Journal of Mathematics The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. The Distortion Theorems for Harmonic Mappings with Analytic Parts Convex or Starlike Functions of Order Mon, 12 Oct 2015 14:23:52 +0000 Some sharp estimates of coefficients, distortion, and growth for harmonic mappings with analytic parts convex or starlike functions of order are obtained. We also give area estimates and covering theorems. Our main results generalise those of Klimek and Michalski. Mengkun Zhu and Xinzhong Huang Copyright © 2015 Mengkun Zhu and Xinzhong Huang. All rights reserved. The Structure of Simple Modules of Birman-Murakami-Wenzl Algebras Mon, 12 Oct 2015 11:17:41 +0000 We study the restriction of simple modules of Birman-Murakami-Wenzl algebras with   being not a root of 1. Precisely, we study the module structure for the restriction of to and describe the socle and head of the restriction of each simple module completely. Xu Xu Copyright © 2015 Xu Xu. All rights reserved. Norm Estimates for Solutions of Polynomial Operator Equations Sun, 04 Oct 2015 16:08:26 +0000 We consider the equations and , where   , , are given linear bounded operators in a Banach space and is to be found. Representations of solutions are derived. In the cases of Euclidean and Hilbert spaces, norm estimates for the solutions are suggested. Michael Gil’ Copyright © 2015 Michael Gil’. All rights reserved. Stability of Fixed Point Sets of a Class of Multivalued Nonlinear Contractions Thu, 01 Oct 2015 12:02:20 +0000 We consider a problem of stability of fixed point sets for a sequence of multivalued mappings defined on a metric space converging to a limit function where the convergence is with respect to the Pompeiu-Hausdorff distance. The members of the sequence are assumed to be multivalued almost contractions. We show that the fixed point sets of this sequence of mappings are stable. Binayak S. Choudhury and Chaitali Bandyopadhyay Copyright © 2015 Binayak S. Choudhury and Chaitali Bandyopadhyay. All rights reserved. On a Theorem of Ziv Ran concerning Abelian Varieties Which Are Product of Jacobians Thu, 01 Oct 2015 09:45:36 +0000 We give a new proof for a theorem of Ziv Ran which generalizes some results of Matsusaka and Hoyt. These results provide criteria for an Abelian variety to be a Jacobian or a product of Jacobians. The advantage of our method is that it works in arbitrary characteristic. Cristian Anghel and Nicolae Buruiana Copyright © 2015 Cristian Anghel and Nicolae Buruiana. All rights reserved. The Partition Function of the Dirichlet Operator on a -Dimensional Rectangle Cavity Tue, 15 Sep 2015 06:16:23 +0000 We study the asymptotic behavior of the free partition function in the limit for a diffusion process which consists of -independent, one-dimensional, symmetric, -stable processes in a hyperrectangular cavity with an absorbing boundary. Each term of the partition function for this polyhedron in -dimensions can be represented by a quermassintegral and the geometrical information conveyed by the eigenvalues of the fractional Dirichlet Laplacian for this solvable model is now transparent. We also utilize the intriguing method of images to solve the same problem, in one and two dimensions, and recover identical results to those derived in the previous analysis. Agapitos N. Hatzinikitas Copyright © 2015 Agapitos N. Hatzinikitas. All rights reserved. Maps Preserving Idempotence on Matrix Spaces Wed, 09 Sep 2015 07:13:00 +0000 Suppose is an arbitrary field. Let be the number of the elements of . Let be the space of all matrices over , let be the subset of consisting of all symmetric matrices, and let be the subset of consisting of all upper-triangular matrices. Let ; a map is said to preserve idempotence if is idempotent if and only if is idempotent for any and . In this paper, the maps preserving idempotence on , , and were characterized in case . Yuqiu Sheng and Hanyu Zhang Copyright © 2015 Yuqiu Sheng and Hanyu Zhang. All rights reserved. Some Applications of Ordinary Differential Operator to Certain Multivalent Functions Tue, 18 Aug 2015 16:28:56 +0000 The aim of this paper is to apply the well-known ordinary differential operator to certain multivalent functions which are analytic in the certain domains of the complex plane and then to determine some criteria concerning analytic and geometric