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Topics referred to by the same term
Look up geq or GEQ in Wiktionary, the free dictionary. GEQ or geq can refer to: Equatorial Guinea, country in Central Africa Greater than or equal to
GEQ
Mathematical optimization concept
{\displaystyle c\geq 0} be the market prices (a unit of good i {\displaystyle i} can sell for c i {\displaystyle c_{i}} ), and let b ≥ 0 {\displaystyle b\geq 0} be
Dual_linear_program
Foundational principle in quantum physics
Hermann Weyl in 1928: σ x σ p ≥ ℏ 2 {\displaystyle \sigma _{x}\sigma _{p}\geq {\frac {\hbar }{2}}} where ℏ = h 2 π {\displaystyle \hbar ={\frac {h}{2\pi
Uncertainty_principle
Solvability theorem for finite systems of linear inequalities
}\mathbf {y} \geq 0} and b ⊤ y < 0. {\displaystyle \mathbf {b} ^{\top }\mathbf {y} <0.} Here, the notation x ≥ 0 {\displaystyle \mathbf {x} \geq 0} means that
Farkas'_lemma
Inequality about exponentiations of ''1+x''
{\displaystyle (1+x)^{r}\geq 1+rx} for every integer r ≥ 1 {\displaystyle r\geq 1} and real number x ≥ − 1 {\displaystyle x\geq -1} . The inequality is
Bernoulli's_inequality
Bound on probability of a random variable being far from its mean
t } ) {\displaystyle \mu (\{x\in X\,:\,\,g\circ f(x)\geq g(t)\})\geq \mu (\{x\in X\,:\,\,f(x)\geq t\})} . The previous statement then follows by defining
Chebyshev's_inequality
Concept in probability theory
\operatorname {P} (X\geq a)\cdot \operatorname {E} (X\mid X\geq a)\geq a\cdot \operatorname {P} (X\geq a)} For X ≥ a {\displaystyle X\geq a} , the expected
Markov's_inequality
Describes approximate behavior of a function
all x ≥ 1 {\displaystyle x\geq 1} . To prove this, let M = 13 {\displaystyle M=13} . Then, for all x ≥ 1 {\displaystyle x\geq 1} : | 6 x 4 − 2 x 3 + 5 |
Big_O_notation
Mathematical inequality
{\displaystyle a_{1}\geq a_{2}\geq \cdots \geq a_{n}\quad } and b 1 ≥ b 2 ≥ ⋯ ≥ b n , {\displaystyle \quad b_{1}\geq b_{2}\geq \cdots \geq b_{n},} then 1 n
Chebyshev's_sum_inequality
Lemma in measure theory
0 {\displaystyle \operatorname {\mathcal {B}} _{{\bar {\mathbb {R} }}_{\geq 0}}} denotes the σ {\displaystyle \sigma } -algebra of Borel sets on [ 0
Fatou's_lemma
Zande language of the CAR
Adamawa–Ubangian Ubangian Zande languages Zande–Nzakara Geme Dialects Geme Tulu Geme Kulagbolu Language codes ISO 639-3 geq Glottolog geme1244 ELP Geme
Geme_language
In mathematics, notion of limit for sequences of sets
_{n\to \infty }A_{n}=\bigcup _{n\geq 1}\bigcap _{j\geq n}A_{j}=\bigcap _{j\geq 1}A_{j}=\bigcap _{n\geq 1}\bigcup _{j\geq n}A_{j}=\limsup _{n\to \infty }A_{n}
Set-theoretic_limit
Theorem of convex functions
) n {\displaystyle \log \!\left({\frac {\sum _{i=1}^{n}x_{i}}{n}}\right)\geq {\frac {\sum _{i=1}^{n}\log \!\left(x_{i}\right)}{n}}} exp ( log ( ∑ i =
Jensen's_inequality
