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The score function u(theta) is the partial derivativeof the log-likelihood function F(theta)=lnL(theta), where L(theta) is the standard likelihood function. Defining the ...

Half a circle. The area of a semicircle of radius r is given by A = int_0^rint_(-sqrt(r^2-x^2))^(sqrt(r^2-x^2))dxdy (1) = 2int_0^rsqrt(r^2-x^2)dx (2) = 1/2pir^2. (3) The ...

A Lie algebra over a field of characteristic zero is called semisimple if its Killing form is nondegenerate. The following properties can be proved equivalent for a ...

A separating family is a set of subsets in which each pair of adjacent elements are found separated, each in one of two disjoint subsets. The 26 letters of the alphabet can ...

The shah function is defined by m(x) = sum_(n=-infty)^(infty)delta(x-n) (1) = sum_(n=-infty)^(infty)delta(x+n), (2) where delta(x) is the delta function, so m(x)=0 for x not ...

The negative derivative S(v)=-D_(v)N (1) of the unit normal N vector field of a surface is called the shape operator (or Weingarten map or second fundamental tensor). The ...

Consider the sum (1) where the x_js are nonnegative and the denominators are positive. Shapiro (1954) asked if f_n(x_1,x_2,...,x_n)>=1/2n (2) for all n. It turns out ...

Two square matrices A and B that are related by B=X^(-1)AX, (1) where X is a square nonsingular matrix are said to be similar. A transformation of the form X^(-1)AX is called ...

Guy's "strong law of small numbers" states that there aren't enough small numbers to meet the many demands made of them. Guy (1988) also gives several interesting and ...

The spherical Hankel function of the second kind h_n^((1))(z) is defined by h_n^((2))(z) = sqrt(pi/(2x))H_(n+1/2)^((2))(z) (1) = j_n(z)-in_n(z), (2) where H_n^((2))(z) is the ...