Chinese Journal of Mathematics
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Open Access journal
ISSN (Online) 2314-8071
Published by Hindawi [333 journals]
- Problems with Mixed Boundary Conditions in Banach Spaces
Abstract: Using Leray-Schauder degree or degree for -condensing maps we obtain the existence of at least one solution for the boundary value problem of the following type: , where is a homeomorphism with reverse Lipschitz constant such that , is a continuous function, is a positive real number, and is a real Banach space.
PubDate: Wed, 15 Mar 2017 10:01:13 +000
- Influence of a Moving Mass on the Dynamic Behaviour of Viscoelastically
Connected Prismatic Double-Rayleigh Beam System Having Arbitrary End
Abstract: This paper deals with the lateral vibration of a finite double-Rayleigh beam system having arbitrary classical end conditions and traversed by a concentrated moving mass. The system is made up of two identical parallel uniform Rayleigh beams which are continuously joined together by a viscoelastic Winkler type layer. Of particular interest, however, is the effect of the mass of the moving load on the dynamic response of the system. To this end, a solution technique based on the generalized finite integral transform, modified Struble’s method, and differential transform method (DTM) is developed. Numerical examples are given for the purpose of demonstrating the simplicity and efficiency of the technique. The dynamic responses of the system are presented graphically and found to be in good agreement with those previously obtained in the literature for the case of a moving force. The conditions under which the system reaches a state of resonance and the corresponding critical speeds were established. The effects of variations of the ratio of the mass of the moving load to the mass of the beam on the dynamic response are presented. The effects of other parameters on the dynamic response of the system are also examined.
PubDate: Sun, 26 Feb 2017 00:00:00 +000
- Variational Problem Involving Operator Curl in a Multiconnected Domain
Abstract: We shall study the problem of minimizing a functional involving the curl of vector fields in a three-dimensional, bounded multiconnected domain with prescribed tangential component on the boundary. The paper is an extension of minimization problem of the curl of vector fields. We shall prove the existence and the estimate of minimizers of more general functional which contains norm of the curl of vector fields.
PubDate: Sun, 27 Nov 2016 09:29:22 +000
- Solution of Singularly Perturbed Differential-Difference Equations with
Mixed Shifts Using Galerkin Method with Exponential Fitting
Abstract: Galerkin method is presented to solve singularly perturbed differential-difference equations with delay and advanced shifts using fitting factor. In the numerical treatment of such type of problems, Taylor’s approximation is used to tackle the terms containing small shifts. A fitting factor in the Galerkin scheme is introduced which takes care of the rapid changes that occur in the boundary layer. This fitting factor is obtained from the asymptotic solution of singular perturbations. Thomas algorithm is used to solve the tridiagonal system of the fitted Galerkin method. The method is analysed for convergence. Several numerical examples are solved and compared to demonstrate the applicability of the method. Graphs are plotted for the solutions of these problems to illustrate the effect of small shifts on the boundary layer solution.
PubDate: Sun, 16 Oct 2016 11:17:16 +000
- Ostrowski Inequalities for Functions Whose First Derivatives Are
Abstract: Some Ostrowski type inequalities for functions whose first derivatives are logarithmically preinvex are established.
PubDate: Tue, 06 Sep 2016 07:16:10 +000
- Some New Generalized Integral Inequalities for GA--Convex Functions via
Hadamard Fractional Integrals
Abstract: We prove new generalization of Hadamard, Ostrowski, and Simpson inequalities in the framework of GA--convex functions and Hadamard fractional integral.
PubDate: Thu, 01 Sep 2016 09:52:32 +000
- Matrix Fourier Transforms for Consistent Mathematical Models
Abstract: We create a matrix integral transforms method; it allows us to describe analytically the consistent mathematical models. An explicit constructions for direct and inverse Fourier matrix transforms with discontinuous coefficients are established. We introduce special types of Fourier matrix transforms: matrix cosine transforms, matrix sine transforms, and matrix transforms with piecewise trigonometric kernels. The integral transforms of such kinds are used for problems solving of mathematical physics in homogeneous and piecewise homogeneous media. Analytical solution of iterated heat conduction equation is obtained. Stress produced in the elastic semi-infinite solid by pressure is obtained in the integral form.
PubDate: Wed, 31 Aug 2016 08:42:00 +000
- Sectional Category of the Ganea Fibrations and Higher Relative Category
Abstract: We first compute James’ sectional category (secat) of the Ganea map of any map in terms of the sectional category of : we show that is the integer part of . Next we compute the relative category (relcat) of . In order to do this, we introduce the relative category of order () of a map and show that is the integer part of . Then we establish some inequalities linking secat and relcat of any order: we show that and . We give examples that show that these inequalities may be strict.
PubDate: Tue, 23 Aug 2016 08:05:24 +000
- Geometric Framework for Unified Field Theory Using Finsler Gauge
Abstract: We study the different types of Finsler space with -metrics which have nonholonomic frames as an application for classical mechanics and dynamics in physics using gauge transformation which helps to derive unified field theory. Further, we set up the application of Finsler geometry to geometrize the electromagnetic field completely.
