We establish some estimates of the right-hand side of Hermite-Hadamard type inequalities for functions whose derivatives absolute values are harmonically s-convex. Several Hermite-Hadamard type inequalities for products of two harmonically s-convex functions are also considered.

Skew Hadamard difference sets have been an interesting topic of study for over 70 years. For a long time, it had been conjectured the classical Paley difference sets (the set of nonzero quadratic residues in Fq where q ≡ 3 mod 4) were the only example in Abelian groups. In 2006, the first author and Yuan disproved this conjecture by showing that the image set of D5(x2, u) is a new skew Hadamard...

We use the newly developed theory of signed groups and some known sequences with zero autocorrelation to derive new results on the asymptotic existence of Hadamard matrices. New values of t are obtained such that, for any odd number p, there exists an Hadamard matrix of order 2tp. These include: t = 2N, where N is the number of nonzero digits in the binary expansion of p, and t = 4[-~ log2((p1)...

We show that if four suitable matrices of order m exist then there are Hadamard matrices of order 28 m, 36 m, and 44 m. In particular we show that Hadamard matrices of orders 14(q + 1), 18(q + 1), and 22(q + 1) exist when q is a prime power and q = l(mod 4). Also we show that if n is the order of a conference matrix there is an Hadamard matrix of order 4mn. As a consequence there are Hadamard m...

Abstract. The purpose of this paper is to introduce new parametric families of complex Hadamard matrices in two different ways. First, we prove that every real Hadamard matrix of order N ≥ 4 admits an affine orbit. This settles a recent open problem of Tadej and Życzkowski [11], who asked whether a real Hadamard matrix can be isolated among complex ones. In particular, we apply our construction...

In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.

We give a formulation, via (1, 1) matrices, of Mathon's construction for conference matrices and derive a new family of conference matrices of order 5·92r+1 + 1, t ≥ 0. This family produces a new conference matrix of order 3646 and a new Hadamard matrix of order 7292. In addition we construct new families of Hadamard matrices of orders 6.92r+1+ 2, 10.92t+1 + 2, 8·49·92, t ≥ 0; q2(q + 3) + 2 whe...

In this paper we establish new Hermite-Hadamard type inequalities involving fractional integrals with respect to another function. Such fractional integrals generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. c ©2016 All rights reserved.

Dihedral Golay sequences are introduced and found for lengths 7,9,15, and 19. Applications include new classes of signed group Hadamard matrices and 19 real Hadamard matrices of orders 2p, p S 4169.

Let n be the order of a Hadamard design, and G any finite group. Then there exists many non-isomorphic Hadamard designs of order 212|G|+13n with automorphism group isomorphic to G.