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Let X(x)=X(x_1,x_2,...,x_n) be a random vector in R^n and let f_X(x) be a probability distribution on X with continuous first and second order partial derivatives. The Fisher ...

A diagram lemma which states that, given the above commutative diagram with exact rows, the following holds: 1. If alpha is surjective, and beta and delta are injective, then ...

The Fourier cosine transform of a real function is the real part of the full complex Fourier transform, F_x^((c))[f(x)](k) = R[F_x[f(x)](k)] (1) = ...

The study of an extension of derivatives and integrals to noninteger orders. Fractional calculus is based on the definition of the fractional integral as ...

A Fredholm integral equation of the first kind is an integral equation of the form f(x)=int_a^bK(x,t)phi(t)dt, (1) where K(x,t) is the kernel and phi(t) is an unknown ...

For a Galois extension field K of a field F, the fundamental theorem of Galois theory states that the subgroups of the Galois group G=Gal(K/F) correspond with the subfields ...

Let the multiples m, 2m, ..., [(p-1)/2]m of an integer such that pm be taken. If there are an even number r of least positive residues mod p of these numbers >p/2, then m is ...

Googolplex is a large number equal to 10^(10^(100)) (i.e., 1 with a googol number of 0s written after it). The term was coined in 1938 after 9-year-old Milton Sirotta, nephew ...

A minimal free resolution of a finitely generated graded module M over a commutative Noetherian Z-graded ring R in which all maps are homogeneous module homomorphisms, i.e., ...

The term "gradient" has several meanings in mathematics. The simplest is as a synonym for slope. The more general gradient, called simply "the" gradient in vector analysis, ...