bluuebunny/crossref_metadata_2025 huggingface dataset:
New formulas concerning Laplace transforms of quadratic forms for general Gaussian sequences
Authors: Kleptsyna M. L. , Le Breton A. , Viot M.
Published: March 2007

Various methods to derive new formulas for the Laplace transforms of some
quadratic forms of Gaussian sequences are discussed. In the general setting, an
approach based on the resolution of an appropriate auxiliary filtering problem is
developed; it leads to a formula in terms of the solutions of Volterra‐type
recursions describing characteristics of the corresponding optimal filter. In the
case of Gauss‐Markov sequences, where the previous equations reduce to
ordinary forward recursive equations, an alternative approach prices another
formula; it involves the solution of a backward recursive equation. Comparing
the different formulas for the Laplace transforms, various relationships between
the corresponding entries are identified. In particular, relationships between the
solutions of matched forward and backward Riccati equations are thus proved
probabilistically; they are proved again directly. In various specific cases, a
further analysis of the concerned equations lead to completely explicit formulas
for the Laplace transform.
Analysis of statistical equilibrium models of geostrophicturbulence
Authors: Ellis Richard S. , Turkington Bruce , Haven Kyle
Published: March 2007

Statistical equilibrium lattice models of coherent structures in geostrophic turbulence,
formulated by discretizing the governing Hamiltonian continuum
dynamics, are analyzed. The first set of results concern large deviation principles
(LDP′s) for a spatially coarse‐grained process with respect to either the canonical
and/or the microcanonical formulation of the model. These principles are derived
from a basic LDP for the coarse‐grained process with respect to product measure,
which in turn depends on Cramér′s Theorem. The rate functions for the LDP′s
give rise to variational principles that determine the equilibrium solutions of the
Hamiltonian equations. The second set of results addresses the equivalence or
nonequivalence of the microcanonical and canonical ensembles. In particular, necessary
and sufficient conditions for a correspondence between microcanonical
equilibria and canonical equilibria are established in terms of the concavity of the
microcanonical entropy. A complete characterization of equivalence of
ensembles is deduced by elementary methods of convex analysis. The
mathematical results proved in this paper complement the physical reasoning and
numerical computations given in a companion paper, where it is argued that the
statistical equilibrium model defined by a prior distribution on potential vorticity
fluctuations and microcanonical conditions on total energy and circulation is
natural from the perspective of geophysical applications.
A Haussmann‐Clark‐Ocone formula for functionals of diffusionprocesses with Lipschitz coefficients
Authors: Bahlali Khaled , Mezerdi Brahim , Ouknine Youssef
Published: March 2007

We establish a martingale representation formula for functionals of diffusion
processes with Lipschitz coefficients, as stochastic integrals with respect to the
Brownian motion.
Complete convergence for negatively dependent random variables
Authors: D. M. Amini , Bozorgnia A.
Published: March 2007

In this paper, we study the complete convergence for the means and via. exponential bounds, where α > 0 and {Xn, n ≥ 1} is a sequence of negatively dependent random variables and {Xnk, 1 ≤ k ≤ n, n ≥ 1} is an array of rowwise pairwise negatively dependent random variables.
Tree‐indexed processes: a high level crossing analysis
Authors: Kelbert Mark , Suhov Yuri
Published: March 2007

Consider a branching diffusion process on R1 starting at the origin. Take a high level u > 0 and count the number R(u, n) of branches reaching u by generation n. Let Fk,n(u) be the probability P(R(u, n) < k), k = 1, 2, …. We study the limit limn→∞Fk,n(u) = Fk(u). More precisely, a natural equation for the probabilities Fk(u) is introduced and the structure of the set of solutions is analysed. We interpret Fk(u) as a potential ruin probability in the situation of a multiple choice of a decision taken at vertices of a ‘logical tree’. It is shown that, unlike the standard risk theory, the above equation has a manifold of solutions. Also an analogue of Lundberg′s bound for branching diffusion is derived.
Functional integro‐differential stochastic evolution equations inHilbert space
Authors: Keck David N. , McKibben Mark A.
Published: March 2007

We investigate a class of abstract functional integro‐differential stochastic evolution equations in a real separable Hilbert space. Global existence results concerning mild and periodic solutions are formulated under various growth and compactness conditions. Also, related convergence results are established and an example arising in the mathematical modeling of heat conduction is discussed to illustrate the abstract theory.
Random fixed point theory in spaces with two metrics
Authors: O′regan Donal , Shahzad Naseer , Agarwal Ravi P.
Published: March 2007

We present new random fixed point theorems in spaces with two metrics. Our results extend recent results of Tan and Yuan [10] and Xu [11].
Integrodifferential equations with analytic semigroups
Authors: Bahuguna D.
Published: March 2007

