let = be a non-negative matrix. denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. if we used instead of the purpose of this paper is to establish a hardy type formula for , where is hausdorff matrix and a similar result is also established for where in particular, we apply our results to the cesaro...

The effect of oleic acid (5 and 10% v/v) and xanthan gum (0.5 and 1% wt) on  partitioning and retention of ethyl acetate and diacetyl from two matrices with a different composition was investigated by applying static head space gas chromatography. Two matrices with different composition have been developed: one containing carbohydrates (xanthan gum) and in the second one, called co...

A matrix ! is completely positive if it has a nonnegative factorization ! = !!! where ! is element wise nonnegative. The smallest number of columns in such a matrix ! is called the cp-rank of !. The !×! completely positive matrices form a closed convex cone and its dual is the cone of co-positive matrices. A completely positive matrix is doubly nonnegative – it is positive semi definite and it ...

design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structures are presented. these include techniques for designing non-separable multidimensional paraunitary matrices. properties of the structures are obtained and proofs given. paraunitary matrices play a central role in signal processing, in particular in the areas of filterbanks and wavelets.

In this study, a method is proposed to determine the fundamental period of layered soil profiles. A model considering the layered soil as shear type structure is used. At first, the soil profile is divided into substructures. Then, the stiffness matrices of the substructures considered as the equivalent shear structures are assembled according to the Finite Element Method. Thereinafter, the sti...

BACKGROUND The purpose of the present study was to introduce a new device specifically designed to evaluate the cutting efficiency of mechanically driven endodontic instruments. MATERIAL AND METHODS Twenty new Reciproc R25 (VDW, Munich, Germany) files were used to be investigated in the new device developed to test the cutting ability of endodontic instruments. The device consists of a main f...

In this paper, the ultraspherical operational matrices of derivatives are constructed. Based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems. The basic idea behind the suggested algorithms is basically built on transforming the eq...

Providing Privacy and security for aggregated data in wireless sensor networks has drawn the attention of practicing engineers researchers globally. Several cryptographic methods have been already proposed to solve integrity problems data. Matrix cryptography is a better option creating secure encryption/decryption algorithms counter quantum attack. However, these higher computational cost incr...