The determinantal ideals of extended Hankel matrices

In this paper, we use the tools of Gr\"{o}bner bases and combinatorial secant varieties to study the determinantal ideals $I_t$ of the extended Hankel matrices. Denote by $c$-chain a sequence $a_1,\...,a_k$ with $a_i+c<a_{i+1}$ for all $i=1,\...,k-1$. Using the results of $c$-chain, we solve the membership problem for the symbolic powers $I_t^{(s)}$ and we compute the primary decomposition of the product $I_{t_1}\... I_{t_k}$ of the determinantal ideals. Passing through the initial ideals and algebras we prove that the product $I_{t_1}\... I_{t_k}$ has a linear resolution and the multi-homogeneous Rees algebra \Rees(I_{t_1},\...,I_{t_k}) is defined by a Gr\"obner basis of quadrics

The standard graded property for vertex cover algebras of Quasi-Trees

J. Herzog, T. Hibi, N. V. Trung and X. Zheng characterize the vertex cover algebras which are standard graded. In this paper we give a simple combinatorial criterion for the standard graded property of vertex cover algebras in the case of quasi-trees. We also give an example of how this criterion works and compute the maximal degree of a minimal generator in that case

On outage probability and throughput performance of cognitive radio inspired NOMA relay system

To improve the throughput and the outage probability of the Cognitive Radio (CR) inspired system, a novel Non-Orthogonal Multiple Access (NOMA) can be deployed to adapt multiple services in 5G wireless communication. In this scheme, after the reception of the superposition coded symbol with a predefined power allocation factors from the primary source, the relay decodes and forwards with a new superposition coded symbol (i.e. allocating another power factors) to the destination. By employing twin antenna design at the relay, the bandwidth efficiency in such scheme will be improved. Assuming Rayleigh fading channels, the closed-form expressions in terms of throughput and the outage performance are derived. Through numerical results, they showed that the outage performance of the proposed scheme using a Single Antenna (SA) scheme at the relay is better than a Twin Antenna (TA) scheme because SA scheme is not affected by its own antenna interference

Cohen-Macaulayness of generically complete intersection monomial ideals

In this paper we discuss the problem of characterizing the Cohen-Macaulay property of certain families of monomial ideals with fixed radical. More precisely, we consider generically complete intersection monomial ideals whose radical corresponds to special classes of simplicial complexes.Comment: To appear in Comm. Al