In this paper we study a class of integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence,
uniqueness, regularity and continuation of solutions to these integrodifferential equations.
Initial and boundary value problems for nonconvex valued multivalued functional differential equations
Authors: Benchohra M. , Ntouyas S. K.
Published: March 2007

In this note we investigate the existence of solutions of initial and boundary value problems defined on a compact interval to some classes of functional differential inclusions.
We shall rely on a fixed point theorem for contraction multivalued maps due to Covitz
and Nadler and Schafer′s theorem combined with lower semicontinuous multivalued operators with decomposable values.
A stochastic version of Fan′s best approximation theorem
Authors: Khan Abdul Rahim , Thaheem A. B. , Hussain Nawab
Published: March 2007

We establish some deterministic and random approximation results with the help of two continuous maps in the context of a metrizable topological vector space. These results
generalize some well known results in approximation theory.
Iterative resolvent methods for general mixed variational inequalities
Authors: Noor Muhammad Aslam , Noor Khalida Inayat
Published: March 2007

In this paper, we use the technique of updating the solution to suggest and analyze a class of new self‐adaptive splitting methods for solving general mixed variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Proof of convergence is very simple. Since general mixed variational include variational inequalities and complementarity problems as special cases, our results continue to hold for these problems.
Classical fluid aspects of nonlinear Schrödinger equations and solitons
Authors: Gilson James G.
Published: March 2007

The author extends his alternative theory for Schrödinger quantum
mechanics by introducing the idea of energy reference strata over configuration
space. It is then shown that the view from various such strata defines, the
content of the system of interest and enables a variety of different descriptions of
events in the same space time region. Thus according to “the point of view” or
energy stratum chosen so the type of Schrödinger equation, linear or otherwise,
appropriate to describe the system is determined. A nonlinear information
channel between two dimensional fluid action in hyperspace into two
dimensional energy hyperspace is shown to exist generally as a background to
nonlinear Schrödinger structures. In addition it is shown how soliton solutions
of the one dimensional Schrödinger equation are related to two dimensional
vortex fields in hyperspace.
Finite, primitive and euclidean spaces
Authors: Khalimsky Efim
Published: March 2007

Integer and digital spaces are playing a significant role in digital image
processing, computer graphics, computer tomography, robot vision,
and many other fields dealing with finitely or countable many objects.
It is proven here that every finite T0‐space is a quotient space of a
subspace of some simplex, i.e. of some subspace of a Euclidean space.
Thus finite and digital spaces can be considered as abstract simplicial
structures of subspaces of Euclidean spaces. Primitive subspaces of
finite, digital, and integer spaces are introduced. They prove to be
useful in the investigation of connectedness structure, which can be
represented as a poset, and also in consideration of the dimension of
finite spaces. Essentially T0‐spaces and finitely connected and
primitively path connected spaces are discussed.
On a duality principle in processes of servicing machines with double control
Authors: Dshalalow Jewgeni
Published: March 2007

This paper examines a doubly controlled process of servicing
machines. The classical system treated by Takács is equipped with
m + 1 unreliable machines served by one repairman. In the present
modification of this model, the failure rates and the repair time may be
controlled with respect to the state of the system. The process
describing the number of intact machines is considered. To derive its
steady state distribution in the form of a simple explicit formula, the
author introduces an auxiliary model with m unreliable machines and a
single repairman who keeps working even when all machines are intact.
This result is based on a duality principle applied to the process above.
Propagation of edge waves in a thinly layered laminated medium with stress couples under initial stresses
Authors: Debnath Lokenath , Roy Pijush Pal
Published: March 2007

The propagation of edge waves in a thinly layered laminated
medium with stress couples under initial stresses is examined. Based
upon an approximate representation of a laminated medium by an
equivalent anisotropic continuum with average initial and couple
stresses, an explicit form of frequency equation is obtained to derive the
phase velocity of edge waves. Edge waves exist under certain
conditions. The inclusion of couple stresses increases the velocity of
wave propagation. For a specific compression, the presence of couple
stresses increases the velocity of wave propagation with the increase of
wave number, whereas the reverse is the case when there is no couple
stress. Numerical computation is performed with graphical
representations. Several special cases are also examined.
Surface integrals approach to solution of some free boundary problems
Authors: Malyshev Igor , Morris Hedley , Naroditsky Vladimir , Romanyuk Leonid
Published: March 2007

Inverse problems in which it is required to determine the coefficients of
an equation belong to the important class of ill‐posed problems. Among these,
of increasing significance, are problems with free boundaries. They can be
found in a wide range of disciplines including medicine, materials engineering,
control theory, etc. We apply the integral equations techniques, typical for
parabolic inverse problems, to the solution of a generalized Stefan problem. The
regularization of the corresponding system of nonlinear integral Volterra
equations, as well as local existence, uniqueness, continuation of its solution,
and several numerical experiments are discussed.
Solutions of nonlinear integrodifferential equations of mixed type in Banach spaces
Authors: Guo Dajun
Published: March 2007

