2011
37
0
0
337
A PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS
2
2
A random walk on a lattice is one of the most fundamental models in probability theory.
When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a
random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT),
and the large deviation principle (LDP) are not fully understood for RWRE. Some known results in the case of LLN and LDP are reviewed.
These results are closely related to the homogenization phenomenon
for HamiltonJacobiBellman equations when both space and time are discretized.
3

5
20


F.
REZAKHANLOU
United States of America
rezakhan@math.berkeley.edu
Random walk in a random environment
law of large numbers
large deviation principle
homogenization
COMPOSITE INTERPOLATION METHOD AND THE
CORRESPONDING DIFFERENTIATION MATRIX
2
2
Properties of the hybrid of blockpulse functions and Lagrange
polynomials based on the LegendreGausstype points are
investigated and utilized to define the composite interpolation
operator as an extension of the wellknown Legendre interpolation
operator. The uniqueness and interpolating properties are
discussed and the corresponding differentiation matrix is also
introduced. The applicability and effectiveness of the method are
illustrated by two numerical experiments.
3

21
34


H.
MARZBAN
Iran
hmarzban@cc.iut.ac.ir


H.
TABRIZIDOOZ
Iran
htabrizidooz@kashanu.ac.ir
Blockpulse functions
Lagrange polynomials
Hybrid functions
Gauss pseudospectral method
differentiation matrices
A SYSTEM OF GENERALIZED VARIATIONAL
INCLUSIONS INVOLVING GetaMONOTONE MAPPINGS
2
2
We introduce a new concept of general
$G$$eta$monotone operator generalizing the general
$(H,eta)$monotone operator cite{arvar2, arvar1}, general
$H$ monotone operator cite{xiahuang} in Banach spaces, and also
generalizing $G$$eta$monotone operator cite{zhang}, $(A,
eta)$monotone operator cite{verma2}, $A$monotone operator
cite{verma0}, $(H, eta)$monotone operator cite{fanghuang},
$H$monotone operator cite{fanghuang1, {fanghuangthompson}},
maximal $eta$monotone operator cite{fanghuang0} and classical
maximal monotone operators cite{zeid} in Hilbert spaces. We provide
some examples and study some properties of general
$G$$eta$monotone operators. Moreover, the generalized proximal
mapping associated with this type of monotone operator is defined
and its Lipschitz continuity is established. Finally, using
Lipschitz continuity of generalized proximal mapping under some
conditions a new system of variational inclusions is solved.
3

35
47


M.
ROOHI
Iran
m.roohi@umz.ac.ir


M.
ALIMOHAMMADY
Iran
amohsen@umz.ac.ir
Variational inclusions
proximal mapping
Monotone Operator
EXACT SOLUTIONS FOR FLOW OF A SISKO FLUID
IN PIPE
2
2
By means of He's homotopy perturbation method
(HPM) an approximate solution of velocity eld is derived for the
ow in straight pipes of nonNewtonian
uid obeying the Sisko
model. The nonlinear equations governing the
ow in pipe are for
mulated and analyzed, using homotopy perturbation method due
to He. Furthermore, the obtained solutions for velocity eld is
graphically sketched and compared with Newtonian
uid to show
the accuracy of this work. Volume
ux, average velocity and pres
sure gradient are also calculated. Results reveal that the proposed
method is very eective and simple for solving nonlinear equations
like nonNewtonian
uids.
3

49
60


N.
MOALLEMI
Iran
nima.moallemi@yahoo.com


I.
SHAFIEENEJAD
Iran
shafieeiman@yahoo.com


A.
NOVINZADEH
Iran
novinzadeh@kntu.ac.ir
NonNewtonian uid
nonlinear equation
Sisko model
homotopy perturbation method (HPM)
APPROXIMATION OF STOCHASTIC PARABOLIC
DIFFERENTIAL EQUATIONS WITH TWO DIFFERENT
FINITE DIFFERENCE SCHEMES
2
2
We focus on the use of two stable and accurate explicit
finite difference schemes in order to approximate the solution of
stochastic partial differential equations of It¨o type, in particular,
parabolic equations. The main properties of these deterministic
difference methods, i.e., convergence, consistency, and stability, are
separately developed for the stochastic cases.
3

