


Paper's Title:
Convergence Speed of Some Random ImplicitKirktype Iterations for Contractivetype Random Operators
Author(s):
H. Akewe, K.S. Eke
Department of Mathematics,
Covenant University,
Canaanland, KM 10, Idiroko Road, P. M. B. 1023, Ota, Ogun State,
Nigeria.
Email: hudson.akewe@covenantuniversity.edu.ng,
kanayo.eke@covenantuniversity.edu.ng
Abstract:
The main aim of this paper is to introduce a stochastic version of multistep type iterative scheme called a modified random implicitKirk multistep iterative scheme and prove strong convergence and stability results for a class of generalized contractivetype random operators. The rate of convergence of the random iterative schemes are also examined through an example. The results show that our new random implicit kirk multistep scheme perform better than other implicit iterative schemes in terms of convergence and thus have good potentials for further applications in equilibrium problems in computer science, physics and economics.
Paper's Title:
A Note On The Global Behavior Of A Nonlinear System of Difference Equations
Author(s):
Norman H. Josephy, Mihaela Predescu and Samuel W. Woolford
Department of Mathematical Sciences,
Bentley University,
Waltham, MA 02452,
U.S.A.
mpredescu@bentley.edu
njosephy@bentley.edu
swoolford@bentley.edu
Abstract:
This paper deals with the global asymptotic stability character of solutions of a discrete time deterministic model proposed by Wikan and Eide in Bulletin of Mathematical Biology, 66, 2004, 16851704. A stochastic extension of this model is proposed and discussed. Computer simulations suggest that the dynamics of the stochastic model includes a mixture of the dynamics observed in the deterministic model.
Paper's Title:
Essential Random Fixed Point Set of Random Operators
Author(s):
Ismat Beg
Centre for Advanced Studies in Mathematics,
Lahore University of Management Sciences (LUMS),
54792Lahore, PAKISTAN.
ibeg@lums.edu.pk
URL: http://web.lums.edu.pk/~ibeg
Abstract:
We obtain necessary and sufficient conditions for the existence of essential random fixed point of a random operator defined on a compact metric space. The structure of the set of essential random fixed points is also studied.
Paper's Title:
Maximal Inequalities for Multidimensionally Indexed Demimartingales and the HájekRényi Inequality for Associated Random Variables
Author(s):
Tasos C. Christofides and Milto Hadjikyriakou
Department of Mathematics and Statistics
University of Cyprus
P.O.Box 20537, Nicosia 1678, Cyprus
tasos@ucy.ac.cy
miltwh@gmail.com
Abstract:
Demimartingales and demisubmartingales introduced by
Newman and
Wright (1982) generalize the notion of martingales and
submartingales respectively. In this paper we define
multidimensionally indexed demimartingales and demisubmartingales
and prove a maximal inequality for this general class of random
variables. As a corollary we obtain a HájekRényi inequality
for multidimensionally indexed associated random variables, the bound of which,
when reduced to the case of single index, is sharper than the bounds already
known in the literature.
Paper's Title:
Asymptotic Distribution of Products of Weighted Sums of Dependent Random Variables
Author(s):
Y. Miao and J. F. Li
College
of Mathematics
and Information
Science,
Henan Normal
University
Henan,
China
yumiao728@yahoo.com.cn
College
of Mathematics
and Information
Science,
Henan Normal
University, 453007
Henan,
China.
junfen_li@yahoo.com.cn
Abstract:
In this paper we establish the asymptotic distribution of products of weighted sums of dependent positive random variable, which extends the results of Rempała and Wesołowski (2002).
Paper's Title:
Bounds on the Jensen Gap, and Implications for MeanConcentrated Distributions
Author(s):
Xiang Gao, Meera Sitharam, Adrian E. Roitberg
Department of Chemistry, and Department
of Computer & Information Science & Engineering,
University of Florida,
Gainesville, FL 32611,
USA.
Email: qasdfgtyuiop@gmail.com
URL:
https://scholar.google.com/citations?user=t2nOdxQAAAAJ
Abstract:
This paper gives upper and lower bounds on the gap in Jensen's inequality, i.e., the difference between the expected value of a function of a random variable and the value of the function at the expected value of the random variable. The bounds depend only on growth properties of the function and specific moments of the random variable. The bounds are particularly useful for distributions that are concentrated around the mean, a commonly occurring scenario such as the average of i.i.d. samples and in statistical mechanics.
Paper's Title:
Approximation of an AQCQFunctional Equation and its Applications
Author(s):
Choonkil Park and Jung Rye Lee
Department of Mathematics,
Research Institute for Natural Sciences,
Hanyang University, Seoul 133791,
Korea;
Department of Mathematics,
Daejin University,
Kyeonggi 487711,
Korea
baak@hanyang.ac.kr
jrlee@daejin.ac.kr
Abstract:
This paper is a survey on the generalized HyersUlam stability of an AQCQfunctional equation in several spaces. Its content is divided into the following sections:
1. Introduction and preliminaries.
2. Generalized HyersUlam stability of an AQCQfunctional equation in Banach spaces: direct method.
3. Generalized HyersUlam stability of an AQCQfunctional equation in Banach spaces: fixed point method.
4. Generalized HyersUlam stability of an AQCQfunctional equation in random Banach spaces: direct method.
5. Generalized HyersUlam stability of an AQCQfunctional equation in random Banach spaces: fixed point method.
6. Generalized HyersUlam stability of an AQCQfunctional equation in nonArchimedean Banach spaces: direct method.
7. Generalized HyersUlam stability of an AQCQfunctional equation in nonArchimedean Banach spaces: fixed point method.
Paper's Title:
Inequalities for Discrete FDivergence Measures: A Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
http://rgmia.org/dragomir
Abstract:
In this paper we survey some recent results obtained by the author in providing various bounds for the celebrated fdivergence measure for various classes of functions f. Several techniques including inequalities of Jensen and Slater types for convex functions are employed. Bounds in terms of KullbackLeibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the fdivergence measure by the use of the celebrated Ostrowski and Trapezoid inequalities are obtained. More accurate approximation formulae that make use of Taylor's expansion with integral remainder are also surveyed. A comprehensive list of recent papers by several authors related this important concept in information theory is also included as an appendix to the main text.
Paper's Title:
A Comparison Between Two Different Stochastic Epidemic Models with Respect to the Entropy
Author(s):
Farzad Fatehi and Tayebe Waezizadeh
Department of Mathematics,
University of Sussex,
Brighton BN1 9QH,
UK.
Email: f.fatehi@sussex.ac.uk
URL:
http://www.sussex.ac.uk/profiles/361251
Department of Pure Mathematics, Faculty
of Mathematics and Computer,
Shahid Bahonar University of Kerman,
Kerman 7616914111,
Iran.
Email: waezizadeh@uk.ac.ir
URL:
http://academicstaff.uk.ac.ir/en/tavaezizadeh
Abstract:
In this paper at first a brief history of mathematical models is presented with the aim to clarify the reliability of stochastic models over deterministic models. Next, the necessary background about random variables and stochastic processes, especially Markov chains and the entropy are introduced. After that, entropy of SIR stochastic models is computed and it is proven that an epidemic will disappear after a long time. Entropy of a stochastic mathematical model determines the average uncertainty about the outcome of that random experiment. At the end, we introduce a chain binomial epidemic model and compute its entropy, which is then compared with the DTMC SIR epidemic model to show which one is nearer to reality.
Paper's Title:
Some Properties of the MarshallOlkin and Generalized CuadrasAugé Families of Copulas
Author(s):
Edward Dobrowolski and Pranesh Kumar
Department of Mathematics and Statistics
University of Northern British Columbia
Prince George, BC,
Canada, V2N 4Z9
Email: Pranesh.Kumar@unbc.ca
Abstract:
We investigate some properties of the families of two parameter MarshallOlkin and Generalized CuadrasAugé copulas. Some new results are proved for copula parameters, dependence measure and mutual information. A numerical application is discussed.
