Caspian Journal of Mathematical Sciences
Volume:7 Issue: 1, Winter Spring 2018

In this paper, we solve higher index differential algebraic equations (DAEs) by transforming them into integral algebraic equations (IAEs). We apply collocation methods on continuous piece-wise polynomials space to solve the obtained higher index IAEs. The efficiency of the given method is improved by using a recursive formula for computing the integral part. Finally, we apply the obtained algorithm to solve a trajectory-prescribed path control problem and a model of simple pendulum. The numerical experiments show efficiency of the given techniques.

In this paper we will present a new method to calculate determinants of square matrices. The method is based on the Chio-Dodgson's condensation formula and our approach automatically affects in reducing the order of determinants by two. Also, using the Chio's condensation method we present an inductive proof of Dodgson's determinantal identity.

The first reformulated Zagreb index $EM_1(G)$ of a simple graph $G$ is defined as the sum of the terms $(d_u+d_v-2)^2$ over all edges $uv$ of $G .$ In this paper, the various upper and lower bounds for the first reformulated Zagreb index of a connected graph interms of other topological indices are obtained.

In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.

While routing in multi-hop packet radio networks (static Ad-hoc wireless networks), it is crucial to minimize power consumption since nodes are powered by batteries of limited capacity and it is expensive to recharge the device. This paper studies the problem of broadcast routing in radio networks. Given a network with an identified source node, any broadcast routing is considered as a directed tree rooted at the source node and spans all nodes. Since the problem is known to be NP-Hard, we try to tackle it heuristically. First we propose an efficient Particle Swarm Optimization (PSO) based algorithm with a proper coding schema. Then we present the second algorithm which combines the global search of the first algorithm with a local search strategy based on noising methods. Comprehensive experimental study is devoted to compare the behavior of the algorithms and to show its priority over the best known previous esults.

‎In the present paper‎, ‎some spectral properties of boundary value problems of Sturm-Liouville type on two disjoint bounded intervals with transmission boundary conditions are investigated‎. ‎Uniqueness theorems for the solution of the inverse problem are proved‎, ‎then we study the reconstructing of the coefficients of the Sturm-Liouville problem by the spectrtal mappings method.

‎In this paper‎, ‎using a generalized translation operator‎, ‎we obtain a generalization of Younis Theorem 5.2 in [3] for the Cherednik-Opdam transform for functions satisfying the $(delta,gamma,p)$-Cherednik-Opdam Lipschitz condition in the space‎ ‎$L^{p}_{alpha,beta}(mathbb{R})$.

In this paper, biochemical reaction problem is given in the form of a system of non-linear differential equations involving Caputo fractional derivative. The aim is to suggest an instrumental scheme to approximate the solution of this problem. To achieve this goal, the fractional derivation terms are expanded as the elements of shifted Legendre scaling functions. Then, applying operational matrix of fractional integration and collocation technique, the main problem is transformed to a set of non-linear algebraic equations. This obtained algebraic system can be solved by available standard iterative procedures. Numerical results of applying the proposed method are investigated in details

In present paper, a numerical approach for solving Cauchy type singular integral equations is discussed. Lagrange interpolation with Gauss Legendre quadrature nodes and Taylor series expansion are utilized to reduce the computation of integral equations into some algebraic equations. Finally, five examples with exact solution are given to show efficiency and applicability of the method. Also, we give the maximum of computed absolute errors for some examples.