Issue 1, Volume 10,
January 2011
Title of the Paper: New Generalized
Delay Integral Inequalities on Time Scales
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Authors: Bin Zheng
Abstract: In this paper, some new delay integral inequalities with two
independent variables on time scales are established, which can be used as a
hand tool in the investigation of qualitative properties of solutions of delay
dynamic equations on time scales. Some applications for the established
inequalities are also presented, and new explicit bounds on unknown functions
of delay dynamic equations are obtained. Our results generalize some of the
results in [16, 17].
Keywords: Delay integral
inequality; Time scale; Integral equation; Differential equation; Dynamic
equation; Bounded
Title of the Paper: A Generalized
VolterraFredholm Type Integral Inequality for Discontinuous Functions
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Authors: Bin Zheng
Abstract: In this paper, a new generalized VolterraFredholm type nonlinear
integral inequality for discontinuous functions is established, which can be
used in analysis for the boundedness of solutions of certain VolterraFredholm
type integral equations. Our results generalize the main results in [18, 19].
Keywords: Integral
inequality discontinuous function Integral equation Differential equation
Bounded
Title of the Paper: Shape of a Drum, a
Constructive Approach
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Authors: P. N.
Shivakumar, Yan Wu, Yang Zhang
Abstract: For the classical question, “Can you hear the shape of the drum?”,
the answer is known to be “yes” for certain convex planar regions with
analytic boundaries. The answer is also known to be “no” for some polygons
with reentrant corners. A large number of mathematicians over four decades
have contributed to the topic from various approaches, theoretical and
numerical. In this article, we develop a constructive analytic approach to
indicate how a preknowledge of the eigenvalues lead to the determination of
the parameters of the boundary. This approach is applied to a general boundary
and in particular to a circle, an ellipse, and a square. In the case of a
square, we obtain an insight into why the analytical procedure does not, as
expected, yield an answer. For the Mathieu equation with a parameter, we
demonstrate the determination of the parameter when the eigenvalues are known.
Keywords: Helmholtz
equation; Eigenvalues; Mathieu equation
Title of the Paper: Linear Models in
Regional and Interregional Modeling
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Authors: Bohuslav
Sekerka, Robert Bata
Abstract: Models, included in this paper, in contrast to the common model of
intersector relations, focuses on products and services, but also activities
with inputs in form of products and services as well. Proposed models also
include regional aspect. There is described solution for the case that number
of elements of products and services and number of activities are not equal,
because there is a problem with finding solution.
Keywords: Decisionmaking,
Models, Uncertainty, Risk, Regions
Issue 2, Volume 10,
February 2011
Title of the Paper: Transient
Temperature Solutions of a Cylindrical Fin
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Authors: G.C. Kuo,
Y.H. Hu, W.L. Liaw, K.J Wang, K.Y. Kung
Abstract: Analytical temperature solutions to the transient heat conduction
for a two dimensional cylindrical fin with arbitrary convective effects on
lateral surface is obtained by the method of superposition and separation
variables. The temperature distributions are generalized for a linear
combination of the product of Bessel function, Fourier series and exponential
type for nine different cases. Relevant connections with some other
closelyrelated recent works are also indicated.
Keywords: Bessel function,
Fourier series, Heat conduction, Temperature distribution, Separation
variables, superposition
Title of the Paper: A Further Improved
(G'/G ) Expansion Method and the Extended Tanh Method for Finding Exact
Solutions of Nonlinear PDEs
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Authors: Elsayed M. E.
Zayed
Abstract: In the present article, we construct the exact traveling wave
solutions of nonlinear PDEs in mathematical physics via the (1 + 1)
dimensional modified Kawahara equation by using the following two methods: (i)
A further improved (G'/G ) expansion method, where G = G(ξ) satisfies the
auxiliary ordinary differential equation [G''(ξ)]^2 = aG^2(ξ) + bG^4(ξ) +
cG^6(ξ), where ξ = x  Vt while a, b, c and V are constants. (ii) The well
known extended tanh function method. We show that the exact solutions
obtained by these two methods are equivalent. Note that the first method (i)
has not been used by anyone before.
Keywords: (G'/G )
expansion method, auxiliary equation, extended tanh function method,
traveling wave solutions, modified Kawahara equation
Title of the Paper: β_{0}Excellent
Graphs
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Authors: A. P.
Pushpalatha, G. Jothilakshmi, S. Suganthi, V. Swaminathan
Abstract: Claude Berge [1] in 1980, introduced B graphs. These are graphs in
which every vertex in the graph is contained in a maximum independent set of
the graph. Fircke et al [3] in 2002 made a beginning of the study of graphs
which are excellent with respect to various graph parameters. For example, a
graph is domination excellent if every vertex is contained in a minimum
dominating set. The Bgraph of Berge was called β0 excellent graph. β0
excellent trees were characterized [3]. A graph is just β0 excellent if every
vertex belongs to exactly one maximum independent set of the graph.This paper
is devoted to the study of β0 excellent graphs and just β0 excellent graphs.