Partial order between random variables
E [ U ( X i ) ] ≥ E [ U ( X j ) ] {\displaystyle \mathbb {E} [U(X_{i})]\geq \mathbb {E} [U(X_{j})]} ". In this case, we say that X i {\displaystyle X_{i}}
Stochastic_dominance
Probabilistic inequality applying on sum of bounded random variables
{\begin{aligned}\operatorname {P} \left(S_{n}-\mathrm {E} \left[S_{n}\right]\geq t\right)&\leq \exp \left(-{\frac {2t^{2}}{\sum _{i=1}^{n}(b_{i}-a_{i})^{
Hoeffding's_inequality
Indicator function of positive numbers
H(x):={\begin{cases}1,&x\geq 0\\0,&x<0\end{cases}}} Using the Iverson bracket notation: H ( x ) := [ x ≥ 0 ] {\displaystyle H(x):=[x\geq 0]} An indicator function:
Heaviside_step_function
Type of probability distribution
| ≥ t ) ∀ t > 0 {\displaystyle P(|X|\geq t)\leq cP(|Z|\geq t)\quad \forall t>0} where c ≥ 0 {\displaystyle c\geq 0} is constant and Z {\displaystyle Z}
Sub-Gaussian_distribution
f_{1}\geq f_{2}\geq \cdots \geq f_{n-1}\geq |f_{n}|} for N = 2n; f 1 ≥ f 2 ≥ ⋯ ≥ f n ≥ 0 {\displaystyle f_{1}\geq f_{2}\geq \cdots \geq f_{n}\geq 0} for
Restricted_representation
Property of a mathematical matrix
non-negative-definite if x T M x ≥ 0 {\displaystyle \mathbf {x} ^{\mathsf {T}}M\mathbf {x} \geq 0} for all x {\displaystyle \mathbf {x} } in R n . {\displaystyle \mathbb
Definite_matrix
Average value of a random variable
Non-negativity: If X ≥ 0 {\displaystyle X\geq 0} (a.s.), then E [ X ] ≥ 0. {\displaystyle \operatorname {E} [X]\geq 0.} Linearity of expectation: The expected
Expected_value
Probability distribution
{F}}(x)=\Pr(X>x)={\begin{cases}\left({\frac {x_{\mathrm {m} }}{x}}\right)^{\alpha }&x\geq x_{\mathrm {m} },\\1&x<x_{\mathrm {m} },\end{cases}}} where xm is the (necessarily
Pareto_distribution
Mathematical inequality
3 2 , {\displaystyle {\frac {a}{b+c}}+{\frac {b}{a+c}}+{\frac {c}{a+b}}\geq {\frac {3}{2}},} with equality only when a = b = c {\displaystyle a=b=c}
Nesbitt's_inequality
Non-parametric statistic used to estimate the survival function
{\displaystyle c_{k}\geq t} ), then τ ~ k ≥ t {\displaystyle {\tilde {\tau }}_{k}\geq t} if and only if τ k ≥ t {\displaystyle \tau _{k}\geq t} . Let k {\displaystyle
Kaplan–Meier_estimator
Exponentially decreasing bounds on tail distributions of random variables
( t > 0 ) {\displaystyle \operatorname {P} \left(X\geq a\right)=\operatorname {P} \left(e^{tX}\geq e^{ta}\right)\leq M(t)e^{-ta}\qquad (t>0)} Since this
Chernoff_bound
Theorem in geometry
[ μ ( A ) ] 1 / n + [ μ ( B ) ] 1 / n , {\displaystyle [\mu (A+B)]^{1/n}\geq [\mu (A)]^{1/n}+[\mu (B)]^{1/n},} where A + B denotes the Minkowski sum:
Brunn–Minkowski_theorem
{\displaystyle v} , A v ≥ 0 {\displaystyle Av\geq 0} implies v ≥ 0 {\displaystyle v\geq 0} , where ≥ {\displaystyle \geq } is the element-wise order on R n {\displaystyle
Monotone_matrix
Complex-differentiable part of a Maass wave function
