Chinese Journal of Mathematics The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. The Fifth Dimension Subgroup for Metabelian 2 Groups Mon, 25 Jul 2016 07:13:32 +0000 Given a finite metabelian -group , the object of this paper is to discuss some cases under which . Further, some examples of groups of class , for which but , are discussed. Shalini Gupta Copyright © 2016 Shalini Gupta. All rights reserved. A Note on the Adaptive Estimation of a Conditional Continuous-Discrete Multivariate Density by Wavelet Methods Thu, 30 Jun 2016 10:35:56 +0000 We investigate the estimation of a multivariate continuous-discrete conditional density. We develop an adaptive estimator based on wavelet methods. We prove its good theoretical performance by determining sharp rates of convergence under the risk with for a wide class of unknown conditional densities. A simulation study illustrates the good practical performance of our estimator. Christophe Chesneau and Hassan Doosti Copyright © 2016 Christophe Chesneau and Hassan Doosti. All rights reserved. Ultra-Quasi-Metrically Tight Extensions of Ultra-Quasi-Metric Spaces Wed, 30 Sep 2015 09:56:09 +0000 The concept of the tight extension of a metric space was introduced and studied by Dress. It is known that Dress theory is equivalent to the theory of the injective hull of a metric space independently discussed by Isbell some years earlier. Dress showed in particular that for a metric space the tight extension is maximal among the tight extensions of . In a previous work with P. Haihambo and H.-P. Künzi, we constructed the tight extension of a -quasi-metric space. In this paper, we continue these investigations by presenting a similar construction in the category of -metric spaces and nonexpansive maps. Collins Amburo Agyingi Copyright © 2015 Collins Amburo Agyingi. All rights reserved. Periodic Solutions for -Species Lotka-Volterra Competitive Systems with Pure Delays Mon, 14 Sep 2015 09:19:50 +0000 We study a class of periodic general -species competitive Lotka-Volterra systems with pure delays. Based on the continuation theorem of the coincidence degree theory and Lyapunov functional, some new sufficient conditions on the existence and global attractivity of positive periodic solutions for the -species competitive Lotka-Volterra systems are established. As an application, we also examine some special cases of the system, which have been studied extensively in the literature. Ahmadjan Muhammadhaji, Rouzimaimaiti Mahemuti, and Zhidong Teng Copyright © 2015 Ahmadjan Muhammadhaji et al. All rights reserved. Classical Ergodicity and Modern Portfolio Theory Sun, 02 Aug 2015 11:35:49 +0000 What role have theoretical methods initially developed in mathematics and physics played in the progress of financial economics? What is the relationship between financial economics and econophysics? What is the relevance of the “classical ergodicity hypothesis” to modern portfolio theory? This paper addresses these questions by reviewing the etymology and history of the classical ergodicity hypothesis in 19th century statistical mechanics. An explanation of classical ergodicity is provided that establishes a connection to the fundamental empirical problem of using nonexperimental data to verify theoretical propositions in modern portfolio theory. The role of the ergodicity assumption in the ex post/ex ante quandary confronting modern portfolio theory is also examined. Geoffrey Poitras and John Heaney Copyright © 2015 Geoffrey Poitras and John Heaney. All rights reserved. On Quasimetrizability of Quasicone Metric Spaces Thu, 09 Jul 2015 11:02:19 +0000 The aim of this work is to extend interesting results on the metrizability of cone metric spaces as it appears in the literature. In this paper we appeal to quasiuniformities and uniformities to prove that a quasicone metric space is qausimetrizable, and from our results we will deduce that every cone metric space is metrizable; our approach is more on bitopological and topological properties and differs from the one used by the papers mentioned above but affirms some of their results. M. Aphane and S. P. Moshokoa Copyright © 2015 M. Aphane and S. P. Moshokoa. All rights reserved. On the Stochastic Stability and Boundedness of Solutions for Stochastic Delay Differential Equation of the Second Order Tue, 31 Mar 2015 13:20:06 +0000 We present two qualitative results concerning the solutions of the following equation: ; the first result covers the stochastic asymptotic stability of the zero solution for the above equation in case , while the second one discusses the uniform stochastic boundedness of all solutions in case . Sufficient conditions for the stability and boundedness of solutions for the considered equation are obtained by constructing a Lyapunov functional. Two examples are also discussed to illustrate the efficiency of the obtained