Journal of Mathematics
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© 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 spacetime 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, discretetime and discretestate, 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 fourstate 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 wellknown 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.
ShangKun Wang and WenWu Pan
Copyright © 2014 ShangKun Wang and WenWu Pan. All rights reserved.

Some Definition of HartleyHilbert and FourierHilbert 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 HartleyHilbert and FourierHilbert transforms on a quotient space of Boehmians. The investigated transforms are welldefined and linear mappings in the space of Boehmians. Further properties are also obtained.
S. K. Q. AlOmari
Copyright © 2014 S. K. Q. AlOmari. 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 BesovLipschitz 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 ThirdOrder 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 thirdorder threepoint 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 fixedpoint 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 NilSymmetric Rings
Thu, 16 Oct 2014 06:56:20 +0000
http://www.hindawi.com/journals/jmath/2014/483784/
The concept of nilsymmetric rings has been introduced as a generalization of symmetric rings and a particular case of nilsemicommutative rings. A ring is called right (left) nilsymmetric if, for , where are nilpotent elements, implies . A ring is called nilsymmetric if it is both right and left nilsymmetric. It has been shown that the polynomial ring over a nilsymmetric ring may not be a right or a left nilsymmetric ring. Further, it is also proved that if is right (left) nilsymmetric, then the polynomial ring is a nilArmendariz 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 EighthOrder 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 eighthorder iterative methods by accelerating the order of convergence of the existing seventhorder 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 eighthorder 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 wellknown 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 RiemannLiouville Fractional Integral
Wed, 10 Sep 2014 13:21:31 +0000
http://www.hindawi.com/journals/jmath/2014/503195/
We present Montgomery identity for RiemannLiouville 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 PenalizedEquationBased Generalized Newton Method for Solving AbsoluteValue Linear Complementarity Problems
Tue, 09 Sep 2014 07:23:17 +0000
http://www.hindawi.com/journals/jmath/2014/560578/
We consider a class of absolutevalue 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 penalizedequationbased 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, HaiShan Han, and DanDan 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 BosonFermion 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 bosonfermion 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 BlochKraemer 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.

SelfDual 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 selfdual normal basis and selfdual normal basis for over , where is considered as a free module over . Moreover, we explain a way to construct selfdual
normal basis using particular system of polynomials. Finally, we show the connection between selfdual normal basis for over and the set of all invertible, circulant, and orthogonal matrices over .
Irwansyah, Intan MuchtadiAlamsyah, 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/AntiOptimal 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 SawadaKotera 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 SawadaKotera equation, discovered recently by Hickman, Hereman, Larue, and Göktaş, and the wellknown old Lax pair of this equation, considered in the form of zerocurvature 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 GrüssType 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 Grüsstype 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.