Journal of Mathematics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . 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 http://www.hindawi.com/journals/jmath/2014/753852/ 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 http://www.hindawi.com/journals/jmath/2014/978941/ 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 http://www.hindawi.com/journals/jmath/2014/972198/ 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 http://www.hindawi.com/journals/jmath/2014/181397/ 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 http://www.hindawi.com/journals/jmath/2014/231909/ 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 http://www.hindawi.com/journals/jmath/2014/573517/ 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 http://www.hindawi.com/journals/jmath/2014/505290/ 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 http://www.hindawi.com/journals/jmath/2014/790161/ 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 http://www.hindawi.com/journals/jmath/2014/702151/ 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 http://www.hindawi.com/journals/jmath/2014/989526/ 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 http://www.hindawi.com/journals/jmath/2014/951947/ 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 http://www.hindawi.com/journals/jmath/2014/483784/ 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 http://www.hindawi.com/journals/jmath/2014/785357/ 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 http://www.hindawi.com/journals/jmath/2014/569719/ 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 http://www.hindawi.com/journals/jmath/2014/160485/ 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. -Regular Sets in Topology and Generalized Topology Sun, 14 Sep 2014 07:33:50 +0000 http://www.hindawi.com/journals/jmath/2014/274592/ We define and study a new class of regular sets called -regular sets. Properties of these sets are investigated for topological spaces and generalized topological spaces. Decompositions of regular open sets and regular closed sets are provided using -regular sets. Semiconnectedness is characterized by using -regular sets. -continuity and almost -continuity are introduced and investigated. Ankit Gupta and Ratna Dev Sarma Copyright © 2014 Ankit Gupta and Ratna Dev Sarma. All rights reserved. Inverse Limit Spaces with Various Shadowing Property Sun, 14 Sep 2014 07:11:56 +0000 http://www.hindawi.com/journals/jmath/2014/169183/ We discuss the relationship between ergodic shadowing property and inverse shadowing property of and that of the shift map σf on the inverse limit space. Ali Barzanouni Copyright © 2014 Ali Barzanouni. All rights reserved. Montgomery Identity and Ostrowski Type Inequalities for Riemann-Liouville Fractional Integral Wed, 10 Sep 2014 13:21:31 +0000 http://www.hindawi.com/journals/jmath/2014/503195/ We present Montgomery identity for Riemann-Liouville fractional integral as well as for fractional integral of a function with respect to another function . We further use them to obtain Ostrowski type inequalities involving functions whose first derivatives belong to spaces. These inequalities are generally sharp in case and the best possible in case . Application for Hadamard fractional integrals is given. Andrea Aglić Aljinović Copyright © 2014 Andrea Aglić Aljinović. All rights reserved. A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems Tue, 09 Sep 2014 07:23:17 +0000 http://www.hindawi.com/journals/jmath/2014/560578/ We consider a class of absolute-value linear complementarity problems. We propose a new approximation reformulation of absolute value linear complementarity problems by using a nonlinear penalized equation. Based on this approximation reformulation, a penalized-equation-based generalized Newton method is proposed for solving the absolute value linear complementary problem. We show that the proposed method is globally and superlinearly convergent when the matrix of complementarity problems is positive definite and its singular values exceed 1. Numerical results show that our proposed method is very effective and efficient. Yuan Li, Hai-Shan Han, and Dan-Dan Yang Copyright © 2014 Yuan Li et al. All rights reserved. On Some New Generalized Difference Sequence Spaces of Nonabsolute Type Tue, 09 Sep 2014 06:19:20 +0000 http://www.hindawi.com/journals/jmath/2014/876813/ We define a new triangle matrix by the composition of the matrices and . Also, we introduce the sequence spaces , and by using matrix domain of the matrix on the classical sequence spaces , and , respectively, where . Moreover, we show that the space is norm isomorphic to for . Furthermore, we establish some inclusion relations concerning those spaces and determine -, -, and -duals of those spaces and construct the Schauder bases , and . Finally, we characterize the classes of infinite matrices where and . Osman Duyar, Serkan Demiriz, and Osman Özdemir Copyright © 2014 Osman Duyar et al. All rights reserved. A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space Mon, 08 Sep 2014 10:59:33 +0000 http://www.hindawi.com/journals/jmath/2014/713690/ Spectral properties of a special class of infinite dimensional Dirac operators on the abstract boson-fermion Fock space associated with the pair of complex Hilbert spaces are investigated, where is a perturbation parameter (a coupling constant in the context of physics) and the unperturbed operator is taken to be a free infinite dimensional Dirac operator. A variety of the kernel of is shown. It is proved that there are cases where, for all sufficiently large with , has infinitely many nonzero eigenvalues even if has no