61
83


A.
SOHEILI
Iran
soheili@um.ac.ir


M.
NIASAR
Iran
bishei@mail.usb.ac.ir


M.
AREZOOMANDAN
Iran
arezoomandan@ mail.usb.ac.ir
Stochastic partial differential equations
finite difference methods
Saul’yev methods
convergence
Stability
Wiener process
PROJECTED DYNAMICAL SYSTEMS AND
OPTIMIZATION PROBLEMS
2
2
We establish a relationship between general constrained
pseudoconvex optimization problems and globally projected dynamical
systems. A corresponding novel neural network model,
which is globally convergent and stable in the sense of Lyapunov,
is proposed. Both theoretical and numerical approaches are considered.
Numerical simulations for three constrained nonlinear optimization
problems are given to show that the numerical behaviors
are in good agreement with the theoretical results.
3

85
100


A.
MALEK
Iran
mala@modares.ac.ir


S.
EZAZIPOUR
Iran
ezazipour@modares.ac.ir


N.
HOSSEINIPOURMAHANI
Iran
n.mahani@modares.ac.ir
Dynamical systems
optimization problems
neural networks
variational inequalities
globally convergence
LINEAR ESTIMATE OF THE NUMBER OF ZEROS OF
ABELIAN INTEGRALS FOR A KIND OF QUINTIC
HAMILTONIANS
2
2
We consider the number of zeros of the integral $I(h) = oint_{Gamma_h} omega$ of real polynomial form $omega$ of degree not greater than $n$ over a family of vanishing cycles on curves $Gamma_h:$ $y^2+3x^2x^6=h$, where the integral is considered as a function of the parameter $h$. We prove that the number of zeros of $I(h)$, for $0 < h < 2$, is bounded above by $2[frac{n1}{2}]+1$.
3

101
116


N.
NYAMORADI
Iran
nyamoradi@math.iut.ac.ir


H.
ZANGENEH
Iran
hamidz@cc.iut.ac.ir
Zeros of Abelian integrals
Hilbert's 16th problem
limit cycles
PAIRED ANISOTROPIC DISTRIBUTION FOR IMAGE
SELECTIVE SMOOTHING
2
2
In this paper, we present a novel approach for image selective smoothing by the evolution of two paired nonlinear
partial differential equations. The distribution coefficient in denoising equation controls the speed of distribution, and is
determined by the edgestrength function. In the previous works, the edgestrength function depends on isotropic
smoothing of the image, which results in failing to preserve corners and junctions, and may also result in failing to resolve
small features that are closely grouped together. The proposed approach obtains the edgestrength function by solving a
nonlinear distribution equation governed by the norm of the image gradient. This edgestrength function is then introduced
into a wellstudied anisotropic distribution model to yield a regularized distribution coefficient for image smoothing. An explicit
numerical scheme is employed to efficiently solve these two paired equations. Compared with the existing methods, the
proposed approach has the advantages of more detailed preservation and implementational simplicity. Experimental results
on the synthesis and real images confirm the validity of the proposed approach.
3

117
131


A.
MADANKAN
Indonesia
amadankan@gmail.com
Computer vision
anisotropic distribution
Image smoothing
partial differential equation
AN INTRODUCTION TO HIGHER CLUSTER
CATEGORIES
2
2
In this survey, we give an overview over some aspects
of the set of tilting objects in an $m$cluster category, with focus
on those properties which are valid for all $m geq 1$. We focus on the
following three combinatorial aspects: modeling the set of tilting
objects using arcs in certain polygons, the generalized assicahedra
of Fomin and Reading, and colored quiver mutation.
3