Paper's Title:
On the Convergence in Law of Iterates of RandomValued Functions
Author(s):
Karol Baron
Uniwersytet
Śląski,
Instytut Matematyki
Bankowa 14,
PL40007 Katowice,
Poland
baron@us.edu.pl
Abstract:
Given a probability space (Ω, A, P) a separable and complete metric space X with the σalgebra B of all its Borel subsets and a B A measurable f : X * Ω → X we consider its iterates f^{n}, n N, defined on X * Ω^{N} by f^{1}(x,ω) = f(x,ω_{1}) and f^{n+1}(x,ω)=f(f^{n}(x,ω),ω_{n+1}), provide a simple criterion for the convergence in law of f^{n}(x,·))_{ n N}, to a random variable independent of x X , and apply this criterion to linear functional equations in a single variable.
Paper's Title:
A note on Inequalities due to Martins, Bennett and Alzer
Author(s):
József Sándor
BabeşBolyai University of Cluj, Department of Mathematics and Computer Sciences
Kogălniceanu Nr.1, ClujNapoca,
Romania.
jjsandor@hotmail.com
jsandor@member.ams.org
Abstract:
A short history of certain inequalities by Martins, Bennett as well as Alzer, is provided. It is shown that, the inequality of Alzer for negative powers [6], or Martin's reverse inequality [7] are due in fact to Alzer [2]. Some related results, as well as a conjecture, are stated.
Paper's Title:
1type PseudoChebyshev Subspaces in Generalized 2normed Spaces
Author(s):
Sh. Rezapour
Department of Mathematics, Azarbaijan University of Tarbiat Moallem,
Azarshahr, Tabriz,
Iran
sh.rezapour@azaruniv.edu
Abstract:
We construct a generalized 2normed space from every normed space. We introduce 1type pseudoChebyshev subspaces in generalized 2normed spaces and give some results in this field.
Paper's Title:
Weak solutions of non coercive stochastic NavierStokes equations in R^{2}
Author(s):
Wilhelm Stannat and Satoshi Yokoyama
Technische Universität Berlin,
Strasse des 17. Juni 136, 10623 Berlin,
Germany.
Graduate School of Mathematical Sciences,
The University of Tokyo,
Komaba, Tokyo 1538914,
Japan.
Email: stannat@math.tuberlin.de
Email: satoshi2@ms.utokyo.ac.jp
Abstract:
We prove existence of weak solutions of stochastic NavierStokes equations in R^{2} which do not satisfy the coercivity condition. The equations are formally derived from the critical point of some variational problem defined on the space of volume preserving diffeomorphisms in R^{2}. Since the domain of our equation is unbounded, it is more difficult to get tightness of approximating sequences of solutions in comparison with the case of a bounded domain. Our approach is based on uniform a priori estimates on the enstrophy of weak solutions of the stochastic 2DNavierStokes equations with periodic boundary conditions, where the periodicity is growing to infinity combined with a suitable spatial cutofftechnique.
Paper's Title:
Antiderivatives and Integrals Involving Incomplete Beta Functions with Applications
Author(s):
R. AlAhmad^{1,2} and H. Almefleh^{1}
Mathematics Department,
Yarmouk University,
Irbid 21163,
Jordan.
Email: rami_thenat@yu.edu.jo
Faculty of Engineering,
Higher Colleges of Technology,
Ras Alkhaimah,
UAE.
Abstract:
In this paper, we prove that incomplete beta functions are antiderivatives of several products and powers of trigonometric functions, we give formulas for antiderivatives for products and powers of trigonometric functions in term of incomplete beta functions, and we evaluate integrals involving trigonometric functions using incomplete beta functions. Also, we extend some properties of the beta functions to the incomplete beta functions. As an application for the above results, we find the moments for certain probability distributions.
Paper's Title:
Bartle Integration in Lie Algebras
Author(s):
Andreas Boukas and Philip Feinsilver
Centro Vito Volterra,
Universita di Roma Tor Vergata,
via Columbia 2, 00133 Roma,
Italy.
Department of Mathematics,
Southern Illinois University,
Carbondale, Illinois 62901,
USA.
Email:
andreasboukas@yahoo.com
Email: pfeinsil@math.siu.edu
Abstract:
Using Bartle's bilinear vector integral we define stochastic integrals of bounded operator valued functions with respect to Stieltjes measures associated with the generators of the Heisenberg and Finite Difference Lie algebras. Our definition also covers the Square of White Noise and sl/2 Lie algebras.
Paper's Title:
Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
http://rgmia.org/dragomir
Abstract:
The main aim of this survey is to present recent results concerning Ostrowski type inequalities for the Lebesgue integral of various classes of complex and realvalued functions. The survey is intended for use by both researchers in various fields of Classical and Modern Analysis and Mathematical Inequalities and their Applications, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.
Paper's Title:
Some Homogeneous Cyclic Inequalities of Three Variables of Degree Three and Four
Author(s):
TETSUYA ANDO
Department of Mathematics and Informatics,
Chiba University, Chiba 2638522, JAPAN
ando@math.s.chibau.ac.jp
Abstract:
We shall show that the three variable cubic inequality
t^{2} (a^{3}+b^{3}+c^{3}) + (t^{4}2t)(ab^{2}+bc^{2}+ca^{2})
≥ (2t^{3}1)(a^{2}b+b^{2}c+c^{2}a)
+ (3t^{4}6t^{3}+3t^{2}6t+3)abc
holds for nonnegative a, b, c, and for any real number t.
We also show some similar three variable cyclic quartic inequalities.
Paper's Title:
On Reformations of 2Hilbert Spaces
Author(s):
M. Eshaghi Gordji, A. Divandari, M. R. Safi and Y. J. Cho
Department of Mathematics, Semnan
University,
P.O. Box 35195363, Semnan,
Iran
meshaghi@semnan.ac.ir, madjid.eshaghi@gmail.com
Department of Mathematics, Semnan
University,
Iran
Department of Mathematics, Semnan
University,
Iran
safi@semnan.ac.ir, SafiMohammadReza@yahoo.com
Department of Mathematics Education and
the RINS,
Gyeongsang National University
Chinju 660701,
Korea
Abstract:
In this paper, first, we introduce the new concept of (complex) 2Hilbert spaces, that is, we define the concept of 2inner product spaces with a complex valued 2inner product by using the 2norm. Next, we prove some theorems on Schwartz's inequality, the polarization identity, the parallelogram laws and related important properties. Finally, we give some open problems related to 2Hilbert spaces.
Paper's Title:
A Wallis Type Inequality and a Double Inequality for Probability Integral
Author(s):
Jian Cao, DaWei Niu and Feng Qi
School of Mathematics and Informatics,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
21caojian@163.com
School of Mathematics and Informatics,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
nnddww@tom.com
Research Institute of Mathematical Inequality Theory,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
qifeng@hpu.edu.cn
fengqi618@member.ams.org
qifeng618@hotmail.com
qifeng618@msn.com
qifeng618@qq.com
URL: http://rgmia.vu.edu.au/qi.html
Abstract:
In this short note, a Wallis type inequality with the best upper and lower bounds is established. As an application, a double inequality for the probability integral is found.
Paper's Title:
Existence of solutions for Neutral Stochastic Functional Differential Systems with Infinite Delay in Abstract Space
Author(s):
P. Balasubramaniam, A. V. A. Kumar and S. K. Ntouyas
Department of Mathematics, Gandhigram Rural Institute,
Deemed University, Gandhigram  624 302,
Tamil Nadu, India.
pbalgri@rediffmail.com
Department of Mathematics, Gandhigram Rural Institute,
Deemed University, Gandhigram  624 302,
Tamil Nadu, India.
nnddww@tom.com
Department of Mathematics, University of Ioannina,
451 10 Ioannina,
Greece.
sntouyas@cc.uoi.gr
URL: http://www.math.uoi.gr/~sntouyas
Abstract:
In this paper we prove existence results for semilinear stochastic neutral functional differential systems with unbounded delay in abstract space. Our theory makes use of analytic semigroups and fractional power of closed operators and Sadovskii fixed point theorem.
Paper's Title:
A Double Inequality for Divided Differences and Some Identities of the Psi and Polygamma Functions
Author(s):
B. N. Guo and F. Qi
School of
Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan
Province, 454010, China
bai.ni.guo@gmail.com,
bai.ni.guo@hotmail.com
School of
Research Institute of Mathematical Inequality Theory, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China
qifeng618@gmail.com,
qifeng618@hotmail.com,
qifeng618@qq.com
URL:http://qifeng618.spaces.live.com
Abstract:
In this short note, from the logarithmically completely monotonic property of the function ^{ }, a double inequality for the divided differences and some identities of the psi and polygamma functions are presented.
