Open Access Method Article

Open Access Short Research Article

On Algebraic Properties of Fuzzy Membership Sequenced Multisets

Yohanna Tella

Journal of Advances in Mathematics and Computer Science, Page 146-164
DOI: 10.9734/BJMCS/2015/15067

Since the original paper by Yager, different definitions of the concept of fuzzy multisets (bags), and the corresponding operations are available in the literature, as well as some extensions of the union, intersection and difference operators of sets, and new algebraic operators. In this paper, a study of some algebraic properties of these operations including idempotency, identity, absorption, associativity, distributivity, demorgan’s laws and the principle of Inclusion/Exclusion is presented in the context of membership sequence of fuzzy multisets. Also, the compatibility of the union and intersection on these structures and sets via their root sets is established.

Open Access Original Research Article

Taylor Series Approach for Solving Multi-level Large Scale Fractional Programming Problem with Stochastic Parameters in Constraints

O. E. Emam, A. Abdo, N. H. Ibrahim

Journal of Advances in Mathematics and Computer Science, Page 79-90
DOI: 10.9734/BJMCS/2015/13568

This paper presents a solution algorithm to solve a multi-level large scale fractional programming problem with individual chance constraints (CH-MLLSFP). We assume that there is randomness in the right-hand side of the constraints only and that the random variables are normally distributed. The basic idea in treating (CH-MLLSFP) is to convert the probabilistic nature of this problem into a deterministic multi-level large scale fractional programming problem (MLLSFPP). A solution of multi-level large scale fractional programming problem is presented using aTaylor series to avoid the complexity of fractional nature. An illustrative example is discussed to demonstrate the correctness of the proposed solution method.

Open Access Original Research Article

Stable Recovery of Sparse Signal in Compressed Sensing via the RIP of Order less than s

Hiroshi Inoue

Journal of Advances in Mathematics and Computer Science, Page 91-101
DOI: 10.9734/BJMCS/2015/13998

Our goal is to reconstruct an unknown sparse signal. In this paper, we consider the feature of the sparse signal and research good conditions for the recovery of sparse signals. In detail, we assume that h ≡ x*−x and h = (h1; h2; · · · ; hn), where x is an unknown signal and x* is the CS-solution. Furthermore for simplicity, we assume that the index of h is sorted by |h1| ≥ |h2| ≥ · · · ≥ |hn| and T0 = {1; 2; · · · ; s}. In this paper, we focus the quality of hT0 . In more details, we shall reseach good conditions for the recovery of sparse signals by investigating the difference between the mean |h1|+|h2|+···+|hs| / s and the mean |h1|+|h2|+···+|hr| / r , r = 1; 2; · · · ; s. We shall show that if δs < 0:366 by the quality of x, and similarly if δ2 / 3*s < 0:436, then we have stable recovery of approximately sparse signals.

Open Access Original Research Article

Periodic Solutions of a Time Delay Stage-structured Prey-predator Model

Yanqiu Li, Wei Duan Duan, Shujian Ma

Journal of Advances in Mathematics and Computer Science, Page 102-111
DOI: 10.9734/BJMCS/2015/14857

The dynamics of a time delay stage-structured prey-predator model is investigated. Firstly, through the analysis of the eigenvalues, the effect of time delay on the stability of the positive equilibrium and the existence of Hopf bifurcation are obtained. Further, the stability and the direction of Hopf bifurcation periodic solution near the first critical value are given utilizing the normal form method and the center manifold theorem.

Open Access Original Research Article

Open Access Original Research Article

Polynomial Operator in the Shifts in Discrete Algebraic Dynamical Systems

Ramamonjy Andriamifidisoa, Juanito Andrianjanahary

Journal of Advances in Mathematics and Computer Science, Page 119-128
DOI: 10.9734/BJMCS/2015/15028

The vector space of the multi-indexed sequences over a field and the vector space of the sequences with finite support are dual to each other, with respect to an appropriate scalar product. It follows that the polynomial operator in the shift which U. Oberst and J. C. Willems have introduced to define time invariant discrete linear dynamical systems can be explained as the adjoint of the polynomial multiplication.