n + 1 {\displaystyle A(q)=\sum _{n\geq 0}{\frac {q^{(n+1)^{2}}(-q;q^{2})_{n}}{(q;q^{2})_{n+1}^{2}}}=\sum _{n\geq 0}{\frac {q^{n+1}(-q^{2};q^{2})_{n}
Mock_modular_form
Geometric figure which has infinite surface area but finite volume
concentric right cylinders whose radii were 1 / b ≥ r ≥ 0 {\displaystyle 1/b\geq r\geq 0} and heights h = 1 / r {\displaystyle h=1/r} . Substituting in the formula
Gabriel's_horn
Property of geometry, also used to generalize the notion of "distance" in metric spaces
B)+d(B,C)&\geq d(A,C)\\[4pt]\Rightarrow \quad d(A,B)&\geq d(A,C)-d(B,C)\\[10pt]d(C,A)+d(A,B)&\geq d(C,B)\\[4pt]\Rightarrow \quad d(A,B)&\geq d(B,C)-d(A
Triangle_inequality
Criterion for igniting a nuclear fusion chain reaction
heating exceeds the losses: f E c h ≥ P l o s s {\displaystyle fE_{\rm {ch}}\geq P_{\rm {loss}}} Substituting in known quantities yields: 1 4 n 2 ⟨ σ v ⟩
Lawson_criterion
Theorems on the convergence of bounded monotonic sequences
all n ≥ N {\displaystyle n\geq N} , hence | a n | ≤ | L | + 1 {\displaystyle |a_{n}|\leq |L|+1} for n ≥ N {\displaystyle n\geq N} . Let M = max { | a 1
Monotone_convergence_theorem
Inequality in mathematics
≥ S 2 ≥ S 3 3 ≥ ⋯ ≥ S n n {\textstyle S_{1}\geq {\sqrt {S_{2}}}\geq {\sqrt[{3}]{S_{3}}}\geq \cdots \geq {\sqrt[{n}]{S_{n}}}} , with equality if and only
Maclaurin's_inequality
Concept in mathematical optimization
{\displaystyle \mathbf {x} \in \mathbf {X} } , μ ≥ 0 {\displaystyle \mathbf {\mu } \geq \mathbf {0} } , then x ∗ {\displaystyle \mathbf {x} ^{\ast }} is an optimal
Karush–Kuhn–Tucker_conditions
Arithmetic mean is greater than or equal to geometric mean
numbers x and y, that is, x + y 2 ≥ x y {\displaystyle {\frac {x+y}{2}}\geq {\sqrt {xy}}} with equality if and only if x = y. This follows from the fact
AM–GM_inequality
Result on density of prime numbers
p_{n}} is the n {\displaystyle n} -th prime, is: for n ≥ 1 {\displaystyle n\geq 1} p n + 1 < 2 p n . {\displaystyle p_{n+1}<2p_{n}.} This hypothesis was
Bertrand's_postulate
Type of statistical analysis
= 1 , ‖ f ‖ ≤ 1 } {\displaystyle {\mathcal {H}}=\{f\in {\mathcal {F}}:f\geq 0,\int _{\mathcal {X}}f(x)dx=1,\lVert f\rVert \leq 1\}} and independent random
Nonparametric_statistics
Mathematical inequality
≥ c {\displaystyle a\geq b\geq c} , and either x ≥ y ≥ z {\displaystyle x\geq y\geq z} or z ≥ y ≥ x {\displaystyle z\geq y\geq x} . Let k ∈ Z + {\displaystyle
Schur's_inequality
Inequality applying to triangles
geq &&0\\\iff &&2a^{2}+2b^{2}+2c^{2}&\geq &&2ab+2bc+2ac\\\iff &&3(a^{2}+b^{2}+c^{2})&\geq &&(a+b+c)^{2}\\\iff &&a^{2}+b^{2}+c^{2}&\geq &&{\sqrt
Weitzenböck's_inequality
Algebra theorem about convex functions
f ( a ) = n f ( a ) . {\displaystyle f(x_{1})+f(x_{2})+\cdots +f(x_{n})\geq f(a)+f(a)+\cdots +f(a)=nf(a).} Dividing by n gives Jensen's inequality. The