Paper's Title:
On Stable Numerical Differentiation
Author(s):
N. S. Hoang and A. G. Ramm
Mathematics Department, Kansas State University
Manhattan, KS 665062602,
U. S. A.
nguyenhs@math.ksu.edu
ramm@math.ksu.edu
URL:http://math.ksu.edu/~ramm
Abstract:
Based on a regularized Volterra equation, two different approaches for numerical differentiation are considered. The first approach consists of solving a regularized Volterra equation while the second approach is based on solving a disretized version of the regularized Volterra equation. Numerical experiments show that these methods are efficient and compete favorably with the variational regularization method for stable calculating the derivatives of noisy functions.
Paper's Title:
A Study of the Effect of Density Dependence in a Matrix Population Model
Author(s):
N. Carter and M. Predescu
Department of Mathematical Sciences,
Bentley University,
Waltham, MA 02452,
U.S.A.
ncarter@bentley.edu
mpredescu@bentley.edu
Abstract:
We study the behavior of solutions of a three dimensional discrete time nonlinear matrix population model. We prove results concerning the existence of equilibrium points, boundedness, permanence of solutions, and global stability in special cases of interest. Moreover, numerical simulations are used to compare the dynamics of two main forms of the density dependence function (rational and exponential).
Paper's Title:
On the Fock Representation of the Central Extensions of the Heisenberg Algebra
Author(s):
L. Accardi and A. Boukas
Centro Vito Volterra, Università di Roma
Tor Vergata,
via Columbia 2, 00133 Roma,
Italy
accardi@volterra.mat.uniroma2.it
URL: http://volterra.mat.uniroma2.it
Department of Mathematics,
American College of Greece,
Aghia Paraskevi, Athens 15342,
Greece
andreasboukas@acg.edu
Abstract:
We examine the possibility of a direct Fock representation of the recently obtained nontrivial central extensions of the Heisenberg algebra, generated by elements and E satisfying the commutation relations , and , where a and are dual, h is selfadjoint, E is the nonzero selfadjoint central element and We define the exponential vectors associated with the Fock space, we compute their Leibniz function (inner product), we describe the action of a, and h on the exponential vectors and we compute the moment generating and characteristic functions of the classical random variable corresponding to the selfadjoint operator
Paper's Title:
Some Functional Inequalities for the Geometric Operator Mean
Author(s):
Mustapha Raissouli
Taibah University, Faculty of Sciences,
Department of Mathematics,
Al Madinah Al Munawwarah, P.O.Box 30097,
Kingdom of Saudi Arabia.
Abstract:
In this paper, we give some new inequalities of functional type for the power geometric operator mean involving several arguments.
Paper's Title:
New Inequalities of Mill's Ratio and Application to The Inverse Qfunction Approximation
Author(s):
Pingyi Fan
Department of Electronic Engineering,
Tsinghua University, Beijing,
China
Abstract:
In this paper, we investigate the Mill's ratio estimation problem and get two new inequalities. Compared to the well known results obtained by Gordon, they becomes tighter. Furthermore, we also discuss the inverse Qfunction approximation problem and present some useful results on the inverse solution. Numerical results confirm the validness of our theoretical analysis. In addition, we also present a conjecture on the bounds of inverse solution on Qfunction.
Paper's Title:
Some New Generalizations of Jensen's Inequality with Related Results and Applications
Author(s):
Steven G. From
Department of Mathematics
University of Nebraska at Omaha
Omaha, Nebraska 681820243.
Email: sfrom@unomaha.edu
Abstract:
In this paper, some new generalizations of Jensen's inequality are presented. In particular, upper and lower bounds for the Jensen gap are given and compared analytically and numerically to previously published bounds for both the discrete and continuous Jensen's inequality cases. The new bounds compare favorably to previously proposed bounds. A new method based on a series of locally linear interpolations is given and is the basis for most of the bounds given in this paper. The wide applicability of this method will be demonstrated. As byproducts of this method, we shall obtain some new HermiteHadamard inequalities for functions which are 3convex or 3concave. The new method works to obtain bounds for the Jensen gap for nonconvex functions as well, provided one or two derivatives of the nonlinear function are continuous. The mean residual life function of applied probability and reliability theory plays a prominent role in construction of bounds for the Jensen gap. We also present an exact integral representation for the Jensen gap in the continuous case. We briefly discuss some inequalities for other types of convexity, such as convexity in the geometric mean, and briefly discuss applications to reliability theory.
Paper's Title:
On Singular Numbers of Hankel Matrices of Markov Functions
Author(s):
Vasily A. Prokhorov
Department of Mathematics and Statistics,
University of South Alabama,
Mobile, Alabama 366880002,
USA.
Email: prokhoro@southalabama.edu
URL:
http://www.southalabama.edu/mathstat/people/prokhorov.shtml
Abstract:
Let E ⊂ (01,1) be a compact set and let μ be a positive Borel measure with support supp μ=E. Let
In the case when E=[a,b]⊂ (1,1) and μ satisfies the condition dμ/dx>0 a.e. on E, we investigate asymptotic behavior of singular numbers σ_{kn,n} of the Hankel matrix D_{n}, where k_{n}/n→θ∈[0,1] as n→∞. Moreover, we obtain asymptotics of the Kolmogorov, Gelfand and linear kwidths, k=k_{n}, of the unit ball A_{n,2} of P_{n}∩L_{2}(Γ) in the space L_{2}(μ,E), where Γ={z:z=1} and P_{n} is the class of all polynomials of the degree at most n.
Paper's Title:
Existence of Solution of Differential and RiemannLiouville Equation Via Fixed Point Approach in Complex Valued bMetric Spaces
Author(s):
K. Afassinou, A. A. Mebawondu, H. A. Abass and O. K. Narain
Department of Science Access,
University of Zululand, KwaDlangezwa,
South Africa.
Email: komia@aims.ac.za
DSTNRF Centre of Excellence in
Mathematical and Statistical Sciences (CoEMaSS),
Johannesburg,
South Africa.
Email: dele@aims.ac.za
DSTNRF Centre of Excellence in
Mathematical and Statistical Sciences (CoEMaSS),
Johannesburg,
South Africa.
Email: hammedabass548@gmail.com
School of Mathematics, Statistics and
Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: naraino@ukzn.ac.za
Abstract:
In this paper, we establish some fixed point and common fixed point results for a new type of generalized contractive mapping using the notion of Cclass function in the framework of complex valued bmetric spaces. As an application, we establish the existence and uniqueness of a solution for RiemannLiouville integral and ordinary differential equation in the framework of a complete complex valued bmetric spaces. The obtained results generalize and improve some fixed point results in the literature.
Paper's Title:
On a Criteria for Strong Starlikeness
Author(s):
V. Ravichandran, M. Darus, and N. Seenivasagan
School Of Mathematical Sciences,
Universiti Sains Malaysia,
11800 Usm Penang, Malaysia
vravi@cs.usm.my
URL: http://cs.usm.my/~vravi
School of Mathematical Sciences, Faculty of Sciences and Technology,
Ukm, Bangi 43600, Malaysia
maslina@pkrisc.cc.ukm.my
Sindhi College, 123, P. H. Road, Numbal,
Chennai 600 077 India
vasagan2000@yahoo.co.in
Abstract:
In this paper, we are concerned with finding sufficient condition for certain normalized analytic function f(z) defined on the open unit disk in the complex plane to be strongly starlike of order α. Also we have obtained similar results for certain functions defined by Ruscheweyh derivatives and Sălăgean derivatives. Further extension of these results are given for certain pvalent analytic functions defined through a linear operator.
Paper's Title:
A New Step Size Rule in Noor's Method for Solving General Variational Inequalities
Author(s):
Abdellah Bnouhachem
School of Management Science and Engineering, Nanjing University,
Nanjing, 210093
P.R. China.
babedallah@yahoo.com
Abstract:
In this paper, we propose a new step size rule in Noor's method for solving general variational inequalities. Under suitable conditions, we prove that the new method is globally convergent. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method.
Paper's Title:
Long Correlations Applied to the Study of Agricultural Indices in Comparison with the S&P500 index
Author(s):
M. C. Mariani, J. Libbin, M.P. Beccar Varela,
V. Kumar Mani, C. Erickson, D.J. Valles Rosales
Department of Mathematical Sciences,
Science Hall 236, New Mexico State University,
Las Cruces, NM 880038001,
USA.
mmariani@nmsu.edu
Abstract:
Longtime correlations in agricultural indices are studied and their behavior is compared to the wellestablished S&P500 index. Hurst exponent and Detrended Fluctuation Analysis (DFA) techniques are used in this analysis. We detected longcorrelations in the agricultural indices and briefly discussed some features specific in comparison to the S&P500 index.
