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Find link is a tool written by Edward Betts.searching for Q-Be 211 found (214 total)

alternate case: q-Be

Sanov's theorem
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Let A be a set of probability distributions over an alphabet X, and let q be an arbitrary distribution over X (where q may or may not be in A). SupposeGaussian q-distribution (861 words) [view diff] no match in snippet view article find links to article

distribution. The limiting uniform distribution is on the range -1 to +1. Let q be a real number in the interval [0, 1). The probability density function ofBreadth-first search (1,494 words) [view diff] no match in snippet view article find links to article

trace the shortest path back to root 1 procedure BFS(G, start_v) is 2 let Q be a queue 3 label start_v as discovered 4 Q.enqueue(start_v) 5 while Q is notKarush–Kuhn–Tucker conditions (2,821 words) [view diff] no match in snippet view article find links to article

constraint. Letting Q {\displaystyle Q} be the quantity of output produced (to be chosen), R ( Q ) {\displaystyle R(Q)} be sales revenue with a positive firstTautological one-form (1,371 words) [view diff] no match in snippet view article find links to article

{\displaystyle Q} be a manifold and M = T ∗ Q {\displaystyle M=T^{*}Q} be the cotangent bundle or phase space. Let π : M → Q {\displaystyle \pi :M\to Q} be the canonicalIsometry (1,784 words) [view diff] no match in snippet view article find links to article

{\displaystyle 2\leq n<\infty } ) into itself. Let d ( p , q ) {\displaystyle d(p,q)} be the distance between points p and q of E n {\displaystyle E^{n}} , and letDirect product of groups (2,887 words) [view diff] no match in snippet view article find links to article

subdirect product is a fiber product. Let G, H, and Q be groups, and let φ: G → Q and χ: H → Q be homomorphisms. The fiber product of G and H over Q,Quotient space (topology) (1,144 words) [view diff] no match in snippet view article

one can determine if q is a quotient map. Two sufficient criteria are that q be open or closed. Note that these conditions are only sufficient, not necessaryPhysical quantity (1,642 words) [view diff] no match in snippet view article find links to article

uniqueley. To clarify these effective template derived quantities, we let q be any quantity within some scope of context (not necessarily base quantities)Serre's multiplicity conjectures (578 words) [view diff] no match in snippet view article find links to article

theory. Let R be a (Noetherian, commutative) regular local ring and P and Q be prime ideals of R. In 1958, Serre realized that classical algebraic-geometric1934 Wimbledon Championships – Women's Singles (156 words) [view diff] no match in snippet view article find links to article

Molesworth 4 5 M Couquerque 4 6 6 Joy Mowbray-Green 6 4 3 M Couquerque 4 3 Q Molly Hargreaves 0 1 P King 6 6 Phyllis King 6 6 P King 6 6 Q BE Frye 2 0Typographical conventions in mathematical formulae (1,132 words) [view diff] no match in snippet view article find links to article

and edge set E...". Theoretically it is admissible to write "Let X = (a, q) be a graph with the vertex set a and edge set q..."; however, this would decreaseArea (5,197 words) [view diff] no match in snippet view article find links to article

is in M. If the rectangle has length h and breadth k then a(R) = hk. Let Q be a set enclosed between two step regions S and T. A step region is formedPassive voice (2,673 words) [view diff] no match in snippet view article find links to article

neqerrluk yukucirtuq neqe-rrluk fish-departed.from.natural.state yuku-cir-tu-q be.moldy-get-IND.INTR-3sg neqe-rrluk yuku-cir-tu-q fish-departed.from.naturalSieve of Sundaram (667 words) [view diff] no match in snippet view article find links to article

the composite odd integers less than 2 n + 2 {\displaystyle 2n+2} . Let q be an odd integer of the form 2 k + 1 {\displaystyle 2k+1} . Then, q is excludedGeneral Leibniz rule (1,055 words) [view diff] no match in snippet view article find links to article

symbol of the composition of differential operators. In fact, let P and Q be differential operators (with coefficients that are differentiable sufficientlyExact functor (2,411 words) [view diff] no match in snippet view article find links to article

but in ways that can still be controlled. Let P and Q be abelian categories, and let F: P→Q be a covariant additive functor (so that, in particular,Scale (map) (5,387 words) [view diff] no match in snippet view article

and longitude λ {\displaystyle \lambda } on the sphere (or ellipsoid). Let Q be a neighbouring point and let α {\displaystyle \alpha } be the angle betweenPower of two (2,853 words) [view diff] no match in snippet view article find links to article

implies that q must divide 16 and be amongst the numbers 1, 2, 4, 8 or 16. Let q be 4, then p must be 124, which is impossible since by hypothesis p is not amongstInteger factorization (2,953 words) [view diff] no match in snippet view article find links to article

some t ∈ N {\displaystyle t\in {\mathbb {N} }} . Let f q {\displaystyle f_{q}} be a random prime form of GΔ with ( Δ q ) = 1 {\displaystyle \left({\tfracFrobenius group (1,270 words) [view diff] no match in snippet view article find links to article

subgroup has arbitrarily large nilpotency class were constructed by Ito: Let q be a prime power, d a positive integer, and p a prime divisor of q −1 with dAkaike information criterion (5,361 words) [view diff] no match in snippet view article find links to article

Note that the distribution of the first population has one parameter. Let q be the probability that a randomly-chosen member of the second population isBernoulli trial (1,161 words) [view diff] no match in snippet view article find links to article

be the probability of success in a Bernoulli trial, and q {\displaystyle q} be the probability of failure. Then the probability of success and the probabilitySkew heap (826 words) [view diff] no match in snippet view article find links to article

Compare roots of two heaps; let p be the heap with the smaller root, and q be the other heap. Let r be the name of the resulting new heap. Let the rootCompressor (6,235 words) [view diff] no match in snippet view article find links to article

differential form of the energy balance for each device Let q {\displaystyle q} be heat, w {\displaystyle w} be work, k e {\displaystyle ke} be kinetic energyLucas–Lehmer primality test (3,431 words) [view diff] no match in snippet view article find links to article

and let q be the smallest prime factor of Mp. Mersenne numbers are odd, so q > 2. Informally, let Z q {\displaystyle \mathbb {Z} _{q}} be the integersMartingale (betting system) (1,671 words) [view diff] no match in snippet view article

rounds. Following is an analysis of the expected value of one round. Let q be the probability of losing (e.g. for American double-zero roulette, it isCross entropy (1,756 words) [view diff] no match in snippet view article find links to article

measure on a Borel σ-algebra). Let P {\displaystyle P} and Q {\displaystyle Q} be probability density functions of p {\displaystyle p} and q {\displaystyleList of rules of inference (1,569 words) [view diff] no match in snippet view article find links to article

