Chinese Journal of Mathematics
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© 2016 , Hindawi Publishing Corporation . All rights reserved.

Sectional Category of the Ganea Fibrations and Higher Relative Category
Tue, 23 Aug 2016 08:05:24 +0000
http://www.hindawi.com/journals/cjm/2016/8320742/
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.
JeanPaul Doeraene
Copyright © 2016 JeanPaul Doeraene. All rights reserved.

Geometric Framework for Unified Field Theory Using Finsler Gauge Transformation
Mon, 22 Aug 2016 14:13:39 +0000
http://www.hindawi.com/journals/cjm/2016/3081840/
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.
Mallikarjuna Yallappa Kumbar, Sachin Jangir, Chowdari Kondasandra Chowdappa, and Narasimhamurthy Senajji Kampalappa
Copyright © 2016 Mallikarjuna Yallappa Kumbar et al. All rights reserved.

Ergodicity Space for MeasurePreserving Transformations
Sun, 21 Aug 2016 14:54:54 +0000
http://www.hindawi.com/journals/cjm/2016/6274839/
We introduce the concept of ergodicity space of a measurepreserving transformation and will present some of its properties as an algebraic weight for measuring the size of the ergodicity of a measurepreserving transformation. We will also prove the invariance of the ergodicity space under conjugacy of dynamical systems.
M. Rahimi and A. Assari
Copyright © 2016 M. Rahimi and A. Assari. All rights reserved.

A Symmetric Algorithm for Golden Ratio in HyperHoradam Numbers
Wed, 10 Aug 2016 07:18:38 +0000
http://www.hindawi.com/journals/cjm/2016/4361582/
We study some ratios related to hyperHoradam numbers such as while by using a symmetric algorithm obtained by the recurrence relation , where is the th hyperHoradam number. Also, we give some special cases of these ratios such as the golden ratio and silver ratio.
Mustafa Bahşi and Süleyman Solak
Copyright © 2016 Mustafa Bahşi and Süleyman Solak. All rights reserved.

The Neutral Stochastic Integrodifferential Equations with Jumps
Thu, 04 Aug 2016 09:15:45 +0000
http://www.hindawi.com/journals/cjm/2016/3285346/
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.
Diem Dang Huan
Copyright © 2016 Diem Dang Huan. All rights reserved.

The Fifth Dimension Subgroup for Metabelian 2 Groups
Mon, 25 Jul 2016 07:13:32 +0000
http://www.hindawi.com/journals/cjm/2016/5342926/
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 ContinuousDiscrete Multivariate Density by Wavelet Methods
Thu, 30 Jun 2016 10:35:56 +0000
http://www.hindawi.com/journals/cjm/2016/6204874/
We investigate the estimation of a multivariate continuousdiscrete 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.

UltraQuasiMetrically Tight Extensions of UltraQuasiMetric Spaces
Wed, 30 Sep 2015 09:56:09 +0000
http://www.hindawi.com/journals/cjm/2015/646018/
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 quasimetric 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 LotkaVolterra Competitive Systems with Pure Delays
Mon, 14 Sep 2015 09:19:50 +0000
http://www.hindawi.com/journals/cjm/2015/856959/
We study a class of periodic general species competitive LotkaVolterra 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 LotkaVolterra 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
http://www.hindawi.com/journals/cjm/2015/737905/
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
http://www.hindawi.com/journals/cjm/2015/392190/
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
http://www.hindawi.com/journals/cjm/2015/358936/
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. AbouElEla, A. I. Sadek, A. M. Mahmoud, and R. O. A. Taie
Copyright © 2015 A. M. A. AbouElEla et al. All rights reserved.