properties of the related complex functions. Müfit Şan, Hüseyin Irmak, and Ayhan Şerbetçi Copyright © 2015 Müfit Şan et al. All rights reserved. Locally Defined Operators in the Space of Functions of Bounded Riesz-Variation Mon, 06 Jul 2015 11:18:12 +0000 We study the locally defined operator on the spaces of bounded Riesz -variation functions and we prove that those operators are the Nemytskii operator. W. Aziz, J. A. Guerrero, K. Maldonado, and N. Merentes Copyright © 2015 W. Aziz et al. All rights reserved. Note on Quasi-Numerically Positive Log Canonical Divisors Sun, 31 May 2015 17:25:50 +0000 We propose a subconjecture that implies the semiampleness conjecture for quasi-numerically positive log canonical divisors and prove the ampleness in some elementary cases. Shigetaka Fukuda Copyright © 2015 Shigetaka Fukuda. All rights reserved. Nonexplosion and Pathwise Uniqueness of Stochastic Differential Equation Driven by Continuous Semimartingale with Non-Lipschitz Coefficients Sun, 17 May 2015 11:50:23 +0000 We study a class of stochastic differential equations driven by semimartingale with non-Lipschitz coefficients. New sufficient conditions on the strong uniqueness and the nonexplosion are derived for -dimensional stochastic differential equations on with non-Lipschitz coefficients, which extend and improve Fei’s results. Jinxia Wang Copyright © 2015 Jinxia Wang. All rights reserved. Boundedness of Marcinkiewicz Integrals on RBMO Spaces over Nonhomogeneous Metric Measure Spaces Sun, 19 Apr 2015 14:23:42 +0000 Let be a metric measures space satisfying the upper doubling conditions and the geometrically doubling conditions in the sense of Hytönen. Under the assumption that the dominating function satisfies the weak reverse doubling condition, the authors prove that Marcinkiewicz integral with kernel satisfying certain stronger Hörmander-type condition is bounded on RBMO space. Ji Cheng and Guanghui Lu Copyright © 2015 Ji Cheng and Guanghui Lu. All rights reserved. On the Range of the Radon Transform on and the Related Volberg’s Uncertainty Principle Mon, 02 Feb 2015 13:21:37 +0000 We characterize the image of exponential type functions under the discrete Radon transform R on the lattice of the Euclidean space . We also establish the generalization of Volberg's uncertainty principle on , which is proved by means of this characterization. The techniques of which we make use essentially in this paper are those of the Diophantine integral geometry as well as the Fourier analysis. Ahmed Abouelaz, Abdallah Ihsane, and Takeshi Kawazoe Copyright © 2015 Ahmed Abouelaz et al. All rights reserved. Inferior Mean of Measures on Curves and Subspaces Sun, 28 Dec 2014 11:16:42 +0000 We obtain new sharp upper bounds of the inferior mean for positive harmonic functions defined by finite boundary measures that lie on curves or subspaces of the boundary of the half-space. Yevgenya Movshovich Copyright © 2014 Yevgenya Movshovich. All rights reserved. Noninvariant Hypersurfaces of a Nearly Trans-Sasakian Manifolds Mon, 22 Dec 2014 11:17:26 +0000 The present paper focuses on the study of noninvariant hypersurfaces of a nearly trans-Sasakian manifold equipped with -structure. Initially some properties of this structure have been discussed. Further, the second fundamental forms of noninvariant hypersurfaces of nearly trans-Sasakian manifolds and nearly cosymplectic manifolds with -structure have been calculated provided is parallel. In addition, the eigenvalues of have been found and proved that a noninvariant hypersurface with -structure of nearly cosymplectic manifold with contact structure becomes totally geodesic. Finally the paper has been concluded by investigating the necessary condition for totally geodesic or totally umbilical noninvariant hypersurface with -structure of a nearly trans-Sasakian manifold. Satya Prakash Yadav and Shyam Kishor Copyright © 2014 Satya Prakash Yadav and Shyam Kishor. All rights reserved. Markov Switching Model Analysis of Implied Volatility for Market Indexes with Applications to S&P 500 and DAX Thu, 18 Dec 2014 00:10:43 +0000 We adopt a regime switching approach to study concrete financial time series with particular emphasis on their volatility characteristics considered in a space-time setting. In particular the volatility parameter is treated as an unobserved state