{\displaystyle p} be the proposition "If it rains today", q {\displaystyle q} be "We will not go on a canoe today" and let r {\displaystyle r} be "We willQ-analog (1,385 words) [view diff] no match in snippet view article find links to article

The Gaussian coefficients count subspaces of a finite vector space. Let q be the number of elements in a finite field. (The number q is then a power ofMersenne prime (9,528 words) [view diff] no match in snippet view article find links to article

23 are both prime, and 11 = 2 × 4 + 3, so 23 divides 211 − 1. Proof: Let q be 2p + 1. By Fermat's little theorem, 22p ≡ 1 (mod q), so either 2p ≡ 1 (modQuadratic reciprocity (9,211 words) [view diff] no match in snippet view article find links to article

the most standard statement is: Law of quadratic reciprocity — Let p and q be distinct odd prime numbers, and define the Legendre symbol as: ( q p ) =Semiautomaton (1,610 words) [view diff] no match in snippet view article find links to article

made into a monoid by adding the identity function. Let M be a monoid and Q be a non-empty set. If there exists a multiplicative operation μ : Q × M → QFloor and ceiling functions (5,401 words) [view diff] no match in snippet view article find links to article

quadratic reciprocity, as modified by Eisenstein, has two basic steps. Let p and q be distinct positive odd prime numbers, and let m = p − 1 2 , {\displaystylePaley graph (1,580 words) [view diff] no match in snippet view article find links to article

digraph, every small subset of vertices is dominated by some other vertex. Let q be a prime power such that q = 1 (mod 4). That is, q should either be an arbitraryClifford algebra (9,139 words) [view diff] no match in snippet view article find links to article

vector space V be real three-dimensional space R3, and the quadratic form Q be the negative of the usual Euclidean metric. Then, for v, w in R3 we haveQuadratic form (4,344 words) [view diff] no match in snippet view article find links to article

(-1)^{n_{-}}.} These results are reformulated in a different way below. Let q be a quadratic form defined on an n-dimensional real vector space. Let A beCurvature (6,016 words) [view diff] no match in snippet view article find links to article

Euclidean space of any dimension. Given two points P and Q on C, let s(P,Q) be the arc length of the portion of the curve between P and Q and let d(P,Q)Max-flow min-cut theorem (3,333 words) [view diff] no match in snippet view article find links to article

that the profit is maximized. Let P be the set of projects not selected and Q be the set of machines purchased, then the problem can be formulated as, maxCEILIDH (823 words) [view diff] no match in snippet view article find links to article

for the same security over basic schemes.[which?] Let q {\displaystyle q} be a prime power. An integer n {\displaystyle n} is chosen such that : TheQuaternion (11,485 words) [view diff] no match in snippet view article find links to article

q ] = 2 p × q . {\displaystyle [p,q]=2p\times q.} In general, let p and q be quaternions and write p = p s + p v , {\displaystyle p=p_{\text{s}}+p_{\text{v}}Octic reciprocity (188 words) [view diff] no match in snippet view article find links to article

be +1 if x is a k-th power modulo the prime p and -1 otherwise. Let p and q be distinct primes congruent to 1 modulo 8, such that (p|q) = (q|p) = +1. LetStereographic projection (4,784 words) [view diff] no match in snippet view article find links to article

stereographic projection relates to the plane inversion in a simple way. Let P and Q be two points on the sphere with projections P′ and Q′ on the plane. Then P′Torsion (algebra) (1,478 words) [view diff] no match in snippet view article

summand of it. Assume that R is a commutative domain and M is an R-module. Let Q be the quotient field of the ring R. Then one can consider the Q-module M QPolar curve (1,238 words) [view diff] no match in snippet view article find links to article

homogeneous polynomial of degree n, and let the homogeneous coordinates of Q be (a, b, c). Define the operator Δ Q = a ∂ ∂ x + b ∂ ∂ y + c ∂ ∂ z . {\displaystyleParabola (13,341 words) [view diff] no match in snippet view article find links to article

{\displaystyle d} , and hence are of equal length. Let line q {\displaystyle q} be the line parallel to m 0 {\displaystyle m_{0}} and passing through pointRational reciprocity law (291 words) [view diff] no match in snippet view article find links to article

be +1 if x is a k-th power modulo the prime p and -1 otherwise. Let p and q be distinct primes congruent to 1 modulo 4, such that (p|q)2 = (q|p)2 = +1.Profinite integer (476 words) [view diff] no match in snippet view article find links to article

integer. Example: Let F ¯ q {\displaystyle {\overline {\mathbf {F} }}_{q}} be the algebraic closure of a finite field F q {\displaystyle \mathbf {F} _{q}}Potts model (2,758 words) [view diff] no match in snippet view article find links to article

XY model, the Heisenberg model and the N-vector model. Let Q = {1, ..., q} be a finite set of symbols, and let Q Z = { s = ( … , s − 1 , s 0 , s 1 , …Fermat's Last Theorem (11,468 words) [view diff] no match in snippet view article find links to article

numbers 1, 2, 3, ..., let Z be the set of integers 0, ±1, ±2, ..., and let Q be the set of rational numbers a/b, where a and b are in Z with b ≠ 0. In whatContinuum mechanics (7,820 words) [view diff] no match in snippet view article find links to article

\rho } be the density of matter in the region, q ¯ {\displaystyle {\bar {q}}} be the entropy flux at the surface, and r {\displaystyle r} be the entropyBarbershop paradox (1,449 words) [view diff] no match in snippet view article find links to article

dissolve Carroll's paradox, since it not only allows, but in fact requires that both "p implies q" and "p implies not-q" be true, so long as p is not true.Kullback–Leibler divergence (8,851 words) [view diff] no match in snippet view article find links to article

(Table 2.1, Example 2.1). Let P {\displaystyle P} and Q {\displaystyle Q} be the distributions shown in the table and figure. P {\displaystyle P} isG-structure on a manifold (2,526 words) [view diff] no match in snippet view article find links to article

restricts to give a mapping of P into Q. (Note that it is sufficient that Q be contained within the image of f*.) The G-structures P and Q are locally isomorphicElliptic curve (7,266 words) [view diff] no match in snippet view article find links to article

relies on the repeated application of Euclidean divisions on E: let P ∈ E(Q) be a rational point on the curve, writing P as the sum 2P1 + Q1 where Q1 isSylvester matrix (1,341 words) [view diff] no match in snippet view article find links to article

