Abstract: The behavior of systems such as periodicity, fixed points, and most importantly chaos has evolved as an integral part of mathematics, especially in dynamical system. This research presents a study on chaos as a property of nonlinear science. Systems with at least two of the following properties are considered to be chaotic in a certain sense: bifurcation and period doubling, period three, transitivity and dense orbit, sensitive dependence to initial conditions, and expansivity. These are termed as the routes to chaos. PubDate: Thu, 08 Mar 2018 00:00:00 +000

Abstract: We study a new family of measures of noncompactness in the locally Sobolev space , equipped with a suitable topology. As an application of the technique associated with this family of measures of noncompactness, we study the existence of solutions for a class of nonlinear Volterra integrodifferential equations. Further, we give an illustrative example to verify the effectiveness and applicability of our results. PubDate: Thu, 15 Feb 2018 00:00:00 +000

Abstract: This paper is devoted to discuss certain aspects of passivity results in dynamic systems and the characterization of the regenerative systems counterparts. In particular, the various concepts of passivity as standard passivity, strict input passivity, strict output passivity, and very strict passivity (i.e., joint strict input and output passivity) are given and related to the existence of a storage function and a dissipation function. Later on, the obtained results are related to external positivity of systems and positivity or strict positivity of the transfer matrices and transfer functions in the time-invariant case. On the other hand, how to achieve or how eventually to increase the passivity effects via linear feedback by the synthesis of the appropriate feed-forward or feedback controllers or, simply, by adding a positive parallel direct input-output matrix interconnection gain is discussed. PubDate: Wed, 24 Jan 2018 08:41:48 +000

Abstract: Using some results about generalized Hermite-Hadamard-Fejér type inequalities related to -convex functions, we give some examples and applications for trapezoid and midpoint type inequalities for differentiable -convex functions. PubDate: Tue, 21 Nov 2017 07:15:56 +000

Abstract: We use -sequences in this article to derive common fixed points for a family of self-mappings defined on a complete -metric space. We imitate some existing techniques in our proofs and show that the tools employed can be used at a larger scale. These results generalize well known results in the literature. PubDate: Sun, 19 Nov 2017 10:02:45 +000

Abstract: The purpose of this paper is to present some existence and uniqueness results for common fixed point theorems for - contraction mappings with two metrics endowed with a directed graph. In addition, by using our main results, we obtain some results about coupled coincidence points endowed with a directed graph. Our results generalize those presented in previous papers. PubDate: Thu, 16 Nov 2017 00:00:00 +000

Abstract: A new modified three-term conjugate gradient (CG) method is shown for solving the large scale optimization problems. The idea relates to the famous Polak-Ribière-Polyak (PRP) formula. As the numerator of PRP plays a vital role in numerical result and not having the jamming issue, PRP method is not globally convergent. So, for the new three-term CG method, the idea is to use the PRP numerator and combine it with any good CG formula’s denominator that performs well. The new modification of three-term CG method possesses the sufficient descent condition independent of any line search. The novelty is that by using the Wolfe Powell line search the new modification possesses global convergence properties with convex and nonconvex functions. Numerical computation with the Wolfe Powell line search by using the standard test function of optimization shows the efficiency and robustness of the new modification. PubDate: Wed, 13 Sep 2017 00:00:00 +000

Abstract: The necessary and sufficient conditions where a second-order linear time-varying system is commutative with another system of the same type have been given in the literature for both zero initial states and nonzero initial states. These conditions are mainly expressed in terms of the coefficients of the differential equation describing system . In this contribution, the inverse conditions expressed in terms of the coefficients of the differential equation describing system have been derived and shown to be of the same form of the original equations appearing in the literature. PubDate: Sun, 27 Aug 2017 00:00:00 +000

Abstract: This paper investigates some fixed point-related questions including the sequence boundedness and convergence properties of mappings defined in spaces, which are parameterized by a scalar , where : are nonexpansive Lipschitz-continuous mappings and is a metric space which is a space. PubDate: Wed, 19 Jul 2017 09:46:44 +000

Abstract: The improved generalized tanh-coth method is used in nonlinear sixth-order solitary wave equation. This method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. The new exact solutions consisted of trigonometric functions solutions, hyperbolic functions solutions, exponential functions solutions, and rational functions solutions. The numerical results were obtained with the aid of Maple. PubDate: Mon, 17 Jul 2017 09:04:11 +000

Abstract: Let be a standard homogeneous Noetherian ring with local base ring and let be a finitely generated graded -module. Let be the th local cohomology module of with respect to . Let be a Serre subcategory of the category of -modules and let be a nonnegative integer. In this paper, if then we investigate some conditions under which the -modules and are in for all . Also, we prove that if , then the graded -module is in for all . Finally, we prove that if is the biggest integer such that , then for all . PubDate: Mon, 03 Jul 2017 00:00:00 +000

Abstract: Let be a Banach space. We introduce a concept of orthogonal symmetry and reflection in . We then establish its relation with the concept of best approximation and investigate its implication on the shape of the unit ball of the Banach space by considering sections over subspaces. The results are then applied to the space of continuous functions on a compact set . We obtain some nontrivial symmetries of the unit ball of . We also show that, under natural symmetry conditions, every odd function is orthogonal to every even function in . We conclude with some suggestions for further investigations. PubDate: Wed, 14 Jun 2017 00:00:00 +000

