Let q ≥ 2 be a positive integer, B be a fractional Brownian motion with Hurst index H ∈ (0, 1), Z be an Hermite random variable of index q, and Hq denote the Hermite polynomial having degree q. For any n ≥ 1, set Vn = ∑n−1 k=0 Hq(Bk+1 − Bk). The aim of the current paper is to derive, in the case when the Hurst index verifies H > 1 − 1/(2q), an upper bound for the total variation distance betwee...

Considered in this short note is the design of output layer nodes of feedforward neural networks for solving multi-class classification problems with r (r ≥ 3) classes of samples. The common and conventional setting of output layer, called “one-to-one approach” in this paper, is as follows: The output layer contains r output nodes corresponding to the r classes. And for an input sample of the i...

Let x ∈ I be an irrational element and n 1, where I is the unit disc in the field of formal Laurent series F((X−1)), we denote by kn(x) the number of exact partial quotients in continued fraction expansion of x, given by the first n digits in the β-expansion of x, both expansions are based on F((X−1)). We obtain that lim inf n→+∞ kn(x) n = degβ 2Q∗(x) , lim sup n→+∞ kn(x) n = degβ 2Q∗(x) , wher...

In this paper, we focus on deriving low-diameter networks, beginning with D = 2, the next best value to that of the complete network, and proceeding to somewhat larger (constant) values leading to more economical networks. We show that perfect difference networks (PDNs), which are based on the mathematical notion of perfect difference sets, offer a diameter of 2 in an asymptotically optimal man...

Ramanujan’s famous deathbed letter to G. H. Hardy concerns the asymptotic properties of modular forms and his so-called mock theta functions. For his mock theta function f(q), he asserts, as q approaches an even order 2k root of unity, that we have f(q)− (−1)(1− q)(1− q)(1− q) · · · ` 1− 2q + 2q − · · · ́ = O(1). We give two proofs of this claim by offering exact formulas for these limiting valu...

We combine the H Coe cients technique and the Coupling technique to improve security bounds of balanced Feistel schemes. For q queries and round functions of n−bits to n−bits, we nd that the CCA Security of 4 + 2r rounds Feistel schemes is upperbounded by 2q r+3 ( 4q 2n ) r+1 2 + q(q−1) 2·22n . This divides by roughly 1.5 the number of needed rounds for a given CCA Security, compared to the pre...

We present an explicit product formula for the spherical functions of the compact Gelfand pairs (G,K1) = (SU(p+ q), SU(p)× SU(q)) with p ≥ 2q, which can be considered as the elementary spherical functions of one-dimensional K-type for the Hermitian symmetric spaces G/K with K = S(U(p)× U(q)). Due to results of Heckman, they can be expressed in terms of Heckman-Opdam Jacobi polynomials of type B...

A graph labeling is an assignment of integers to the vertices (or) edges or both subject to certain conditions. Graceful labeling was introduced by Rosa [6] while the concept of odd graceful labeling was introduced by Gnanajothi [2]. A Graph G (V, E), |V(G)| = p, |E(G)| = q is said to be odd graceful if there is an injection from V(G) to {0, 1, 2, .... 2q-1} such that when each edge xy is assig...

Abstract. Zero-sum problems in abelian groups and covers of the integers by residue classes, are two different active topics initiated by P. Erdős more than 40 years ago and investigated by many researchers separately since then. In an earlier announcement [Electron. Res. Announc. Amer. Math. Soc. 9(2003), 51-60], the author claimed some surprising connections among these seemingly unrelated fa...

The effect of eggshell particles on the mechanical properties of epichlorohydrin crosslinked chitosan/eggshell composites had been studied. The content of eggshell particles in each composites was varied from 2.5 to 13.4% (w/w). The tensile strength was 60% improved, compared to the control chitosan. The composite with 13.4% (w/w) content of eggshell particles showed the optimum tensile strengt...