Sylvester matrices are named after James Joseph Sylvester. Formally, let p and q be two nonzero polynomials, respectively of degree m and n. Thus: p ( z ) =Shor's algorithm (5,224 words) [view diff] no match in snippet view article find links to article

{\displaystyle z=f(x)} . Let ω = e 2 π i Q {\displaystyle \omega =e^{\frac {2\pi i}{Q}}} be a Q {\displaystyle Q} -th root of unity, r {\displaystyle r} be the periodPoincaré disk model (3,273 words) [view diff] no match in snippet view article find links to article

constructed by: let P' be the inversion in the boundary circle of point P let Q' be the inversion in the boundary circle of point Q let M be the midpoint ofSeparable polynomial (768 words) [view diff] no match in snippet view article find links to article

be a prime number which does not divide the leading coefficient of P. Let Q be the polynomial over the finite field with p elements, which is obtained byChange of basis (3,098 words) [view diff] no match in snippet view article find links to article

taking Rn to Rm), and let t1 and t2 be their respective matrices. Let p and q be the matrices of the change-of-coordinates automorphisms φ2−1 ∘ φ1 on Rn andFoliation (8,184 words) [view diff] no match in snippet view article find links to article

allowing the following Definition. Let M and Q be manifolds of dimension n and q≤n respectively, and let f : M→Q be a submersion, that is, suppose that theFree category (726 words) [view diff] no match in snippet view article find links to article

itself, then the free category on Q has as arrows 1, f, f∘f,f∘f∘f, etc. Let Q be the quiver with two vertices a, b and two edges e, f from a to b and b toLucas pseudoprime (3,454 words) [view diff] no match in snippet view article find links to article

0 and D = P 2 − 4 Q {\displaystyle D=P^{2}-4Q} , let Uk(P, Q) and Vk(P, Q) be the corresponding Lucas sequences. Let n be a positive integer and let (Runge–Kutta methods (6,509 words) [view diff] no match in snippet view article find links to article

solutions. Let B {\displaystyle B} , M {\displaystyle M} and Q {\displaystyle Q} be three s × s {\displaystyle s\times s} matrices defined by B = diag ( bHyperbolic angle (1,735 words) [view diff] no match in snippet view article find links to article

and P2 the point (x2, 1/x2), then the parallel condition requires that Q be the point (x1x2, 1/x11/x2). It thus makes sense to define the hyperbolicSectrix of Maclaurin (2,640 words) [view diff] no match in snippet view article find links to article

curve is not algebraic and is dense in the plane. Let Q {\displaystyle Q} be the point of intersection of the two lines and let ψ {\displaystyle \psiCyclic quadrilateral (3,696 words) [view diff] no match in snippet view article find links to article

{\displaystyle \omega } be a circle whose diameter is the segment, EF, and let P and Q be Pascal points on sides AB and CD formed by the circle ω {\displaystyle \omegaBombieri norm (843 words) [view diff] no match in snippet view article find links to article

property of this norm is the Bombieri inequality: let P , Q {\displaystyle P,Q} be two homogeneous polynomials respectively of degree d ∘ ( P ) {\displaystylePrime number theorem (5,877 words) [view diff] no match in snippet view article find links to article

of the classical prime number theorem. To state it precisely, let F = GF(q) be the finite field with q elements, for some fixed q, and let Nn be the numberRegular semi-algebraic system (557 words) [view diff] no match in snippet view article find links to article

{\displaystyle P_{>}:=\{p>0\mid p\in P\}} . Let Q {\displaystyle {\mathcal {Q}}} be a quantifier-free formula of k [ x ] {\displaystyle \mathbf {k} [\mathbfTree rotation (1,302 words) [view diff] no match in snippet view article find links to article

right child to be Q. [Set Q's parent to P] Left rotation of node P: Let Q be P's right child. Set P's right child to be Q's left child. [Set Q's left-child'sHagen–Poiseuille equation (5,039 words) [view diff] no match in snippet view article find links to article

let n be the concentration of free charged particles (in m−3) and let q* be the charge of each particle (in coulombs). (For electrons, q* = e = 1.6×10−19 CTorus knot (1,714 words) [view diff] no match in snippet view article find links to article

points. The intersection gives a submanifold of the hypersphere. Let p and q be coprime integers, greater than or equal to two. Consider the holomorphicFarey sequence (4,284 words) [view diff] no match in snippet view article find links to article

and at most r {\displaystyle r} columns of cells. Let Q {\displaystyle Q} be the set of vectors ( q , p ) {\displaystyle (q,p)} such that 1 ≤ q ≤ r {\displaystyleQuantile regression (3,282 words) [view diff] no match in snippet view article find links to article

different values of u. Consider τ = 0.5 {\displaystyle \tau =0.5} and let q be an initial guess for q τ {\displaystyle q_{\tau }} . The expected loss evaluatedReduced ring (711 words) [view diff] no match in snippet view article find links to article

1 ] {\displaystyle R\to R[S^{-1}]} . Let q {\displaystyle {\mathfrak {q}}} be the pre-image of a maximal ideal. Then q {\displaystyle {\mathfrak {q}}}Uncertain inference (633 words) [view diff] no match in snippet view article find links to article

Rijsbergen proposes that the measure of uncertainty of a document d to a query q be the probability of its logical implication, i.e.: P ( d → q ) {\displaystyleHomological conjectures in commutative algebra (1,048 words) [view diff] no match in snippet view article find links to article

{\displaystyle R\subseteq S} be a map of complete local domains, and let Q be a height one prime ideal of S lying over x R {\displaystyle xR} , where RGroup ring (3,725 words) [view diff] no match in snippet view article find links to article

or less than the group ring of the infinite cyclic group Z over R. 3. Let Q be the quaternion group with elements { e , e ¯ , i , i ¯ , j , j ¯ , k , kRank of a partition (1,326 words) [view diff] no match in snippet view article find links to article

notations are used to specify how many partitions have a given rank. Let n, q be a positive integers and m be any integer. The total number of partitionsExact differential (2,149 words) [view diff] no match in snippet view article find links to article

functions). If A {\displaystyle A} has an antiderivative, let Q {\displaystyle Q} be an antiderivative of A {\displaystyle A} and this Q {\displaystyle Q} satisfiesCayley transform (1,955 words) [view diff] no match in snippet view article find links to article

fact, Q must have determinant +1, so is special orthogonal. Conversely, let Q be any orthogonal matrix which does not have −1 as an eigenvalue; then A = (List of problems in loop theory and quasigroup theory (3,461 words) [view diff] no match in snippet view article find links to article