Karamata's_inequality
Memoryless property of a stochastic process
{\displaystyle X} is called time-homogeneous if for all t , s ≥ 0 {\displaystyle t,s\geq 0} the weak Markov property holds: P ( X t + s ∈ A ∣ F s ) = P ( X t ∈ A
Markov_property
Inequality in probability theorem
X − E [ X ] ≥ λ ) ≤ σ 2 σ 2 + λ 2 , {\displaystyle \Pr(X-\mathbb {E} [X]\geq \lambda )\leq {\frac {\sigma ^{2}}{\sigma ^{2}+\lambda ^{2}}},} where X {\displaystyle
Cantelli's_inequality
Problem in statistical estimation
}}x\geq m\end{cases}}\\={}&[x<m]+[x\geq m]\sum _{n=x+1}^{\infty }{\frac {k-1}{k}}{\frac {\binom {m-1}{k-1}}{\binom {N}{k}}}\\[4pt]={}&[x<m]+[x\geq m]{\frac
German_tank_problem
English saying meaning "equivalent retaliation"
)}}}{1}}\cdot {\frac {6}{\cancel {1-\delta }}}&\geq 9+2\delta \\6+6\delta &\geq 9+2\delta \\4\delta &\geq 3\\\delta &\geq {\frac {3}{4}}\end{aligned}}} Continue
Tit_for_tat
Mathematical relation making a non-equal comparison
e^{x}\geq 1+x.} If x > 0 and p > 0, then 1 p ( x p − 1 ) ≥ ln ( x ) ≥ 1 p ( 1 − 1 x p ) . {\displaystyle {\frac {1}{p}}\left(x^{p}-1\right)\geq \ln(x)\geq
Inequality_(mathematics)
Graph whose vertices correspond to combinations of a set of n elements
Kneser graph K ( n , k ) {\displaystyle K(n,k)} for n ≥ 2 k {\displaystyle n\geq 2k} is exactly n − 2k + 2; for instance, the Petersen graph requires three
Kneser_graph
Mathematical structure that describes the dynamics in a Markovian open quantum system
t ≥ 0 {\displaystyle {\mathcal {T}}:=\left({\mathcal {T}}_{t}\right)_{t\geq 0}} , with the following properties: T 0 ( a ) = a {\displaystyle {\mathcal
Quantum_Markov_semigroup
Probability theorem
{\displaystyle (A_{k})_{k\geq 1}} is non-decreasing, we have P ( ⋃ k ≥ 1 A k ) = lim k → ∞ P ( A k ) {\displaystyle \mathbb {P} \left(\bigcup _{k\geq 1}A_{k}\right)=\lim
Continuous_mapping_theorem
Distance from zero to a number
x ≥ 0 − x , if x < 0. {\displaystyle |x|={\begin{cases}x,&{\text{if }}x\geq 0\\-x,&{\text{if }}x<0.\end{cases}}} The absolute value of x {\displaystyle
Absolute_value
Theorem on eigenvalues and eigenvectors of Hermitian matrices
order). We have λ i ≥ μ i ≥ λ n − r + i , {\displaystyle \lambda _{i}\geq \mu _{i}\geq \lambda _{n-r+i},} An algebraic proof, based on the variational interpretation
Poincaré_separation_theorem
Iterative algorithm on numbers
z ≥ 0 , u ≥ 0 ) . {\displaystyle n=6x+2y+9z+2u\quad (x\geq 1,\ y\geq 1,\ z\geq 0,\ u\geq 0)\,.} ... Sequence of 124578’s, 09’s, 123456789’s and 36’s
Kaprekar's_routine
Highest power of p dividing a given number
\log _{p}n} ; this follows directly from n ≥ p ν p ( n ) {\displaystyle n\geq p^{\nu _{p}(n)}} . The p-adic valuation can be extended to the rational numbers
P-adic_valuation
Method of notation of very large integers
