http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Sun, 16 Jun 2013 10:42:22 +0000 http://www.hindawi.com/journals/jmath/2013/574213/ We have discussed the dynamical behaviour of a single-species population model in a polluted environment which describes the effect of toxicants on ecological system. Boundedness, positivity, and stability analysis of the model at various equilibrium points is discussed thoroughly. We have also studied the effect of single discrete delay as well as double discrete delays on the population model. Existence conditions of the Hopf bifurcation for single time delay are investigated. The length of delay preserving the stability is also estimated. The direction and the stability criteria of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. The stability of the model with double time delays is investigated by using the Nyquist criteria. By choosing one of the delays as a bifurcation parameter, the model is found to undergo a Hopf bifurcation. Some numerical simulations for justifying the theoretical results are also illustrated by using MATLAB, which shows the reliability of our model from the practical point of view. Swarnali Sharma and G. P. Samanta Copyright © 2013 Swarnali Sharma and G. P. Samanta. All rights reserved. Thu, 13 Jun 2013 10:56:26 +0000 http://www.hindawi.com/journals/jmath/2013/738491/ We investigate a new class of cocoercive operators named generalized -cocoercive operators in Hilbert spaces. We prove that generalized -cocoercive operator is single-valued and Lipschitz continuous and extends the concept of resolvent operators associated with -cocoercive operators to the generalized -cocoercive operators. Some examples are given to justify the definition of generalized -cocoercive operators. Further, we consider a generalized set-valued variational-like inclusion problem involving generalized -cocoercive operator. In terms of the new resolvent operator technique, we give the approximate solution and suggest an iterative algorithm for the generalized set-valued variational-like inclusions. Furthermore, we discuss the convergence criteria of iterative algorithm under some suitable conditions. Our results can be viewed as a generalization of some known results in the literature. Shamshad Husain, Sanjeev Gupta, and Vishnu Narayan Mishra Copyright © 2013 Shamshad Husain et al. All rights reserved. Wed, 12 Jun 2013 12:52:35 +0000 http://www.hindawi.com/journals/jmath/2013/404626/ This paper studies the quantitative behavior of a class of one-dimensional cellular automata, named weakly permutive cellular automata, acting on the space of all doubly infinite sequences with values in a finite ring , . We calculate the measure-theoretic entropy and the topological entropy of weakly permutive cellular automata with respect to any invariant measure on the space . As an application, it is shown that the uniform Bernoulli measure is the unique maximal measure for linear cellular automata among the Markov measures. Chih-Hung Chang and Yu-Wen Chen Copyright © 2013 Chih-Hung Chang and Yu-Wen Chen. All rights reserved. Tue, 11 Jun 2013 11:51:45 +0000 http://www.hindawi.com/journals/jmath/2013/685212/ We will have an attempt to present a method for constructing variational problems without having a desired one-parameter transformation group as a variational symmetry. For this, we use the notation of μ-symmetry which was introduced by Giuseppe Gaeta and Paola Morando in 2004. Moreover, our given method enabled us to solve those constructed variational problems using μ-symmetries. Mehdi Nadjafikhah, Saeed Dodangeh, and Parastoo Kabi-Nejad Copyright © 2013 Mehdi Nadjafikhah et al. All rights reserved. Mon, 10 Jun 2013 13:29:50 +0000 http://www.hindawi.com/journals/jmath/2013/407068/ We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on a twin Frobenius algebra, by providing a description of this category in terms of generators and relations. A twin Frobenius algebra consists of a commutative Frobenius algebra , a symmetric Frobenius algebra , and an algebra homomorphism with dual , satisfying some extra conditions. We also introduce a generalized 2-dimensional Topological Quantum Field Theory defined on singular 2-dimensional cobordisms and show that it is equivalent to a twin Frobenius algebra in a symmetric monoidal category. Carmen Caprau Copyright © 2013 Carmen Caprau. All rights reserved. Wed, 05 Jun 2013 15:02:27 +0000 http://www.hindawi.com/journals/jmath/2013/490524/ A finite -group is said to have the property , if, for any abelian subgroup of , there is . We show that if satisfies , then has the following two types: (1) is isoclinic to some stem groups of order , which form an isoclinic family. (2) is isoclinic to a special -group of exponent . Elementary structures of groups with are determined. Yuemei Mao and Qianlu Li Copyright © 2013 Yuemei Mao and Qianlu Li. All rights reserved. Sun, 02 Jun 2013 14:10:23 +0000 http://www.hindawi.com/journals/jmath/2013/510790/ We characterize intra-regular LA-semihypergroups by using the properties of their left and right hyperideals, and we investigate some useful conditions for an LA-semihypergroup to become an intra-regular LA-semihypergroup. Naveed Yaqoob, Piergiulio Corsini, and Faisal Yousafzai Copyright © 2013 Naveed Yaqoob et al. All rights reserved. Thu, 30 May 2013 09:28:31 +0000 http://www.hindawi.com/journals/jmath/2013/921952/ We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equation , where , are two matrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems. Zhenhua Hu and Shuqing Zhou Copyright © 2013 Zhenhua Hu and Shuqing Zhou. All rights reserved. Sun, 26 May 2013 16:06:30 +0000 http://www.hindawi.com/journals/jmath/2013/590462/ This paper investigates the synchronization rate for identical synchronization of chaotic dynamical systems, achieved by using controllers. The paper stresses on the hybrid feedback control technique and the tracking control technique and determines their corresponding maximum, minimum, and average synchronization rates. The results obtained are applied on the Shimizu-Morioka chaotic system, and some necessary and sufficient conditions for synchronization are obtained. Comparison of the two controllers is undertaken on the basis of their synchronization rates, in the context of the Shimizu-Morioka system. The results are analyzed both theoretically and numerically. Moreover, a method of graphical analysis is proposed to completely characterize the set of hybrid controllers for a given system. Mitul Islam, Bipul Islam, and Nurul Islam Copyright © 2013 Mitul Islam et al. All rights reserved. Thu, 23 May 2013 19:02:58 +0000 http://www.hindawi.com/journals/jmath/2013/502635/ We investigate a variant of the stochastic logistic model that allows individual variation and time-dependent infection and recovery rates. The model is described as a heterogeneous density dependent Markov chain. We show that the process can be approximated by a deterministic process defined by an integral equation as the population size grows. Yilun Shang Copyright © 2013 Yilun Shang. All rights reserved. Wed, 22 May 2013 11:08:27 +0000 http://www.hindawi.com/journals/jmath/2013/721868/ A mathematical model to control the vibrations of a rectangular plate is constructed with an aim to assist engineers in designing and fabrication of various structures used in the field of science and technology, mostly used in satellite and aeronautical engineering. The present study is related to the analysis of free vibrations of nonhomogeneous rectangular plate clamped at all the four edges. Authors studied the bilinear effect of thickness as well as temperature variations in both and directions. Variation in Poisson's ratio is also considered linearly in -direction due to nonhomogeneity. Rayleigh-Ritz method is used to analyze the frequencies for the first two modes of vibrations for different values of thermal gradient, nonhomogeneity constant, taper constants and aspect ratio. All the numerical computations have been performed for an alloy of aluminum, that is, duralumin. All the results are presented in the form of graphs. Anupam Khanna and Ashish Singhal Copyright © 2013 Anupam Khanna and Ashish Singhal. All rights reserved. Mon, 20 May 2013 10:52:43 +0000 http://www.hindawi.com/journals/jmath/2013/967045/ A fixed point theorem is presented for single-valued map with using generalized -weak contractive condition involving various combinations of on a complete metric space. Our result is an extension as well as a generalization of Alber and Guerre-Delabriere (1997) in particular. It also generalizes the results of Rhoades (2001), Choudhury and Dutta, (2000), and Dutta and Choudhury, (2008). Penumurthy Parvateesam Murthy and K. N. V. V. Vara Prasad Copyright © 2013 Penumurthy Parvateesam Murthy and K. N. V. V. Vara Prasad. All rights reserved. Sun, 12 May 2013 14:13:20 +0000 http://www.hindawi.com/journals/jmath/2013/821762/ This paper is devoted to study further properties of generalized Mittag-Leffler function associated with Weyl fractional integral and differential operators. A new integral operator depending on Weyl fractional integral operator and containing in its kernel is defined and studied, namely, its boundedness. Also, composition of Weyl fractional integral and differential operators with the new operator is established. Ahmad Faraj, Tariq Salim, Safaa Sadek, and Jamal Ismail Copyright © 2013 Ahmad Faraj et al. All rights reserved. Thu, 09 May 2013 12:52:16 +0000 http://www.hindawi.com/journals/jmath/2013/841837/ We define two new general integral operators for certain analytic functions in the unit disc and give some sufficient conditions for these integral operators on some subclasses of analytic functions. H. Özlem Güney and Serap Bulut Copyright © 2013 H. Özlem Güney and Serap Bulut. All rights reserved. Wed, 08 May 2013 10:39:20 +0000 http://www.hindawi.com/journals/jmath/2013/609218/ We begin by recalling a group which is an enlargement of the diffeomorphisms on an ordinary manifold. We used this larger group to unify the gravitational and electroweak fields, which are mediated by bosons. Unfortunately, we could not include the neutrinos, because geometrical theories based on an ordinary manifold generally cannot include fermions. Therefore, in this paper, we introduce an analogous group that contains the superdiffeomorphisms on a DeWitt supermanifold as a proper subgroup. Dave Pandres Jr. Copyright © 2013 Dave Pandres Jr. All rights reserved. Tue, 07 May 2013 13:11:43 +0000 http://www.hindawi.com/journals/jmath/2013/793824/ Frame theory is the study of topology based on its open set lattice, and it was studied extensively by various authors. In this paper, we study quotients of intuitionistic fuzzy filters of an intuitionistic fuzzy coframe. The quotients of intuitionistic fuzzy filters are shown to be filters of the given intuitionistic fuzzy coframe. It is shown that the collection of all intuitionistic fuzzy filters of a coframe and the collection of all intutionistic fuzzy quotient filters of an intuitionistic fuzzy filter are coframes. Rajesh K. Thumbakara Copyright © 2013 Rajesh K. Thumbakara. All rights reserved. Thu, 02 May 2013 16:02:29 +0000 http://www.hindawi.com/journals/jmath/2013/457631/ We study a mixed problem with an integral two-space-variables condition for parabolic equation with the Bessel operator. The existence and uniqueness of the solution in functional weighted Sobolev space are proved. The proof is based on a priori estimate “energy inequality” and the density of the range of the operator generated by the problem considered. Bouziani Abdelfatah, Oussaeif Taki-Eddine, and Ben Aoua Leila Copyright © 2013 Bouziani Abdelfatah et al. All rights reserved. Sun, 28 Apr 2013 08:45:55 +0000 http://www.hindawi.com/journals/jmath/2013/645752/ For the famous Darboux-Pöschl-Teller equation, we present new wronskian representation both for the potential and the related eigenfunctions. The simplest application of this new formula is the explicit description of dynamics of the DPT potentials and the action of the KdV hierarchy. The key point of the proof is some evaluation formulas for special wronskian determinant. Pierre Gaillard and Vladimir Matveev Copyright © 2013 Pierre Gaillard and Vladimir Matveev. All rights reserved. Tue, 23 Apr 2013 10:54:43 +0000 http://www.hindawi.com/journals/jmath/2013/146836/ The aim of this paper is to extend the use of homotopy perturbation method (HPM) to study the solutions for some important generalized nonlinear partial differential equations (PDEs) such as Fisher equation with convection term, Sharma-Tasso-Olver (STO) equation, and Fitzhugh-Nagumo (FN) equation. Marwan Alquran, Mahmoud Mohammad, and Ahmad Ababneh Copyright © 2013 Marwan Alquran et al. All rights reserved. Mon, 22 Apr 2013 13:08:39 +0000 http://www.hindawi.com/journals/jmath/2013/630934/ We introduce and study a subclass of analytic functions related to Robertson functions. Here we discuss the coefficient estimate for function in this class. Muhammad Arif and Mumtaz Ali Copyright © 2013 Muhammad Arif and Mumtaz Ali. All rights reserved. Thu, 18 Apr 2013 10:21:16 +0000 http://www.hindawi.com/journals/jmath/2013/920528/ The hyperbolic cosines and sines theorems for the curvilinear triangle bounded by circular arcs of three intersecting circles are formulated and proved by using the general complex calculus. The method is based on a key formula establishing a relationship between exponential function and the cross-ratio. The proofs are carried out on Euclidean plane. Robert M. Yamaleev Copyright © 2013 Robert M. Yamaleev. All rights reserved. Thu, 18 Apr 2013 08:17:29 +0000 http://www.hindawi.com/journals/jmath/2013/650480/ Maji et al. introduced the concept of intuitionistic fuzzy soft sets, which is an extension of soft sets and intuitionistic fuzzy sets. In this paper, we apply the concept of intuitionistic fuzzy soft sets to rings. The concept of intuitionistic fuzzy soft rings is introduced and some basic properties of intuitionistic fuzzy soft rings are given. Intersection, union, AND, and OR operations of intuitionistic fuzzy soft rings are defined. Then, the deffinitions of intuitionistic fuzzy soft ideals are proposed and some related results are considered. B. A. Ersoy, S. Onar, K. Hila, and B. Davvaz Copyright © 2013 B. A. Ersoy et al. All rights reserved. Wed, 17 Apr 2013 08:19:56 +0000 http://www.hindawi.com/journals/jmath/2013/430965/ We have examined the spectra of the operator on the sequence spaces and . Binod Chandra Tripathy and Avinoy Paul Copyright © 2013 Binod Chandra Tripathy and Avinoy Paul. All rights reserved. Tue, 16 Apr 2013 18:49:19 +0000 http://www.hindawi.com/journals/jmath/2013/467351/ Let , and let be an even function. In this paper, we consider some Lagrange interpolation polynomials and the Gauss-Jacobi quadrature formula