{\displaystyle M(G,2)} when G {\displaystyle G} is a 2-generated group. Let p and q be distinct odd primes. If q is not congruent to 1 modulo p, are all MoufangLegendre symbol (2,207 words) [view diff] no match in snippet view article find links to article

which are used in primality testing. See Wall–Sun–Sun prime. Let p and q be distinct odd primes. Using the Legendre symbol, the quadratic reciprocityFermat's principle (7,842 words) [view diff] no match in snippet view article find links to article

generally a function of location and direction. Now let Q be a point on W close to P, and let Q′ be a point on W′ close to P′. Then, by the constructionBetter-quasi-ordering (1,147 words) [view diff] no match in snippet view article find links to article

{\displaystyle \omega } , is given the usual product topology. Let Q {\displaystyle Q} be a quasi-ordering and endow Q {\displaystyle Q} with the discrete topologyVery smooth hash (1,983 words) [view diff] no match in snippet view article find links to article

{\displaystyle c} be a fixed constant and p {\displaystyle p} , q {\displaystyle q} be primes with p = 2 q + 1 {\displaystyle p=2q+1} and let k ≤ ( log p ) cCubic Hermite spline (2,845 words) [view diff] no match in snippet view article find links to article

the two points with the given tangents. Proof. Let P , Q {\displaystyle P,Q} be two third degree polynomials satisfying the given boundary conditions. DefineSchoof's algorithm (4,098 words) [view diff] no match in snippet view article find links to article

_{l}).} For l ∈ S {\displaystyle l\in S} do: Let q ¯ {\displaystyle {\bar {q}}} be the unique integer such that q ≡ q ¯ ( mod l ) {\displaystyle q\equiv {\barPocklington primality test (2,197 words) [view diff] no match in snippet view article find links to article

let p e {\displaystyle p^{e}} be the maximum power of p dividing A. Let q be a prime factor of N. For the a p {\displaystyle a_{p}} from the corollaryWieferich prime (6,804 words) [view diff] no match in snippet view article find links to article

Iwasawa invariants). Furthermore, the following result was obtained: Let q be an odd prime number, k and p are primes such that p = 2k + 1, k ≡ 3 (modNon-extensive self-consistent thermodynamical theory (1,005 words) [view diff] no match in snippet view article find links to article

S_{q}=S_{q}^{FD}+S_{q}^{BE}} where S q F D {\displaystyle S_{q}^{FD}} is the non-extended version of the Fermi–Dirac entropy and S q B E {\displaystyle S_{q}^{BE}} isKnowledge argument (4,518 words) [view diff] no match in snippet view article find links to article

properties of experiences (and experiences are physical processes). Let Q be such a property. Mary can know all about Q and she can know that a givenČech cohomology (2,409 words) [view diff] no match in snippet view article find links to article

i ) i ∈ { 0 , … , q } {\displaystyle \sigma =(U_{i})_{i\in \{0,\ldots ,q\}}} be such a q-simplex. The j-th partial boundary of σ is defined to be the (q−1)-simplexJordan normal form (6,791 words) [view diff] no match in snippet view article find links to article

(A-\lambda I)\cap \mathrm {Ker} (A-\lambda I)\neq \{0\},} let the dimension of Q be s ≤ r. Each vector in Q is an eigenvector of A' corresponding to eigenvalueList coloring (1,585 words) [view diff] no match in snippet view article find links to article

vertices, and these colors may be chosen arbitrarily. More generally, let q be a positive integer, and let G be the complete bipartite graph Kq,qq. LetJ-structure (1,446 words) [view diff] no match in snippet view article find links to article

connected normal subgroup. Let K have characteristic not equal to 2. Let Q be a quadratic form on the vector space V over K with associated bilinear formCarmichael's theorem (646 words) [view diff] no match in snippet view article find links to article

that D = P 2 − 4 Q > 0 {\displaystyle D=P^{2}-4Q>0} and PQ ≠ 0, let Un(P,Q) be the Lucas sequence of the first kind defined by U 0 ( P , Q ) = 0 , U 1Bombieri–Vinogradov theorem (519 words) [view diff] no match in snippet view article find links to article

simplified by Patrick X. 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 . {\displaystyleDerived category (3,039 words) [view diff] no match in snippet view article find links to article

abelian categories, but their (bounded) derived categories are equivalent. Let Q be any quiver and P be a quiver obtained from Q by reversing some arrows. InSpectral sequence (9,486 words) [view diff] no match in snippet view article find links to article

cohomological spectral sequence. Let E r p , q {\displaystyle E_{r}^{p,q}} be a first-quadrant spectral sequence converging to H with the decreasing filtrationQuadratic residue (5,547 words) [view diff] no match in snippet view article find links to article

the analytic formula for the class number of binary quadratic forms. Let q be a prime number, s a complex variable, and define a Dirichlet L-function asComplex differential form (1,207 words) [view diff] no match in snippet view article find links to article

differential forms is defined in the same way as with real forms. Let p and q be a pair of non-negative integers ≤ n. The space Ωp,q of (p,q)-forms is definedSingleton bound (1,430 words) [view diff] no match in snippet view article find links to article

objects in finite projective geometry. Let P G ( N , q ) {\displaystyle PG(N,q)} be the finite projective space of (geometric) dimension N {\displaystyle N}Conference matrix (1,657 words) [view diff] no match in snippet view article find links to article

Antisymmetric matrices can also be produced by the Paley construction. Let q be a prime power with residue 3 (mod 4). Then there is a Paley digraph of orderWitt's theorem (527 words) [view diff] no match in snippet view article find links to article

of an isomorphism between quadratic spaces may be "cancelled". Let (V, q) be a quadratic space over a field k. Then it admits a Witt decomposition: (Angle of parallelism (1,070 words) [view diff] no match in snippet view article find links to article

motions), one can establish the relation of φ to a with Euclidean geometry. Let Q be the semicircle with diameter on the x-axis that passes through the pointsBlock design (4,344 words) [view diff] no match in snippet view article find links to article

