To predict the clustering of inclusions at liquid steel and inert gas interface, it is essential to calculate pairwise attractive (inertial) force on correctly. In most studies, inertial calculated from three successive inter-particle distances with a certain time interval, in which assumed be identical first two distances. Considering nature force, new iteration scheme proposed where non-ident...

In this paper, we obtain a direct result and Voronovskaya type asymptotic formula for the exponential-type operators in simultaneous approximation with polynomial growth. In the end, we obtain the recurrence formulae for the central moments, direct results and Voronovskaya type asymptotic formulae for the various mixed summation-integral type operators. 2000 AMS Subject Classification. 41A28, 4...

A rational secret sharing scheme is a game in which each party responsible for reconstructing a secret tries to maximize his utility by obtaining the secret alone. Quantum secret sharing schemes, either derived from quantum teleportation or from quantum error correcting code, do not succeed when we assume rational participants. This is because all existing quantum secret sharing schemes conside...

A new set of modified Legendre rational functions which are mutually orthogonal in L2(0,+∞) is introduced. Various projection and interpolation results using the modified Legendre rational functions are established. These results form the mathematical foundation of related spectral and pseudospectral methods for solving partial differential equations on the half line. A spectral scheme using th...

The combinatorial effect of an exponential backoff scheme and retransmission cutoff on the stability of frequencyhopping slotted ALOHA systems with finite population is investigated in terms of the catastrophe theory. In the systems, the packet retransmission probabilities are geometrically distributed with respect to the number of experienced unsuccessful transmissions and a packet will be dis...

The parameters of metric, cometric, symmetric association schemes with q 6= ±1 (the same as the parameters of the underlying orthogonal polynomials) can be given in general by evaluating a single rational function of degree (4, 4) in the complex variable q j . But in all known examples, save the simple n-gons, these reduce to polynomials of degree at most 2 in q j with q an integer. One reason ...

In a traditional (H,r) combination network, each user connects to unique set of r relays. However, few research efforts have considered the (H,r,u) multiaccess network problem wherein relays is connected by u users. this paper, we focus on designing coded caching schemes for network. By directly applying well-known coding method (proposed Zewail and Yener) scheme (called ZY scheme) obtained. it...

Due to the explosion of smart devices, data traffic over cellular networks has seen an exponential rise in recent years. This increase in mobile data traffic has caused an immediate need for offloading traffic from operators. Device-to-Device(D2D) communication is a promising solution to boost the capacity of cellular networks and alleviate the heavy burden on backhaul links. However, dir...

Throughout this paper Z, Q, C, Zp, Qp and Cp will respectively denote the ring of rational integers, the field of rational numbers, the filed of complex numbers, the ring p-adic rational integers, the field of p-adic rational numbers, and the completion of the algebraic closure of Qp. Let vp be the normalized exponential valuation of Cp such that |p|p = p −vp(p) = p. If q ∈ Cp, we normally assu...