Journal of Advances in Applied Mathematics

8

Authors: Ren Gao, Yun Zhang, Long Tang

How to get quality of service (QoS) support in the MAC layer is a hot topic in wireless ad hoc network (MANET). In this paper, a novel adaptive QoS model is presented in MANET, and its feasibility and reliability is analyzed and verified. Compared with traditional SWAN model, the proposed approach is improved by differentiated services in MAC layer in order to achieve high control rate of low-priority transactions. The simulations of the presented model are carried out and the results show that can improve the bandwidth utilization and increase the network throughput, as well as reduce transmission delay in MANET.

12

Authors: Lucian M. Ionescu

The current research regarding the Riemann zeros suggests the existence of a non-trivial algebraic/analytic structure on the set of Riemann zeros [1,2,3]. The duality between primes and Riemann zeta function zeros suggests some new goals and aspects to be studied: adelic duality and the POSet of prime numbers. The article presents computational evidence of the structure of the imaginary parts t of the non-trivial zeros of the Riemann zeta function ρ = 1/2 + it, called in this article the Riemann Spectrum, using the study of their distribution, as in [3]. The novelty represents in considering the associated characters pit, towards an algebraic point of view, than rather in the sense of Analytic Number Theory. This structure is tentatively interpreted in terms of adelic characters, and the duality of the rationals. Second, the POSet structure of prime numbers studied in [4], is tentatively mirrored via duality in the Riemann spectrum. A direct study of the convergence of their Fourier series, along Pratt trees, is proposed. Further considerations, relating the Riemann Spectrum, adelic characters and distributions, in terms of Hecke idelic characters, local zeta integrals (Mellin transform) and !-eigen-distributions, are explored following [5].