In this paper, the author combines the topological degree theory and the
monotone iterative technique to investigate the existence of solutions
and also minimal and maximal solutions of the initial value problem
for nonlinear integrodifferential equations of mixed type in Banach
space. Two main theorems are obtained and two examples are given.
Existence and uniqueness theorems for a third‐order generalized boundary value problem
Authors: Gupta Chaitan P.
Published: March 2007

Let f : [0, 1] × ℝ3 → ℝ be a function satisfying Caratheodory′s conditions,
e(x) ∈ L1[0, 1], η ∈ [0, 1], h ≥ 0, k ≥ 0, h + k > 0. This paper studies existence
and uniqueness questions for the third‐order three‐point generalized boundary
value problem

urn:x-wiley:20903332:media:ista918359:ista918359-math-0001

,

urn:x-wiley:20903332:media:ista918359:ista918359-math-0002

,
and the associated special cases corresponding to one or both of h and k equal to
infinity. The conditions on the nonlinearity f turn out to be related to the spectrum of the linear boundary value problem u‴ = λu′, u(η) = 0, u″(0) − hu′(0) = u″(1) + ku′(1) = 0, in a natural way.
An existence theorem for nonlinear delay differential equations
Authors: Balachandran Krishnan
Published: March 2007

In this paper we prove a theorem on the existence of solutions of
nonlinear delay differential equations, with implicit derivatives. The
result is established using the measure of noncompactness of a set and
Darbo′s fixed point theorem.
A sharp upper bound for discrete inequalities of Gronwall‐Bellman type
Authors: Thandapani E.
Published: March 2007

A sharp upper bound is given for solutions of a discrete inequality of the Gronwall‐Bellman type. The
bound, which is the exact solution of the corresponding discrete equation, is obtained by reducing the
equation to a system of difference equations.
Nonlinear boundary value problems for first order impulsive integro‐differential equations
Authors: Liu Xinzhi
Published: March 2007

In this paper, we investigate a class of first order impulsive integro‐differential equations subject to certain nonlinear boundary conditions and prove,
with the help of upper and lower solutions, that the problem has a solution lying
between the upper and lower solutions. We also develop monotone iterative technique and show the existence of multiple solutions of a class of periodic boundary
value problems.
Markov chains with quasitoeplitz transition matrix: first zero hitting
Authors: Dukhovny Alexander M.
Published: March 2007

This paper continues the investigation of Markov
Chains with a quasitoeplitz transition matrix. Generating functions of first zero hitting probabilities and
mean times are found by the solution of special Riemann boundary value problems on the unit circle.
Duality is discussed.
Solutions of nonstandard initial value problems for a first order ordinary differential equation
Authors: Venkatesulu M. , Srinivas P. D. N.
Published: March 2007

Differential equations of the form y′ = f(t, y, y′), where f is not necessarily
linear in its arguments, represent certain physical phenomena and have been
known to mathematicians for quite a long time. But a fairly general
existence theory for solutions of the above type of problems does not exist
because the (nonstandard) initial value problem y′ = f(t, y, y′), y(t0) = y0 does
not permit an equivalent integral equation of the conventional form. Hence,
our aim here is to present a systematic study of solutions of the NSTD IVPs
mentioned above.

First, we establish the equivalence of the NSTD IVP with a functional
equation and prove the local existence of a unique solution of the NSTD IVP
via the functional equation. Secondly, we prove the continuous dependence
of the solutions on initial conditions and parameters. Finally, we prove a
global existence result and present an example to illustrate the theory.
Euler‐type approximation for systems of stochastic differential equations
Authors: Golec J. , Ladde G.
Published: March 2007

By developing a stochastic version of the Taylor formula, the mean‐square convergence of the Euler‐type approximation for the solution of systems of Itô‐type
stochastic differential equations is investigated. Sufficient conditions are given
to obtain time‐varying and time‐invariant error estimates.
The cauchy‐poisson waves in an inviscid rotating stratified liquid
Authors: Debnath Lokenath , Guha Uma B. , Basu Manjusri
Published: March 2007

Based upon the Boussinesq approximation, an initial
value investigation is made of the axisymmetric free
surface flows generated in an inviscid rotating stratified liquid of infinite depth by the prescribed free
surface disturbance. The asymptotic analysis of the
integral solution is carried out by the stationary phase
method to describe the solution for large time and
large distance from the source of the disturbance. The
asymptotic solution is found to consist of the classical free surface gravity waves and the internal‐inertial
waves.
Strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with integrals
Authors: Byszewski Ludwik
Published: March 2007

