Search Results for ""

The nth-order Sierpiński carpet graph is the connectivity graph of black squares in the nth iteration of the Sierpiński carpet fractal. The first three iterations are shown ...

A smooth function is a function that has continuous derivatives up to some desired order over some domain. A function can therefore be said to be smooth over a restricted ...

Let A_r=a_(ij) be a sequence of N symmetric matrices of increasing order with i,j=1, 2, ..., r and r=1, 2, ..., N. Let lambda_k(A_r) be the kth eigenvalue of A_r for k=1, 2, ...

Let sigma_0(n) and sigma_1(n) denote the number and sum of the divisors of n, respectively (i.e., the zeroth- and first-order divisor functions). A number n is called sublime ...

Let (K,|·|) be a non-Archimedean field. Its valuation ring R is defined to be R={x in K:|x|<=1}. The valuation ring has maximal ideal M={x in K:|x|<1}, and the field R/M is ...

int_0^inftyJ_0(ax)cos(cx)dx={0 a<c; 1/(sqrt(a^2-c^2)) a>c (1) int_0^inftyJ_0(ax)sin(cx)dx={1/(sqrt(c^2-a^2)) a<c; 0 a>c, (2) where J_0(z) is a zeroth order Bessel function of ...

When p is a prime number, then a p-group is a group, all of whose elements have order some power of p. For a finite group, the equivalent definition is that the number of ...

A Latin square is said to be odd if it contains an odd number of rows and columns that are odd permutations. Otherwise, it is said to be even. Let the number of even Latin ...

A generalized quadrangle is a generalized polygon of order 4. An order-(s,t) generalized quadrangle contains s+1 points in each line and has t+1 lines through every point, ...

A katadrome is a number whose hexadecimal digits are in strict descending order. The first few are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 32, 33, 48, 49, ... ...