Paper's Title:
Topological Aspects of Scalarization in Vector Optimization Problems.
Author(s):
Peter I. Kogut, Rosanna Manzo and Igor V. Nechay
Department of Differential Equations,
Dnipropetrovsk National University, Naukova
STR.,
13,
49010 Dnipropetrovsk,
Ukraine
p.kogut@i.ua
Università di Salerno,
Dipartimento di Ingegneria dell'Informazione e Matematica Applicata,
Via Ponte don Melillo, 84084 Fisciano (SA),
Italy
manzo@diima.unisa.it
Department of Technical Cybernetics,
Dnipropetrovsk Technical University,
Acad. Lazarjan
STR., 2,
49010 Dnipropetrovsk,
Ukraine
i.nechay@i.ua
Abstract:
In this paper, we study vector optimization problems in partially ordered Banach spaces. We suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We derive sufficient conditions for existence of efficient solutions of the above problems and discuss the role of topological properties of the objective space. We discuss the scalarization of vector optimization problems when the objective functions are vectorvalued mappings with a weakened property of lower semicontinuity. We also prove the existence of the socalled generalized efficient solutions via the scalarization process. All principal notions and assertions are illustrated by numerous examples.
Paper's Title:
Shape Diagrams for 2D Compact Sets  Part III: Convexity Discrimination for Analytic and Discretized Simply Connected Sets.
Author(s):
S. Rivollier, J. Debayle and J.C. Pinoli
Ecole Nationale Supérieure des Mines de SaintEtienne,
CIS  LPMG, UMR CNRS
5148,
158 cours Fauriel,
42023 SaintEtienne Cedex 2, France.
rivollier@emse.fr;
debayle@emse.fr; pinoli@emse.fr
Abstract:
Shape diagrams are representations in the Euclidean plane introduced to study 3dimensional and 2dimensional compact convex sets. However, they can also been applied to more general compact sets than compact convex sets. A compact set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow twentytwo shape diagrams to be built. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these twentytwo shape diagrams. The two first parts of this study are published in previous papers 8,9. They focus on analytic compact convex sets and analytic simply connected compact sets, respectively. The purpose of this paper is to present the third part, by focusing on the convexity discrimination for analytic and discretized simply connected compact sets..
Paper's Title:
On the Inequality
Author(s):
A. Coronel and F. Huancas
Departamento de Ciencias Básicas,
Facultad de Ciencias, Universidad del BíoBío, Casilla 447,
Campus Fernando May, Chillán, Chile.
acoronel@roble.fdomay.ubiobio.cl
Departamento Académico de Matemática,
Facultad de Ciencias Físicas y Matemáticas,
Universidad Nacional Pedro Ruiz Gallo, Juan XIII s/n,
Lambayeque, Perú
Abstract:
In this paper we give a complete proof of for all positive real numbers a, b and c. Furthermore, we present another way to prove the statement for
Paper's Title:
Expected Utility with Subjective Events
Author(s):
Jacob Gyntelberg and Frank Hansen
Bank for International Settlements,
Basel,
Switzerland
Tohoku University, Institute for International Education,
Sendai,
Japan
Abstract:
We provide a new theory of expected utility with subjective events modeled by a lattice of projections. This approach allows us to capture the notion of a ``small world'' as a context dependent or local state space embedded into a subjective set of events, the ``grand world''. For each situation the decision makers' subjective ``small world'' reflects the events perceived to be relevant for the act under consideration. The subjective set of events need not be representable by a classical state space. Maintaining preference axioms similar in spirit to the classical axioms, we obtain an expected utility representation which is consistent across local state spaces and separates subjective probability and utility. An added benefit is that this alternative expected utility representation allows for an intuitive distinction between risk and uncertainty.
Paper's Title:
On Some Estimates for the Logarithmic Mean
Author(s):
Shuhei Wada
Department of Information and Computer
Engineering,
Kisarazu National College of Technology,
Kisarazu, Chiba 2920041,
Japan.
Email: wada@j.kisarazu.ac.jp
Abstract:
We show some estimates for the logarithmic mean that are obtained from operator inequalities between the Barbour path and the Heinz means.
Paper's Title:
New Stochastic Calculus
Author(s):
Moawia Alghalith
Department of Economics,
University of the West Indies, St. Augustine,
Trinidad and Tobago.
Email:
malghalith@gmail.com
Abstract:
We present new stochastic differential equations, that are more general and simpler than the existing Itobased stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.
Paper's Title:
The Conservativeness of Girsanov Transformed for Symmetric Jumpdiffusion Process
Author(s):
Mila Kurniawaty and Marjono
Department of Mathematics,
Universitas Brawijaya,
Malang,
Indonesia.
Email: mila_n12@ub.ac.id,
marjono@ub.ac.id
Abstract:
We study about the Girsanov transformed for symmetric Markov processes with jumps associated with regular Dirichlet form. We prove the conservativeness of it by dividing the regular Dirichlet form into the "small jump" part and the "big jump" part.
Paper's Title:
Solving Two Point Boundary Value Problems by Modified Sumudu Transform Homotopy Perturbation Method
Author(s):
Asem AL Nemrat and Zarita Zainuddin
School of Mathematical Sciences,
Universiti Sains Malaysia,
11800 Penang,
Malaysia.
Email: alnemrata@yahoo.com
zarita@usm.my
Abstract:
This paper considers a combined form of the Sumudu transform with the modified homotopy perturbation method (MHPM) to find approximate and analytical solutions for nonlinear two point boundary value problems. This method is called the modified Sumudu transform homotopy perturbation method (MSTHPM). The suggested technique avoids the roundoff errors and finds the solution without any restrictive assumptions or discretization. We will introduce an appropriate initial approximation and furthermore, the residual error will be canceled in some points of the interval (RECP). Only a first order approximation of MSTHPM will be required, as compared to STHPM, which needs more iterations for the same cases of study. After comparing figures between approximate, MSTHPM, STHPM and numerical solutions, it is found through the solutions we have obtained that they are highly accurate, indicating that the MSTHPM is very effective, simple and can be used to solve other types of nonlinear boundary value problems (BVPs).
Paper's Title:
A new approach to the study of fixed point for simulation functions with application in Gmetric spaces
Author(s):
Komi Afassinou and Ojen Kumar Narain
Department of Mathematical Sciences,
University of Zululand,
KwaDlangezwa,
South Africa.
Email: komia@aims.ac.za
School of Mathematics, Statistics and
Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: naraino@ukzn.ac.za
Abstract:
The purpose of this work is to generalize the fixed point results of Kumar et al. [11] by introducing the concept of (α,β)Zcontraction mapping, Suzuki generalized (α,β)Zcontraction mapping, (α,β)admissible mapping and triangular (α,β)admissible mapping in the frame work of Gmetric spaces. Fixed point theorems for these class of mappings are established in the frame work of a complete Gmetric spaces and we establish a generalization of the fixed point result of Kumar et al. [11] and a host of others in the literature. Finally, we apply our fixed point result to solve an integral equation.
Paper's Title:
Several Applications of a Local Nonconvex Youngtype Inequality
Author(s):
Loredana Ciurdariu, Sorin Lugojan
Department of Mathematics,
"Politehnica" University of Timisoara,
Pta. Victoriei, No.2, 300006Timisoara,
Romania.
Email: ltirtirau87@yahoo.com
Abstract:
A local version of the Young inequality for positive numbers is used in order to deduce some inequalities about determinants and norms for real quadratic matrices and norms of positive operators on complex Hilbert spaces.
Paper's Title:
Inequalities of Gamma Function Appearing in Generalizing Probability Sampling Design
Author(s):
Mohammadkheer M. AlJararha And Jehad M. AlJararha
Department of Mathematics,
Yarmouk University,
Irbid 21163,
Jordan.
Email: mohammad.ja@yu.edu.jo
Department of Statistics,
Yarmouk University,
Irbid 21163,
Jordan.