In [4] and [5], the author studied strong maximum principles for nonlinear parabolic
problems with initial and nonlocal inequalities, respectively. Our purpose here is to extend
results in [4] and [5] to strong maximum principles for nonlinear parabolic problems with
nonlocal inequalities together with integrals. The results obtained in this paper can be
applied in the theories of diffusion and heat conduction, since considered here integrals in
nonlocal inequalities can be interpreted as mean amounts of the diffused substance or mean
temperatures of the investigated medium.
On the nonexistence of a law of the iterated logarithm for weighted sums of identically distributed random variables
Authors: Adler André
Published: March 2007

For weighted sums of independent and identically distributed
random variables, conditions are placed under which a generalized law of the iterated logarithm cannot hold, thereby extending the usual nonweighted situation.
On nonstandard potentials in a Stefan problem
Authors: Malyshev Igor
Published: March 2007

We report some results on nonstandard potentials and their application to solution
of the Stefan problem.
An existence theorem for a Volterra integral equation with deviating arguments
Authors: Balachandran K. , Ilamaran S.
Published: March 2007

An existence theorem is proved for a nonlinear Volterra integral equation with
deviating arguments.
A theorem on many fixed points for nonlinear operator
Authors: Sun Jingxian , Sun Yong
Published: March 2007

Multiple fixed points of weakly inward mappings are investigated
by means of ordinary differential equations in abstract spaces.
Analysis of stability problems via matrix Lyapunov functions
Authors: Martynyuk Anatoly A.
Published: March 2007

The stability of nonlinear systems is analyzed by the direct Lyapunov′s
method in terms of Lyapunov matrix functions. The given paper surveys the
main theorems on stability, asymptotic stability and nonstability. They are
applied to systems of nonlinear equations, singularly‐perturbed systems and
hybrid systems. The results are demonstrated by an example of a two‐component system.
On a Volterra integral equation with deviating arguments
Authors: Balachandran Krishnan
Published: March 2007

We prove an existence theorem for nonlinear Volterra integral
equation with deviating arguments without assuming the Lipschitz condition.
Nonnegative solutions of two‐point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces
Authors: Guo Dajun
Published: March 2007

In this paper, we combine the fixed point theory, fixed point index
theory and cone theory to investigate the nonnegative solutions of two‐point
BVP for nonlinear second order integrodifferential equations in Banach spaces.
As application, we get some results for the third order case. Finally, we give
several examples for both infinite and finite systems of ordinary nonlinear
integrodifferential equations.
Surface waves in higher order visco‐elastic media under theinfluence of gravity
Authors: Mukherjee Animesh , Sengupta P. R. , Debnath Lokenath
Published: March 2007

Based upon Biot′s [1965] theory of initial stresses of hydrostatic nature produced by
the effect of gravity, a study is made of surface waves in higher order visco‐elastic
media under the influence of gravity. The equation for the wave velocity of Stonely
waves in the presence of viscous and gravitational effects is obtained. This is followed
by particular cases of surface waves including Rayleigh waves and Love waves in the
presence of viscous and gravity effects. In all cases the wave‐velocity equations are
found to be in perfect agreement with the corresponding classical results when the
effects of gravity and viscosity are neglected.
Unique solution to periodic boundary value problems
Authors: Sun Yong
Published: March 2007

Existence of unique solution to periodic boundary value problems of differential equations with continuous or discontinuous right‐hand side is considered by utilizing the method of lower and upper solutions and the monotone properties of the operator. This is subject to discussion in the present paper.
On the parabolic potentials in degenerate‐type heat equation
Authors: Malyshev Igor
Published: March 2007

Using distributions theory technique we introduce parabolic
potentials for the heat equation with one time‐dependent coefficient
(not everywhere positive and continuous) at the highest space‐derivative, discuss their properties, and apply obtained results to three illustrative problems. Presented technique allows to deal with some equation
of the degenerate/mixed type.
The non‐parameter penalty function method in constrained optimal control problems
Authors: Xing An-Qing
Published: March 2007

This paper is concerned with the generalization, numerical
implementation and testing of the non‐parameter penalty function algorithm
which was initially developed for solving n‐dimensional optimization problems.
It uses this method to transform a constrained optimal control problem into a
sequence of unconstrained optimal control problems. It is shown that the
solutions to the original constrained problem. Convergence results are proved
both theoretically and numerically.
Nonlinear evolution equations on Banach space
Authors: Ahmed N. U.
Published: March 2007

In this paper we consider the questions of existence and
uniqueness of solutions of certain semilinear and quasilinear evolution
equations on Banach space. We consider both deterministic and
stochastic systems. The approach is based on semigroup theory and
fixed point theorems. Our results allow the nonlinear perturbations in all
the semilinear problems to be bounded or unbounded with reference to
the base space, thereby increasing the scope for applications to partial
differential equations. Further, quasilinear stochastic evolution equations
seemingly have never been considered in the literature.
On generalized thermoelastic disturbances in an elastic solid with a spherical cavity
Authors: Mukhopadhyay Basudeb , Bera Rasajit , Debnath Lokenath
Published: March 2007

