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If x_1/n_1 and x_2/n_2 are the observed proportions from standard normally distributed samples with proportion of success theta, then the probability that ...

The invariance of domain theorem states that if f:M->N is a one-to-one and continuous map between n-manifolds without boundary, then f is an open map.

Given a module M over a unit ring R, the set End_R(M) of its module endomorphisms is a ring with respect to the addition of maps, (f+g)(x)=f(x)+g(x), for all x in M, and the ...

The involute of the epicycloid x = (a+b)cost-bcos[((a+b)/b)t] (1) y = (a+b)sint-bsin[((a+b)/b)t] (2) is another epicycloid given by x = (a+2b)/a{(a+b)cost+bcos[((a+b)/b)t]} ...

The conjecture that Frey's elliptic curve was not modular. The conjecture was quickly proved by Ribet (Ribet's theorem) in 1986, and was an important step in the proof of ...

An endomorphism is called ergodic if it is true that T^(-1)A=A implies m(A)=0 or 1, where T^(-1)A={x in X:T(x) in A}. Examples of ergodic endomorphisms include the map X->2x ...

The Gaussian joint variable theorem, also called the multivariate theorem, states that given an even number of variates from a normal distribution with means all 0, (1) etc. ...

2^(30)=1024^3=1073741824 bytes. Although the term gigabyte is sometimes used to refer to 1024^3 bytes, such usage is deprecated in favor of the standard SI naming convention ...

The Hajós number h(G) of a graph G is the maximum k such that G contains a subdivision of the complete graph K_k.

The study, first developed by Boole, of shift-invariant operators which are polynomials in the differential operator D^~. Heaviside calculus can be used to solve any ordinary ...