variable whose value in time is given as the outcome of an unobserved, discrete-time and discrete-state, stochastic process represented by a suitable Markov chain. We will take into account two different approaches for inference on Markov switching models, namely, the classical approach based on the maximum likelihood techniques and the Bayesian inference method realized through a Gibbs sampling procedure. Then the classical approach shall be tested on data taken from the Standard & Poor’s 500 and the Deutsche Aktien Index series of returns in different time periods. Computations are given for a four-state switching model and obtained numerical results are put beside by explanatory graphs which report the outcomes obtained exploiting both smoothing and filtering algorithms used in the estimation/calibration procedures we proposed to infer on the switching model parameters. Luca Di Persio and Samuele Vettori Copyright © 2014 Luca Di Persio and Samuele Vettori. All rights reserved. Erratum to “Pointwise Analog of the Stečkin Approximation Theorem” Sun, 14 Dec 2014 07:00:17 +0000 Włodzimierz Łenski Copyright © 2014 Włodzimierz Łenski. All rights reserved. On Complex Intuitionistic Fuzzy Soft Sets with Distance Measures and Entropies Sun, 14 Dec 2014 00:10:39 +0000 We introduce the concept of complex intuitionistic fuzzy soft sets which is parametric in nature. However, the theory of complex fuzzy sets and complex intuitionistic fuzzy sets are independent of the parametrization tools. Some real life problems, for example, multicriteria decision making problems, involve the parametrization tools. In order to get their new entropies, some important properties and operations on the complex intuitionistic fuzzy soft sets have also been discussed. On the basis of some well-known distance measures, some new distance measures for the complex intuitionistic fuzzy soft sets have also been obtained. Further, we have established correspondence between the proposed entropies and the distance measures of complex intuitionistic fuzzy soft sets. Tanuj Kumar and Rakesh Kumar Bajaj Copyright © 2014 Tanuj Kumar and Rakesh Kumar Bajaj. All rights reserved. The Relationship between Some Regular Subsemigroups of Mon, 08 Dec 2014 00:10:18 +0000 The concept of regular subsemigroups plays an important role in the theory of semigroup. In this work, we study the relationship between some regular subsemigroups on the monoid of all generalized hypersubstitutions of type . Weerapong Wongpinit and Sorasak Leeratanavalee Copyright © 2014 Weerapong Wongpinit and Sorasak Leeratanavalee. All rights reserved. Power Weighted Versions of Bennett, Alpert, and Goldstein’s Wed, 03 Dec 2014 00:10:11 +0000 A weighted version of Bennett, Alpert, and Goldstein’s S, denoted by , is studied. It is shown that the special cases of are often ordered in the same way. It is also shown that many special cases of tend to produce values close to unity, especially when the number of categories of the rating scale is large. It is argued that the application of as an agreement coefficient is not without difficulties. Matthijs J. Warrens Copyright © 2014 Matthijs J. Warrens. All rights reserved. Periodic Solutions for a Class of Singular Hamiltonian Systems on Time Scales Sun, 30 Nov 2014 10:50:34 +0000 We are concerned with a class of singular Hamiltonian systems on time scales. Some results on the existence of periodic solutions are obtained for the system under consideration by means of the variational methods and the critical point theory. Xiaofang Meng and Yongkun Li Copyright © 2014 Xiaofang Meng and Yongkun Li. All rights reserved. Nontrivial Solutions for Dirichlet Boundary Value Systems with the -Laplacian Wed, 19 Nov 2014 07:56:09 +0000 Using critical point theory due to Bonanno (2012), we prove the existence of at least one nontrivial solution for Dirichlet boundary value systems with the -Laplacian. Shang-Kun Wang and Wen-Wu Pan Copyright © 2014 Shang-Kun Wang and Wen-Wu Pan. All rights reserved. Some Definition of Hartley-Hilbert and Fourier-Hilbert Transforms in a Quotient Space of Boehmians Thu, 06 Nov 2014 11:57:32 +0000 We investigate the Hartley-Hilbert and Fourier-Hilbert transforms on a quotient space of Boehmians. The investigated transforms are well-defined and linear mappings in the space of Boehmians. Further properties