notation is as follows (for a ≥ 0 , n ≥ 1 , b ≥ 0 {\displaystyle a\geq 0,n\geq 1,b\geq 0} ): a ↑ n b = H n + 2 ( a , b ) = a [ n + 2 ] b . {\displaystyle
Knuth's_up-arrow_notation
Real function with secant line between points above the graph itself
its tangents: f ( x ) ≥ f ( y ) + f ′ ( y ) ( x − y ) {\displaystyle f(x)\geq f(y)+f'(y)(x-y)} for all x {\displaystyle x} and y {\displaystyle y} in the
Convex_function
Notions of probabilistic convergence, applied to estimation and asymptotic analysis
n ( x ) = 1 {\displaystyle F_{n}(x)=1} for all x ≥ 1 n {\displaystyle x\geq {\frac {1}{n}}} when n > 0 {\displaystyle n>0} . However, for this limiting
Convergence of random variables
Convergence_of_random_variables
Problem in discrete geometry
g_{3}(n)\geq \Omega _{*}(n^{3/5})} , by applying the recursion relation of to the result g 2 ( n ) ≥ Ω ∗ ( n ) {\displaystyle g_{2}(n)\geq \Omega _{*}(n)}
Erdős distinct distances problem
Erdős_distinct_distances_problem
Generalization of mass, length, area and volume
For all E ∈ Σ , μ ( E ) ≥ 0 {\displaystyle E\in \Sigma ,\ \ \mu (E)\geq 0} Countable additivity (or σ-additivity): For all countable collections
Measure_(mathematics)
Triangles without a right angle
1 2 . {\displaystyle \cos ^{3}A+\cos ^{3}B+\cos ^{3}C+\cos A\cos B\cos C\geq {\frac {1}{2}}.} For an acute triangle, sin 2 A + sin 2 B + sin 2 C
Acute_and_obtuse_triangles
Subclass of matrices
dominant if | a i i | ≥ ∑ j ≠ i | a i j | ∀ i {\displaystyle |a_{ii}|\geq \sum _{j\neq i}|a_{ij}|\ \ \forall \ i} where a i j {\displaystyle a_{ij}}
Diagonally_dominant_matrix
Class of statistical survival models
{\sum _{j:Y_{j}\geq Y_{i}}\theta _{j}X_{j}X_{j}^{\prime }}{\sum _{j:Y_{j}\geq Y_{i}}\theta _{j}}}-{\frac {\left[\sum _{j:Y_{j}\geq Y_{i}}\theta
Proportional_hazards_model
Integral inequality
. {\displaystyle \|h\|_{1}:=\int _{\mathbb {R} ^{n}}h(x)\,\mathrm {d} x\geq \left(\int _{\mathbb {R} ^{n}}f(x)\,\mathrm {d} x\right)^{1-\lambda }\left(\int
Prékopa–Leindler_inequality
Lemma that defines a property of regular languages
\exists p\geq 1,\forall w\in L,|w|\geq p\implies \\\qquad \exists x,y,z\in \Sigma ^{*},(w=xyz)\land (|y|\geq 1)\land (|xy|\leq p)\land (\forall n\geq 0,xy^{n}z\in
Pumping lemma for regular languages
Pumping_lemma_for_regular_languages
Norm on a vector space of matrices
{\displaystyle \ A,B\in K^{m\times n}\ ,} ‖ A ‖ ≥ 0 {\displaystyle \|A\|\geq 0\ } (positive-valued) ‖ A ‖ = 0 ⟺ A = 0 m , n {\displaystyle \|A\|=0\iff
Matrix_norm
Concept in homological algebra
D ≤ 0 , D ≥ 0 ) {\displaystyle ({\mathcal {D}}^{\leq 0},{\mathcal {D}}^{\geq 0})} of a triangulated category or stable infinity category which abstract
T-structure
Property of a color
{\displaystyle R\geq G\geq B} Orange 60 ∘ ⋅ G − B R − B {\displaystyle 60^{\circ }\cdot {\frac {G-B}{R-B}}} G > R ≥ B {\displaystyle G>R\geq B} Chartreuse
Hue
Lower bound on variance of an estimator