2, another type of ovoid is known – the Suzuki–Tits ovoid. Theorem. Let q be a positive integer, at least 2. (a) If q is odd, then any ovoid is projectivelyCartesian oval (1,093 words) [view diff] no match in snippet view article find links to article

the same linear combination of distances from two fixed points. Let P and Q be fixed points in the plane, and let d(P,S) and d(Q,S) denote the EuclideanReductive group (7,844 words) [view diff] no match in snippet view article find links to article

to some H/Z-torsor over k, as discussed in the next section. Example: Let q be a nondegenerate quadratic form of even dimension 2n over a field k of characteristicDisk laser (1,858 words) [view diff] no match in snippet view article find links to article

power scaling can revealed from a simple model. Let Q {\displaystyle Q~} be the saturation intensity, of the medium, η 0 = ω s / ω p {\displaystyleDolbeault cohomology (4,031 words) [view diff] no match in snippet view article find links to article

subquotient of the space of complex differential forms of degree (p,q). Let Ωp,q be the vector bundle of complex differential forms of degree (p,q). In the articleLiouville number (4,504 words) [view diff] no match in snippet view article find links to article

{p}{q}}\right|<{\frac {1}{q^{n}}}\,.} From this the claimed conclusion follows. Let p and q be any integers with q > 1. Then we have, | x − p q | = | c d − p q | = | cPoincaré half-plane model (3,312 words) [view diff] no match in snippet view article find links to article

perpendicular p from the Euclidean center of the circle to the x-axis. Let point q be the intersection of this line and the x- axis. Draw a line tangent to theTrisectrix of Maclaurin (703 words) [view diff] no match in snippet view article find links to article

{\displaystyle P_{1}} has angle 3 θ {\displaystyle 3\theta } . Let Q {\displaystyle Q} be the point of intersection, then the angle formed by the lines at Q {\displaystyleBloom filter (9,749 words) [view diff] no match in snippet view article find links to article

Mitzenmacher and Upfal. After all n items have been added to the Bloom filter, let q be the fraction of the m bits that are set to 0. (That is, the number of bitsWeinberg–Witten theorem (2,577 words) [view diff] no match in snippet view article find links to article

(p-p')} isn't null, which means that the momentum transfer is spacelike. Let q be the eigenvalue of those states for the charge operator Q, so that: q δ 3Lens space (1,328 words) [view diff] no match in snippet view article find links to article

-actions. More precisely, let p {\displaystyle p} and q {\displaystyle q} be coprime integers and consider S 3 {\displaystyle S^{3}} as the unit sphereCauchy's theorem (geometry) (758 words) [view diff] no match in snippet view article

of plates and hinges will necessarily form a rigid structure. Let P and Q be combinatorially equivalent 3-dimensional convex polytopes; that is, theyError catastrophe (1,201 words) [view diff] no match in snippet view article find links to article

of the two groups be x , y with reproduction rates a>b, respectively; let Q be the probability of a virus in the first group (x) mutating to a member ofBoolean model of information retrieval (1,091 words) [view diff] no match in snippet view article find links to article

{\text{Bayesian epistemology}}\}\end{aligned}}} Let the query Q {\textstyle Q} be: Q = probability ∧ decision-making {\displaystyle Q={\text{probability}}\landFinite element method in structural mechanics (2,950 words) [view diff] no match in snippet view article find links to article

can be directly set up from data input. Let q {\displaystyle \mathbf {q} } be the vector of nodal displacements of a typical element. The displacementsThaine's theorem (291 words) [view diff] no match in snippet view article find links to article

Mihăilescu's theorem (Schoof 2008). Let p {\displaystyle p} and q {\displaystyle q} be distinct odd primes with q {\displaystyle q} not dividing p − 1 {\displaystyleUltraparallel theorem (996 words) [view diff] no match in snippet view article find links to article

abscissa of the Cartesian plane. Let p {\displaystyle p} and q {\displaystyle q} be semicircles above the abscissa with diameters a b {\displaystyle ab} andProof by infinite descent (2,172 words) [view diff] no match in snippet view article find links to article

rational and can be expressed as m⁄n for natural numbers m and n, and let q be the largest integer no greater than √k. Then k = m n = m ( k − q ) n ( kGill Sans (11,329 words) [view diff] no match in snippet view article find links to article

sans-serifs.) Morison also intervened to insist that the letters "J" and "Q" be allowed to elegantly descend below the baseline, something not normal forGeneralized quadrangle (1,298 words) [view diff] no match in snippet view article find links to article

incidence is the natural one. This is a (q-1,q+1)-generalized quadrangle. Let q be a prime power (odd or even) and consider a symplectic polarity θ {\displaystyleRandom cluster model (674 words) [view diff] no match in snippet view article find links to article

subgraph of all open edges ω ( e ) = 1 {\displaystyle \omega (e)=1} ). Let q be a positive real. Then define the new weighted measure as μ ( ω ) = 1 Z qDuality (projective geometry) (5,637 words) [view diff] no match in snippet view article

line OP is called the polar of the point P with respect to circle C. Let q be a line not passing through O. Drop a perpendicular from O to q, meeting qThomae's function (1,453 words) [view diff] no match in snippet view article find links to article

R ∖ Q {\displaystyle \;\alpha \in \mathbb {R} \smallsetminus \mathbb {Q} \;} be any irrational number and define for all i ∈ N , {\displaystyle \;i\inTrammel of Archimedes (867 words) [view diff] no match in snippet view article find links to article

the outer end of the rod, and A, B be the pivots of the sliders. Let p and q be the distances from A to B and B to C, respectively. Let us assume that slidersProbabilistic automaton (1,489 words) [view diff] no match in snippet view article find links to article

subset. Let F = Q accept ⊆ Q {\displaystyle F=Q_{\text{accept}}\subseteq Q} be the set of "accepting" or "final" states of the automaton. By abuse of notationHomomorphic signatures for network coding (3,186 words) [view diff] no match in snippet view article find links to article

q {\displaystyle E/\mathbb {F} _{q}} be an elliptic curve and let F ¯ q {\displaystyle \mathbb {\bar {F}} _{q}} be an algebraic closure of F q {\displaystyleErdős–Mordell inequality (1,028 words) [view diff] no match in snippet view article find links to article