of entire functions associated with Erdös-type weights , , and we will estimate the error terms. Gou Nakamura, Ryozi Sakai, and Noriaki Suzuki Copyright © 2013 Gou Nakamura et al. All rights reserved. Tue, 16 Apr 2013 13:04:36 +0000 http://www.hindawi.com/journals/jmath/2013/719324/ First we prove common fixed point theorems for weakly compatible maps which generalize the results of Chen (2012). Secondly, we prove common fixed point theorems using property E.A. along with weakly compatible maps. At the end, we prove common fixed point theorems using common limit range property (CLR property) along with weakly compatible maps. Manoj Kumar, Pankaj Kumar, and Sanjay Kumar Copyright © 2013 Manoj Kumar et al. All rights reserved. Tue, 16 Apr 2013 10:52:06 +0000 http://www.hindawi.com/journals/jmath/2013/207176/ We study the inverses of block Toeplitz matrices based on the analysis of the block cyclic displacement. New formulas for the inverses of block Toeplitz matrices are proposed. We show that the inverses of block Toeplitz matrices can be decomposed as a sum of products of block circulant matrices. In the scalar case, the inverse formulas are proved to be numerically forward stable, if the Toeplitz matrix is nonsingular and well conditioned. Xiao-Guang Lv and Ting-Zhu Huang Copyright © 2013 Xiao-Guang Lv and Ting-Zhu Huang. All rights reserved. Tue, 16 Apr 2013 10:14:24 +0000 http://www.hindawi.com/journals/jmath/2013/126347/ The widespread and rapid proliferation of logical systems in several areas of computer science has led to a resurgence of interest in various methods for combining logical systems and in investigations into the properties inherited by the resulting combinations. One of the oldest such methods is fibring. In fibring the shared connectives of the combined logics inherit properties from both component logical systems, and this leads often to inconsistencies. To deal with such undesired effects, Sernadas et al. (2011, 2012) have recently introduced a novel way of combining logics, called meet-combination, in which the combined connectives share only the common logical properties they enjoy in the component systems. In their investigations they provide a sound and concretely complete calculus for the meet-combination based on available sound and complete calculi for the component systems. In this work, an effort is made to abstract those results to a categorical level amenable to categorical abstract algebraic logic techniques. George Voutsadakis Copyright © 2013 George Voutsadakis. All rights reserved. Wed, 10 Apr 2013 09:34:47 +0000 http://www.hindawi.com/journals/jmath/2013/105848/ Certain properties of the S-transform are given and composition of S-transform is defined. We study the fractional S-transform on spaces of type . It is shown that the fractional S-transform is a continuous linear map of the space of type defined on into the space of type defined on . Sunil Kumar Singh Copyright © 2013 Sunil Kumar Singh. All rights reserved. Tue, 09 Apr 2013 13:29:09 +0000 http://www.hindawi.com/journals/jmath/2013/489863/ The aim of this paper is to study magneto-thermoelastic interactions in an initially stressed isotropic homogeneous half-space in the context of fractional order theory of generalized thermoelasticity. State space formulation with the Laplace transform technique is used to obtain the general solution, and the resulting formulation is applied to the ramp type increase in thermal load and zero stress. Solutions of the problem in the physical domain are obtained by using a numerical method of the Laplace inverse transform based on the Fourier expansion technique, and the expressions for the displacement, temperature, and stress inside the half-space are obtained. Numerical computations are carried out for a particular material for illustrating the results. Results obtained for the field variables are displayed graphically. Some comparisons have been shown in figures to present the effect of fractional parameter, ramp parameter, magnetic field, and initial stress on the field variables. Some particular cases of special interest have been deduced from the present investigation. Sunita Deswal, Sandeep Singh Sheoran, and Kapil Kumar Kalkal Copyright © 2013 Sunita Deswal et al. All rights reserved. Tue, 09 Apr 2013 11:44:29 +0000 http://www.hindawi.com/journals/jmath/2013/912643/ Let be a commutative Noetherian local ring and let be a finitely generated -module of dimension . Then the following statements hold: (a) if width for all with , then is co-Cohen-Macaulay of Noetherian dimension ; (b) if is an unmixed -module and depth , then is co-Cohen-Macaulay of Noetherian dimension if and only if is either zero or co-Cohen-Macaulay of Noetherian dimension . As consequence, if is co-Cohen-Macaulay of Noetherian dimension for all with , then is co-Cohen-Macaulay of Noetherian dimension . Hero Saremi and Amir Mafi Copyright © 2013 Hero Saremi and Amir Mafi. All rights reserved.