Email: jehad@yu.edu.jo
Abstract:
In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities can be used to generalize different probability distribution functions. Also, they can be used to generalize some statistical designs, e.g., the probability proportional to the size without replacement design.
Paper's Title:
On Admissible Mapping via Simulation Function
Author(s):
Anantachai Padcharoen and Pakeeta Sukprasert
Department of Mathematics,
Faculty of Science and Technology,
Rambhai Barni Rajabhat University,
Chanthaburi 22000,
Thailand.
Email: anantachai.p@rbru.ac.th
Department of Mathematics and Computer Science
Faculty of Science and Technology
Rajamangala University of Technology Thanyaburi (RMUTT),
Thanyaburi, Pathumthani 12110,
Thailand.
Email: pakeeta_s@rmutt.ac.th
Abstract:
In this paper, we present some fixed point results in complete metric spaces by using generalized admissible mapping embedded in the simulation function. Its applications, Our results used to study the existence problem of nonlinear Hammerstein integral equations.
Paper's Title:
Long Time Behavior for a Viscoelastic Problem with a Positive Definite Kernel
Author(s):
Nassereddine Tatar
King Fahd
University of Petroleum and Mineral, Department of Mathematical Sciences,
Dhahran, 31261 Saudi Arabia
tatarn@kfupm.edu.sa
Abstract:
We study the asymptotic behavior of solutions for an integrodifferential problem which arises in the theory of viscoelasticity. It is proved that solutions go to rest in an exponential manner under new assumptions on the relaxation function in the memory term. In particular, we consider a new family of kernels which are not necessarily decreasing.
Paper's Title:
Viability
Theory And Differential Lanchester Type Models For Combat.
Differential Systems.
Author(s):
G. Isac and A. Gosselin
Department Of
Mathematics, Royal Military College Of Canada,
P.O. Box 17000, Stn Forces, Kingston,
Ontario, Canada K7k 7b4
isacg@rmc.ca
gosselina@rmc.ca
URL:
http://www.rmc.ca/academic/math_cs/isac/index_e.html
URL:
http://www.rmc.ca/academic/math_cs/gosselin/index_e.html
Abstract:
In 1914, F.W. Lanchester proposed several mathematical models based on differential equations to describe combat situations [34]. Since then, his work has been extensively modified to represent a variety of competitions including entire wars. Differential Lanchester type models have been studied from many angles by many authors in hundreds of papers and reports. Lanchester type models are used in the planning of optimal strategies, supply and tactics. In this paper, we will show how these models can be studied from a viability theory stand point. We will introduce the notion of winning cone and show that it is a viable cone for these models. In the last part of our paper we will use the viability theory of differential equations to study Lanchester type models from the optimal theory point of view.
Paper's Title:
Positive Solution For Discrete ThreePoint Boundary Value Problems
Author(s):
WingSum Cheung And Jingli Ren
Department of Mathematics,
The University of Hong Kong,
Pokfulam, Hong Kong
wscheung@hku.hk
Institute of Systems Science,
Chinese Academy of Sciences,
Beijing 100080, P.R. China
renjl@mx.amss.ac.cn
Abstract:
This paper is concerned with the existence of positive solution to the discrete threepoint boundary value problem
_{
},
_{
}
where _{ }, and f is allowed to change sign. By constructing available operators, we shall apply the method of lower solution and the method of topology degree to obtain positive solution of the above problem for _{ } on a suitable interval. The associated Green’s function is first given.
Paper's Title:
Refinement Inequalities Among Symmetric Divergence Measures
Author(s):
Inder Jeet Taneja
Departamento de Matemática,
Universidade Federal de Santa Catarina, 88.040900
Florianópolis, Sc, Brazil
taneja@mtm.ufsc.br
URL: http://www.mtm.ufsc.br/~taneja
Abstract:
There are three classical divergence measures in the literature on information theory and statistics, namely, JeffryesKullbackLeiber’s Jdivergence, SibsonBurbeaRao’s Jensen Shannon divegernce and Taneja’s arithemtic  geometric mean divergence. These bear an interesting relationship among each other and are based on logarithmic expressions. The divergence measures like Hellinger discrimination, symmetric χ^{2}−divergence, and triangular discrimination are not based on logarithmic expressions. These six divergence measures are symmetric with respect to probability distributions. In this paper some interesting inequalities among these symmetric divergence measures are studied. Refinements of these inequalities are also given. Some inequalities due to Dragomir et al. [6] are also improved.
Paper's Title:
A general theory of decision making
Author(s):
Frank Hansen
Department of Economics,
University of Copenhagen,
Studiestraede 6, DK1455 Copenhagen K
Denmark
Frank.Hansen@econ.ku.dk
URL: http://www.econ.ku.dk/okofh
Abstract:
We formulate a general theory of decision making based on a lattice of observable events, and we exhibit a large class of representations called the general model. Some of the representations are equivalent to the so called standard model in which observable events are modelled by an algebra of measurable subsets of a state space, while others are not compatible with such a description. We show that the general model collapses to the standard model, if and only if an additional axiom is satisfied. We argue that this axiom is not very natural and thus assert that the standard model may not be general enough to model all relevant phenomena in economics. Using the general model we are (as opposed to Schmeidler [16]) able to rationalize Ellsberg's paradox without the introduction of nonadditive measures.
Paper's Title:
Two Mappings Related to Steffensen's Inequalities
Author(s):
LiangCheng Wang
School of Mathematical Science,
Chongqing Institute of Technology,
Xingsheng Lu 4,
Yangjiaping 400050, Chongqing City,
China.
wangliangcheng@163.com
Abstract:
In this paper, we define two mappings closely connected with Steffensen's inequalities, investigate their main properties, give some refinements for Steffensen's inequalities and obtain new inequalities.
Paper's Title:
On Perturbed Reflection Coefficients
Author(s):
J. L. DíazBarrero and J. J. Egozcue
Applied Mathematics III,
Universidad Politécnica de Cataluña,
Barcelona, Spain
jose.luis.diaz@upc.edu
juan.jose.egozcue@upc.edu
Abstract:
Many control and signal processing applications require testing stability of polynomials. Classical tests for locating zeros of polynomials are recursive, but they must be stopped whenever the so called "singular polynomials" appear. These ``singular cases'' are often avoided by perturbing the "singular polynomial". Perturbation techniques although always successful are not proven to be wellfounded. Our aim is to give a mathematical foundation to a perturbation method in order to overcome "singular cases" when using Levinson recursion as a testing method. The nonsingular polynomials are proven to be dense in the set of all polynomials respect the L²norm on the unit circle . The proof is constructive and can be used algorithmically.
Paper's Title:
A New HardyHilbert's Type Inequality for Double Series and its Applications
Author(s):
Mingzhe Gao
Department of Mathematics and Computer Science, Normal College Jishou University,
Jishou Hunan, 416000,
People's Republic of China
mingzhegao1940@yahoo.com.cn
Abstract:
In this paper, it is shown that a new HardyHilbert’s type inequality for double series can be established by introducing a parameter _{ }and the weight function of the form _{} where c is Euler constant and And the coefficient is proved to be the best possible. And as the mathematics aesthetics, several important constants _{ }and _{} appear simultaneously in the coefficient and the weight function when _{} In particular, for case _{} some new Hilbert’s type inequalities are obtained. As applications, some extensions of HardyLittlewood’s inequality are given.
Paper's Title:
Reconstruction of Discontinuities of Functions Given Noisy Data
Author(s):
Eric D. Mbakop
67A Beaver Park Rd,
Framingham, MA, 01702,
U. S. A.
ericsteve86@yahoo.fr
Abstract:
Suppose one is given noisy data of a discontinuous piecewisesmooth function along with a bound on its second derivative. The locations of the points of discontinuity of f and their jump sizes are not assumed known, but are instead retrieved stably from the noisy data. The novelty of this paper is a numerical method that allows one to locate some of these points of discontinuity with an accuracy that can be made arbitrarily small.
Paper's Title:
Generalizations of HermiteHadamard's Inequalities for LogConvex Functions
Author(s):
AiJun Li
School of Mathematics and Informatics,
Henan Polytechnic University,
Jiaozuo City, Henan Province,
454010, China.
liaijun72@163.com
Abstract:
In this article, HermiteHadamard's inequalities are extended in terms of the weighted power mean and logconvex function. Several refinements, generalizations and related inequalities are obtained.
