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...

A new construction of complex Hadamard matrices of composite order d = pq, with primes p, q, is presented which is based on pairs of mutually unbiased bases containing only product states. We illustrate the method for many product dimensions d < 100 by analytically deriving complex Hadamard matrices, both with zero and non-zero defect. In particular, we obtain at least 12 new isolated Butson-ty...

If A and B are n× n nonsingular M -matrices, a new lower bound for the minimum eigenvalue τ(A◦B) for the Hadamard product of A and B is derived. This bound improves the result of [R. Huang. Some inequalities for the Hadamard product and the Fan product of matrices. Linear Algebra Appl., 428:1551–1559, 2008.].

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 ...

In [8] a notion of generalized Hadamard product was introduced. We show that when certain kinds of tensors interact with the eigenvalues of symmetric matrices the resulting formulae can be nicely expressed using the generalized Hadamard product and two simple linear operations on the tensors. The Calculus-type rules developed here will be used in [9] to routinize, to a large extend, the differe...

Abstract. For the Hadamard product A ◦ A of an M -matrix A and its inverse A, some new lower bounds for the minimum eigenvalue of A ◦ A are given. These bounds improve the results of [H.B. Li, T.Z. Huang, S.Q. Shen, and H. Li. Lower bounds for the minimum eigenvalue of Hadamard product of an M -matrix and its inverse. Linear Algebra Appl., 420:235-247, 2007] and [Y.T. Li, F.B. Chen, and D.F. Wa...