PubDate: Mon, 22 Aug 2016 14:13:39 +000
- Ergodicity Space for Measure-Preserving Transformations
Abstract: We introduce the concept of ergodicity space of a measure-preserving transformation and will present some of its properties as an algebraic weight for measuring the size of the ergodicity of a measure-preserving transformation. We will also prove the invariance of the ergodicity space under conjugacy of dynamical systems.
PubDate: Sun, 21 Aug 2016 14:54:54 +000
- A Symmetric Algorithm for Golden Ratio in Hyper-Horadam Numbers
Abstract: We study some ratios related to hyper-Horadam numbers such as while by using a symmetric algorithm obtained by the recurrence relation , where is the th hyper-Horadam number. Also, we give some special cases of these ratios such as the golden ratio and silver ratio.
PubDate: Wed, 10 Aug 2016 07:18:38 +000
- The Neutral Stochastic Integrodifferential Equations with Jumps
Abstract: We study the existence and uniqueness of mild solutions for neutral stochastic integrodifferential equations with Poisson jumps under global and local Carathéodory conditions on the coefficients by means of the successive approximation. Furthermore, we give the continuous dependence of solutions on the initial value. Finally, an example is provided to illustrate the effectiveness of the obtained results.
PubDate: Thu, 04 Aug 2016 09:15:45 +000
- The Fifth Dimension Subgroup for Metabelian 2 Groups
Abstract: 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.
PubDate: Mon, 25 Jul 2016 07:13:32 +000
- A Note on the Adaptive Estimation of a Conditional Continuous-Discrete
Multivariate Density by Wavelet Methods
Abstract: 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.
PubDate: Thu, 30 Jun 2016 10:35:56 +000
- Ultra-Quasi-Metrically Tight Extensions of Ultra-Quasi-Metric Spaces
Abstract: 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.
PubDate: Wed, 30 Sep 2015 09:56:09 +000
- Periodic Solutions for -Species Lotka-Volterra Competitive Systems with
Abstract: 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.
PubDate: Mon, 14 Sep 2015 09:19:50 +000
- Classical Ergodicity and Modern Portfolio Theory
Abstract: 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.
PubDate: Sun, 02 Aug 2015 11:35:49 +000
- On Quasimetrizability of Quasicone Metric Spaces
Abstract: 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.
PubDate: Thu, 09 Jul 2015 11:02:19 +000
- On the Stochastic Stability and Boundedness of Solutions for Stochastic
Delay Differential Equation of the Second Order
Abstract: 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.
PubDate: Tue, 31 Mar 2015 13:20:06 +000
- On Transitive Points in a Generalized Shift Dynamical System
Abstract: 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 .
PubDate: Mon, 05 Jan 2015 06:54:37 +000
- On Some Integral Inequalities Related to Hermite-Hadamard-Fejér
Inequalities for Coordinated Convex Functions
Abstract: 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.
PubDate: Mon, 17 Nov 2014 00:00:00 +000
- Differential Subordination with Generalized Derivative Operator of
Abstract: 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.
PubDate: Wed, 20 Aug 2014 10:48:28 +000
- A Few Inequalities Established by Using Fractional Calculus and Their
Applications to Certain Multivalently Analytic Functions
Abstract: 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.
PubDate: Wed, 18 Jun 2014 09:37:02 +000
- Existence and Multiplicity of Positive Solutions for a System of
Fourth-Order Boundary Value Problems
Abstract: 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.
PubDate: Wed, 18 Jun 2014 06:26:37 +000
- On Hermite-Hadamard Type Inequalities for Riemann-Liouville Fractional
Integrals via Two Kinds of Convexity
Abstract: 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.
PubDate: Sun, 15 Jun 2014 09:28:29 +000
- Linear Independent Solutions and Operational Representations for
Hypergeometric Functions of Four Variables
Abstract: 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 partialdifferential 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.
PubDate: Sun, 15 Jun 2014 00:00:00 +000
- New Čebyšev Type Inequalities and Applications for Functions of
Self-Adjoint Operators on Complex Hilbert Spaces
Abstract: 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.
PubDate: Thu, 05 Jun 2014 12:01:45 +000
- Study of a Forwarding Chain in the Category of Topological Spaces between
and with respect to One Point Compactification Operator
Abstract: 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 topologicalspaces 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.
PubDate: Wed, 30 Apr 2014 13:52:41 +000
- The Collatz Problem in the Light of an Infinite Free Semigroup
Abstract: 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.
PubDate: Wed, 30 Apr 2014 11:07:12 +000
- An Approximation of Hedberg’s Type in Sobolev Spaces with Variable
Exponent and Application
Abstract: 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.
PubDate: Tue, 29 Apr 2014 08:54:00 +000