In this paper, a generalized dynamical theory of thermoelasticity
is employed to study disturbances in an infinite elastic solid containing a
spherical cavity which is subjected to step rise in temperature in its inner
boundary and an impulsive dynamic pressure on its surface. The
problem is solved by the use of the Laplace transform on time. The
short time approximations for the stress, displacement and temperature
are obtained to examine their discontinuities at the respective
wavefronts. It is shown that the instantaneous change in pressure and
temperature at the cavity wall gives rise to elastic and thermal
disturbances which travel with finite velocities v1 and v2(>v1)
respectively. The stress, displacement and temperature are found to
experience discontinuities at the respective wavefronts. One of the
significant findings of the present analysis is that there is no diffusive
nature of the waves as found in classical theory.
Relative stability and weak convergence in non‐decreasingstochastically monotone Markov chains
Authors: Todorovic P.
Published: March 2007

Let {ξn} be a non‐decreasing stochastically monotone Markov
chain whose transition probability Q(..) has Q(x, {x}) = β(x) > 0 for
some function β(.) that is non‐decreasing with β(x)↑1 as x → +∞, and
each Q(x.) is non‐atomic otherwise. A typical realization of {ξn} is a
Markov renewal process {(Xn, Tn)}, where ξj = Xn, for Tn consecutive
values of j, Tn geometric on {1, 2, …} with parameter β(Xn).
Conditions are given for Xn, to be relatively stable and for Tn to be
weakly convergent.
On modulated random measures
Authors: Dshalalow Jewgeni H.
Published: March 2007

In this paper the author introduces the notion of a modulated marked
random measure, Zξ, on the class of locally compact and σ‐compact spaces
with countable bases. As special cases, are marked processes modulated by ξ
are considered where ξ is a semi‐Markov or semi‐regenerative process. For
either case, the intensities are evaluated in terms of
parameters of ξ. Examples and applications to inventories, queueing processes
and economics are discussed.
Neural networks with memory
Authors: Burton T. A.
Published: March 2007

This paper is divided into four parts. Part 1 contains a survey of
three neural networks found in the literature and which motivate this
work. In Part 2 we model a neural network with a very general integral
form of memory, prove a boundedness result, and obtain a first result on
asymptotic stability of equilibrium points. The system is very general
and we do not solve the stability problem. In the third section we show
that the neural networks are very robust. The fourth section concerns
simplification of the systems from the second part. Several asymptotic
stability results are obtained for the simplified systems.
Numerical solutions of nonstandard first order initial value problems
Authors: Venkatesulu M. , Srinivasu P. D. N.
Published: March 2007

Differential equations of the form y′ = f(t, y, y′), where f is not
necessarily linear in its arguments, represent certain physical phenomena and
are known for quite some time. The well known Clairut′s and Chrystal′s
equations fall into this category. Earlier, we established the existence of a
(unique) solution of the nonstandard initial value problem (NSTD IV P)
y′ = f(t, y, y′), y(t0) = y0 under certain natural hypotheses on f. In this paper
we present some first order convergent numerical methods for finding the
approximate solutions of the NST D I V Ps.
Integral manifolds of impulsive differential equations
Authors: Bainov D. D. , Kostadinov S. I. , Van Minh N. , Thai N. Hong , Zabreiko P. P.
Published: March 2007

The present paper is concerned with the existence of integral manifolds
of impulsive differential equations as t → +∞. Under the assumption of
exponential trichotomy on the linear part of the right‐hand side of the
equation, it is proved that if the nonlinear perturbation is small enough, then
there exist integral manifolds as t → +∞ for the perturbed equations.
Impulsive integral equations in Banach spaces and applications
Authors: Guo Dajun
Published: March 2007

In this paper, we first use the fixed point theory to prove two existence
theorems of positive solutions for the impulsive Fredholm integral Equations
in Banach spaces. And then, we offer some applications to the two‐point
boundary value problems for the second order impulsive differential equations
in Banach spaces.
An existence theorem for differential inclusions on Banach space
Authors: Ahmed N. U.
Published: March 2007

In this paper we consider the question of existence of solutions
for a large class of nonlinear differential inclusions on Banach space
arising from control theory.
Asymptotic classification of aliasing structures
Authors: Izmailov R. N. , Pokrovskii A. V.
Published: March 2007

The effects of quantization of quickly oscillating functions are
considered. An asymptotical classification of aliasing spots is considered.
The results obtained may be used in the restoring of certain features of
initial functions.
Existence of solution for a mixed neutral system
Authors: Balachandran K. , Anguraj A.
Published: March 2007

We prove the existence of unique solution of the mixed neutral
system

urn:x-wiley:20903332:media:ista263705:ista263705-math-0001

and also prove the continuous dependence of the solution.
On a multilevel controlled bulk queueing system MX/Gr,R/1
Authors: Abolnikov Lev , Dshalalow Jewgeni H.
Published: March 2007

The authors introduce and study a class of bulk queueing systems with
a compound Poisson input modulated by a semi‐Markov process, multilevel
control service time and a queue length dependent service delay discipline. According to this discipline, the server immediately starts the next service act if
the queue length is not less than r; in this case all available units, or R (capacity of the server) of them, whichever is less, are taken for service. Otherwise,
the server delays the service act until the number of units in the queue reaches
or exceeds level r.