results. A. M. A. Abou-El-Ela, A. I. Sadek, A. M. Mahmoud, and R. O. A. Taie Copyright © 2015 A. M. A. Abou-El-Ela et al. All rights reserved. On Transitive Points in a Generalized Shift Dynamical System Mon, 05 Jan 2015 06:54:37 +0000 Considering point transitive generalized shift dynamical system for discrete with at least two elements and infinite , we prove that is countable and has at most elements. Then, we find a transitive point of the dynamical system for with and show that point transitive , for infinite countable , is a factor of . Bahman Taherkhani and Fatemah Ayatollah Zadeh Shirazi Copyright © 2015 Bahman Taherkhani and Fatemah Ayatollah Zadeh Shirazi. All rights reserved. On Some Integral Inequalities Related to Hermite-Hadamard-Fejér Inequalities for Coordinated Convex Functions Mon, 17 Nov 2014 00:00:00 +0000 Several new mappings associated with coordinated convexity are proposed, by which we obtain some new Hermite-Hadamard-Fejér type inequalities for coordinated convex functions. We conclude that the results obtained in this work are the generalizations of the earlier results. Ruiyin Xiang and Feixiang Chen Copyright © 2014 Ruiyin Xiang and Feixiang Chen. All rights reserved. Differential Subordination with Generalized Derivative Operator of Analytic Functions Wed, 20 Aug 2014 10:48:28 +0000 Motivated by generalized derivative operator defined by the authors (El-Yagubi and Darus, 2013) and the technique of differential subordination, several interesting properties of the operator are given. Entisar El-Yagubi and Maslina Darus Copyright © 2014 Entisar El-Yagubi and Maslina Darus. All rights reserved. A Few Inequalities Established by Using Fractional Calculus and Their Applications to Certain Multivalently Analytic Functions Wed, 18 Jun 2014 09:37:02 +0000 By making use of different techniques given in Miller and Mocanu (2000) (and also in Jack (1971)), some recent results consisting of certain multivalently analytic functions given both in Irmak (2005) and in Irmak (2010) are firstly restated and some of their applications are then pointed out. Hüseyin Irmak Copyright © 2014 Hüseyin Irmak. All rights reserved. Existence and Multiplicity of Positive Solutions for a System of Fourth-Order Boundary Value Problems Wed, 18 Jun 2014 06:26:37 +0000 We study the existence and multiplicity of positive solutions for the system of fourth-order boundary value problems , and where . We use fixed point index theory to establish our main results based on a priori estimates achieved by utilizing some integral identities and inequalities and -monotone matrices. Shoucheng Yu and Zhilin Yang Copyright © 2014 Shoucheng Yu and Zhilin Yang. All rights reserved. On Hermite-Hadamard Type Inequalities for Riemann-Liouville Fractional Integrals via Two Kinds of Convexity Sun, 15 Jun 2014 09:28:29 +0000 We obtain some Hermite-Hadamard type inequalities for products of two -convex functions via Riemann-Liouville integrals. The analogous results for -convex functions are also established. Feixiang Chen Copyright © 2014 Feixiang Chen. All rights reserved. Linear Independent Solutions and Operational Representations for Hypergeometric Functions of Four Variables Sun, 15 Jun 2014 00:00:00 +0000 In investigation of boundary-value problems for certain partial differential equations arising in applied mathematics, we often need to study the solution of system of partial differential equations satisfied by hypergeometric functions and find explicit linearly independent solutions for the system. Here we choose the Exton function among his 21 functions to show how to find the linearly independent solutions of partial differential equations satisfied by this function . Based upon the classical derivative and integral operators, we introduce a new operational images for hypergeometric function . By means of these operational images, a number of finite series and decomposition formulas are then found. Maged G. Bin-Saad and Anvar Hasanov Copyright © 2014 Maged G. Bin-Saad and Anvar Hasanov. All rights reserved. New Čebyšev Type Inequalities and Applications for Functions of Self-Adjoint Operators on Complex Hilbert Spaces Thu, 05 Jun 2014 12:01:45 +0000 Several new error bounds for the Čebyšev functional under various assumptions are proved. Applications for functions of self-adjoint operators on complex Hilbert spaces are provided as well. Mohammad W. Alomari Copyright © 2014 Mohammad W. Alomari. All rights reserved. Study of a Forwarding Chain in the Category of Topological Spaces between and with respect to One Point Compactification Operator Wed, 30 Apr 2014 13:52:41 +0000 In the following text, we want to study the behavior of one point compactification operator in the chain := Metrizable, Normal, , KC, SC, US, , , , , Top of subcategories of category of topological spaces, Top (where we denote the subcategory of Top, containing all topological spaces with property , simply by ). Actually we want to know, for and , the one point compactification of topological space belongs to which elements of . Finally we find out that the chain Metrizable, , KC, SC, US, T1, , , , Top is a forwarding chain with respect to one point compactification operator. Fatemah Ayatollah Zadeh Shirazi, Meysam Miralaei, and Fariba Zeinal Zadeh Farhadi Copyright © 2014 Fatemah Ayatollah Zadeh Shirazi et al. All rights reserved. The Collatz Problem in the Light of an Infinite Free Semigroup Wed, 30 Apr 2014 11:07:12 +0000 The Collatz (or ) problem is examined in terms of a free semigroup on which suitable diophantine and rational functions are defined. The elements of the semigroup, called T-words, comprise the information about the Collatz operations which relate an odd start number to an odd end number, the group operation being the concatenation of T-words. This view puts the concept of encoding vectors, first introduced in 1976 by Terras, in the proper mathematical context. A method is described which allows to determine a one-parameter family of start numbers compatible with any given T-word. The result brings to light an intimate relationship between the Collatz problem and the problem. Also, criteria for the rise or fall of a Collatz sequence are derived and the important notion of anomalous T-words is established. Furthermore, the concept of T-words is used to elucidate the question what kind of cycles—trivial, nontrivial, rational—can be found in the Collatz problem and also in the problem. Furthermore, the notion of the length of a Collatz sequence is discussed and applied to average sequences. Finally, a number of conjectures are proposed. Manfred Trümper Copyright © 2014 Manfred Trümper. All rights reserved. An Approximation of Hedberg’s Type in Sobolev Spaces with Variable Exponent and Application Tue, 29 Apr 2014 08:54:00 +0000 The aim of this paper is to extend the usual framework of PDE with to include a large class of cases with , whose coefficient satisfies conditions (including growth conditions) which guarantee the solvability of the problem . This new framework is conceptually more involved than the classical one includes many more fundamental examples. Thus our main result can be applied to various types of PDEs such as reaction-diffusion equations, Burgers type equation, Navier-Stokes equation, and p-Laplace equation. Abdelmoujib Benkirane, Mostafa El Moumni, and Aziz Fri Copyright © 2014 Abdelmoujib Benkirane et al. All rights reserved. Some Fixed Point Theorems under Weak Semicompatibility Sun, 27 Apr 2014 12:24:55 +0000 The aim of the present paper is to prove some fixed point theorems by using the recent notion “weak semicompatibility.” The new notion is proper generalization of semicompatibility and can be applicable on commuting and compatible maps. We used compatible and absorbing mappings to prove theorems which also include (E.A.) property. A. S. Saluja and Mukesh Kumar Jain Copyright © 2014 A. S. Saluja and Mukesh Kumar Jain. All rights reserved. On Quasi-Pseudometric Type Spaces Tue, 15 Apr 2014 00:00:00 +0000 We introduce the concept of a quasi-pseudometric type space and prove some fixed point theorems. Moreover, we connect this concept to the existing notion of quasi-cone metric space. Eniola Funmilayo Kazeem, Collins Amburo Agyingi, and Yaé Ulrich Gaba Copyright © 2014 Eniola Funmilayo Kazeem et al. All rights reserved. Inclusion Properties of New Classes of Analytic Functions Mon, 31 Mar 2014 14:06:43 +0000 The purpose of the present paper is to introduce certain new subclasses of analytic functions defined by Srivastava-Attiya operator and study their inclusion relationships and to obtain some interesting consequences of the inclusion relations. Mohan Das, Ramesha Chendady, and Indira Kasarkod Pal Copyright © 2014 Mohan Das et al. All rights reserved. Dynamic Behaviour under Moving Distributed Masses of Nonuniform Rayleigh Beam with General Boundary Conditions Sun, 23 Mar 2014 06:14:40 +0000 This paper investigates the flexural vibration of a finite nonuniform Rayleigh beam resting on an elastic foundation and under travelling distributed loads. For the solution of this problem, in the first instance, the generalized Galerkin method was used. The resulting Galerkin’s equations were then simplified using the modified asymptotic method of Struble. The simplified second-order ordinary differential equation was then solved using the method of integral transformation. The closed form solution obtained was analyzed and results show that, an increase in the values of foundation moduli and rotatory inertia correction factor reduces the response amplitudes of both the clamped-clamped nonuniform Rayleigh beam and the clamped-free nonuniform Rayleigh beam. Also for the same natural frequency, the critical speed for the moving distributed mass problem is smaller than that for the moving distributed