Paper's Title:
Existence of Solutions for Third Order Nonlinear Boundary Value Problems
Author(s):
Yue Hu and Zuodong Yang
School of Mathematics and Computer Science, Nanjing Normal University, Jiangsu Nanjing 210097,
China.
huu3y2@163.com
College of Zhongbei, Nanjing Normal University, Jiangsu Nanjing 210046,
China.
zdyang_jin@263.net
yangzuodong@njnu.edu.cn
Abstract:
In this paper, the existence of solution for a class of third order quasilinear ordinary differential equations with nonlinear boundary value problems
(Φ_{p}(u"))'=f(t,u,u',u"), u(0)=A, u'(0)=B, R(u'(1),u"(1))=0
is established. The results are obtained by using upper and lower solution methods.
Paper's Title:
Isoperimetric Inequalities for Dual Harmonic Quermassintegrals
Author(s):
Yuan Jun, Zao Lingzhi and Duan Xibo
School of Mathematics and Computer Science,
Nanjing Normal University, Nanjing, 210097,
China.
yuanjun_math@126.com
Department of Mathematics, Nanjing Xiaozhuang University,
Nanjing, 211171,
China.
lzhzhao@163.com
Department of Mathematics, Shandong Water Polytechnic,
Shandong, 276826,
China
dxb1111@sohu.com
Abstract:
In this paper, some isoperimetric inequalities for the dual harmonic quermassintegrals are established.
Paper's Title:
Positive Solutions for Systems of Threepoint Nonlinear Boundary Value Problems
Author(s):
J. Henderson and S. K. Ntouyas
Department of Mathematics, Baylor University
Waco, Texas
767987328 USA.
Johnny_Henderson@baylor.edu
URL: http://www3.baylor.edu/~Johnny_Henderson
Department of Mathematics, University of Ioannina
451 10 Ioannina,
Greece.
sntouyas@cc.uoi.gr
URL: http://www.math.uoi.gr/~sntouyas
Abstract:
Values of λ are determined for which there exist positive solutions of the system of threepoint boundary value problems, u''(t)+ λa(t)f(v(t))=0, v''(t)+λb(t)g(u(t))=0, for 0 < t <1, and satisfying, u(0) = 0, u(1)=α u(η), v(0) = 0, v(1)=α v(η). A GuoKrasnosel'skii fixed point theorem is applied.
Paper's Title:
The Bernoulli Inequality in Uniformly Complete falgebras with Identity
Author(s):
Adel Toumi and Mohamed Ali Toumi
Laboratoire de Physique des Liquides Critiques, Département de Physique, Faculté des Sciences de Bizerte,
7021, Zarzouna, Bizerte, TUNISIA
Adel.Toumi@fst.rnu.tn
Département de Mathématiques, Faculté des Sciences de Bizerte, 7021, Zarzouna,
Bizerte, TUNISIA
MohamedAli.Toumi@fsb.rnu.tn
Abstract:
The main purpose of this paper is to establish with a constructive proof the Bernoulli inequality: let A be a uniformly complete falgebra with e as unit element, let 1<p<∞, then
(e+a)^{p}≥e+pa
for all a∈A_{+}. As an application we prove the Hölder inequality for positive linear functionals on a uniformly complete falgebra with identity by using the Minkowski inequality.
Paper's Title:
Some Properties of the Solution of a Second Order Elliptic Abstract Differential Equation
Author(s):
A. Aibeche and K. Laidoune
Mathematics Department, Faculty of Sciences,
University Ferhat Abbas, Setif,
Route de Scipion, 19000,
Setif,
Algeria
aibeche@univsetif.dz
Abstract:
In this paper we study a class of non regular boundary value problems for elliptic differentialoperator equation of second order with an operator in boundary conditions. We give conditions which guarantee the coerciveness of the solution of the considered problem, the completeness of system of root vectors in Banachvalued functions spaces and we establish the Abel basis property of this system in Hilbert spaces. Finally, we apply this abstract results to a partial differential equation in cylindrical domain.
Paper's Title:
Hyperbolic Barycentric Coordinates
Author(s):
Abraham A. Ungar
Department of Mathematics, North Dakota State University,
Fargo, ND 58105,
USA
Abraham.Ungar@ndsu.edu
URL: http://math.ndsu.nodak.edu/faculty/ungar/
Abstract:
A powerful and novel way to study Einstein's special theory of relativity and its underlying geometry, the hyperbolic geometry of Bolyai and Lobachevsky, by analogies with classical mechanics and its underlying Euclidean geometry is demonstrated. The demonstration sets the stage for the extension of the notion of barycentric coordinates in Euclidean geometry, first conceived by Möbius in 1827, into hyperbolic geometry. As an example for the application of hyperbolic barycentric coordinates, the hyperbolic midpoint of any hyperbolic segment, and the centroid and orthocenter of any hyperbolic triangle are determined.
Paper's Title:
On the product of Mmeasures in lgroups
Author(s):
A. Boccuto, B. Riěcan, and A. R. Sambucini
Dipartimento di Matematica e Informatica,
via Vanvitelli, 1 I06123 Perugia,
Italy.
boccuto@dipmat.unipg.it
URL:
http://www.dipmat.unipg.it/~boccuto
Katedra Matematiky, Fakulta Prírodných Vied,
Univerzita Mateja Bela,
Tajovského, 40, Sk97401 Banská Bystrica,
Slovakia.
riecan@fpv.umb.sk
Dipartimento di Matematica e Informatica,
via Vanvitelli, 1 I06123 Perugia,
Italy.
matears1@unipg.it
URL:
http://www.unipg.it/~matears1
Abstract:
Some extensiontype theorems and compactness
properties for the
product of lgroupvalued Mmeasures are proved.
Paper's Title:
The RiemannStieltjes Integral on Time Scales
Author(s):
D. Mozyrska, E. Pawłuszewicz, D. Torres
Faculty Of Computer Science,
Białystok University Of Technology,
15351 Białystok,
Poland
d.mozyrska@pb.edu.pl
Department Of Mathematics,
University Of Aveiro,
3810193 Aveiro,
Portugal
ewa@ua.pt
Department Of Mathematics,
University Of Aveiro,
3810193 Aveiro,
Portugal
delfim@ua.pt
Abstract:
We study the process of integration on time scales in the sense of RiemannStieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given
Paper's Title:
Generalized Efficient Solutions to One Class of Vector Optimization Problems in Banach Space
Author(s):
Peter I. Kogut, Rosanna Manzo, and Igor V. Nechay
Department of Differential Equations,
Dnipropetrovsk National University,
Naukova str., 13,
49050 Dnipropetrovsk,
Ukraine
p.kogut@i.ua
Dipartimento di Ingegneria
Dell’informazione e Matematica Applicata,
Università di Salerno,
Via
Ponte
Don Melillo,
84084 Fisciano
(Sa),
Italy
manzo@diima.unisa.it
Department of Technical Cybernetics,
Dnipropetrovsk Technical University,
Acad. Lazarjan str., 2,
49010
Dnipropetrovsk,
Ukraine
i.nechay@i.ua
Abstract:
In this paper, we study vector optimization problems in Banach spaces for essentially nonlinear operator equations with additional control and state constraints. We assume that an objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. Using the penalization approach we derive both sufficient and necessary conditions for the existence of efficient solutions of the above problems. We also prove the existence of the socalled generalized efficient solutions via the scalarization of some penalized vector optimization problem.
Paper's Title:
Nontrivial Solutions of Singular Superlinear Threepoint Boundary Value Problems at Resonance
Author(s):
Feng Wang, Fang Zhang
School of Mathematics and Physics,
Changzou University,
Changzhou, 213164,
China.
fengwang188@163.com
Abstract:
The singular superlinear second order threepoint boundary value problems at resonance
are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where n ∈ (0,1) is a constant, f is allowed to be singular at both t=0 and t=1. The existence results of nontrivial solutions are given by means of the topological degree theory.
Paper's Title:
Shape Diagrams for 2D Compact Sets  Part I: Analytic Convex Sets.