Keywords: β0excellent and
just β0 excellent, Harary graphs, Generalized Petersen graph
Title of the Paper: Analysis of a
Deteriorating Cold Standby System with Priority
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Authors: Lixia Ma, Genqi
Xu, Nikos E. Mastorakis
Abstract: A deteriorating cold standby repairable system consisting of two
dissimilar components and one repairman is studied in this paper. Suppose that
the life of each component satisfies the exponentially distribution and repair
time of the component satisfies the general distribution, the component 1 has
priority in use and repair. Firstly, a mathematical model is built via the
differential and partial differential equations. And then using the
C0semigroup theory of bounded linear operators, the existence and uniqueness
of the solution, the nonnegative steadystate solution and the exponential
stability of the system are derived. Based on the stability result, some
reliability indices of the system and an optimization problem are presented at
the end of the paper.
Keywords: C0 Semigroup,
WellPosedness, Asymptotic Stability, Exponential Stability, Availability
Issue 3, Volume 10,
March 2011
Title of the Paper: A Heuristic for the
Multiknapsack Problem
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Authors: Jose Grandon,
Ivan Derpich
Abstract: In this work a heuristic for the problem multiknapsack , based on
directions of ascent is presented. These directions are generated from a
center of the polyhedron and they conduct to good approximations of the
integer solutions. For it a center of the polyhedron of the relaxed problem is
obtained. Then an interior ellipse is constructed in this polyhedron and those
eigenvectors of the ellipse that present the best objective ascent of the
function are selected as ascent direction. For determine how many eigenvectors
to use, an angle that relate the eigenvector with the objective function, was
used. The heuristic algorithm has been proved with problems from the
ORlibrary. Four groups of problems were proved with 30 instances every one,
combining 100 and 250 variables with 5 and 10 constraints. The results show
process time that are from a little seconds for little problems, to 400
seconds for bigger problems. The Cpu time average is 190 seconds. The errors
of the best solution found measured using the integrality gap are in order to
3% in the worst case.
Keywords: Heuristics,
Integer Programming, Multiknapsack
Title of the Paper: Introduction to the
Rectangular Trigonometry in Euclidian 2DSpace
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Authors: Claude Bayeh
Abstract: Trigonometry is a branch of mathematics that deals with relations
between sides and angles of triangles. It has some relationship to geometry,
though there is disagreement on exactly what that relationship is. For some,
trigonometry is just a subtopic of geometry. The trigonometric functions are
very important in technical subjects like Astronomy, Relativity, science,
engineering, architecture, and even medicine. In this paper, the rectangular
trigonometry is introduced in order to be in the future a part of the General
trigonometry topic. Thus, the definition of this original part is presented.
The rectangular trigonometric functions are also defined. The importance of
these functions is by producing multi signal forms by varying some parameters
of a single function. Different signals and forms are analyzed and discussed.
The concept of the rectangular Trigonometry is completely different from the
traditional trigonometry in which the study of angles is not the relation
between sides of a right triangle that describes a circle as the previous one,
but the idea here is to use the relation between angles and sides of a
rectangular form with the internal and external circles formed by the
intersection of the rectangular form and the positive parts of x’ox and y’oy
axis in the Euclidian 2D space and their projections. This new concept of
relations will open a huge gate in the mathematical domain and it can resolve
many complicated problems that are difficult or almost impossible to solve
with the traditional trigonometry, and it can describe a huge number of multi
form periodic signals.
Keywords: Mathematics,
geometry, trigonometry, angular function, multi form signal, power electronics
Title of the Paper: Exact Traveling Wave
Solutions of Nonlinear Variable Coefficients Evolution Equations with Forced
Terms using the Generalized (G'/G) Expansion Method
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Authors: Elsayed Zayed,
Mahmoud Abdelaziz
Abstract: The exact traveling wave solutions of the nonlinear variable
coefficients BurgersFisher equation and the generalized Gardner equation with
forced terms can be found in this article using the generalized
(G'/G)expansion method. As a result, hyperbolic, trigonometric and rational
function solutions with parameters are obtained. When these parameters are
taken special values, the solitary wave solutions are derived from the
hyperbolic function solutions. It is shown that the proposed method is direct,
effective and can be applied to many other nonlinear evolution equations in
the mathematical physics.
