Iranian Journal of Mathematical Sciences and Informatics
Year:2018 | Volume:13 | Issue:2|Papers Count:13

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E (G) | such that the sum of the labels of the edges incident with any vertex v is equal to (1+|E (G) |) deg (v) /2.Degree-magic graphs extend supermagic regular graphs. In this paper we find the necessary and sufficient conditions for the existence of balanced degree-magic labelings of graphs obtained by taking the join, composition, Cartesian product, tensor product and strong product of complete bipartite graphs.

‎The sequences of the form {Embgn} m,nÎZ, where Emb is the modulation operator‎, ‎b>0 and gn is the‎ ‎window function in L2(R)‎, ‎construct Fourier-like‎ ‎systems‎. ‎We try to consider some sufficient conditions on the window‎ ‎functions of Fourier-like systems‎, ‎to make a frame and find a dual‎ ‎frame with the same structure‎. ‎We also extend the given two Bessel‎ ‎Fourier-like systems to make a pair of dual frames and prove that‎ ‎the window functions of Fourier-like Bessel sequences share the‎ ‎compactly supported property with their extensions‎. ‎But for‎ ‎polynomials windows‎, ‎a result of this type does not happen.

This paper studies some existence results for generalized e-vector equilibrium problems and generalized e-vector variational inequalities. The existence results for solutions are derived by using the celebrated KKM theorem. The results achieved in this paper generalize and improve the works of many authors in references.

Let G be a simple connected graph. In this paper, Szeged dimension and PIv dimension of graph G are introduced. It is proved that if G is a graph of Szeged dimension 1 then line graph of G is 2-connected. Trees of Szeged dimension 1 are characterized. The Szeged dimension and PIv dimension of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components are computed. Also explicit formulas of Szeged and PIv indices for these composite graphs are obtained.

A submanifold Mn of the Euclidean space En+m is said to be biharmonic if its position map x: Mn®En+m satisfies the condition D2x=0, where D stands for the Laplace operator. A well-known conjecture of Bang-Yen Chen says that, the only biharmonic submani-folds of Euclidean spaces are the minimal ones. In this paper, we consider a modified version of the conjecture, replacing D by its extension, L1-operator (namely, L1-conjecture). The L1-conjecture states that any L1-biharmonic Euclidean hyper surface is 1-minimal. We prove that the L1-conjecture is true for L1-biharmonic hyper surfaces with three distinct principal curvatures and constant mean curvature of a Euclidean space of arbitrary dimension.

Fejer Hadamard inequality is generalization of Hadamard inequality. In this paper we prove certain Fejer Hadamard inequalities for k-fractional integrals. We deduce Fejer Hadamard-type inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities fork-fractional as well as fractional integrals are given.

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In this paper we investigate the notion of I-statistical convergence and introduce I-st limit points and I-st cluster points of real number sequence and also studied some of its basic properties.

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered.First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem. The suggested technique transforms this type of equations to the solution of a system of algebraic equations. In the next step, the error analysis of the proposed method is investigated. Finally, the technique is applied to some problems to show its validity and applicability.

The equivalence relation isoclinism partitions the class of all pairs of groups into families. In this paper, a complete classification of the set of all pairs (G, G’) is established whenever, p is a prime number greater than 3 and G is a p-group of order at most p5. Moreover, the classification of pairs (H, H’) for extra special p-groups H is also given.

The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre polynomials as the eigenfunctions of two non-classical Sturm-Liouville problems. We prove some important properties of these operators such as: These sets of functions are orthogonal with respect to a positive definite inner product defined over the compact intervals [-1; 1] and [0,¥), respectively and also these sequences form two new orthogonal bases for the corresponding Hilbert spaces. Finally, the spectral and Rayleigh-Ritz methods are carry out using these basis functions to solve some examples. Our numerical results are compared with other existing results to confirm the efficiency and accuracy of our method.

We define the notion of almost n-layered QTAG-modules and study their basic properties. One of the main result is that almost 1-layered modules are almost (w+1) -projective exactly when they are almost direct sum of countably generated modules of length less than or equal to (w+1). Some other characterizations of this new class are also established.