For a matrix A = [aij ] m,n i,j=1 ∈ Fm×n, the transpose of A is the matrix A> = [aji] n,m j,i=1 ∈ Fn×m. A square matrix A ∈ Rn×n is called symmetric if aji = aij for all i, j ∈ {1, . . . , n} and is called skew-symmetric or anti-symmetric if aji = −aij for all i, j ∈ {1, . . . , n}. A basis will be denoted B = {u1,u2, . . . ,un} when the ordering of the basis vectors is not important and B = [u...

This paper discusses minimum mean-square error quantization for symmetric distributions. If the distribution satisfies a logconcavity condition, the optimal quantizer is itself symmetric. For the gamma distribution often used to model speech signals, the log-concavity condition is not satisfied. It is shown that for this distribution both the uniformly spaced and the nonuniformly spaced optimal...

We present a simple proof of the factorization of (complex) symmetric matrices into a product of a square matrix and its transpose, and discuss its application in establishing a uniqueness property of certain antilinear operators.

The optimal constant over square root of n error bound in the central limit theorem for distribution functions of sums of independent symmetric Bernoulli random variables is 1/ √ 2πn.

Three-moment chi-square and four moment F approximations are given which can be used for testing a unit root in AR(1) model when the innovations have one of a very wide family of symmetric distributions (Student’s t).

Schrödinger equation with the imaginary, PT symmetric potential V (x) = i x is studied and discussed in momentum representation, via a solvable square-well approximation of its kinetic term.

An encryption technique is widely used to keep data confidential. Most of the block symmetric algorithms use substitution functions. Often this functions use so called S-BOX matrix. In this paper author presents one software tool for testing and measuring square s-boxes. Based of information theory functions for testing static and dynamic criteria are presented. These criterions are mathematica...

We present a detailed calculation of the recently published exact solution of a random tiling model possessing an eight-fold symmetric phase. The solution is obtained using Bethe Ansatz and provides closed expressions for the entropy and phason elastic constants. Qualitatively, this model has the same features as the square-triangle random tiling model. We use the method of P. Kalugin, who solv...

A novel, compact, probe-fed microstrip patch antenna for operation in dual-polarization mode is proposed. The novel design is achieved by etching out a symmetric pattern of crossed slots from the surface of a square probe-fed patch. Reduction in patch size of up to 51% with respect to a traditional dual-polarized square patch operating at the same frequency is obtained. Results show linear pola...