On Transitive Points in a Generalized Shift Dynamical System
Mon, 05 Jan 2015 06:54:37 +0000
http://www.hindawi.com/journals/cjm/2015/519357/
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 HermiteHadamardFejér Inequalities for Coordinated Convex Functions
Mon, 17 Nov 2014 00:00:00 +0000
http://www.hindawi.com/journals/cjm/2014/796132/
Several new mappings associated with coordinated convexity are proposed, by which we obtain some new HermiteHadamardFejér 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
http://www.hindawi.com/journals/cjm/2014/656258/
Motivated by generalized derivative operator defined by the authors (ElYagubi and Darus, 2013) and the technique of differential subordination, several interesting properties of the operator are given.
Entisar ElYagubi and Maslina Darus
Copyright © 2014 Entisar ElYagubi 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
http://www.hindawi.com/journals/cjm/2014/349719/
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 FourthOrder Boundary Value Problems
Wed, 18 Jun 2014 06:26:37 +0000
http://www.hindawi.com/journals/cjm/2014/717290/
We study the existence and multiplicity of positive solutions for the system of fourthorder 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 HermiteHadamard Type Inequalities for RiemannLiouville Fractional Integrals via Two Kinds of Convexity
Sun, 15 Jun 2014 09:28:29 +0000
http://www.hindawi.com/journals/cjm/2014/173293/
We obtain some HermiteHadamard type inequalities for products of two convex functions via RiemannLiouville 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
http://www.hindawi.com/journals/cjm/2014/273064/
In investigation of boundaryvalue 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. BinSaad and Anvar Hasanov
Copyright © 2014 Maged G. BinSaad and Anvar Hasanov. All rights reserved.

New Čebyšev Type Inequalities and Applications for Functions of SelfAdjoint Operators on Complex Hilbert Spaces
Thu, 05 Jun 2014 12:01:45 +0000
http://www.hindawi.com/journals/cjm/2014/363050/
Several new error bounds for the Čebyšev functional under various assumptions are proved. Applications for functions of selfadjoint 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
http://www.hindawi.com/journals/cjm/2014/541538/
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
http://www.hindawi.com/journals/cjm/2014/756917/
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 Twords, 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 Twords. 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 oneparameter family of start numbers compatible with any given Tword. 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 Twords is established. Furthermore, the concept of Twords 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
http://www.hindawi.com/journals/cjm/2014/549051/
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 reactiondiffusion equations, Burgers type equation, NavierStokes equation, and pLaplace 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
http://www.hindawi.com/journals/cjm/2014/618965/
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 QuasiPseudometric Type Spaces
Tue, 15 Apr 2014 00:00:00 +0000
http://www.hindawi.com/journals/cjm/2014/198685/
We introduce the concept of a quasipseudometric type space and prove some fixed point theorems. Moreover, we connect this concept to the existing notion of quasicone 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
http://www.hindawi.com/journals/cjm/2014/974175/
The purpose of the present paper is to introduce certain new subclasses of analytic functions defined by SrivastavaAttiya 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
http://www.hindawi.com/journals/cjm/2014/565826/
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 secondorder 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 clampedclamped nonuniform Rayleigh beam and the clampedfree 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 CoOrdinated Convex Functions
Wed, 19 Mar 2014 09:54:17 +0000
http://www.hindawi.com/journals/cjm/2014/741291/
A generalized lemmas is proved and several new inequalities for differentiable coordinated convex and concave functions in two variables are obtained.
Feixiang Chen
Copyright © 2014 Feixiang Chen. All rights reserved.

A New Optimal EighthOrder OstrowskiType Family of Iterative Methods for Solving Nonlinear Equations
Thu, 13 Mar 2014 13:38:23 +0000
http://www.hindawi.com/journals/cjm/2014/369713/
Based on Ostrowski's method, a new family of eighthorder 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 KungTraub 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 NonArchimedean Case
Wed, 05 Mar 2014 00:00:00 +0000
http://www.hindawi.com/journals/cjm/2014/813924/
We study Liouville numbers in the nonArchimedean case. We deal with the concept of a Liouville sequence in the nonArchimedean case and we give some results both in the padic numbers field and the functions field .
Hamza Menken and Abdulkadir Aşan
Copyright © 2014 Hamza Menken and Abdulkadir Aşan. All rights reserved.