The authors establish a necessary and sufficient criterion for the
ergodicity of the embedded queueing process in terms of generating functions
of the entries of the corresponding transition probability matrix and of the
roots of a certain associated functions in the unit disc of the complex plane.
The stationary distribution of this process is found by means of the results of a
preliminary analysis of some auxiliary random processes which arise in the
“first passage problem” of the queueing process over level r. The stationary
distribution of the queueing process with continuous time parameter is
obtained by using semi‐regenerative techniques. The results enable the authors
to introduce and analyze some functionals of the input and output processes
via ergodic theorems. A number of different examples (including an optimization problem) illustrate the general methods developed in the article.
Boundedness and asymptotic stability in the large of solutions of an ordinary differential system y′ = f(t, y, y′)
Authors: Venkatesulu M. , Srinivasu P. D. N.
Published: March 2007

Differential equations of the form y′ = f(t, y, y′), where f is not
necessarily linear in its arguments, represent certain physical phenomena
and solutions have been known for quite some time. The well known
Clairut′s and Chrystal′s equations fall into this category. Earlier
existence of solutions of first order initial value problems and stability of
solutions of first order ordinary differential system of the above type were
established. In this paper we study boundedness and asymptotic stability
in the large of solutions of an ordinary differential system of the above
type under certain natural hypotheses on f.
Lyapunov stability theory for dynamic systems on time scales
Authors: Kaymakçalan Billur
Published: March 2007

By use of the necessary calculus and the fundamental existence
theory for dynamic systems on time scales, in this paper, we develop
Lyapunov′s second method in the framework of general comparison
principle so that one can cover and include several stability results for
both types of equations at the same time.
Multipoint focal boundary value problems on infinite intervals
Authors: Umamaheswaram S. , Rama M. Venkata
Published: March 2007

For the differential equation y(n) = f(x, y), we state a set of
necessary and sufficient conditions for the existence of a solution (i) on a
semi‐infinite interval for a k‐point right focal boundary value problem
and (ii) on (−∞, ∞) for a (n − 1)‐point right focal boundary value
problem. The conditions are in terms of the existence of a pair of
solutions u(x), v(x) satisfying some auxiliary boundary conditions and
algebraic inequatilities.
Number of real roots of a random trigonometric polynomial
Authors: Farahmand K.
Published: March 2007

We study the expected number of real roots of the random
equation g1cosθ + g2cos2θ + …+gncosnθ = K where the coefficients
gj′s are normally distributed, but not necessarily all identical. It is
shown that although this expected number is independent of the means
of gj, (j = 1, 2, …, n), it will depend on their variances. The previous
works in this direction considered the identical distribution for the
coefficients.
On (h0, h)‐stability of autonomous systems
Authors: Liu Xinzhi
Published: March 2007

In this paper, we discuss the qualitative behavior of a map h
along solutions of an autonomous system whose initial values are
measured by a second map h0. By doing this, we may deal with, in a
unified way, several concepts and associated problems, which are usually
considered separately. Five theorems on asymptotic stability are given
and two examples are worked out.
Existence of approximate solution to abstract nonlocal Cauchy problem
Authors: Byszewski L.
Published: March 2007

The aim of the paper is to prove a theorem about the existence
of an approximate solution to an abstract nonlinear nonlocal Cauchy
problem in a Banach space. The right‐hand side of the nonlocal
condition belongs to a locally closed subset of a Banach space. The
paper is a continuation of papers [1], [2] and generalizes some results
from [3].
Strong laws of large numbers for arrays of rowwise conditionally independent random elements
Authors: Patterson Ronald Frank , Bozorgnia Abolghassem , Taylor Robert Lee
Published: March 2007

Let {Xnk} be an array of rowwise conditionally independent
random elements in a separable Banach space of type p, 1 ≤ p ≤ 2.
Complete convergence of to 0, 0 < r < p ≤ 2 is obtained
by using various conditions on the moments and conditional means. A
Chung type strong law of large numbers is also obtained under suitable
moment conditions on the conditional means.
Application of Lakshmikantham′s monotone‐iterative technique to the solution of the initial value problem for impulsiveintegro‐differential equations
Authors: Bainov D. D. , Hristova S. G.
Published: March 2007