θ ^ ) ≥ 1 I ( θ ) {\displaystyle \operatorname {var} ({\hat {\theta }})\geq {\frac {1}{I(\theta )}}} where the Fisher information I ( θ ) {\displaystyle
Cramér–Rao_bound
Mathematical graph relating to chess
{\displaystyle n\geq 2} and m ≥ 2 {\displaystyle m\geq 2} ) Girth 4 (if n ≥ 3 {\displaystyle n\geq 3} and m ≥ 5 {\displaystyle m\geq 5} ) Properties bipartite
Knight's_graph
Distribution result for probability mathematics
{\displaystyle \mathbb {P} \left(\sup _{0\leq s\leq t}W(s)\geq a\right)=2\mathbb {P} (W(t)\geq a)} Assuming W ( 0 ) = 0 {\displaystyle W(0)=0} , due to
Reflection principle (Wiener process)
Reflection_principle_(Wiener_process)
Geometric inequality applicable to any closed curve
\operatorname {vol} (A+B_{\epsilon })\geq (\operatorname {vol} (A)^{1/n}+\operatorname {vol} (B_{\epsilon })^{1/n})^{n}\geq \operatorname {vol} (A)+n\operatorname
Isoperimetric_inequality
Concept in algebraic geometry
{\displaystyle d\geq 0} , and very ample if and only if d ≥ 1 {\displaystyle d\geq 1} . It follows that O(d) is ample if and only if d ≥ 1 {\displaystyle d\geq 1}
Ample_line_bundle
Conjecture on zeros of the zeta function
log | t | {\displaystyle \sigma \geq 1-{\frac {1}{5.558691\log |t|}}} whenever | t | ≥ 2 {\displaystyle |t|\geq 2} , σ ≥ 1 − 1 55.241 ( log | t |
Riemann_hypothesis
Mathematical inequality
. {\displaystyle \operatorname {E} [X^{2}/Y]\geq \operatorname {E} [|X|]^{2}/\operatorname {E} [Y]\geq \operatorname {E} [X]^{2}/\operatorname {E} [Y]
Titu's_lemma
Relation between pairs of arithmetic functions
{\displaystyle g(n)=\sum _{d\mid n}f(d)\quad {\text{for every integer }}n\geq 1} then f ( n ) = ∑ d ∣ n μ ( d ) g ( n d ) for every integer n ≥ 1 {\displaystyle
Möbius_inversion_formula
Statement that all non empty subsets of positive numbers contains a least element
≤ a ) ) ] {\displaystyle \forall A\left[\left(A\subseteq \mathbb {Z} _{\geq 0}\land A\neq \varnothing \right)\rightarrow \left(\exists m\in A\,\forall
Well-ordering_principle
Method to solve optimization problems
\\&{\text{subject to}}&&A\mathbf {x} \leq \mathbf {b} \\&{\text{and}}&&\mathbf {x} \geq \mathbf {0} .\end{aligned}}} Here the components of x {\displaystyle \mathbf
Linear_programming
Theorem in probability theory
}\operatorname {E} \!{\bigl [}|X_{n}|1_{\{N\geq n\}}{\bigr ]}\leq C\sum _{n=1}^{\infty }\operatorname {P} (N\geq n),} and the last series equals the expectation
Wald's_equation
Probability distribution
}}x<\mu \\1-{\frac {1}{2}}\exp \left(-{\frac {x-\mu }{b}}\right)&{\mbox{if }}x\geq \mu \end{cases}}\\&={\tfrac {1}{2}}+{\tfrac {1}{2}}\operatorname {sgn}(x-\mu
Laplace_distribution
Agent-based segregation model
will choose to relocate to a vacant spot where B ≥ B a {\displaystyle B\geq B_{\textrm {a}}} . This continues until every agent is satisfied. Every agent
Schelling's model of segregation