Author(s):
S. Rivollier, J. Debayle and J.C. Pinoli
Ecole Nationale Supérieure des Mines de SaintEtienne,
CIS  LPMG, UMR CNRS 5148, 158 cours Fauriel,
42023 SaintEtienne Cedex 2, France.
rivollier@emse.fr;
debayle@emse.fr; pinoli@emse.fr
Abstract:
Shape diagrams are representations in the Euclidean plane introduced to study 3dimensional and 2dimensional compact convex sets. Such a set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow thirtyone shape diagrams to be built. Most of these shape diagrams can also been applied to more general compact sets than compact convex sets. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these thirtyone shape diagrams. The purpose of this paper is to present the first part of this study, by focusing on analytic compact convex sets. A set will be called analytic if its boundary is piecewise defined by explicit functions in such a way that the six geometrical functionals can be straightforwardly calculated. The second and third part of the comparative study are published in two following papers [19.20]. They are focused on analytic simply connected sets and convexity discrimination for analytic and discretized simply connected sets, respectively.
Paper's Title:
Shape Diagrams for 2D Compact Sets  Part II: Analytic Simply Connected Sets.
Author(s):
S. Rivollier, J. Debayle and J.C. Pinoli
Ecole Nationale Supérieure des Mines de SaintEtienne,
CIS  LPMG, UMR CNRS 5148, 158 cours Fauriel,
42023 SaintEtienne Cedex 2, France.
rivollier@emse.fr;
debayle@emse.fr; pinoli@emse.fr
Abstract:
Shape diagrams are representations in the Euclidean plane introduced to study 3dimensional and 2dimensional compact convex sets. However, they can also been applied to more general compact sets than compact convex sets. A compact set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow twentytwo shape diagrams to be built. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these twentytwo shape diagrams. The first part of this study is published in a previous paper 16. It focused on analytic compact convex sets. A set will be called analytic if its boundary is piecewise defined by explicit functions in such a way that the six geometrical functionals can be straightforwardly calculated. The purpose of this paper is to present the second part, by focusing on analytic simply connected compact sets. The third part of the comparative study is published in a following paper 17. It is focused on convexity discrimination for analytic and discretized simply connected compact sets.
Paper's Title:
A Generalization of a Trace Inequality for Positive Definite Matrices
Author(s):
E. V. Belmega, M. Jungers, and S. Lasaulce
Université ParisSud Xi, SUPELEC,
Laboratoire Des Signaux Et Systèmes,
GifSurYvette,
France.
belmega@lss.supelec.fr
http://veronica.belmega.lss.supelec.fr
CNRS, ENSEM, CRAN, Vandoeuvre,
France.
marc.jungers@cran.uhpnancy.fr
http://perso.ensem.inplnancy.fr/Marc.Jungers/
CNRS, SUPELEC, Laboratoire des Signaux et
Systèmes,
GifSurYvette,
France.
lasaulce@lss.supelec.fr
http://samson.lasaulce.lss.supelec.fr
Abstract:
In this note, we provide a generalization of the trace inequality derived in [Belmega].
More precisely, we prove that for arbitrary K ≥ 1 where Tr(∙) denotes the matrix trace operator, A_{1}, B_{1} are any positive definite matrices and A_{k}, B_{k} for all k∈{2,...,k}, are any positive semidefinite matrices.
Paper's Title:
Necessary and Sufficient Conditions for Cyclic Homogeneous Polynomial Inequalities of Degree Four in Real Variables
Author(s):
Vasile Cirtoaje and Yuanzhe Zhou
Department of Automatic Control and Computers
University of Ploiesti
Romania.
vcirtoaje@upgploiesti.ro.
High School Affiliated to Wuhan University, China
Abstract:
In this paper, we give two sets of necessary and sufficient conditions that the inequality f_{4}(x,y,z) ≥ 0 holds for any real numbers x,y,z, where f_{4}(x,y,z) is a cyclic homogeneous polynomial of degree four. In addition, all equality cases of this inequality are analysed. For the particular case in which f_{4}(1,1,1)=0, we get the main result in [3]. Several applications are given to show the effectiveness of the proposed methods.
Paper's Title:
A_{p} Functions and Maximal Operator
Author(s):
Chunping Xie
Department of Mathematics,
Milwaukee School of Engineering,
1025 N. Broadway,
Milwaukee, Wisconsin 53202,
U. S. A.
Email: xie@msoe.edu
URL: http://www.msoe.edu/people/chunping.xie
Abstract:
The relationship between A_{p} functions and HardyLittlewood maximal operator on L^{p,λ}(w), the weighted Morrey space, has been studied. Also the extropolation theorem of L^{p,λ}(w) has been considered.
Paper's Title:
On the HyersUlam Stability of Homomorphisms and Lie Derivations
Author(s):
Javad Izadi and Bahmann Yousefi
Department of Mathematics, Payame Noor
University,
P.O. Box: 193953697, Tehran,
Iran.
Email: javadie2003@yahoo.com,
b_yousefi@pnu.ac.ir
Abstract:
Let A be a Lie Banach^{*}algebra. For each elements (a, b) and (c, d) in A^{2}:= A * A, by definitions
(a, b) (c, d)= (ac, bd),
(a, b)= a+ b,
(a, b)^{*}= (a^{*}, b^{*}),
A^{2} can be considered as a Banach^{*}algebra. This Banach^{*}algebra is called a Lie Banach^{*}algebra whenever it is equipped with the following definitions of Lie product:
for all a, b, c, d in A. Also, if A is a Lie Banach^{*}algebra, then D: A^{2}→A^{2} satisfying
D ([ (a, b), (c, d)])= [ D (a, b), (c, d)]+ [(a, b), D (c, d)]
for all $a, b, c, d∈A, is a Lie derivation on A^{2}. Furthermore, if A is a Lie Banach^{*}algebra, then D is called a Lie^{*} derivation on A^{2} whenever D is a Lie derivation with D (a, b)^{*}= D (a^{*}, b^{*}) for all a, b∈A. In this paper, we investigate the HyersUlam stability of Lie Banach^{*}algebra homomorphisms and Lie^{* }derivations on the Banach^{*}algebra A^{2}.
Paper's Title:
Hyponormal and KQuasiHyponormal Operators On SemiHilbertian Spaces
Author(s):
Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali
Mathematics Department,
College of Science,
Aljouf University,
Aljouf 2014,
Saudi Arabia.
Email:
sididahmed@ju.edu.sa
Mathematics Department, Faculty of
Science,
Hassiba Benbouali, University of Chlef,
B.P. 151 Hay Essalem, Chlef 02000,
Algeria.
Email:
benali4848@gmail.com
Abstract:
Let H be a Hilbert space and let A be a positive bounded operator on H. The semiinner product < uv>_{A}:=<Auv>, u,v ∈ H induces a seminorm  ._{A} on H. This makes H into a semiHilbertian space. In this paper we introduce the notions of hyponormalities and kquasihyponormalities for operators on semi Hilbertian space (H,._{A}), based on the works that studied normal, isometry, unitary and partial isometries operators in these spaces. Also, we generalize some results which are already known for hyponormal and quasihyponormal operators. An operator T ∈ B_{A} (H) is said to be (A, k)quasihyponormal if
Paper's Title:
Credibility Based Fuzzy Entropy Measure
Author(s):
G. Yari, M. Rahimi, B. Moomivand and P. Kumar
Department of Mathematics,
Iran University
of Science and Technology,
Tehran,
Iran.
Email:
Yari@iust.ac.ir
Email:
Mt_Rahimi@iust.ac.ir
URL:
http://www.iust.ac.ir/find.php?item=30.11101.20484.en
URL:
http://webpages.iust.ac.ir/mt_rahimi/en.html
Qarzolhasaneh
Mehr Iran Bank, Tehran,
Iran.
Email:
B.moomivand@qmb.ir
Department of Mathematics and Statistics,
University of Northern British Columbia,
Prince George, BC,
Canada.
Email:
Pranesh.Kumar@unbc.ca
Abstract:
Fuzzy entropy is the entropy of a fuzzy variable, loosely representing the information of uncertainty. This paper, first examines both previous membership and credibility based entropy measures in fuzzy environment, and then suggests an extended credibility based measure which satisfies mostly in Du Luca and Termini axioms. Furthermore, using credibility and the proposed measure, the relative entropy is defined to measure uncertainty between fuzzy numbers. Finally we provide some properties of this Credibility based fuzzy entropy measure and to clarify, give some examples.
Paper's Title:
A Generalization of Viete's Infinite Product and New Mean Iterations
Author(s):
Ryo Nishimura
Department of Frontier Materials
Nagoya Institute of Technology
Gokisocho, Showaku, Nagoya
Aichi, 4668555, Japan.
