Abstract. Recently, the authors established a number of inequalities involving integer powers of the Hadamard product of two positive de nite Hermitian matrices. Here these results are extended in two ways. First, the restriction to integer powers is relaxed to include all real numbers not in the open interval ( 1; 1). Second, the results are extended to the Hadamard product of any nite number ...

AHadamard matrix is said to be completely non-cyclic (CNC) if there are no two rows (or two columns) that are shift equivalent in its reduced form. In this paper, we present three new constructions of CNC Hadamard matrices. We give a primary construction using a flipping operation on the submatrices of the reduced form of a Hadamard matrix. We show that, up to some restrictions, the Kronecker p...

*Correspondence: [email protected]; [email protected]; [email protected] 1School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, P.R. China Full list of author information is available at the end of the article Abstract In this paper, we investigate the closure property ofH-tensors under the Hadamard product. It is shown that the Hadamard products of Had...

In [1], Constantine proposed that a variant of the codes constructed in Theorem 1 might be a useful substitute for Hadamard matrices at orders where no Hadamard matrix is known to exist. His main result is a plug-in construction for codes of order 4q with 8q codewords and minimum distance 2q−2 using a Goethals-Seidel type array. He provides component matrices for odd prime powers q. Theorem 1 s...

In this work, we calculate the limit distribution of the total cost incurred by splitting a tree selected at random from the set of all finite free trees. This total cost is considered to be an additive functional induced by a toll equal to the square of the size of tree. The main tools used are the recent results connecting the asymptotics of generating functions with the asymptotics of...

The aim of the present paper is to introduce and investigate a new subclass of Bazilevi'{c} functions in the punctured unit disk $mathcal{U}^*$ which have been described through using of the well-known fractional $q$-calculus operators, Hadamard product and a linear operator. In addition, we obtain some sufficient conditions for the func...