Keywords: Nonlinear
evolution equations; Generalized (G'/G)expansion method; Variable
coefficients BurgersFisher equation with the forced term; Variable
coefficients generalized Gardner equation with the forced term, Exact
solutions
Issue 4, Volume 10,
April 2011
Title of the Paper: Spectral Analysis of
a Two Unit Deteriorating Standby System with Repair
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Authors: Wenzhi Yuan,
Genqi Xu
Abstract: In this paper, we analyze the spectra and stability of a system
consisting of a working unit and repair unit, in which the working unit
consists of one main unit and one standby unit, while the standby unit may
deteriorate in its standby mode. Firstly, we formulate the problem into a
suitable Banach space. And then we carry out a detailed spectral analysis of
the system operator. Based on the spectral analysis and C0semigroup theory,
we prove the existence of positive solution and finite expansion of the
solution according to its eigenvectors. As a consequence we get that its
dynamic solutions converges exponentially to the steadystate solution.
Finally, we derive some reliability indices of the system.
Keywords: C0semigroup
theory, dynamic solution, steadystate, exponential stability, availability
Title of the Paper: MichelPenot
Subdifferential and Lagrange Multiplier Rule
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Authors: Triloki Nath,
S. R. Singh
Abstract: In this paper, we investigate some properties of Michel Penot
subdifferentials of locally Lipschitz functions and establish Lagrange
multiplier rule in terms of MichelPenot subdifferentials for nonsmooth
mathematical programming problem.
Keywords: Nonsmooth
optimization; approximate subdifferentials; generalized gradient; Michel Penot
subdifferential; Banach space
Title of the Paper: Inverse Model to
Determine the Optimal Number of Drops of RDC Column Using Fuzzy Approach
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Authors: Hafez Ibrahim,
Jamalludin Talib, Normah Maan
Abstract: Inverse modeling is natural in many real world application including
industrial chemical engineering problems. This paper describes the process of
determines optimal input and output of number of drops in various stage of
rotating disc contactor column using fuzzy model. An algorithm of the fuzzy
model is developed to simulate the above process.
Keywords: LiquidLiquid
Extraction, RDC Column, Drop Distribution, Inverse Model, Fuzzy Environment,
Fuzzy Algorithm
Issue 5, Volume 10,
May 2011
Title of the Paper: Almost RungeKutta
Methods of Orders up to Five
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Authors: Abraham
Ochoche, Peter Ndajah
Abstract: In this paper, we have sought to investigate the viability of a type
of general linear methods called Almost RungeKutta (ARK) methods, as a means
of obtaining acceptable numerical approximations of the solution of problems
in continuous mathematics. We have outlined the derivation and implementation
of this class of methods up to order five. Extensive numerical experiments
were carried out and the results clearly show that ARK methods are indeed a
viable alternative to existing traditional methods.
Keywords: Almost, Order,
Alternative, Euler, Runge – Kutta, General Linear Methods
Title of the Paper: Spectrum of A Class
of Delay Differential Equations and Its Solution Expansion
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Authors: Yaxuan Zhang
Abstract: In this paper we study the spectrum and solution expansion of the
differential equation with multiple delays. Firstly, we present explicitly the
asymptotic expressions of the eigenvalues under certain conditions. Then we
prove that the root vectors of the system fail to form a basis for the state
Hilbert space. However, by a trick, we expand the solution of the system
according to the root vectors. As an application, we explain how to apply
solution expansion to the numerical simulation of this kind of delay
differential equations.
Keywords: Delay
differential equation, multiple delays, spectrum, root vector, expansion of
solution, numerical simulation
Title of the Paper: Turing Instability
and Wave Patterns for a Symmetric Discrete Competitive LotkaVolterra System
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Authors: YuTao Han, Bo
Han, Lu Zhang, Li Xu, MeiFeng Li,Guang Zhang
Abstract: In this paper, Turing instability of a symmetric discrete
competitive LotkaVolterra system is considered. To this end, conditions for
producing Turing instability of a general discrete system is attained and this
conclusion is applied to the discrete competition LotkaVolterra system. Then
a series of numerical simulations of the discrete model are performed with
different parameters. Results show that the discrete competitive
LotkaVolterra system can generate a large variety of wave patterns in the
Turing instability region. Particularly, the diffusion coefficients can be
equivalent, that is, there is neither ”activator” nor ”inhibitor”. Similar
results can not be obtained for the corresponding continuous models. On the
other hand, the number of the eigenvalues is illuminated by calculation and
the unstable spaces can be clearly expressed. Thus, the Turing mechanism is
also explained.
Keywords: Turing
instability, Diffusion, Discrete system, Eigenvalue, LotkaVolterra system,
Wave pattern
Issue 6, Volume 10,
June 2011
Title of the Paper: An Algebraic
Approach to Multidimensional Minimax Location Problems with Chebyshev Distance
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Authors: Nikolai
Krivulin
Abstract: Minimax single facility location problems in multidimensional space
with Chebyshev distance are examined within the framework of idempotent
algebra. The aim of the study is twofold: first, to give a new algebraic
solution to the location problems, and second, to extend the area of
application of idempotent algebra. A new algebraic approach based on
investigation of extremal properties of eigenvalues for irreducible matrices
is developed to solve multidimensional problems that involve minimization of
functionals defined on idempotent vector semimodules. Furthermore, an
unconstrained location problem is considered and then represented in the
idempotent algebra settings. A new algebraic solution is given that reduces
the problem to evaluation of the eigenvalue and eigenvectors of an appropriate
matrix. Finally, the solution is extended to solve a constrained location
problem.