Email: rrnishimura@gmail.com
Abstract:
In this paper, we generalize Viéte's infinite product formula by use of Chebyshev polynomials. Furthermore, the infinite product formula for the lemniscate sine is also generalized. Finally, we obtain new mean iterations by use of these infinite product formulas.
Paper's Title:
New Refinements of Hölder's Inequality
Author(s):
XiuFen Ma
College of Mathematical and Computer,
Chongqing Normal University Foreign Trade and Business College,
No.9 of Xuefu Road, Hechuan District 401520,
Chongqing City,
The People's Republic of China.
Email: maxiufen86@163.com
Abstract:
In this paper, we define two mappings, investigate their properties, obtain some new refinements of Hölder's inequality.
Paper's Title:
New Exact Taylor's Expansions without the Remainder: Application to Finance
Author(s):
Moawia Alghalith
Economics Dept.,
University of the West Indies,
St Augustine,
Trinidad and Tobago.
Email: malghalith@gmail.com
Abstract:
We present new exact Taylor's expansions with fixed coefficients and without the remainder. We apply the method to the portfolio model.
Corrigendum.
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Paper's Title:
A kind of Function Series and Its Applications
Author(s):
Yang Tianze
Mechanical Engineering,
Shandong University, Xinglongshan Campus,
Jinan, Shandong,
China.
Email: qdyangtianze@163.com
Abstract:
A kind of new function series is obtained in this paper. Their theorems and proofs are shown, and some applications are given. We give the expansion form of general integral and the series expansion form of function and the general expansion form of derivative. Using them in the mathematics,we get some unexpected result.
Paper's Title:
Existence and Estimate of the Solution for the Approximate Stochastic Equation to the Viscous Barotropic Gas
Author(s):
R. Benseghir and A. Benchettah
LANOS Laboratory,
Badji Mokhtar University,
PO Box 12,
Annaba, Algeria.
Email:
benseghirrym@ymail.com,
abenchettah@hotmail.com
Abstract:
A stochastic equation of a viscous barotropic gas is considered. The application of Ito formula to a specific functional in an infinite dimensional space allows us to obtain an estimate which is useful to analyse the behavior of the solution. As it is difficult to exploit this estimate, we study an approximate problem. More precisely, we consider the equation of a barotropic viscous gas in Lagrangian coordinates and we add a diffusion of the density. An estimate of energy is obtained to analyse the behavior of the solution for this approximate problem and Galerkin method is used to prove the existence and uniqueness of the solution.
Paper's Title:
Cubic Alternating Harmonic Number Sums
Author(s):
Anthony Sofo
Victoria University,
College of Engineering and Science,
Melbourne City,
Australia.
Email:
Anthony.Sofo@vu.edu.au
Abstract:
We develop new closed form representations of sums of cubic alternating harmonic numbers and reciprocal binomial coefficients. We also identify a new integral representation for the ζ (4) constant.
Paper's Title:
An Existence of the Solution to Neutral Stochastic Functional Differential Equations Under the Holder Condition
Author(s):
YoungHo Kim
Department of Mathematics,
Changwon National University,
Changwon, Gyeongsangnamdo 51140,
Korea.
Email: iyhkim@changwon.ac.kr
Abstract:
In this paper, we show the existence and uniqueness of solution of the neutral stochastic functional differential equations under weakened H\"{o}lder condition, a weakened linear growth condition, and a contractive condition. Furthermore, in order to obtain the existence of a solution to the equation we used the Picard sequence.
Paper's Title:
Some New Mappings Related to Weighted Mean Inequalities
Author(s):
XiuFen Ma
College of Mathematical and Computer,
Chongqing Normal University Foreign Trade and Business College,
No.9 of Xuefu Road, Hechuan District 401520,
Chongqing City,
The People's Republic of China.
Email: maxiufen86@163.com
Abstract:
In this paper, we define four mappings related to weighted mean inequalities, investigate their properties, and obtain some new refinements of weighted mean inequalities.
Paper's Title:
Global Analysis on Riemannian Manifolds
Author(s):
Louis Omenyi and Michael Uchenna
Department of Mathematics, Computer
Science, Statistics and Informatics,
Alex Ekwueme Federal University, NdufuAlike,
Nigeria.
Email: omenyi.louis@funai.edu.ng,
michael.uchenna@funai.edu.ng
URL: http://www.funai.edu.ng
Abstract:
In this paper, an exposition of the central concept of global analysis on a Riemannan manifold is given. We extend the theory of smooth vector fields from open subsets of Euclidean space to Riemannan manifolds. Specifically, we prove that a Riemannian manifold admits a unique solution for a system of ordinary differential equations generated by the flow of smooth tangent vectors. The idea of partial differential equations on Riemannian manifold is highlighted on the unit sphere.
Paper's Title:
Some fixed point results in partial Smetric spaces
Author(s):
M. M. Rezaee, S. Sedghi, A. Mukheimer, K. Abodayeh, and Z. D. Mitrovic
Department of Mathematics, Qaemshahr
Branch,
Islamic Azad University, Qaemshahr,
Iran.
Email: Rezaee.mohammad.m@gmail.com
Department of Mathematics, Qaemshahr
Branch,
Islamic Azad University, Qaemshahr,
Iran.
Email: sedghi.gh@qaemiau.ac.ir
Department of Mathematics and General
Sciences,
Prince Sultan University, Riyadh,
KSA.
Email: mukheimer@psu.edu.sa
Department of Mathematics and General
Sciences,
Prince Sultan University, Riyadh,
KSA.
Email: kamal@psu.edu.sa
Nonlinear Analysis Research Group,
Faculty of Mathematics and Statistics,
Ton Duc Thang University, Ho Chi Minh City,
Vietnam.
Email: zoran.mitrovic@tdtu.edu.vn
Abstract:
We introduce in this article a new class of generalized metric spaces, called partial Smetric spaces. In addition, we also give some interesting results on fixed points in the partial Smetric spaces and some applications.
Paper's Title:
Weyl's theorem for class Q and k  quasi class Q Operators
Author(s):
S. Parvatham and D. Senthilkumar
Department of Mathematics and Humanities,
Sri Ramakrishna Institute of Technology, Coimbatore10, Tamilnadu,
India.
Email: parvathasathish@gmail.com
Post Graduate and Research Department of
Mathematics,
Govt. Arts College, Coimbatore641018, Tamilnadu,
India.
Email: senthilsenkumhari@gmail.com
Abstract:
In this paper, we give some properties of class Q operators. It is proved that every class Q operators satisfies Weyl's theorem under the condition that T^{2} is isometry. Also we proved that every k quasi class Q operators is Polaroid and the spectral mapping theorem holds for this class of operator. It will be proved that single valued extension property, Weyl and generalized Weyl's theorem holds for every k quasi class Q operators.
Paper's Title:
Sharp Inequalities Between Hölder and Stolarsky Means of Two Positive Numbers
Author(s):
M. Bustos Gonzalez and A. I. Stan
The University of Iowa,
Department of Mathematics,
14 MacLean Hall,
Iowa City, Iowa,
USA.
Email:
margaritabustosgonzalez@uiowa.edu
The Ohio State University at Marion,
Department of Mathematics,
1465 Mount Vernon Avenue,
Marion, Ohio,
USA.
Email: stan.7@osu.edu
Abstract:
Given any index of the Stolarsky means, we find the greatest and least indexes of the H\"older means, such that for any two positive numbers, the Stolarsky mean with the given index is bounded from below and above by the Hölder means with those indexes, of the two positive numbers. Finally, we present a geometric application of this inequality involving the FermatTorricelli point of a triangle.
Paper's Title:
Lie Group Theoretic Approach of OneDimensional BlackScholes Equation
Author(s):
P. L. Zondi and M. B. Matadi
Department of Mathematical sciences,
Faculty of Sciences & Agriculture, University of Zululand,
P Bag X1001, KwaDlangezwa 3886,
South Africa.
Email: matadim@unizulu.ac.za
zondip@unizulu.ac.za
Abstract:
This study discusses the Lie Symmetry Analysis of BlackScholes equation via a modified local oneparameter transformations. It can be argued that the transformation of the BlackScholes equation is firstly obtained by means of riskless rate. Thereafter, the corresponding determining equations to the reduced equation are found. Furthermore, new symmetries of the BlackScholes equation are constructed and lead to invariant solutions.
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