137
157


A.
BUAN
Norway
aslakb@math.ntnu.no
Cluster categories
tilting
triangulated categories
ALGEBRAS WITH CYCLEFINITE STRONGLY SIMPLY
CONNECTED GALOIS COVERINGS
2
2
Let $A$ be a nite dimensional $k$algebra and $R$ be a
locally bounded category such that $R rightarrow R/G = A$ is a Galois covering
dened by the action of a torsionfree group of automorphisms
of $R$. Following [30], we provide criteria on the convex subcategories
of a strongly simply connected category R in order to be a cycle
nite category and describe the module category of $A$. We provide
criteria for $A$ to be of polynomial growth
3

159
186


J.
DE LA PENA
Mexico
jap@matem.unam.mx
Module category of an algebra
infinite radical
Galois coverings
cycles of modules
CLUSTER ALGEBRAS AND CLUSTER CATEGORIES
2
2
These are notes from introductory survey lectures given
at the Institute for Studies in Theoretical Physics and Mathematics
(IPM), Teheran, in 2008 and 2010. We present the definition and
the fundamental properties of FominZelevinsky’s cluster algebras.
Then, we introduce quiver representations and show how they can
be used to construct cluster variables, which are the canonical generators
of cluster algebras. From quiver representations, we proceed
to the cluster category, which yields a complete categorification of
the cluster algebra and its combinatorial underpinnings.
3

187
234


B.
KELLER
France
keller@math.jussieu.fr
Cluster algebra
quiver representation
cluster category
triangulated category
Rings of Singularities
2
2
This paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``Advanced School and Conference on homological and geometrical methods in representation theory'' at the International Centre for Theoretical Physics (ICTP), Miramare  Trieste, Italy, 1129 January 2010.
We show how to associate to a triple of positive integers $(p_1,p_2,p_3)$ a twodimensional isolated graded singularity by an elementary procedure that works over any field $k$ (with no assumptions on characteristic, algebraic closedness or cardinality). This assignment starts from the triangle singularity $x_1^{p_1}+x_2^{p_2}+x_3^{p_3}$ and when applied to the Platonic (or Dynkin) triples, it produces the famous list of ADEsingularities. As another particular case, the procedure yields Arnold's famous strange duality list consisting of the 14 exceptional unimodular singularities (and an infinite sequence of further singularities not treated here in detail).
As we are going to show, weighted projective lines and various triangulated categories attached to them play a key role in the study of the triangle and associated singularities.
3

235
271


H.
LENZING
Germany
helmut@math.unipaderborn.de
Weighted projective line
(extended) canonical algebra
simple singularity
Arnold's strange duality
stable category of vector bundles
RIGID DUALIZING COMPLEXES
2
2
Let $X$ be a sufficiently nice scheme.
We survey some recent progress on dualizing complexes. It turns
out that a complex in $kinj X$ is dualizing if and only if
tensor product with it induces an equivalence of categories
from Murfet's new
category $kmpr X$ to the category
$kinj X$. In these terms, it
becomes interesting to wonder how to glue such equivalences.
3

273
290


A.
NEEMAN
Australia
Amnon.Neeman@anu.edu.au
Dualizing complex
Grothendieck duality
ON THE USE OF KULSHAMMER TYPE INVARIANTS
IN REPRESENTATION THEORY
2
2
Since 2005 a new powerful invariant of an algebra has
emerged using the earlier work of Horvath, Hethelyi, Kulshammer
and Murray. The authors studied Morita invariance of a sequence
of ideals of the center of a nite dimensional algebra over a eld
of nite characteristic. It was shown that the sequence of ideals is
actually a derived invariant, and most recently a slightly modied
version of it is an invariant under stable equivalences of Morita
type. The invariant was used in various contexts to distinguish
derived and stable equivalence classes of pairs of algebras in very
subtle situations. Generalisations to non symmetric algebras and to
higher Hochschild (co)homology were given. This article surveys
the results and gives some of the constructions in more details.
3

291
341


A.
ZIMMERMANN
France
alexander.zimmermann@upicardie.fr
Derived equivalences
stable equivalences
tame algebras
periodic algebras