This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...

In this paper we did a generalization of Hadamard product of Fibonacci Q matrix and Fibonacci Q−n matrix for continuous domain. We obtained Hadamard product of the golden matrices in the terms of the symmetrical hyperbolic Fibonacci functions and investigated some properties of Hadamard product of the golden matrices. Mathematics Subject Classification: Primary 11B25, 11B37, 11B39, Secondary 11C20

The visual explanation of learned representation of models helps to understand the fundamentals of learning. The attentional models of previous works used to visualize the attended regions over an image or text using their learned weights to confirm their intended mechanism. Kim et al. (2016) show that the Hadamard product in multimodal deep networks, which is well-known for the joint function ...

J. Dziok Institute of Mathematics, University of Rzeszów, ul. Rejtana 16A, 35-310 Rzeszów, Poland Correspondence should be addressed to J. Dziok, [email protected] Received 2 July 2009; Revised 21 November 2009; Accepted 5 January 2010 Academic Editor: Vladimir Mityushev Copyright q 2010 J. Dziok. This is an open access article distributed under the Creative Commons Attribution License, wh...

Equivalence operations for n-dimensional proper Hadamard matrices are defined. Their equivalence classes are investigated and bounds on the number of such equivalence classes are found to be associated with the number of equivalence classes of 2-dimensional Hadamard matrices. Properties of planes (2-dimensional sections) in an n-dimensional proper Hadamard matrix are investigated. It is shown t...

Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent func...

The Hadamard and SJT product of matrices are two types of special matrix product. The latter was first defined by Chen [1]. In this study, they are applied to the differential quadrature (DQ) solution of geometrically nonlinear bending of isotropic and orthotropic rectangular plates. By using the Hadamard product, the nonlinear formulations are greatly simplified, while the SJT product approach...

Motivated by the Hadamard product of matrices we define the Hadamard product of multivariate polynomials and study its arithmetic circuit and branching program complexity. We also give applications and connections to polynomial identity testing. Our main results are the following. • We show that noncommutative polynomial identity testing for algebraic branching programs over rationals is comple...