nonzero eigenvalues. Also Fredholm property of restricted to a subspace of is discussed. Asao Arai Copyright © 2014 Asao Arai. All rights reserved. New Interpretations of Cohen’s Kappa Wed, 03 Sep 2014 06:21:10 +0000 http://www.hindawi.com/journals/jmath/2014/203907/ Cohen’s kappa is a widely used association coefficient for summarizing interrater agreement on a nominal scale. Kappa reduces the ratings of the two observers to a single number. With three or more categories it is more informative to summarize the ratings by category coefficients that describe the information for each category separately. Examples of category coefficients are the sensitivity or specificity of a category or the Bloch-Kraemer weighted kappa. However, in many research studies one is often only interested in a single overall number that roughly summarizes the agreement. It is shown that both the overall observed agreement and Cohen’s kappa are weighted averages of various category coefficients and thus can be used to summarize these category coefficients. Matthijs J. Warrens Copyright © 2014 Matthijs J. Warrens. All rights reserved. Self-Dual Normal Basis of a Galois Ring Mon, 01 Sep 2014 12:40:57 +0000 http://www.hindawi.com/journals/jmath/2014/258187/ Let and be two Galois rings. In this paper, we show how to construct normal basis in the extension of Galois rings, and we also define weakly self-dual normal basis and self-dual normal basis for over , where is considered as a free module over . Moreover, we explain a way to construct self-dual normal basis using particular system of polynomials. Finally, we show the connection between self-dual normal basis for over and the set of all invertible, circulant, and orthogonal matrices over . Irwansyah, Intan Muchtadi-Alamsyah, Aleams Barra, and Ahmad Muchlis Copyright © 2014 Irwansyah et al. All rights reserved. Basicity of the System of Exponents with a Linear Phase in Sobolev Weight Space Mon, 01 Sep 2014 09:57:34 +0000 http://www.hindawi.com/journals/jmath/2014/481425/ In the present paper a criterion for basicity of exponential system with linear phase is obtained in Sobolev weight space . Togrul Muradov and Valid Salmanov Copyright © 2014 Togrul Muradov and Valid Salmanov. All rights reserved. Weight Distribution of Periodic Errors and Optimal/Anti-Optimal Linear Codes Sun, 31 Aug 2014 08:12:46 +0000 http://www.hindawi.com/journals/jmath/2014/971410/ The paper discusses weight distribution of periodic errors and then the optimal case on bounds of parity check digits for (, ) linear codes over that corrects all periodic errors of order in the first block of length and all periodic errors of order in the second block of length and no others. Further, we extend the study to the case when the errors are in the form of periodic errors of order (and ) or more in the two subblocks. Pankaj Kumar Das Copyright © 2014 Pankaj Kumar Das. All rights reserved. A Note on Lax Pairs of the Sawada-Kotera Equation Sun, 24 Aug 2014 12:04:31 +0000 http://www.hindawi.com/journals/jmath/2014/906165/ We prove that the new Lax pair of the Sawada-Kotera equation, discovered recently by Hickman, Hereman, Larue, and Göktaş, and the well-known old Lax pair of this equation, considered in the form of zero-curvature representations, are gauge equivalent to each other if and only if the spectral parameter is nonzero, while for zero spectral parameter a nongauge transformation is required. Sergei Sakovich Copyright © 2014 Sergei Sakovich. All rights reserved. On Some Grüss-Type Fractional Inequalities Using Saigo Fractional Integral Operator Sun, 24 Aug 2014 09:44:14 +0000 http://www.hindawi.com/journals/jmath/2014/527910/ The main aim of this paper is to establish some new fractional integral inequalities of Grüss-type via the Saigo fractional integral operator. Vaijanath L. Chinchane and Deepak B. Pachpatte Copyright © 2014 Vaijanath L. Chinchane and Deepak B. Pachpatte. All rights reserved. On Iterated Entire Functions with ()th Order Sun, 17 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/jmath/2014/908798/ We prove some results relating to the comparative growth properties of iterated entire functions using (p, q)th order ((p, q)th lower order). Sanjib Kumar Datta, Tanmay Biswas, and Chinmay Biswas Copyright © 2014 Sanjib Kumar Datta et al. All rights reserved. Associate, Hyperdomainlike, and Presimplifiable Hyperrings Thu, 14 Aug 2014 13:27:03 +0000 http://www.hindawi.com/journals/jmath/2014/458603/ Based on the works of Axtell et al., Anderson et al., and Ghanem on associate, domainlike, and presimplifiable rings, we introduce new hyperrings called associate, hyperdomainlike, and presimplifiable hyperrings. Some elementary properties of these new hyperrings and their relationships are presented. Agboola Adesina Abdul Akeem and Davvaz Bijan Copyright © 2014 Agboola Adesina Abdul Akeem and Davvaz Bijan. All rights reserved. A New Hyperbolic Area Formula of a Hyperbolic Triangle and Its Applications Wed, 13 Aug 2014 13:04:03 +0000 http://www.hindawi.com/journals/jmath/2014/838497/ We study some characterizations of hyperbolic geometry in the Poincaré disk. We first obtain the hyperbolic area and length formula of Euclidean disk and a circle represented by its Euclidean center and radius. Replacing interior angles with vertices coordinates, we also obtain a new hyperbolic area formula of a hyperbolic triangle. As its application, we give the hyperbolic area of a Lambert quadrilateral and some geometric characterizations of Lambert quadrilaterals and Saccheri quadrilaterals. Hui Bao and Xingdi Chen Copyright © 2014 Hui Bao and Xingdi Chen. All rights reserved.