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For any two nonzero p-adic numbers a and b, the Hilbert symbol is defined as (a,b)={1 if z^2=ax^2+by^2 has a nonzero solution; -1 otherwise. (1) If the p-adic field is not ...

An algorithm for partitioning (or clustering) N data points into K disjoint subsets S_j containing N_j data points so as to minimize the sum-of-squares criterion ...

The first few numbers whose abundance absolute values are odd squares (excluding the trivial cases of powers of 2) are 98, 2116, 4232, 49928, 80656, 140450, 550564, 729632, ...

For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...

A longimeter is a transparent sheet of plastic with a regular grid of lines inclined at an angle of 30 degrees to the sides of the sheet. By counting the number of squares ...

Given n matches (i.e., rigid unit line segments), find the number of topologically distinct planar arrangements which can be made (Gardner 1991). In this problem, two matches ...

Maximum likelihood, also called the maximum likelihood method, is the procedure of finding the value of one or more parameters for a given statistic which makes the known ...

A merit function, also known as a figure-of-merit function, is a function that measures the agreement between data and the fitting model for a particular choice of the ...

Tiling of a Möbius strip can be performed immediately by carrying over a tiling of a rectangle with the same two-sided surface area. However, additional tilings are possible ...

A square-shaped neighborhood that can be used to define a set of cells surrounding a given cell (x_0,y_0) that may affect the evolution of a two-dimensional cellular ...