In the present paper, a technique of V. Lakshmikantham is
applied to approximate finding of extremal quasisolutions of an initial
value problem for a system of impulsive integro‐differential equations of
Volterra type.
Uniqueness criterion for solution of abstract nonlocal Cauchy problem
Authors: Byszewski L.
Published: March 2007

The aim of the paper is to prove an uniqueness criterion for a
solution of an abstract nonlocal Cauchy problem. A dissipative operator
in the nonlocal problem and an arbitrary functional in the nonlocal
condition are considered. The paper is a continuation of papers [1]‐[3]
and generalizes some results from [4].
On nonlinear boundary value problems with deviating arguments and discontinuous right hand side
Authors: Dhage B. C. , Heikkilä S.
Published: March 2007

In this paper we shall study the existence of the extremal
solutions of a nonlinear boundary value problem of a second order
differential equation with general Dirichlet/Neumann form boundary
conditions. The right hand side of the differential equation is assumed to
contain a deviating argument, and it is allowed to possess discontinuities
in all the variables. The proof is based on a generalized iteration
method.
Random fixed point theorems on product spaces
Authors: Beg Ismat , Shahzad Naseer
Published: March 2007

The existence of random fixed point of a locally contractive
random operator in first variable on product spaces is proved. The
concept “continuous random height‐selection” is discussed. Some
random fixed point theorems for nonexpansive self and nonself maps are
also obtained in product spaces.
On distributed parameter control systems in the abnormal case and in the case of nonoperator equality constraints
Authors: Ledzewicz Urszula
Published: March 2007

In this paper, a general distributed parameter control problem in
Banach spaces with integral cost functional and with given initial and
terminal data is considered. An extension of the Dubovitskii‐Milyutin
method to the case of nonregular operator equality constraints, based on
Avakov′s generalization of the Lusternik theorem, is presented. This
result is applied to obtain an extension of the Extremum Principle for
the case of abnormal optimal control problems. Then a version of this
problem with nonoperator equality constraints is discussed and the
Extremum Principle for this problem is presented.
A note on controllability of neutral Volterra integrodifferential systems
Authors: Balachandran K. , Balasubramaniam P.
Published: March 2007

Sufficient conditions for the controllability of nonlinear neutral
Volterra integrodifferential systems are established. The results are
obtained using the Schauder fixed point theorem.
Optimal controllability of impulsive control systems
Authors: McRae Farzana A.
Published: March 2007

The problem of optimal controllability of a nonlinear impulsive
control system is studied using the method of vector Lyapunov functions
and the generalized comparison principle.
Impulsive nonlocal nonlinear parabolic differential problems
Authors: Byszewski Ludwik
Published: March 2007

The aim of the paper is to prove a theorem about a weak
impulsive nonlinear parabolic differential inequality together with weak
impulsive nonlocal nonlinear inequalities. A weak maximum principle
for an impulsive nonlinear parabolic differential inequality together with
weak impulsive nonlocal nonlinear inequalities and an uniqueness
criterion for the existence of the classical solution of an impulsive
nonlocal nonlinear parabolic differential problem are obtained as a
consequence of the theorem about the weak impulsive nonlinear parabolic
differential inequality together with weak impulsive nonlocal nonlinear
inequalities.
On the existence of solutions for Volterra integral inclusions in Banach spaces
Authors: Avgerinos Evgenios P.
Published: March 2007

In this paper we examine a class of nonlinear integral inclusions
defined in a separable Banach space. For this class of inclusions of
Volterra type we establish two existence results, one for inclusions with a
convex‐valued orientor field and the other for inclusions with nonconvex‐valued orientor field. We present conditions guaranteeing that the
multivalued map that represents the right‐hand side of the inclusion is α‐condensing using for the proof of our results a known fixed point theorem
for α‐condensing maps.
Converge, Version 3.0
Authors: Tadj Lotfi
Published: March 2007

Although intended for college teachers/students, Converge
presents a feature that may interest all scientists: it allows an easy export
of graphic files to most known word processors, specifically to the 𝔼𝕏ℙ,
Version 2.1, a powerful WYSIWYG mathematical word processor.
Stability analysis in terms of two measures for dynamic systems on time scales
Authors: Kaymakçalan Billûr
Published: March 2007

Using the theory of Lyapunov′s second method developed earlier
for time scales, we extend our stability results to two measures which
give rise to unification of several stability concepts in a single set up.
The probabilistic approach to the analysis of the limiting behavior of an integro‐diffebential equation depending on a small parameter, and its application to stochastic processes
Authors: Borisenko O. V. , Borisenko A. D. , Malyshev I. G.
Published: March 2007

Using connection between stochastic differential equation with
Poisson measure term and its Kolmogorov′s equation, we investigate the
limiting behavior of the Cauchy problem solution of the integro
differential equation with coefficients depending on a small parameter.
We also study the dependence of the limiting equation on the order of
the parameter.
Oscillatory properties and asymptotic behavior of the solutions of a class of operator‐differential equations
Authors: Bainov D. D. , Dimitrova M. B.
Published: March 2007