Keywords: Single facility
location problem, Chebyshev distance, Idempotent semifield, Eigenvalue,
Eigenvector
Title of the Paper: Turing Instability
for a Two Dimensional SemiDiscrete Oregonator Model
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Authors: Li Xu, Guang
Zhang, JunFeng Ren
Abstract: In this paper, a semidiscrete (time continuous but twodimensional
spatially discrete) Oregonator model has been given in the microscopic domain,
and Turing instability theory analysis is discussed in detail. Turing
instability conditions have been deduced by combining linearization method and
inner product technique. Various patterns such as spiral wave, target wave,
stripes and spotlike patterns are selectively obtained from numerical
simulations in the Turing instability region. In particular, the effect of
both system parameters and initial value on pattern formation is numerically
proved.
Keywords: Semidiscrete
Oregonator model; Turing instability; pattern formation; initial value;
linearization method; inner product
Title of the Paper: Effect of Variable
Viscosity on Convective Heat and Mass Transfer by Natural Convection from
Horizontal Surface in Porous Medium
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Authors: M. B. K.
Moorthy, K. Senthilvadivu
Abstract: The aim of this paper is to investigate the effect of variable
viscosity on free convective heat and mass transfer from a horizontal plate
embedded in a saturated porous medium. The governing equations of continuity,
momentum, energy and concentration are transformed into non linear ordinary
differential equations using similarity transformations and then solved by
using Runge – Kutta – Gill method along with shooting technique. Governing
parameters for the problem under study are the variable viscosity (θc), the
buoyancy ratio (N) and the Lewis number (Le). The velocity, temperature and
concentration distributions are presented and discussed. The Nusselt and
Sherwood number is also derived. The numerical values of local Nusselt and
local Sherwood numbers have also been computed for a wide range of governing
parameters θc, N and Le. The viscous and thermal boundary layer thicknesses
are discussed.
Keywords: Free convection,
Heat transfer, Mass transfer, Variable viscosity, Porous medium
Issue 7, Volume 10,
July 2011
Title of the Paper: The Effects of the
Change of Bond Insurance Premium and Capital Regulatory Ratio on Loan and
Deposit Rates: An OptionPricing Model
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Authors: ShihHeng Pao,
JyhHorng Lin, ShuHui Chang
Abstract: We propose an optionbased model that examines the relationships
among municipal bonds with prepackaged insurance, capital insurance, and
optimal bank interest margins. If the elasticity effect is positive
(negative), then an increase in the bond insurance premium will increase the
bank’s optimal loan rate (optimal deposit rate). If the elasticity effect is
negative (positive), then an increase in the capitaltodeposit ratio will
increase (decrease) the bank’s optimal loan rate. But an increase in the
capitalto deposit ratio increase the bank’s optimal deposit rate under the
positive elasticity effect.
Keywords: Municipal bond,
Capitaltodeposit ratio, Interest margins, Bond insurance, Elasticity, option
Title of the Paper: The Asymptotic
Behavior of a Doubly Nonlinear Parabolic Equation with a Absorption Term
Related to the Gradient
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Authors:
Huashui Zhan
Title of the Paper: GronwallBellman
Type Inequalities On Time Scales And Their Applications
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Authors: Qinghua Feng,
Fanwei Meng
Abstract: In this work, we investigate some new GronwallBellman type dynamic
inequalities on time scales in two independent variables, which provide a
handy tool in deriving explicit bounds on unknown functions in certain dynamic
equations on time scales. The established results generalize the main results
on integral inequalities for continuous functions in [1] and their
corresponding discrete analysis in [2].
Keywords: Dynamic
inequality; GronwallBellman inequality; Time scales; Dynamic equation;
Bounded
Issue 8, Volume 10,
August 2011
Title of the Paper: Traveling Wave
Solutions for Some Nonlinear Evolution Equations by the First Integral Method
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Authors: Bin Zheng
Abstract: In this paper, based on the known first integral method, we try to
seek the traveling wave solutions of several nonlinear evolution equations. As
a result, some exact travelig wave solutions and solitary solutions for
WhithamBroerKaup (WBK) equations, Gardner equation, BoussinesqBurgers
equations, nonlinear schrodinger equation and mKDV equation are established
successfully.
