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A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control Problem
Tue, 21 Feb 2017 00:00:00 +0000
http://www.hindawi.com/journals/jmath/2017/6901467/
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.
Qingjin Xu and Zhaojie Zhou
Copyright © 2017 Qingjin Xu and Zhaojie Zhou. All rights reserved.

The Mean Value for Infinite Volume Measures, Infinite Products, and Heuristic Infinite Dimensional Lebesgue Measures
Mon, 30 Jan 2017 00:00:00 +0000
http://www.hindawi.com/journals/jmath/2017/9853672/
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.
JeanPierre Magnot
Copyright © 2017 JeanPierre Magnot. All rights reserved.

A Generalization of the Krätzel Function and Its Applications
Thu, 26 Jan 2017 00:00:00 +0000
http://www.hindawi.com/journals/jmath/2017/2195152/
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.
Neşe Dernek, Ahmet Dernek, and Osman Yürekli
Copyright © 2017 Neşe Dernek et al. All rights reserved.

Differential Calculus on Graded Manifolds
Tue, 17 Jan 2017 06:52:23 +0000
http://www.hindawi.com/journals/jmath/2017/8271562/
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 localringed 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.
G. Sardanashvily and W. Wachowski
Copyright © 2017 G. Sardanashvily and W. Wachowski. All rights reserved.

Approximate Solution of Perturbed VolterraFredholm Integrodifferential Equations by ChebyshevGalerkin Method
Thu, 12 Jan 2017 09:31:33 +0000
http://www.hindawi.com/journals/jmath/2017/8213932/
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 ChebyshevGalerkin 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.
K. Issa and F. Salehi
Copyright © 2017 K. Issa and F. Salehi. All rights reserved.

Different Characterizations of Large Submodules of QTAGModules
Tue, 03 Jan 2017 07:07:55 +0000
http://www.hindawi.com/journals/jmath/2017/2496246/
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 QTAGmodules 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 restrictionfree. This motivates us to find the necessary and sufficient conditions for a submodule of a QTAGmodule to be large and characterize them. Also, we investigate some properties of large submodules shared by modules, summable modules, summable modules, and so on.
Fahad Sikander, Alveera Mehdi, and Sabah A. R. K. Naji
Copyright © 2017 Fahad Sikander et al. All rights reserved.

Mathematical Analysis of a Reactive Viscous Flow through a Channel Filled with a Porous Medium
Tue, 27 Dec 2016 09:50:46 +0000
http://www.hindawi.com/journals/jmath/2016/1350578/
An investigation has been carried out to study entropy generation in a viscous, incompressible, and reactive fluid flowing steadily through a channel with porous materials. Approximate solutions for both velocity and temperature fields are obtained by using a rapidly convergent Adomian decomposition method (ADM). These solutions are then used to determine the heat irreversibility and Bejan number of the problem. Variations of other important fluid parameters are conducted, presented graphically, and discussed.
Samuel O. Adesanya, J. A. Falade, J. C. Ukaegbu, and K. S. Adekeye
Copyright © 2016 Samuel O. Adesanya et al. All rights reserved.

Fuzzy Soft Compact Topological Spaces
Sun, 25 Dec 2016 13:27:25 +0000
http://www.hindawi.com/journals/jmath/2016/2480842/
In this paper, we have studied compactness in fuzzy soft topological spaces which is a generalization of the corresponding concept by R. Lowen in the case of fuzzy topological spaces. Several basic desirable results have been established. In particular, we have proved the counterparts of Alexander’s subbase lemma and Tychonoff theorem for fuzzy soft topological spaces.
Seema Mishra and Rekha Srivastava
Copyright © 2016 Seema Mishra and Rekha Srivastava. All rights reserved.

Graphs Generated by Measures
Mon, 19 Dec 2016 09:32:32 +0000
http://www.hindawi.com/journals/jmath/2016/1706812/
In this paper, a graph is assigned to any probability measure on the algebra of Borel sets of a topological space. Using this construction, it is proved that given any number (finite or infinite) there exists a nonregular graph such that its clique, chromatic, and dominating number equals .
A. Assari and M. Rahimi
Copyright © 2016 A. Assari and M. Rahimi. All rights reserved.

