In this paper, some inequalities Hadamard-type for (h, r)-convex functions are given. Furthermore, we also proved some Hadamard-type inequalities for product of two (h, r)-convex functions. Mathematics Subject Classification: 26D15

In this paper, some inequalities Hadamard-type for h -convex functions are given. We also proved some Hadamard-type inequalities for products of two h -convex functions. Mathematics subject classification (2000): 26D07, 26D15.

Two Hadamard matrices of order 764 of Goethals– Seidel type are constructed. Recall that a Hadamard matrix of order m is a {±1}-matrix A of size m × m such that AA T = mI m , where T denotes the transpose and I m the identity matrix. We refer the reader to one of [2, 4] for the survey of known results about Hadamard matrices. In our previous note [1], written about 13 years ago, we listed 17 in...

From past literature it is evident that the search for self-dual codes has been hampered by the computational difficulty of generating the Hadamard matrices required. The use of the cocyclic construction of Hadamard matrices has permitted substantial cut-downs in the search time, but the search space still grows exponentially. Here we look at an adaptation of image-processing techniques for the...

This paper presents a new transform known as natural-ordered complex Hadamard transform (NCHT) which is derived from the Walsh–Hadamard transform (WHT) through the direct block matrix operation. Some of its properties, including the exponential property of the NCHT and the shift invariant property of the NCHT power spectrum, are presented. The relationship of the NCHT with the sequency-ordered ...

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...

We introduce power Hadamard matrices, in order to study the structure of (group) generalized Hadamard matrices, Butson (generalized) Hadamard matrices and other related orthogonal matrices, with which they share certain common characteristics. The new objects turn out to be as interesting, and perhaps as useful, as the objects that motivated them. We develop a basic theory of power Hadamard mat...

Kounias and Farmakis, in 'On the excess of Hadamard matrices', Discrete Math. 68 (1988) 59-69, showed that the maximal excess (or sum of the elements) of an Hadamard matrix of order h, o(h) for h = 4m(m -1) is given by o(4m(m 1))≤4(m 1)2(2m + 1). Kharaghani in 'An infinite class of Hadamard matrices of maximal excess' (to appear) showed this maximal excess can be attained if m is the order of a...

This paper proposes a method to estimate the flicker severity index using the Walsh Hadamard transform (WHT). A weighting filter in the sequency domain is utilized for direct computation of the flicker index. The proposed method is compared with a flicker meter in the frequency domain that uses the Fast Fourier Transform (FFT). It is seen by numerical simulations that the proposed method yields...