ABC. Let D, E, F be the orthogonal projections of P onto BC, CA, AB. M, N, Q be the orthogonal projections of P onto tangents to (O) at A, B, C respectivelySzemerédi regularity lemma (3,910 words) [view diff] no match in snippet view article find links to article

simultaneously for all irregular pairs). Let Q {\displaystyle {\mathcal {Q}}} be a common refinement of P {\displaystyle {\mathcal {P}}} by A i , j {\displaystyleCyclotomic polynomial (4,826 words) [view diff] no match in snippet view article find links to article

consider Φ n ( N ) {\displaystyle \Phi _{n}(N)} . Let q {\displaystyle q} be a prime factor of Φ n ( N ) {\displaystyle \Phi _{n}(N)} (to see that ΦGeometric Algebra (909 words) [view diff] no match in snippet view article find links to article

dilation he writes, "Let two distinct points P and Q and their images P′ and Q′ be given." To suggest the role of incidence in geometry, a dilation is specifiedEdge-graceful labeling (852 words) [view diff] no match in snippet view article find links to article

{\displaystyle E(G)} and the vertices by V ( G ) {\displaystyle V(G)} . Let q be the cardinality of E ( G ) {\displaystyle E(G)} and p be that of V ( G )IP (complexity) (5,514 words) [view diff] no match in snippet view article

length of φ. Now let F be a finite field with order q > 2n; also demand that q be at least 1000. For each 0 ≤ i ≤ n, define a function fi on F, having parametersMethod of conditional probabilities (3,103 words) [view diff] no match in snippet view article find links to article

the expected number of cut edges was at least |E|/2. Let random variable Q be the number of edges cut. To keep the conditional probability of failure belowAmple line bundle (5,357 words) [view diff] no match in snippet view article find links to article

degree 4 in P 2 {\displaystyle \mathbb {P} ^{2}} ) over C, and let p and q be distinct complex points of X. Then the line bundle L = O ( 2 p − q ) {\displaystyleYao's principle (729 words) [view diff] no match in snippet view article find links to article

algorithm chosen according to p {\displaystyle p} . Let q {\displaystyle q} be a probability distribution over the inputs X {\displaystyle {\mathcal {X}}}Dedekind–MacNeille completion (2,694 words) [view diff] no match in snippet view article find links to article

different partially ordered set. If P is any partially ordered set, let Q be a partial order whose elements contain two copies of P: for each elementF-divergence (1,159 words) [view diff] no match in snippet view article find links to article

ƒ-divergences, Csiszár-Morimoto divergences or Ali-Silvey distances. Let P and Q be two probability distributions over a space Ω such that P is absolutely continuousConductor-discriminant formula (635 words) [view diff] no match in snippet view article find links to article

Q ( ζ p n ) / Q {\displaystyle L=\mathbf {Q} (\zeta _{p^{n}})/\mathbf {Q} } be a cyclotomic extension of the rationals. The Galois group G {\displaystyleMass matrix (1,136 words) [view diff] no match in snippet view article find links to article

is defined by ni free Cartesian coordinates (where ni is 1, 2, or 3). Let q be the column vector comprising all those coordinates. The mass matrix M isManin triple (331 words) [view diff] no match in snippet view article find links to article

a Lie bialgebra then one can construct a Manin triple from it by letting q be the dual of p and defining the commutator of p and q to make the bilinearThin set (Serre) (1,017 words) [view diff] no match in snippet view article

avoiding some given finite set. For example take K = Q: it is required that V(Q) be dense in Π V(Qp) for all products over finite sets of prime numbers p, notMethod of image charges (2,357 words) [view diff] no match in snippet view article find links to article

similar way). In the figure, this is represented by the green point. Let q be the charge of this point. The image of this charge with respect to the groundedMAX-3SAT (1,392 words) [view diff] no match in snippet view article find links to article

queries. This is valid because the number of queries remains constant. Let q be the number of queries. Enumerating all random strings Ri ∈ V, we obtain poly(x)Polynomial greatest common divisor (8,173 words) [view diff] no match in snippet view article find links to article

to satisfy the need of efficiency of computer algebra systems. Let p and q be polynomials with coefficients in an integral domain F, typically a fieldPseudo-arc (1,273 words) [view diff] no match in snippet view article find links to article

C^{*}=\bigcup _{S\in C}S.} The pseudo-arc is defined as follows: Let p and q be distinct points in the plane and { C i } i ∈ N {\displaystyle \left\{{\mathcalSemi-invariant of a quiver (1,403 words) [view diff] no match in snippet view article find links to article

Sato and Kimura described the ring of semi-invariants in such case. Let Q be a Dynkin quiver, d a dimension vector. Let ∑ be the set of weights σ suchDomino computer (744 words) [view diff] no match in snippet view article find links to article

needed if one wants a logical connective with output 0 for input 1. Let P$Q be the gate in which the sequence to be turned down by P is broken by that byCyclic sieving (1,230 words) [view diff] no match in snippet view article find links to article

generated by an element c of order n. Suppose C acts on a set X. Let X(q) be a polynomial with integer coefficients. Then the triple (X, X(q), C) isCantor's first set theory article (7,230 words) [view diff] no match in snippet view article find links to article

\ldots } ⋮ {\displaystyle \ \ \vdots } Let [ p , q ] {\displaystyle [p,q]} be an interval such that no term of sequence (1) lies in it. For example, letKhabibullin's conjecture on integral inequalities (694 words) [view diff] no match in snippet view article find links to article

Khabibullin's conjecture (version 3). Let q {\displaystyle \displaystyle q} be a non-negative continuous function on the half-line [ 0 , + ∞ ) {\displaystyleOppenheim conjecture (727 words) [view diff] no match in snippet view article find links to article

of the conjecture were formulated by Oppenheim and Harold Davenport. Let Q be a real nondegenerate indefinite quadratic form in n variables. Suppose thatPlimpton 322 (5,835 words) [view diff] no match in snippet view article find links to article

corresponds to an angle of 0°. He found that, maintaining the requirement that q be a single-digit sexagesimal number, there are 23 pairs in addition to theInformation theory and measure theory (1,754 words) [view diff] no match in snippet view article find links to article

Kullback–Leibler divergence: let P {\displaystyle P} and Q {\displaystyle Q} be probability measures over the same space. Then if P {\displaystyle P} isPolar space (660 words) [view diff] no match in snippet view article find links to article

is collinear to all points of ℓ. Let P G ( n , q ) {\displaystyle PG(n,q)} be the projective space of dimension n {\displaystyle n} over the finite fieldValuation ring (3,898 words) [view diff] no match in snippet view article find links to article