Classifying Quadratic Forms Over in Three Variables
Tue, 13 Dec 2016 08:40:35 +0000
http://www.hindawi.com/journals/jmath/2016/7407638/
The quadratic forms in three variables over the field are classified. Some remarks are made about the group of equivalences of the quadratic forms.
Gerard Thompson
Copyright © 2016 Gerard Thompson. All rights reserved.

A Generalized HermiteHadamard Inequality for Coordinated Convex Function and Some Associated Mappings
Tue, 13 Dec 2016 07:28:35 +0000
http://www.hindawi.com/journals/jmath/2016/1631269/
We have discussed the generalization of HermiteHadamard inequality introduced by Lupaş for convex functions on coordinates defined in a rectangle from the plane. Also we define that mappings are related to it and their properties are discussed.
Atiq Ur Rehman, Gulam Farid, and Sidra Malik
Copyright © 2016 Atiq Ur Rehman et al. All rights reserved.

Some Relations between Isologic and Varietal Perfect Groups
Mon, 12 Dec 2016 14:50:17 +0000
http://www.hindawi.com/journals/jmath/2016/5093983/
In 1940, Hall introduced the notion of isologism, with respect to a given variety of groups . In the present article, we study the concepts of perfect groups, subgroup, and quotient irreducible groups, with respect to a given variety of groups . Also we prove and obtain some results.
Shokufeh Lotfi and S. Mostafa Taheri
Copyright © 2016 Shokufeh Lotfi and S. Mostafa Taheri. All rights reserved.

Differentiation Theory over InfiniteDimensional Banach Spaces
Thu, 08 Dec 2016 10:25:18 +0000
http://www.hindawi.com/journals/jmath/2016/2619087/
We study, for any positive integer and for any subset of , the Banach space of the bounded real sequences and a measure over that generalizes the dimensional Lebesgue one. Moreover, we expose a differentiation theory for the functions defined over this space. The main result of our paper is a change of variables’ formula for the integration of the measurable real functions on . This change of variables is defined by some infinitedimensional functions with properties that generalize the analogous ones of the standard finitedimensional diffeomorphisms.
Claudio Asci
Copyright © 2016 Claudio Asci. All rights reserved.

Sectional and Ricci Curvature for ThreeDimensional Lie Groups
Sun, 04 Dec 2016 11:09:39 +0000
http://www.hindawi.com/journals/jmath/2016/3681529/
Formulas for the Riemann and Ricci curvature tensors of an invariant metric on a Lie group are determined. The results are applied to a systematic study of the curvature properties of invariant metrics on threedimensional Lie groups. In each case the metric is reduced by using the automorphism group of the associated Lie algebra. In particular, the maximum and minimum values of the sectional curvature function are determined.
Gerard Thompson and Giriraj Bhattarai
Copyright © 2016 Gerard Thompson and Giriraj Bhattarai. All rights reserved.

KhatriRao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces
Mon, 28 Nov 2016 13:31:02 +0000
http://www.hindawi.com/journals/jmath/2016/8301709/
We introduce the notion of KhatriRao product for operator matrices acting on the direct sum of Hilbert spaces. This notion generalizes the tensor product and Hadamard product of operators and the KhatriRao product of matrices. We investigate algebraic properties, positivity, and monotonicity of the KhatriRao product. Moreover, there is a unital positive linear map taking TracySingh products to KhatriRao products via an isometry.
Arnon Ploymukda and Pattrawut Chansangiam
Copyright © 2016 Arnon Ploymukda and Pattrawut Chansangiam. All rights reserved.

Presic Type Fixed Point Theorem for Four Maps in Metric Spaces
Tue, 22 Nov 2016 06:27:48 +0000
http://www.hindawi.com/journals/jmath/2016/2121906/
We obtained a Presic type fixed point theorem for two pairs of jointly weakly compatible maps in metric spaces. We also have given an example to illustrate our main theorem.
K. P. R. Rao, Sk. Sadik, and S. Manro
Copyright © 2016 K. P. R. Rao et al. All rights reserved.

MultipleTerm Refinements of Young Type Inequalities
Wed, 16 Nov 2016 13:34:34 +0000
http://www.hindawi.com/journals/jmath/2016/4346712/
Recently, a multipleterm refinement of Young’s inequality has been proved. In this paper, we show its reverse refinement. Moreover, we will present multipleterm refinements of Young’s inequality involving Kantorovich constants. Finally, we will apply scalar inequalities to operators.
Daeshik Choi
Copyright © 2016 Daeshik Choi. All rights reserved.

