positive real numbers, representing the possible annual gross domestic product. It is

two function, which is a strictly increasing function over the positive real numbers and therefore has a unique inverse. Alternatively, it may be defined

Marc Chamberland. He showed that the conjecture does not hold for positive real numbers since there are infinitely many fixed points, as well as orbits

and ‖ ⋅ ‖ ′ {\displaystyle \|\cdot \|'} on Rn you can always find positive real numbers α , β > 0 {\displaystyle \alpha ,\beta >0} , such that α ⋅ ‖ x ‖

{\displaystyle {\widehat {p\,}}^{k}} not exceeding x, x runs over the positive real numbers, and Λ ( n ) {\displaystyle \Lambda (n)} is the von Mangoldt function

distance between the zeros of ζ (1/2 + it) on intervals of large positive real numbers. In the following, N(T) is the total number of real zeros and N0(T)

be shown to be invalid by using a specific value of the set of positive real numbers for A: Value [ A ∨ ¬ A ] = Value [ A ] ∪ Value [ ¬ A ] = Value [

with the usual definition of the arithmetic–geometric mean for positive real numbers. See The Arithmetic-Geometric Mean of Gauss by David A. Cox. Milne

higher order derivatives of F are smooth functions of x on the positive real numbers; (T-2). We require that the function F is rapidly decreasing in

{\displaystyle \sigma (T_{0})} is a discrete, countable subset of positive real numbers, and all the eigenspaces are finite-dimensional. Since F {\displaystyle

{\displaystyle rU,} where r > 0 {\displaystyle r>0} ranges over the positive real numbers, induces a topological vector space topology on X . {\displaystyle

cumulative distribution function of a probability measure on the positive real numbers. The distribution is therefore defined, and any of its multiples

)-regularity]. Suppose δ j , d j {\displaystyle \delta _{j},d_{j}} are positive real numbers and r ≥ 1 {\displaystyle r\geq 1} is an integer. G ( j ) {\displaystyle

discoveries was the notion of the arithmetic-geometric mean (AGM) of two positive real numbers. Systematic investigations on the AGM led him to discover an unusually

characterized by a fixed rate of occurrence Log-normal distribution, for positive real numbers that are assumed to grow exponentially, such as incomes or prices

positive number as its base. The same is true for the logarithm of positive real numbers as long as the logarithm base is positive and not 1. Irrational

is a formal product of a fractional ideal of K and a vector of positive real numbers with components indexed by the infinite places of K. A replete divisor

when the arguments of the logarithm and the square root are non-positive real numbers. The principal value of the square root is thus defined outside

({\boldsymbol {wB}})} . Suppose that the Borel transform converges for all positive real numbers to a function growing sufficiently slowly that the following integral

{\displaystyle \epsilon _{1}} and ϵ 2 {\displaystyle \epsilon _{2}} are positive real numbers that control the squareness of the shape. The surface of the superellipsoid

)=(AB,\beta )} This right group is the direct product of a group (positive real numbers under multiplication) and a right zero semigroup induced by the

the convolution algebra of the locally compact abelian group of positive real numbers with multiplication. The Mellin transform of the function f ( x

number ωx = { 0, r ωxL | s ωxR }, where r and s range over the positive real numbers. If x < y then ωy is "infinitely greater" than ωx, in that it is

p>1} and let b 1 , … , b n {\displaystyle b_{1},\dots ,b_{n}} be positive real numbers. Set S k = ∑ i = 1 k b i {\displaystyle S_{k}=\sum _{i=1}^{k}b_{i}}

(a_{n})} with a n → a {\displaystyle a_{n}\to a} and a sequence of positive real numbers ( p n ) {\displaystyle (p_{n})} with 1 p 1 + ⋯ + p n → 0 {\displaystyle

{\displaystyle f} be a function of compact support that maps into the positive real numbers f : Ω → R 0 + . {\displaystyle f:\Omega \rightarrow \mathbb {R}

(pitch) of their fundamental, and thus are parametrized by the positive real numbers, R+. Musical tones that differ by an octave (a doubling of frequency)

{\displaystyle a} , b {\displaystyle b} , c {\displaystyle c} are positive real numbers (see List of trigonometric identities). A special case is π = arctan

{\varepsilon } =(\varepsilon _{0},\varepsilon _{1},\dots )} of positive real numbers, there is a positive integer S {\displaystyle S} such that for every

r_{\bullet }=\left(r_{i}\right)_{i=1}^{\infty }\to \infty } of positive real numbers such that the sequence ( r i f i ) i = 1 ∞ {\displaystyle

and non-negative respectively describe matrices with exclusively positive real numbers as elements and matrices with exclusively non-negative real numbers

power, always producing a positive result, so logb(x) for any two positive real numbers b and x, where b is not equal to 1, is always a unique real number y

{\displaystyle b} , x {\displaystyle x} , and y {\displaystyle y} are positive real numbers and b ≠ 1 {\displaystyle b\neq 1} , and c {\displaystyle c} and

integral. The volume formula can be generalized even further. For positive real numbers p1, …, pn, define the (p1, …, pn) ball with limit L ≥ 0 to be B

example, a square root calculating function that works only on positive real numbers might be specified as follows: SQRTP(x:real)r:real pre x >=0 post

\partial {z_{n}}^{k_{n}}}}} It is possible to define a combination of positive real numbers { r ν   ( ν = 1 , … , n ) } {\displaystyle \{r_{\nu }\ (\nu =1,\dots

)x\subseteq (0,1)K} if and only if there exists a divergent sequence of positive real numbers t 1 , t 2 , t 3 , ⋯ → ∞ {\displaystyle t_{1},t_{2},t_{3},\cdots

{\displaystyle m_{\bullet }=\left(m_{i}\right)_{i=1}^{\infty }} of positive real numbers such that | t i | ≤ m i {\displaystyle \left|t_{i}\right|\leq m_{i}}

arguments ( R + + {\displaystyle \mathbb {R} _{++}} denotes the set of positive real numbers). For instance, the trading function of the constant product market

whether the collection of positive integers and the collection of positive real numbers "can be corresponded so that each individual of one collection corresponds

a 2 , … , {\displaystyle a_{1},a_{2},\ldots ,} is a sequence of positive real numbers, let c k = a 1 + 1 a 2 + 1 a 3 + 1 ⋱ + 1 a k {\displaystyle c_{k}=a_{1}+{\cfrac

stability. Given a time-series x ( t ) {\displaystyle x(t)} , for any positive real numbers T , τ {\displaystyle T,\tau } , define the real number sequence

following property, known as the Riesz property: There exists two positive real numbers A {\displaystyle A} and B {\displaystyle B} such that for any square

possible to determine a positive quantity δ so that for every pair of positive real numbers a, b with | b − a | < δ {\displaystyle |b-a|<\delta } , every transformed