are also obtained. S. K. Q. Al-Omari Copyright © 2014 S. K. Q. Al-Omari. All rights reserved. Weighted -Inequalities for the Dunkl Transform Thu, 06 Nov 2014 08:47:02 +0000 We give, for , weighted -inequalities for the Dunkl transform, using, respectively, the modulus of continuity of radial functions and the Dunkl convolution in the general case. As application, we obtain, in particular, the integrability of this transform on Besov-Lipschitz spaces. Chokri Abdelkefi and Faten Rached Copyright © 2014 Chokri Abdelkefi and Faten Rached. All rights reserved. Parameter Dependence of Stable Invariant Manifolds for Delay Differential Equations under -Dichotomies Mon, 27 Oct 2014 07:14:24 +0000 We obtain the existence of stable invariant manifolds for the nonlinear equation provided that the linear delay equation admits a nonuniform -dichotomy and is a sufficiently small Lipschitz perturbation. We show that the stable invariant manifolds are dependent on parameter . Namely, the stable invariant manifolds are Lipschitz in the parameter . In addition, we also show that nonuniform -contraction persists under sufficiently small nonlinear perturbations. Lijun Pan Copyright © 2014 Lijun Pan. All rights reserved. Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem Sun, 19 Oct 2014 11:40:10 +0000 We are concerned with the existence of positive solutions for the nonlinear third-order three-point boundary value problem , , , , where , , is a positive parameter, is continuous. We construct Green’s function for the associated linear boundary value problem and obtain some useful properties of Green’s function. Finally, by using fixed-point index theorem in cones, we establish the existence results of positive solutions for the boundary value problem an example illustrates the application of the results obtained. Tiaoxia Dun and Pengyu Chen Copyright © 2014 Tiaoxia Dun and Pengyu Chen. All rights reserved. On Nil-Symmetric Rings Thu, 16 Oct 2014 06:56:20 +0000 The concept of nil-symmetric rings has been introduced as a generalization of symmetric rings and a particular case of nil-semicommutative rings. A ring is called right (left) nil-symmetric if, for , where are nilpotent elements, implies . A ring is called nil-symmetric if it is both right and left nil-symmetric. It has been shown that the polynomial ring over a nil-symmetric ring may not be a right or a left nil-symmetric ring. Further, it is also proved that if is right (left) nil-symmetric, then the polynomial ring is a nil-Armendariz ring. Uday Shankar Chakraborty and Krishnendu Das Copyright © 2014 Uday Shankar Chakraborty and Krishnendu Das. All rights reserved. Coupled Fixed Point Theorems with Rational Type Contractive Condition in a Partially Ordered -Metric Space Mon, 29 Sep 2014 11:47:38 +0000 Coupled fixed point theorems for a map satisfying mixed monotone property and a nonlinear, rational type contractive condition are established in a partially ordered -metric space. The conditions for uniqueness of the coupled fixed point are discussed. We also present results for the existence of coupled coincidence points of two maps. K. Chakrabarti Copyright © 2014 K. Chakrabarti. All rights reserved. An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics Mon, 15 Sep 2014 00:00:00 +0000 The prime objective of this paper is to design a new family of optimal eighth-order iterative methods by accelerating the order of convergence of the existing seventh-order method without using more evaluations for finding simple root of nonlinear equations. Numerical comparisons have been carried out to demonstrate the efficiency and performance of the proposed method. Finally, we have compared new method with some existing eighth-order methods by basins of attraction and observed that the proposed scheme is more efficient. Anuradha Singh and J. P. Jaiswal Copyright © 2014 Anuradha Singh and J. P. Jaiswal. All rights reserved. Some Inequalities for the Derivative of Polynomials Sun, 14 Sep 2014 09:49:32 +0000 If is a polynomial of degree , having no zeros in , then Aziz (1989) proved , where . In this paper, we consider a class of polynomial of degree , defined as and present certain generalizations of above inequality and some other well-known results. Sunil Hans, Dinesh Tripathi, and Babita Tyagi Copyright © 2014 Sunil Hans et al. All rights reserved.