Stability Analysis of the Periodic Solutions of Some Kinds of PredatorPrey Dynamical Systems
Thu, 10 Nov 2016 06:49:40 +0000
http://www.hindawi.com/journals/jmath/2016/7308609/
Analysis of predatorprey dynamical systems that have the functional response which generalizes the other types of functional responses in two dimensions is mainly studied in this paper. The main problems for this study are to detect the if and only if conditions for attaining the periodic solution of the considered system and to find the condition for global asymptotic stability of this solution for some different types of predatorprey systems that are obtained from that system. To get the desired results, some aspects of semigroup theory for stability analysis and coincidence degree theory are used.
Neslihan Nesliye Pelen
Copyright © 2016 Neslihan Nesliye Pelen. All rights reserved.

On Parametric Metric Spaces and FixedPoint Type Theorems for Expansive Mappings
Mon, 07 Nov 2016 06:46:50 +0000
http://www.hindawi.com/journals/jmath/2016/4746732/
We introduce the notion of a parametric metric space as generalization of a parametric metric space. Using some expansive mappings, we prove a fixedpoint theorem on a parametric metric space. It is important to obtain new fixedpoint theorems on a parametric metric space because there exist some parametric metrics which are not generated by any parametric metric. We expect that many mathematicians will study various fixedpoint theorems using new expansive mappings (or contractive mappings) in a parametric metric space.
Nihal Taş and Nihal Yılmaz Özgür
Copyright © 2016 Nihal Taş and Nihal Yılmaz Özgür. All rights reserved.

A Study on Characteristic Roots of Lattice Matrices
Mon, 31 Oct 2016 08:56:30 +0000
http://www.hindawi.com/journals/jmath/2016/3964351/
This paper deals with the characteristic roots of different types of lattice matrices and proves that a matrix and its transpose have the same characteristic roots. Also this paper introduces the concept of similar lattice matrices and proves that similar lattice matrices have the same characteristic roots.
Kapiarumalayil Varkey Thomas and Geena Joy
Copyright © 2016 Kapiarumalayil Varkey Thomas and Geena Joy. All rights reserved.

End Point Results in Metric Spaces Endowed with a Graph
Sun, 30 Oct 2016 13:12:30 +0000
http://www.hindawi.com/journals/jmath/2016/9130107/
We introduce the notion of end point of multivalued mappings in the setting of metric space endowed with a graph and prove some existence results in this context. The mappings are assumed to satisfy certain generalized multivalued almost contractive type inequalities. Further, the consequences of the corresponding results in the cases of singlevalued mappings are also discussed with examples.
Binayak S. Choudhury, Nikhilesh Metiya, and Pradip Debnath
Copyright © 2016 Binayak S. Choudhury et al. All rights reserved.

On the Adjacency, Laplacian, and Signless Laplacian Spectrum of Coalescence of Complete Graphs
Tue, 25 Oct 2016 09:25:47 +0000
http://www.hindawi.com/journals/jmath/2016/5906801/
Coalescence as one of the operations on a pair of graphs is significant due to its simple form of chromatic polynomial. The adjacency matrix, Laplacian matrix, and signless Laplacian matrix are common matrices usually considered for discussion under spectral graph theory. In this paper, we compute adjacency, Laplacian, and signless Laplacian energy ( energy) of coalescence of pair of complete graphs. Also, as an application, we obtain the adjacency energy of subdivision graph and line graph of coalescence from its energy.
S. R. Jog and Raju Kotambari
Copyright © 2016 S. R. Jog and Raju Kotambari. All rights reserved.

Nonsolvable Subalgebras of
Tue, 18 Oct 2016 13:55:56 +0000
http://www.hindawi.com/journals/jmath/2016/2570147/
All the simple and then semisimple subalgebras of are found. Each such semisimple subalgebra acts by commutator on . In each case the invariant subspaces are found and the results are used to determine all possible subalgebras of that are not solvable.
Ryad Ghanam and Gerard Thompson
Copyright © 2016 Ryad Ghanam and Gerard Thompson. All rights reserved.