Schelling's_model_of_segregation
Parallel sorting algorithm
⋯ ≤ x m ≥ ⋯ ≥ x n − 1 . {\displaystyle x_{0}\leq \cdots \leq x_{m}\geq \cdots \geq x_{n-1}.} A bitonic sorter can only sort inputs that are bitonic. Bitonic
Bitonic_sorter
Mathematical inequality explaining concentration of random variables
) ≥ Φ ( a ) ) ≤ E ( Φ ( X ) ) Φ ( a ) . {\displaystyle \Pr(X\geq a)=\Pr(\Phi (X)\geq \Phi (a))\leq {\frac {\operatorname {E} (\Phi (X))}{\Phi (a)}}
Concentration_inequality
\varepsilon >0,\Pr(\forall n_{0}\geq 0,\,\exists n\geq n_{0},\,|X_{n}|<\varepsilon )=1} However, for m ≥ 3 {\displaystyle m\geq 3} , ∀ A > 0 , Pr ( ∃ n 0 ≥
Chung–Fuchs_theorem
Concept in Hlibert spaces mathematics
\alpha _{1}\geq \alpha _{2}\geq \cdots \geq \alpha _{n}} and β 1 ≥ β 2 ≥ ⋯ ≥ β n {\displaystyle \beta _{1}\geq \beta _{2}\geq \cdots \geq \beta _{n}}
Trace_inequality
Mode of convergence of a function sequence
natural number N {\displaystyle N} such that for all n ≥ N {\displaystyle n\geq N} and for all x ∈ E {\displaystyle x\in E} | f n ( x ) − f ( x ) | < ε
Uniform_convergence
Mathematical result
Pr\left({\frac {1}{k}}\sum _{i}Q_{i}^{2}\geq 1+\epsilon \right)\geq {\frac {k}{2}}(\epsilon -\ln(1+\epsilon ))\geq {\frac {k}{2}}(\epsilon ^{2}/2-\epsilon
Johnson–Lindenstrauss_lemma
Theorem in functional analysis
ordered in descending order λ 1 ≥ . . . ≥ λ n {\textstyle \lambda _{1}\geq ...\geq \lambda _{n}} . Let v 1 , . . . , v n {\textstyle v_{1},...,v_{n}} be
Min-max_theorem
Equivalence of optimization problems
d_{uv}\geq 1} ). The constraints d s v + z v ≥ 1 {\displaystyle d_{sv}+z_{v}\geq 1} (equivalent to d s v ≥ 1 − z v {\displaystyle d_{sv}\geq 1-z_{v}}
Max-flow_min-cut_theorem
On the existence of hyperplanes separating disjoint convex sets
that ⟨ x , v ⟩ ≥ c and ⟨ y , v ⟩ ≤ c {\displaystyle \langle x,v\rangle \geq c\,{\text{ and }}\langle y,v\rangle \leq c} for all x {\displaystyle x} in
Hyperplane_separation_theorem
Continuous probability distribution
{k}{\lambda }}\left({\frac {x}{\lambda }}\right)^{k-1}e^{-(x/\lambda )^{k}},&x\geq 0,\\0,&x<0,\end{cases}}} where k > 0 is the shape parameter and λ > 0 is
Weibull_distribution
Trying to map moments to a measure that generates them
\Lambda (x^{n})=m_{n}} and Λ ( f 2 ) ≥ 0 {\displaystyle \Lambda (f^{2})\geq 0} (non-negative for sum of squares of polynomials). Assume Λ {\displaystyle
Moment_problem
Criterion for the convergence of a series
(1;r)} such that there exists a natural number n 0 ≥ 2 {\displaystyle n_{0}\geq 2} satisfying a n 0 ≠ 0 {\displaystyle a_{n_{0}}\neq 0} and | a n + 1 a n
Ratio_test
Mathematics of general relativity
{\displaystyle \rho +p\geq 0.} The weak energy condition stipulates that ρ ≥ 0 , ρ + p ≥ 0. {\displaystyle \rho \geq 0,\;\;\rho +p\geq 0.} The dominant energy
Energy_condition
Technique in numerical linear algebra