Keywords: First integral
method; Traveling wave solution; WBK equations, Gardner equation;
BoussinesqBurgers equations; nonlinear schrodinger equation; mKDV equation;
Exact solution; Solitary solution
Title of the Paper: Relatively Relaxed
Proximal Point Algorithms for Generalized Maximal Monotone Mappings and
DouglasRachford Splitting Methods
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Authors: Ram Verma
Abstract: The theory of maximal setvalued monotone mappings provide a
powerful framework to the study of convex programming and variational
inequalities. Based on the notion of relatively maximal relaxed monotonicity,
the approximation solvability of a general class of inclusion problems is
discussed, while generalizing most of investigations on weak convergence using
the proximal point algorithm in a real Hilbert space setting. A wellknown
method of multipliers of constrained convex programming is a special case of
the proximal point algorithm. The obtained results can be used to generalize
the Yosida approximation, which, in turn, can be applied to generalize
firstorder evolution equations to the case of evolution inclusions.
Furthermore, we observe that the DouglasRachford splitting method for finding
the zero of the sum of two monotone operators is a specialization of the
proximal point algorithm as well. This allows a further generalization and
unification of a wide range of convex programming algorithms.
Keywords: Variational
inclusion problems; Relatively maximal relaxed monotone mapping; Generalized
resolvent
Title of the Paper: The Modified (G'/G)
Expansion Method and its Applications to Construct Exact Solutions for
Nonlinear PDEs
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Authors: Elsayed M. E.
Zayed, Khaled A. Gepreel
Abstract: In the present article, we construct the traveling wave solutions
involving parameters of some nonlinear PDEs; namely the nonlinear Klein 
Gordon equations, the nonlinear reaction diffusion equation, the nonlinear
modified Burgers equation and the nonlinear Eckhaus equation by using the
modified (G'/G) expansion method, where G satisfies a second order linear
ordinary differential equation. When these parameters are taken special
values, the solitary waves are derived from the traveling waves. The traveling
waves solutions are expressed by hyperbolic, trigonometric and the rational
functions.
Keywords: Expansion
method, nonlinear PDEs, exact solution
Title of the Paper: A Stability Result
for a Generalized TrigonometricQuadratic Functional Equation with one
Unbounded Function
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Authors: Charinthip
Hengkrawit, Vichian Laohakosol, Janyarak Tongsomporn
Abstract: A generalized trigonometricquadratic functional equation of the
form over the domain of an abelian group and the range of the complex field is
considered. Its stability is established based on the assumption that the
function K is unbounded. Subject to certain natural conditions, explicit
shapes of the functions H and K are determined. Several existing related
results are derived as direct consequences.
Keywords: Quadratic
functional equation, trigonometric functional equation, stability,
unboundedness, abelian group, additive function
Issue 9, Volume 10,
September 2011
Title of the Paper: The Consistency
Analysis of Coefficient Regularized Classification with Convex Loss
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Authors: Sheng Baohuai,
Xiang Daohong
Abstract: It is known that the learning rates are the quantitative description
of the consistency of a learning al gorithm. In the present paper, we provide
the learning rates for the coefficient regularized classification learning
algorithm with a K?functional whose explicit rates are estimated when the loss
functions are least square loss and the hinge loss.
Keywords: Coefficient
regularized classification, machine learning, convex loss, differentiable
loss,Kfunctional, learning rates
Title of the Paper: Insitu Combustion
Simulation for Heavy Oil Reservoirs
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Authors: Rasaq O.
Olayiwola, Reuben O. Ayeni
Abstract: In this paper we study the continuity, momentum and coupled
nonlinear energy and species convectiondiffusion equations describing the
insitu combustion process in porous media. We assume the fuel depends on the
space variablex. We examine the properties of solution under certain
conditions. Using large activation energy asymptotics and shooting method we
provide a numerical solution of the problem and obtained temperature and
concentration profiles.
Keywords: Insitu,
combustion, porous media, simulation, heavy oil, reservoirs
Title of the Paper: Stability Analysis
of Periodic Solutions for Stochastic ReactionDiffusion HighOrder
CohenGrossbergType Bam Neural Networks with Delays
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Authors: Yunquan Ke,
Chunfang Miao
Abstract: In this paper, the mean square exponential stability of the periodic
solution for stochastic reaction diffusion highorder CohenGrossbergType
BAM neural networks with time delays is investigated. By construct ing
suitable Lyapunov function, applying It?o formula and Poincar/e mapping, we
give some sufficient conditions to guarantee the mean square exponential
stability of the periodic solution. An illustrative example are also given in
the end to show the effectiveness of our results.
Keywords: Stochastic
reactiondiffusion CohenGrossbergtype BAM neural networks; Ito formula;
Poincare mapping; periodic solution; mean square exponential stability
Title of the Paper: Robust Portfolio
Selection Problem for an Insurer with Exponential Utility Preference
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Authors: Hui Zhao, Ximin
Rong, Jiling Cao
Abstract: In this paper, we consider the robust portfolio selection problem
for an insurer in the sense of maximiz ing the exponential utility of his
wealth. This special robust investment problem, where underwriting results and
a riskfree asset are considered, differs from ordinary robust portfolio
selection problems. The insurer has the option of investing in a riskfree
asset and multiple risky assets whose returns are described by the factor
model. The rate of underwriting return is also assumed to be correlated with
returns of risky assets. When the parameters are perturbed in a joint
uncertainty set, the robust investment problem for an insurer is established
and this problem is reformulated and solved as a cone programming problem.