Abstract: Let be a commutative graded ring with unity . A proper graded ideal of is a graded ideal of such that . Let be any function, where denotes the set of all proper graded ideals of . A homogeneous element is -prime to if where is a homogeneous element in ; then . An element is -prime to if at least one component of is -prime to . Therefore, is not -prime to if each component of is not -prime to . We denote by the set of all elements in that are not -prime to . We define to be -primal if the set (if ) or (if ) forms a graded ideal of . In the work by Jaber, 2016, the author studied the generalization of primal superideals over a commutative super-ring with unity. In this paper we generalize the work by Jaber, 2016, to the graded case and we study more properties about this generalization. PubDate: Sun, 04 Jun 2017 07:12:32 +000

Abstract: We consider the interaction of traveling curved fronts in bistable reaction-diffusion equations in two-dimensional spaces. We first characterize the growth of the traveling curved fronts at infinity; then by constructing appropriate subsolutions and supersolutions, we prove that the solution of the Cauchy problem converges to a pair of diverging traveling curved fronts in under appropriate initial conditions. PubDate: Sun, 07 May 2017 00:00:00 +000

Abstract: We describe symplectic and complex toric spaces associated with the five regular convex polyhedra. The regular tetrahedron and the cube are rational and simple, the regular octahedron is not simple, the regular dodecahedron is not rational, and the regular icosahedron is neither simple nor rational. We remark that the last two cases cannot be treated via standard toric geometry. PubDate: Thu, 23 Mar 2017 00:00:00 +000

Abstract: This research studies the chromatic numbers of the suborbital graphs for the modular group and the extended modular group. We verify that the chromatic numbers of the graphs are or . The forest conditions of the graphs for the extended modular group are also described in this paper. PubDate: Sun, 05 Mar 2017 09:44:49 +000

Abstract: We would like to generalize to non-Newtonian real numbers the usual Lebesgue measure in real numbers. For this purpose, we introduce the Lebesgue measure on open and closed sets in non-Newtonian sense and examine their basic properties. PubDate: Tue, 28 Feb 2017 00:00:00 +000

Abstract: Suppose that and are two Cayley graphs on the cyclic additive group , where is an even integer, , , and are the inverse-closed subsets of . In this paper, it is shown that is a distance-transitive graph, and, by this fact, we determine the adjacency matrix spectrum of . Finally, we show that if and is an even integer, then the adjacency matrix spectrum of is , , , (we write multiplicities as exponents). PubDate: Mon, 27 Feb 2017 00:00:00 +000

Abstract: In this paper, we investigate a mixed discontinuous Galerkin approximation of time dependent convection diffusion optimal control problem with control constraints based on the combination of a mixed finite element method for the elliptic part and a discontinuous Galerkin method for the hyperbolic part of the state equation. The control variable is approximated by variational discretization approach. A priori error estimates of the state, adjoint state, and control are derived for both semidiscrete scheme and fully discrete scheme. Numerical example is given to show the effectiveness of the numerical scheme. PubDate: Tue, 21 Feb 2017 00:00:00 +000

Abstract: One of the goals of this article is to describe a setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure and of the concentration property on metric measured spaces, inspired from classical examples of means. In some cases, we get a linear extension of the limit at infinity. Then, the mean value on an infinite product is defined, first for cylindrical functions and secondly taking the uniform limit. Finally, the mean value for the heuristic Lebesgue measure on a separable infinite dimensional topological vector space (e.g., on a Hilbert space) is defined. This last object, which is not the classical infinite dimensional Lebesgue measure but its “normalized” version, is shown to be invariant under translation, scaling, and restriction. PubDate: Mon, 30 Jan 2017 00:00:00 +000

Abstract: In this paper, we introduce new functions as a generalization of the Krätzel function. We investigate recurrence relations, Mellin transform, fractional derivatives, and integral of the function . We show that the function is the solution of differential equations of fractional order. PubDate: Thu, 26 Jan 2017 00:00:00 +000

Abstract: The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, over -graded commutative rings and on -graded manifolds is developed. This is a straightforward generalization of the conventional differential calculus over commutative rings and also is the case of the differential calculus over Grassmann algebras and on -graded manifolds. We follow the notion of an -graded manifold as a local-ringed space whose body is a smooth manifold . A key point is that the graded derivation module of the structure ring of graded functions on an -graded manifold is the structure ring of global sections of a certain smooth vector bundle over its body . Accordingly, the Chevalley–Eilenberg differential calculus on an -graded manifold provides it with the de Rham complex of graded differential forms. This fact enables us to extend the differential calculus on -graded manifolds to formalism of nonlinear differential operators, by analogy with that on smooth manifolds, in terms of graded jet manifolds of -graded bundles. PubDate: Tue, 17 Jan 2017 06:52:23 +000

Abstract: In this work, we obtain the approximate solution for the integrodifferential equations by adding perturbation terms to the right hand side of integrodifferential equation and then solve the resulting equation using Chebyshev-Galerkin method. Details of the method are presented and some numerical results along with absolute errors are given to clarify the method. Where necessary, we made comparison with the results obtained previously in the literature. The results obtained reveal the accuracy of the method presented in this study. PubDate: Thu, 12 Jan 2017 09:31:33 +000

Abstract: A module over an associative ring with unity is a -module if every finitely generated submodule of any homomorphic image of is a direct sum of uniserial modules. The study of large submodules and its fascinating properties makes the theory of QTAG-modules more interesting. A fully invariant submodule of is large in if , for every basic submodule of The impetus of these efforts lies in the fact that the rings are almost restriction-free. This motivates us to find the necessary and sufficient conditions for a submodule of a QTAG-module to be large and characterize them. Also, we investigate some properties of large submodules shared by -modules, summable modules, -summable modules, and so on. PubDate: Tue, 03 Jan 2017 07:07:55 +000