This article points out that the differential quadrature (DQ) and differential cubature (DC) methods, due to their global domain property, are more efficient for nonlinear problems than the traditional numerical techniques such as finite element and finite difference methods. By introducing the Hadamard product of matrices, we obtain an explicit matrix formulation for the DQ and DC solutions of...

in this paper, we deal with the subdierential concept onhadamard spaces. flat hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in hadamard spaces is nonempty. proximal subdierentialin hadamard spaces is addressed and some basic properties are high-lighted. finally, a density theorem for subdierential set is establi...

Let A and B be n n positive semidefinite Hermitian matrices, let c and/ be real numbers, let o denote the Hadamard product of matrices, and let Ak denote any k )< k principal submatrix of A. The following trace and eigenvalue inequalities are shown: tr(AoB) <_tr(AoBa), c_<0or_> 1, tr(AoB)a_>tr(AaoBa), 0_a_ 1, A1/a(A o Ba) <_ Al/(Az o B), a <_ /,a O, Al/a[(Aa)k] <_ A1/[(A)k], a <_/,a/ 0. The equ...

Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.

In this paper, we deal with the subdierential concept onHadamard spaces. Flat Hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in Hadamard spaces is nonempty. Proximal subdierentialin Hadamard spaces is addressed and some basic properties are high-lighted. Finally, a density theorem for subdierential set is established.

1 Hadamard matrices in Space Communications One hundred years ago, in 1893, Jacques Hadamard 21] found square matrices of orders 12 and 20, with entries 1, which had all their rows (and columns) orthogonal. These matrices, X = (x ij), satissed the equality of the following inequality jdet Xj 2 n i=1 n X j=1 jx ij j 2 and had maximal determinant. Hadamard actually asked the question of matrices ...