Finally, some computational results are given for raw market data.
Keywords: Robust
optimization, Investment for insurers, Joint uncertainty set, Underwriting
result, Cone programming, Factor model
Issue 10, Volume
10, October 2011
Title of the Paper: Global Exponential
Stability of HighOrder BAM Neural Networks with Stype Distributed Delays and
Reaction Diffusion Terms
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Authors: Chengrong Ma,
Fengyan Zhou
Abstract: In this paper, by constructing suitable Lyapunov functional, using
differential mean value theorem and homeomorphism, we analyze the global
exponential stability of highorder bidirectional associative memory (BAM)
neural networks with reactiondiffusion terms and Stype distributed delays.
Some sufficient theorems have been derived under different conditions to
guarantee the global exponential stability of the networks. Moreover, two
numerical examples are presented to illustrate the feasibility and
effectiveness of the results.
Keywords: Highorder BAM
Neural Networks; reaction diffusion terms; Stype distributed delays;
Lyapunov functional; exponential stability
Title of the Paper: Weighted Generalized
Kernel Discriminant Analysis Using Fuzzy Memberships
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Authors: Jing Yang, Liya
Fan
Abstract: Linear discriminant analysis (LDA) is a classical approach for
dimensionality reduction. However, LDA has limitations in that one of the
scatter matrices is required to be nonsingular and the nonlinearly clustered
struc ture is not easily captured. In order to overcome these problems, in
this paper, we present several generalizations of kernel fuzzy discriminant
analysis (KFDA) which include KFDA based on generalized singular value
decomposition (KFDA/GSVD), pseudoinverse KFDA (PIKFDA) and range space KFDA
(RSKFDA). These KFDAbased algorithms adopts kernel methods to accommodate
nonlinearly separable cases. In order to remedy the problem that KFDAbased
algorithms fail to consider that different contribution of each pair of class
to the discrimination, weighted schemes are incorporated into KFDA extensions
in this paper and called them weighted generalized KF DA algorithms.
Experiments on three realworld data sets are performed to test and evaluate
the effectiveness of the proposed algorithms and the effect of weights on
classification accuracy. The results show that the effect of weighted schemes
is very significantly.
Keywords: Kernel fuzzy
discriminant analysis; fuzzy membership; undersampled problem; weighting
function; classification accuracy
Title of the Paper: Kernelbased
Weighted Discriminant Analysis with QR Decomposition and Its Application to
Face Recognition
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Authors: Jianqiang Gao,
Liya Fan
Abstract: Kernel discriminant analysis (KDA) is a widely used approach in
feature extraction problems. However, for highdimensional multiclass tasks,
such as faces recognition, traditional KDA algorithms have a limitation that
the Fisher criterion is nonoptimal with respect to classification rate.
Moreover, they suffer from the small sample size problem. This paper presents
two variants of KDA called based on QR decomposition weighted kernel
discriminant analysis (WKDA/QR), which can effectively deal with the above two
problems, and based on singular value decomposition weighted kernel
discriminant analysis (WKDA/SVD). Since the QR decomposition on a small size
matrix is adopted, the superiority of the proposed method is its computational
efficiency and can avoid the singularity problem. In addition, we compare
WKDA/QR with WKDA/SVD under the parameters of weighted function and kernel
function. Experimental results on face recognition show that the WKDA/QR and
WKDA/SVD are more effective than KDA, and WKDA/QR is more effective and
feasible than WKDA/SVD.
Keywords: QR
decomposition, Kernel discriminant analysis (KDA), Feature extraction, Face
recognition, small sample size (SSS)
Title of the Paper: Research on Delayed
Complexity Based on Nonlinear Price Game of Insurance Market
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Authors: Junling Zhang,
Junhai Ma
Abstract: Based on the study of scholars, supposing that one of the two
competitors in the market makes decision only with bounded rationality without
delay, and the other competitor makes the delayed decision with one period and
two periods, we established the dynamic price game models respectively. In
this paper we mainly analyzed the stable points and their stabilities of the
dynamic system with twoperiod delayed decision, and made computer simulations
for the system stability under different decision rules and the complexity
such as the bifurcations, chaos and so on. The numerical simulation results
showed that, the delayed decision can not change the system’s Nash equilibrium
point, however it can improve the system’s stability; the changes of delayed
period and weights of delay variables will make the system’s stability area
change correspondingly; when the company make decision with delay, they should
consider the introducing time. Because the proper delayed periods and weights
of variables will obviously improve his competition advantages.