Convergence Rate of Some TwoStep Iterative Schemes in Banach Spaces
Mon, 10 Oct 2016 05:58:44 +0000
http://www.hindawi.com/journals/jmath/2016/9641706/
This article proves some theorems to approximate fixed point of Zamfirescu operators on normed spaces for some twostep iterative schemes, namely, PicardMann iteration, Ishikawa iteration, Siteration, and Thianwan iteration, with their errors. We compare the aforementioned iterations using numerical approach; the results show that Siteration converges faster than other iterations followed by PicardMann iteration, while Ishikawa iteration is the least in terms of convergence rate. These results also suggest the best among twostep iterative fixed point schemes in the literature.
O. T. Wahab, R. O. Olawuyi, K. Rauf, and I. F. Usamot
Copyright © 2016 O. T. Wahab et al. All rights reserved.

Multivalued Fixed Point Theorems for Generalized Contractions and Their Applications
Wed, 05 Oct 2016 14:00:48 +0000
http://www.hindawi.com/journals/jmath/2016/5190718/
We give common hybrid fixed point results for generalized weak contraction satisfying and properties in the framework of metric spaces. An application to functional equations is also discussed.
Muhammad Shoaib and Muhammad Sarwar
Copyright © 2016 Muhammad Shoaib and Muhammad Sarwar. All rights reserved.

Effective RootFinding Methods for Nonlinear Equations Based on Multiplicative Calculi
Wed, 05 Oct 2016 07:58:17 +0000
http://www.hindawi.com/journals/jmath/2016/8174610/
In recent studies, papers related to the multiplicative based numerical methods demonstrate applicability and efficiency of these methods. Numerical rootfinding methods are essential for nonlinear equations and have a wide range of applications in science and engineering. Therefore, the idea of rootfinding methods based on multiplicative and Volterra calculi is selfevident. NewtonRaphson, Halley, Broyden, and perturbed rootfinding methods are used in numerical analysis for approximating the roots of nonlinear equations. In this paper, NewtonRaphson methods and consequently perturbed rootfinding methods are developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed rootfinding methods is exposed by examples, and the results are compared with some ordinary methods. One of the striking results of the proposed method is that the rate of convergence for many problems are considerably larger than the original methods.
Ali Özyapıcı, Zehra B. Sensoy, and Tolgay Karanfiller
Copyright © 2016 Ali Özyapıcı et al. All rights reserved.

Slightly Regular Measures and Measureable Sets
Mon, 03 Oct 2016 11:46:57 +0000
http://www.hindawi.com/journals/jmath/2016/1456039/
Outer and inner measures of a measure are defined and used to prove results involving them on a lattice and its complement . The results concern slightly regular measures and sets such as which is the collection of measureable sets.
James Camacho Jr.
Copyright © 2016 James Camacho Jr. All rights reserved.

On a Special Form of Torsion Tensor in Finsler Space
Thu, 29 Sep 2016 12:11:52 +0000
http://www.hindawi.com/journals/jmath/2016/3694017/
A special form of () torsion tensor was introduced which may be considered generalization of Finsler space and reducible Finsler space and then some properties of this space were studied. We also introduce connection and give some case and condition of torsion tensor
Brijesh Kumar Tripathi and K. B. Pandey
Copyright © 2016 Brijesh Kumar Tripathi and K. B. Pandey. All rights reserved.

One Form of Lyapunov Operator for Stochastic Dynamic System with Markov Parameters
Thu, 29 Sep 2016 07:15:19 +0000
http://www.hindawi.com/journals/jmath/2016/1694935/
The form of weak infinitesimal operator of Lyapunov type on solutions of stochastic dynamic systems of random structure with constant delay which exist under the action of Markov perturbations is obtained.
Taras Lukashiv
Copyright © 2016 Taras Lukashiv. All rights reserved.

Computation of New DegreeBased Topological Indices of Graphene
Mon, 26 Sep 2016 11:35:31 +0000
http://www.hindawi.com/journals/jmath/2016/4341919/
Graphene is one of the most promising nanomaterials because of its unique combination of superb properties, which opens a way for its exploitation in a wide spectrum of applications ranging from electronics to optics, sensors, and biodevices. Inspired by recent work on Graphene of computing topological indices, here we propose new topological indices, namely, ArithmeticGeometric index ( index), SK index, SK1 index, and SK2 index of a molecular graph and obtain the explicit formulae of these indices for Graphene.
V. S. Shigehalli and Rachanna Kanabur
Copyright © 2016 V. S. Shigehalli and Rachanna Kanabur. All rights reserved.