{\displaystyle p(D')} is a valuation ring of k ( p ) {\displaystyle k(p)} and let q be the corresponding place; the rest is mechanical.) If D is a valuation ringSupermatrix (2,273 words) [view diff] no match in snippet view article find links to article

independent of the choice of basis, just as in the ungraded case. Let Rp|q be the space of column supervectors—supermatrices of dimension (p|q)×(1|0).Differential dynamic programming (1,843 words) [view diff] no match in snippet view article find links to article

min [ ] {\displaystyle \min[]} operator in Eq. 2, let Q {\displaystyle Q} be the variation of this quantity around the i {\displaystyle i} -th ( x ,Maass wave form (8,502 words) [view diff] no match in snippet view article find links to article

{\displaystyle y\to \infty } . Let c ∈ Q {\displaystyle c\in \mathbb {Q} } be another cusp. Then there exists θ ∈ S L 2 ( Z ) {\displaystyle \theta \inPreference ranking organization method for enrichment evaluation (2,458 words) [view diff] no match in snippet view article find links to article

actions and let F = { f 1 , . . , f q } {\displaystyle F=\{f_{1},..,f_{q}\}} be a consistent family of q criteria. Without loss of generality, we willRaven Oak (2,583 words) [view diff] exact match in snippet view article find links to article

universe as Class-M Exile, will also be released in 2017. Her short story "Q-Be" will be published on October 1, 2016 in Untethered: A Magic iPhone AnthologySemi-abelian category (468 words) [view diff] no match in snippet view article find links to article

non Hausdorff) bornological spaces is semi-abelian. Let Q {\displaystyle Q} be the quiver 1 → 2 ← 3 ↓ ↓ ↓ 4 → 5 ← 6 {\displaystyle {\begin{array}{ccc}1&{\xrightarrowQuotient by an equivalence relation (349 words) [view diff] no match in snippet view article find links to article

sheaves. Let X be a set and consider some equivalence relation on it. Let Q be the set of all equivalence classes in X. Then the map q : X → Q {\displaystyleQuartic reciprocity (4,790 words) [view diff] no match in snippet view article find links to article

beyond the character of 2, let the prime p = a2 + b2 where b is even, and let q be a prime such that ( p q ) = 1. {\displaystyle ({\tfrac {p}{q}})=1.} QuadraticComputability logic (2,538 words) [view diff] no match in snippet view article find links to article

and ⊓x(p(x)⩛¬p(x)) the problem of recursively approximating p. Let p and q be two unary predicates. Then ⊓x(p(x)⊔¬p(x))⟜⊓x(q(x)⊔¬q(x)) expresses the problemNear-field (mathematics) (1,752 words) [view diff] no match in snippet view article

The construction of Dickson proceeds as follows. Let q {\displaystyle q} be a prime power and choose a positive integer n {\displaystyle n} such thatMonodromy theorem (1,328 words) [view diff] no match in snippet view article find links to article

f:U\to \mathbb {C} } be a complex-analytic function. Let Q {\displaystyle Q} be another point in the complex plane. If there exists a family of curves γPer Enflo (4,309 words) [view diff] no match in snippet view article find links to article

property of this norm is the Bombieri inequality: Let P , Q {\displaystyle P,Q} be two homogeneous polynomials respectively of degree d ∘ ( P ) {\displaystyleSperner's theorem (2,012 words) [view diff] no match in snippet view article find links to article

field of order q, let L ( p , F q ) {\displaystyle {\mathcal {L}}(p,F_{q})} be the family of all subspaces. When partially ordered by set inclusion, thisIdeal lattice (5,823 words) [view diff] no match in snippet view article find links to article

polynomial x n + 1 {\displaystyle x^{n}+1} is irreducible. Let q {\displaystyle q} be a prime number such that 2 n {\displaystyle 2n} divides q − 1 {\displaystyleLyapunov–Schmidt reduction (968 words) [view diff] no match in snippet view article find links to article

dim Y 2 < ∞ {\displaystyle \dim Y_{2}<\infty } . Let Q {\displaystyle Q} be the projection operator onto Y 1 {\displaystyle Y_{1}} . Consider also theSignature of a knot (948 words) [view diff] no match in snippet view article find links to article

→ Q {\displaystyle tr:\mathbb {Q} [\mathbb {Z} ]/\Delta K\to \mathbb {Q} } be any linear function which is invariant under the involution t ⟼ t − 1 {\displaystyleCauchy's functional equation (2,080 words) [view diff] no match in snippet view article find links to article

maps. Theorem: Let f : Q → Q {\displaystyle f:\mathbb {Q} \to \mathbb {Q} } be an additive function. Then f {\displaystyle f} is linear. Proof: We wantMurray's law (1,964 words) [view diff] no match in snippet view article find links to article

assumption of mass-conservation this will yield the law. Let Q {\displaystyle Q} be the laminar flow rate in this channel, which is assumed to be fixed. TheKullback's inequality (1,428 words) [view diff] no match in snippet view article find links to article

{\displaystyle P.} The Cramér–Rao bound is a corollary of this result. Let P and Q be probability distributions (measures) on the real line, whose first momentsOriginal proof of Gödel's completeness theorem (4,737 words) [view diff] no match in snippet view article find links to article

previously unused variables of the same length as x and y respectively, and let Q be a previously unused relation symbol that takes as many arguments as the sumInfo-gap decision theory (19,660 words) [view diff] no match in snippet view article find links to article

the pernicious and propitious facets of uncertainty. Let q {\displaystyle q} be a decision vector of parameters such as design variables, time of initiationGeneralized relative entropy (1,929 words) [view diff] no match in snippet view article find links to article

{\displaystyle Q} be the orthogonal projection onto the positive eigenspace of ρ − σ {\displaystyle \rho -\sigma } , and let Q ¯ {\displaystyle {\bar {Q}}} be theExact couple (1,645 words) [view diff] no match in snippet view article find links to article

spectral sequences horizontal and vertical.) Let K p , q {\displaystyle K^{p,q}} be a double complex. With the notation G p = ⨁ i ≥ p K i , ∗ {\displaystyleUnital (geometry) (1,133 words) [view diff] no match in snippet view article

unitals, based on Ree groups was constructed by H. Lüneburg. Let Γ = R(q) be the Ree group of type 2G2 of order (q3 + 1)q3(q − 1) where q = 32m+1. LetLadyzhenskaya–Babuška–Brezzi condition (696 words) [view diff] no match in snippet view article find links to article

spaces and bilinear forms. Let V {\displaystyle V} and Q {\displaystyle Q} be Hilbert spaces, and let a : V × V → R {\displaystyle a:V\times V\to \mathbbProofs of quadratic reciprocity (3,693 words) [view diff] no match in snippet view article find links to article