Keywords: Duopoly, delayed
decision, bifurcation, chaotic, nonlinear price game, insurance market
Issue 11, Volume
10, November 2011
Title of the Paper: Applied Research on
the Coexistence Relationship between Tianjin Port and Inland Transportation
System based on Population Ecology Model
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Authors: Jun Wang,
Junhai Ma
Abstract: First, this article takes container throughput of Tianjin Port as an
example to estimate the future port scale by using genetic algorithms. Then
this article applies BP neural network to compare the advantages and
disadvantages of Tianjin Port and its competitors by analyzing the data of
listed port companies. Finally, this article does some research on the
coexistence relationship between port and transportation. The results show
that Tianjin Port’s scale is beyond the inflection point of Growth curve, its
speed of development will slow down. High administration cost and the lag of
inland transportation construction are two major factors which constrain
Tianjin Port’s development. After coexistence relationship analysis we find
that the develop speeds of port and inland transportation should reach a
reasonable proportion to remain symbiotic relationships.
Keywords: Port, population
ecology model, genetic algorithms, BP neural network, inherent complexities,
mathmatics
Title of the Paper: Rich Dynamical
Behaviors of a PredatorPrey System with State Feedback Control and a General
Functional Responses
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Authors: Yongzhen Pei,
Haiyong Wang
Abstract: In this paper, we study dynamics of a logistical predatorprey
system with state feedback control and a general functional responses. By
using the Poincare map, some conditions for the existence and stability of
semitrivial solution and positive periodic solution are obtained. Numerical
results are carried out to illustrate the feasibility of our main results, and
it is shown that a chaotic solution is generated via a cascade of
perioddoubling bifurcations, which implies that the presence of pulses makes
the dynamic behavior more complex.
Keywords: Preypredator
system; State feedback control; Periodic solution; Extinction; Bifurcation
Title of the Paper: Dynamic Behavior in
a HIV Infection Model for the Delayed Immune Response
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Authors: Yongzhao Wang,
Dongwei Huang, Shuangde Zhang, Hongjie Liu
Abstract: Considering full Logistic proliferation of CD4+ Tcells and retarded
immune response, we analyze a HIV model in this paper. Global asymptotic
stability of the infectionfree equilibrium and immuneabsent equilibrium is
investigated, and some conditions for Hopf bifurcation around infected
equilibrium to occur are also obtained by using the time delayed as a
bifurcation parameter. Numerical simulating works are presented to illustrate
the main results, and we can observe the effects of the proliferation rate of
CD4+ Tcells for the dynamics of system. This result can be used to explain
the complexity of the immune state of AIDS.
Keywords: Global
stability; Delayed immune response; Logistic proliferation
Title of the Paper: About the Weak
Efficiencies in Vector Optimization
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Authors: Cristina
Stamate
Abstract: We present the principal properties of the weak efficient points
given in the literature. We study a vector optimization problems for
multifunctions, defined with infimal and supremal efficient points in locally
convex spaces ordered by convex, pointed closed cones with nonempty interior.
We introduce and study the solutions for these problems using the algebraic
and topological results for the efficient points. Also, we’ll present the
links between our problems and 2 special problems, the scalar and the
approximate problems as well as some saddle points theorems and duality
results using a suitable Lagrangian adapted for the INFSUP problem, a
generalization of the MINMAX problem.
Keywords: Order vector
spaces, convex cones, efficient points
Issue 12, Volume
10, December 2011
Title of the Paper: On the Sophie
Germain Prime Conjecture
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Authors: Fengsui Liu
Abstract: By extending the operations +,X on natural numbers to the
operations on finite sets of natural numbers, we founded a new formal system
of a second order arithmetic <P(N),N,+,X,0,1,є>. We
designed a recursive sieve method on residue classes and obtained recursive
formulas of a set sequence and its subset sequence of Sophie Germain primes,
both the set sequences converge to the set of all Sophie Germain primes.
Considering the numbers of elements of this two set sequences, one is strictly
monotonically increasing and the other is monotonically increasing, the order
topological limits of two cardinal sequences exist and these two limits are
equal, we concluded that the counting function of Sophie Germain primes
approaches infinity. The cardinal function is sequentially continuous with
respect to the order topology, we proved that the cardinality of the set of
all Sophie Germain primes is ℵ0 using modular arithmetical and analytic
techniques on the set sequences. Further we extended this result to attack on
Twin primes, Cunningham chains and so on.
Keywords: Second order
arithmetic,Recursive sieve method,Order topology,Limit of set sequences,Sophie
Germain primes, Twin primes, Cunningham chain, RossLittwood paradox
Title of the Paper: Generalized Integral
Inequalities for Discontinuous Functions with One or Two Independent Variables
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Authors: Qinghua Feng,
Fanwei Meng
Abstract: In this paper, some new integral inequalities for discontinuous
functions with one or two independent variables are established, which provide
new bounds for unknown functions in certain integral equations. The
established inequalities generalize the main results in [14,15,16,17].