σ 1 ≥ σ 2 ≥ ⋯ ≥ σ m ≥ 0 {\displaystyle \sigma _{1}\geq \sigma _{2}\geq \cdots \geq \sigma _{m}\geq 0} . We claim that the best rank- k {\displaystyle
Low-rank_approximation
Complete, full information, perfectly competitive markets are Pareto efficient
{\displaystyle \mathbf {x_{i}} \geq _{i}\mathbf {x_{i}^{*}} } then p ⋅ x i ≥ w i {\displaystyle \mathbf {p} \cdot \mathbf {x_{i}} \geq w_{i}} To see why, imagine
Fundamental theorems of welfare economics
Fundamental_theorems_of_welfare_economics
Stochastic process in probability theory
process is a stochastic process X = { X t : t ≥ 0 } {\displaystyle X=\{X_{t}:t\geq 0\}} that satisfies the following properties: X 0 = 0 {\displaystyle X_{0}=0\
Lévy_process
Theorem about the radii of convergence of power series
{\displaystyle f(z)=\sum _{\alpha \geq 0}c_{\alpha }(z-a)^{\alpha }:=\sum _{\alpha _{1}\geq 0,\ldots ,\alpha _{n}\geq 0}c_{\alpha _{1},\ldots ,\alpha
Cauchy–Hadamard_theorem
Recurrence relations of binomial coefficients in Pascal's triangle
identity or Chu's Theorem, states that if n ≥ r ≥ 0 {\displaystyle n\geq r\geq 0} are integers, then ( r r ) + ( r + 1 r ) + ( r + 2 r ) + ⋯ + ( n r
Hockey-stick_identity
Type of automaton
_{\epsilon },x_{1},x_{2},\ldots ,x_{m}\in \Gamma ^{*},m\geq 0,y_{1},y_{2},\ldots ,y_{n}\in \Gamma ^{*},n\geq 0} Construct the following transitions for the PDA:
Pushdown_automaton
Value to which an infinite sequence tends
{\displaystyle N} such that, for every natural number n ≥ N {\displaystyle n\geq N} , we have | x n − x | < ε {\displaystyle |x_{n}-x|<\varepsilon } . In
Limit_of_a_sequence
Data structure for priority queue operations
induction) that F d + 2 ≥ φ d {\displaystyle F_{d+2}\geq \varphi ^{d}} for all integers d ≥ 0 {\displaystyle d\geq 0} , where φ = ( 1 + 5 ) / 2 ≈ 1.618 {\displaystyle
Fibonacci_heap
Mathematical criterion about whether a series converges
(a_{n})_{n\geq 1}} and ( b n ) n ≥ 1 {\displaystyle (b_{n})_{n\geq 1}} be two sequences of real numbers. Assume that ( b n ) n ≥ 1 {\displaystyle (b_{n})_{n\geq
Convergence_tests
Infinitely many prime numbers exist
{1}{p}}}}&=\prod _{p\in P_{k}}\sum _{i\geq 0}{\frac {1}{p^{i}}}\\&=\left(\sum _{i\geq 0}{\frac {1}{2^{i}}}\right)\cdot \left(\sum _{i\geq 0}{\frac {1}{3^{i}}}\right)\cdot
Euclid's_theorem
GEQ
GEQ
GEQ
GEQ
Male
Russian
Hawaiian and Russian form of Greek Loukas, LUKA means "from Lucania."
Girl/Female
Hindu, Indian
Love Goddess; Wife of Kaamadeva
Girl/Female
Tamil
Devanshi | தேவாநà¯à®·à¯€
Divine
Female
Egyptian
, the mother of the royal scribe Pet-amen.
Biblical
my height; throwing forth waters
Boy/Male
Arabic, Muslim
Slave of the Giver
Girl/Female
Hindu, Indian
Full Moon
Boy/Male
Hindu, Indian, Marathi
Excellence; Superiority
Girl/Female
Indian
Counsel, Protector
Boy/Male
Biblical
To hide, demolished.
GEQ
GEQ
GEQ
GEQ
GEQ