force problem. Hence resonance is reached earlier in the former. Furthermore, resonance conditions for the dynamical system are attained significantly by both and for the illustrative end conditions considered. Emem Ayankop Andi and Sunday Tunbosun Oni Copyright © 2014 Emem Ayankop Andi and Sunday Tunbosun Oni. All rights reserved. Generalizations of Inequalities for Differentiable Co-Ordinated Convex Functions Wed, 19 Mar 2014 09:54:17 +0000 A generalized lemmas is proved and several new inequalities for differentiable co-ordinated convex and concave functions in two variables are obtained. Feixiang Chen Copyright © 2014 Feixiang Chen. All rights reserved. A New Optimal Eighth-Order Ostrowski-Type Family of Iterative Methods for Solving Nonlinear Equations Thu, 13 Mar 2014 13:38:23 +0000 Based on Ostrowski's method, a new family of eighth-order iterative methods for solving nonlinear equations by using weight function methods is presented. Per iteration the new methods require three evaluations of the function and one evaluation of its first derivative. Therefore, this family of methods has the efficiency index which equals 1.682. Kung and Traub conjectured that a multipoint iteration without memory based on evaluations could achieve optimal convergence order . Thus, we provide a new class which agrees with the conjecture of Kung-Traub for . Numerical comparisons are made to show the performance of the presented methods. Taher Lotfi and Tahereh Eftekhari Copyright © 2014 Taher Lotfi and Tahereh Eftekhari. All rights reserved. On Liouville Sequences in the Non-Archimedean Case Wed, 05 Mar 2014 00:00:00 +0000 We study Liouville numbers in the non-Archimedean case. We deal with the concept of a Liouville sequence in the non-Archimedean case and we give some results both in the p-adic numbers field and the functions field . Hamza Menken and Abdulkadir Aşan Copyright © 2014 Hamza Menken and Abdulkadir Aşan. All rights reserved. On the Estimation of Parameter of Weighted Sums of Exponential Distribution Tue, 04 Mar 2014 07:30:57 +0000 The random variable , with and   being independent exponentially distributed random variables with mean one, is considered. Van Leeuwaarden and Temme (2011) attempted to determine good approximation of the distribution of . The main problem is estimating the parameter that has the main state in applicable research. In this paper we show that estimating the parameter by using the relation between and mode is available. The mean square error values are obtained for estimating by mode, moment method, and maximum likelihood method. N. Abbasi, A. Namju, and N. Safari Copyright © 2014 N. Abbasi et al. All rights reserved. Growth Rates of Meromorphic Functions Focusing Relative Order Sun, 02 Mar 2014 14:00:22 +0000 A detailed study concerning some growth rates of composite entire and meromorphic functions on the basis of their relative orders (relative lower orders) with respect to entire functions has been made in this paper. Sanjib Kumar Datta, Tanmay Biswas, and Sarmila Bhattacharyya Copyright © 2014 Sanjib Kumar Datta et al. All rights reserved. Wiener Polarity Index of Cycle-Block Graphs Thu, 27 Feb 2014 16:26:08 +0000 The Wiener polarity index of a graph is the number of unordered pairs of vertices of such that the distance between and is 3. Cycle-block graph is a connected graph in which every block is a cycle. In this paper, we determine the maximum and minimum Wiener polarity index of cycle-block graphs and describe their extremal graphs; the extremal graphs of 4-uniform cactus with respect to Wiener polarity index are also discussed. Zhen Jia, Fuyi Wei, and Yang Wu Copyright © 2014 Zhen Jia et al. All rights reserved. Existence for a Second-Order Impulsive Neutral Stochastic Integrodifferential Equations with Nonlocal Conditions and Infinite Delay Thu, 27 Feb 2014 06:29:02 +0000 The current paper is concerned with the existence of mild solutions for a class of second-order impulsive neutral stochastic integrodifferential equations with nonlocal conditions and infinite delays in a Hilbert space. A sufficient condition for the existence results is obtained by using the Krasnoselskii-Schaefer-type fixed point theorem combined with theories of a strongly continuous cosine family of bounded linear operators. Finally, an application to the stochastic nonlinear wave equation with infinite delay is given. Dang Huan Diem Copyright © 2014 Dang Huan Diem. All rights reserved. Disjointness Preserving and Functional Type Disjointness Preserving Operators Tue, 25 Feb 2014 08:55:10 +0000 A new concept called functional type disjointness preserving operators is introduced and structure of disjointness preserving and functional type disjointness preserving operators on some function spaces are analysed. C. Ganesa Moorthy and C. T. Ramasamy Copyright © 2014 C. Ganesa Moorthy and C. T. Ramasamy. All rights reserved.