Keywords: Integral
inequality, Discontinuous function, Integral equation, Bounded, Qualitative
analysis
Title of the Paper: Fuzzy Time Series
Model Incorporating Predictor Variables and Interval Partition
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Authors: HsienLun Wong,
ChiChen Wang
Abstract: Prediction is a critical component in decisionmaking process for
business management. Fuzzy Markov model is a common approach for dealing with
the prediction of time series. However, not many studies devoted their
attention to the effect of the parameters on model fitting for fuzzy Markov
model. In the paper, we examine the prediction ability for fuzzy Markov model,
based on the data of Taiwan’s exports and foreign exchange rate. The empirical
results indicate that fuzzy Markov model performs better for longer period
forecasting; moreover, neither increment information nor increasing window
basis would improve the performance for fuzzy Markov model. An advantage of
the paper provides a beneficial knowledge when using Markov model for
prediction.
Keywords: Fuzzy time
series, Fuzzy Markov model, High order fuzzy relationship, Increment
information, Interval partition, Taiwan exports
Title of the Paper: Population Dynamics:
A Geometrical Approach of Some Epidemic Models
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Authors: M. E. Kahil
Abstract: Recently, the behavior of different epidemic models and their
relation both to different types of ge ometries and to some biological models
has been revisited. Path equations representing the behavior of epidemic
models and their corresponding deviation vectors are examined. A comparison
between paths and their deviation vectors in Riemannian and Finslerian
Geometries is presented.
Keywords: Epidemic model,
Path equation, Geometrical method
Title of the Paper: Ergodic Theorems
with Respect to Lebesgue
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Authors: Eleonora
Catsigeras
Abstract: We study, from the ergodic viewpoint, the asymptotic dynamics in the
future of a full Lebesgue set of initial states. The dynamical systems under
research are deterministic and evolving with discrete time n ∈ N by the
forward iterations of any continuous map f : M 7→ M acting on a
finitedimensional, compact and Riemannian manifold M. First, we revisit the
classic definition of physical or SRB probability measures, and its
generalized notion of weak physical probabilities. Then, inspired in the
statistical meaning of the ergodic attractors defined by Pugh and Schub, which
support ergodic physical measures, we define the more general concept of
ergodiclike attractor. We prove that any such generalized attractor is the
support of weak physical probabilities and conversely. Then, we revisit the
proof of existence of weak physical probabilities and conclude that any
continuous dynamics exhibits at least one ergodiclike attractor.
Keywords: Ergodic theory,
physical measures, ergodic attractors, topological dynamics, theoretical
measure dynamics
Title of the Paper: A General Iterative
Algorithm for Equilibrium Problems and Strict PseudoContractions in Hilbert
Spaces
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Authors: Ming Tian, Lei
Liu
Abstract: In this paper an iterative scheme is presented for finding a common
element of the set of solutions of the variational inequality, fixed points of
strict pseudocontraction and solutions of equilibrium problem in Hilbert
spaces. Under suitable conditions, it is proved that implicit and explicit
schemes are of strong convergence properties. Obtained results improve and
extend the existed results.
Keywords: Nonexpansive
mapping, Fixed point, Equilibrium problem, Strict pseudocontraction,
Variational inequality, Iterative algorithm
Title of the Paper: Exponential
p−Stability of Impulsive Stochastic Fuzzy Cellular Neural Networks with Mixed
Delays
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Authors: Qianhong Zhang,
Lihui Yang
Abstract: This paper deals with an impulsive stochastic fuzzy cellular neural
networks with both timevarying and infinite distributed delays. Based on
Mmatrix theory and stochastic analysis technique, a sufficient condition is
obtained to ensure the existence, uniqueness, and global exponential
p−stability of the equilibrium point for the addressed impulsive stochastic
fuzzy cellular neural network with mixed delays. Moreover a numerical example
is given to illustrate the effectiveness of stability results.
Keywords: Stochastic fuzzy
cellular neural networks, Brownian motion, Global exponential p−stability,
Mixed delays, Impulse
Title of the Paper: Positive Solutions
for Singular ThirdOrder Nonhomogeneous Boundary Value Problems with Nonlocal
Boundary Conditions
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Authors: Ping Kang
Abstract: Under various weaker conditions, we establish various results on the
existence and nonexistence of positive solutions for singular thirdorder
nonhomogeneous boundary value problems with nonlocal boundary conditions. The
arguments are based upon the fixed point theorem of cone expansion and
compression. Finally, we give two examples to demonstrate our results.
Keywords: Positive
solutions, Fixed points, Boundary value problems, Nonhomogeneous, Ordinary
differential equations
