A problem due to Martin LaBar is to find a 3x3 magic square with 9 distinct perfect square entries or prove that such a magic square cannot exist (LaBar [1]). This problem has been tied to various domains including arithmetic progressions, rational right triangles, and elliptic curves (Robertson [2]). However, there are some interesting properties that can be derived without ever leaving the do...

In this paper a general analytical solution is obtained to find stress distribution in a finite elastic plate with a circular or square hole subjected to arbitrary biaxial partial loading using modified boundary condition by assuming plane stress conditions. The method employed is based on solution of circular hole in finite rectangular plate. This plate is mapped to circular ones and the parti...

This paper is concerned with weighted least mean square design of two-dimensional (2-D) zero-phase FIR lters with quadrantally symmetric and antisymmetric frequency responses. The optimal solutions are rst characterized by certain integral equations, and the existence, and uniqueness of the weighted least mean square solution for 2-D FIR lter design are then established using contraction mappin...

A square complex matrix A is called if it can be written in the form EP   1 0 U A U  with U being fixed unitary and 1 A being arbitrary matrix in . We give necessary and sufficient conditions for the existence of the solution to the system of complex matrix equation r r   r EP , AX B XC D   and present an expression of the solution to the system when the solvability conditions are satisf...

In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation Ax = b, where A is an m×n full-rank matrix, b is a column-vector of dimension m, and m (the number of equations) is larger than or equal to n (the dimension of the unknown vector x). Generally, the equations are inconsistent and there is no feasible solution for x unless b belongs t...

a meshless method namely, discrete least square method (dlsm), is presented in the paper for the solution of free surface seepage problem. in this method computational domain is discredited by some nodes and then the set of simultaneous equations are built using moving least square (mls) shape functions and least square technique. the proposed method does not need any background mesh therefore ...