Gal ( L / Q ) {\displaystyle \phi \in \operatorname {Gal} (L/\mathbf {Q} )} be the Frobenius automorphism associated to β; the characteristic propertyInversive congruential generator (2,258 words) [view diff] no match in snippet view article find links to article

1} and q ≥ 2 {\displaystyle q\geq 2} let C k ( q ) {\displaystyle C_{k}(q)} be the set of nonzero lattice points ( h 1 , … , h k ) ∈ Z k {\displaystyleAdele ring (16,865 words) [view diff] no match in snippet view article find links to article

, {\displaystyle \alpha =(\alpha _{p})_{p}\in \mathbb {A} _{\mathbb {Q} },} be arbitrary and p {\displaystyle p} be a prime for which | α p | > 1. {\displaystyleGeometric separator (2,131 words) [view diff] no match in snippet view article find links to article

a wide variety of optimality measures) may be found in O(Nd) steps. Let Q be a set of n points in the plane such that the minimal distance between pointsUncertainty theory (3,798 words) [view diff] no match in snippet view article find links to article

(Liu, Holder's Inequality) Let p {\displaystyle p} and q {\displaystyle q} be positive numbers with 1 / p + 1 / q = 1 {\displaystyle 1/p+1/q=1} , andAerodynamic potential-flow code (1,530 words) [view diff] no match in snippet view article find links to article

point in the volume V Let S be the surface boundary of the volume V. Let Q be a point on the surface S, and R = | P − Q | {\displaystyle R=|P-Q|} . AsKostant's convexity theorem (1,870 words) [view diff] no match in snippet view article find links to article

let a {\displaystyle {\mathfrak {a}}} be a maximal Abelian subspace. Let Q be the orthogonal projection of p {\displaystyle {\mathfrak {p}}} onto a {\displaystyleGrill (cryptology) (10,407 words) [view diff] no match in snippet view article

S does exist, however, so for no [initial position] will the expression Q be equal to each other, but among them will be a certain similarity for a particularProfinite word (997 words) [view diff] no match in snippet view article find links to article

words. Those notions are now defined. Let M and N be monoids, and let p and q be elements of the monoid M. Let φ be a morphism of monoids from M to N. ItPermutation polynomial (2,726 words) [view diff] no match in snippet view article find links to article

interleaver component of error detection and correction algorithms. Let Fq = GF(q) be the finite field of characteristic p, that is, the field having q elementsDependent random choice (1,779 words) [view diff] no match in snippet view article find links to article

U_{3-i}} . Formally, let u , n , r , m , t , q {\displaystyle u,n,r,m,t,q} be some positive integers with q > r {\displaystyle q>r} , and let α > 0 {\displaystyleClausen function (7,576 words) [view diff] no match in snippet view article find links to article

{j+p}{2p}}\right)\right]} Let p {\displaystyle \,p\,} and q {\displaystyle \,q\,} be positive integers, such that q / p {\displaystyle \,q/p\,} is a rationalOscillator representation (21,581 words) [view diff] no match in snippet view article find links to article

proofs for R. Let A be a finite abelian group, written additively, and let Q be a non-degenerate quadratic form on A with values in T. Thus ( a , b ) = QPlanted motif search (4,665 words) [view diff] no match in snippet view article find links to article

k (for k ≤ l) such that each of these occurs in every input string. Let Q be a collection of k-mers in M. Note that, in every input string si, there willCoding theory approaches to nucleic acid design (5,640 words) [view diff] no match in snippet view article find links to article

which complementary pair it belongs to. Let q {\displaystyle {\mathit {q}}} be a DNA sequence. The sequence b ( q ) {\displaystyle {\mathit {b(q)}}} obtainedInterval scheduling (1,958 words) [view diff] no match in snippet view article find links to article

C = { c 1 , c 2 , . . . , c q } {\displaystyle C=\{c_{1},c_{2},...,c_{q}\}} be a set of clauses over X such that (1) each clause in C has at most threePolynomial method in combinatorics (1,366 words) [view diff] no match in snippet view article find links to article

method. Finite Field Kakeya Conjecture: Let F q {\displaystyle \mathbb {F} _{q}} be a finite field with q {\displaystyle q} elements. Let K ⊆ F q n {\displaystyleDynamic epistemic logic (7,976 words) [view diff] no match in snippet view article find links to article

{\displaystyle p} be the proposition stating that A is dirty, and q {\displaystyle q} be the proposition stating that B is dirty. We represent the initial situationQualitative variation (14,863 words) [view diff] no match in snippet view article find links to article

et al. and was used to compare differences between chromosomes. Let P and Q be two collections of r finite probability distributions. Let these distributionsRanking SVM (2,452 words) [view diff] no match in snippet view article find links to article

Recall} . Let r ∗ {\displaystyle r^{*}} and r f ( q ) {\displaystyle r_{f(q)}} be the expected and proposed ranking methods of a database respectively, theComplementation of Büchi automaton (1,138 words) [view diff] no match in snippet view article find links to article

p,q ∈ Q and i ∈ {0,1}, let Ai,p,q = ( {0,1}×Q, Σ, Δ1∪Δ2, {(0,p)}, {(i,q)} ) be a nondeterministic finite automaton, where Δ1 = { ((0,q1),(0,q2)) | (q1Arithmetic Fuchsian group (3,838 words) [view diff] no match in snippet view article find links to article

field F {\displaystyle F} , let r = [ F : Q ] {\displaystyle r=[F:\mathbb {Q} ]} be its degree, D F {\displaystyle D_{F}} its discriminant and ζ F {\displaystyleGross substitutes (indivisible items) (2,301 words) [view diff] no match in snippet view article

items whose price decreased more. Formally, let p , q {\displaystyle p,q} be two price-vectors and let Δ := q − p {\displaystyle \Delta :=q-p} be theVisual Turing Test (3,771 words) [view diff] no match in snippet view article find links to article

{\displaystyle q\in Q} can be the proposed question, and X q {\displaystyle X_{q}} be the answer to the question q {\displaystyle q} . Then, find the conditional