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searching for Q-Be 211 found (214 total)

alternate case: q-Be

Sanov's theorem (378 words) [view diff] no match in snippet view article find links to article

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). Suppose
Gaussian 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 of
Breadth-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 not
Karush–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 first
Tautological 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 canonical
Isometry (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 let
Direct 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 necessary
Physical 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-geometric
1934 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 0
Typographical 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 decrease
Area (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 formed
Passive 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.natural
Sieve 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 excluded
General 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 sufficiently
Exact 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 between
Power 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 amongst
Integer 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({\tfrac
Frobenius 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 d
Akaike 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 is
Bernoulli 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 probability
Skew 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 root
Compressor (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 energy
Lucas–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 integers
Martingale (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 is
Cross 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 {\displaystyle
List 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 will
Q-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 of
Mersenne 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 (mod
Quadratic 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 → Q
Floor 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 , {\displaystyle
Paley 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 arbitrary
Clifford 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 have
Quadratic 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 be
Curvature (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, max
CEILIDH (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 : The
Quaternion (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. Let
Stereographic 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 Q
Polar 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 . {\displaystyle
Parabola (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 point
Rational 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 what
Continuum 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 entropy
Barbershop 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} is
G-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 isomorphic
Elliptic 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 is
Sylvester 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 period
Poincaré 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 of
Separable 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 by
Change 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 and
Foliation (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 the
Free 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 to
Lucas 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 ⁡ ( b
Hyperbolic 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 hyperbolic
Sectrix 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 \psi
Cyclic 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 \omega
Bombieri 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 ) {\displaystyle
Prime 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 number
Regular 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} [\mathbf
Tree 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's
Hagen–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 C
Torus 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 holomorphic
Farey 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 {\displaystyle
Quantile 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 evaluated
Reduced 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 ) {\displaystyle
Homological 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 R
Group 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 , k
Rank 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 partitions
Exact 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} satisfies
Cayley 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 Moufang
Legendre 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 reciprocity
Fermat'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 Qbe a point on W′ close to P′. Then, by the construction
Better-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 topology
Very 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 ) c
Cubic 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. Define
Schoof'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 {\bar
Pocklington 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 corollary
Wieferich 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 (mod
Non-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}} is
Knowledge 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 given
Čech 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)-simplex
Jordan 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 eigenvalue
List 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. Let
J-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 form
Carmichael'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 1
Bombieri–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 . {\displaystyle
Derived 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. In
Spectral 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 filtration
Quadratic 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 as
Complex 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 defined
Singleton 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 order
Witt'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 points
Block 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 projectively
Cartesian 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 Euclidean
Reductive 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 characteristic
Disk 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     {\displaystyle
Dolbeault 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 article
Liouville 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 | = | c
Poincaré 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 the
Trisectrix 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 {\displaystyle
Bloom 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 bits
Weinberg–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 3
Lens 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 sphere
Cauchy'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, they
Error 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 of
Boolean 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}}\land
Finite 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 displacements
Thaine'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 {\displaystyle
Ultraparallel 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} and
Proof 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 ( k
Gill 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 for
Generalized 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 {\displaystyle
Random 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 q
Duality (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 q
Thomae'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\in
Trammel 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 sliders
Probabilistic 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 notation
Homomorphic 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 {\displaystyle
Erdős–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 respectively
Szemerédi 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 {\displaystyle
Cyclotomic 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 Φ
Geometric 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 Qbe given." To suggest the role of incidence in geometry, a dilation is specified
Edge-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 parameters
Method 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 below
Ample 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 ) {\displaystyle
Yao'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 element
F-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 continuous
Conductor-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 {\displaystyle
Mass 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 is
Manin 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 bilinear
Thin 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, not
Method 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 grounded
MAX-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 field
Pseudo-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\{{\mathcal
Semi-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 such
Domino 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 by
Cyclic 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) is
Cantor'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, let
Khabibullin'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 , + ∞ ) {\displaystyle
Oppenheim 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 that
Plimpton 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 the
Information 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} is
Polar 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 field
Valuation 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 ring
Supermatrix (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 \in
Preference 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 will
Raven 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 Anthology
Semi-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&{\xrightarrow
Quotient 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 {\displaystyle
Quartic 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.} Quadratic
Computability 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 problem
Near-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 that
Monodromy 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 γ
Per 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 ) {\displaystyle
Sperner'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, this
Ideal 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 {\displaystyle
Lyapunov–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 the
Signature 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 {\displaystyle
Cauchy'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 want
Murray'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. The
Kullback'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 moments
Original 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 sum
Info-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 initiation
Generalized 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 the
Exact 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 , ∗ {\displaystyle
Unital (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. Let
Ladyzhenskaya–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 \mathbb
Proofs 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 property
Inversive 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 {\displaystyle
Adele 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. {\displaystyle
Geometric 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 points
Uncertainty 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} , and
Aerodynamic 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|} . As
Kostant'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 {\displaystyle
Grill (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 particular
Profinite 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. It
Permutation 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 elements
Dependent 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 {\displaystyle
Clausen 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 rational
Oscillator 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 ) = Q
Planted 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 will
Coding 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)}}} obtained
Interval 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 three
Polynomial 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 {\displaystyle
Dynamic 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 situation
Qualitative 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 distributions
Ranking 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, the
Complementation 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)) | (q1
Arithmetic 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 {\displaystyle
Gross 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 the
Visual 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