In the present paper an operator‐differential equation is
investigated. Sufficient conditions for the presence of Kneser′s properties
are found.
A class of singularly perturbed evolution systems
Authors: Ahmed N. U.
Published: March 2007

In this paper we study a class of evolution equations where the semigroup
generators are singularly perturbed by a nonnegative real valued function of time.
Sufficient conditions for existence of evolution operators and their compactness
are given including continuous dependence on the perturbation. Further, for a
coupled system of singularly perturbed semilinear systems in two Banach spaces,
existence of periodic solutions and their stability are studied.
Generalized functionals of Brownian motion
Authors: Ahmed N. U.
Published: March 2007

In this paper we discuss some recent developments in the theory of generalized functionals of Brownian motion. First we give a brief summary of the
Wiener‐Ito multiple Integrals. We discuss some of their basic properties, and
related functional analysis on Wiener measure space. then we discuss the generalized functionals constructed by Hida. The generalized functionals of Hida are
based on L2‐Sobolev spaces, thereby, admitting only Hs, s ∈ R valued kernels in
the multiple stochastic integrals. These functionals are much more general than
the classical Wiener‐Ito class. The more recent development, due to the author,
introduces a much more broad class of generalized functionals which are based on
Lp‐Sobolev spaces admitting kernels from the spaces 𝒲p,s, s ∈ R. This allows
analysis of a very broad class of nonlinear functionals of Brownian motion, which
can not be handled by either the Wiener‐Ito class or the Hida class. For s ≤ 0,
they represent generalized functionals on the Wiener measure space like Schwarz
distributions on finite dimensional spaces. In this paper we also introduce some
further generalizations, and construct a locally convex topological vector space of
generalized functionals. We also present some discussion on the applications of
these results.
On Markovian traffic with applications to TES processes
Authors: Jagerman David L. , Melamed Benjamin
Published: March 2007

Markov processes are an important ingredient in a variety of stochastic applications. Notable instances include queueing systems and traffic processes offered
to them. This paper is concerned with Markovian traffic, i.e., traffic processes
whose inter‐arrival times (separating the time points of discrete arrivals) form a
real‐valued Markov chain. As such this paper aims to extend the classical results
of renewal traffic, where interarrival times are assumed to be independent, identically distributed. Following traditional renewal theory, three functions are addressed: the probability of the number of arrivals in a given interval, the corresponding mean number, and the probability of the times of future arrivals. The
paper derives integral equations for these functions in the transform domain.
These are then specialized to a subclass, TES+, of a versatile class of random sequences, called TES (Transform-Expand-Sample), consisting of marginally uniform autoregressive schemes with modulo‐1 reduction, followed by various transformations. TES models are designed to simultaneously capture both first‐order
and second‐order statistics of empirical records, and consequently can produce
high‐fidelity models. Two theoretical solutions for TES+ traffic functions are derived: an operator‐based solution and a matric solution, both in the transform
domain. A special case, permitting the conversion of the integral equations to differential equations, is illustrated and solved. Finally, the results are applied to
obtain instructive closed‐form representations for two measures of traffic
burstiness: peakedness and index of dispersion, elucidating the relationship
between them.
Large deviations for unbounded additive functionals of a Markov process with discrete time (noncompact case)
Authors: Gulinskii O. V. , Lipster Robert S. , Lototskii S. V.
Published: March 2007

We combine the Donsker and Varadhan large deviation principle (l.d.p) for
the occupation measure of a Markov process with certain results of Deuschel and
Stroock, to obtain the l.d.p. for unbounded functionals. Our approach relies on
the concept of exponential tightness and on the Puhalskii theorem. Three
illustrative examples are considered.
Non‐compact random generalized games and random quasi‐variational inequalities
Authors: Yuan Xian-Zhi
Published: March 2007

In this paper, existence theorems of random maximal elements, random
equilibria for the random one‐person game and random generalized game with a
countable number of players are given as applications of random fixed point
theorems. By employing existence theorems of random generalized games, we
deduce the existence of solutions for non‐compact random quasi‐variational inequalities. These in turn are used to establish several existence theorems of noncompact generalized random quasi‐variational inequalities which are either
stochastic versions of known deterministic inequalities or refinements of corresponding results known in the literature.
Random fixed point theorems for nonexpansive and contractive‐type random operators on Banach spaces
Authors: Beg Ismat , Shahzad Naseer
Published: March 2007

The existence of random fixed points. for nonexpansive and pseudocontractive
random multivalued operators defined on unbounded subsets of a Banach space is
proved. A random coincidence point theorem for a pair of compatible random
multivalued operators is established.
Some properties of the Feynman‐Kac functional
Authors: Graversen S. , Pop-Stojanović Z. R. , Rao K. Murali
Published: March 2007

The Feynman‐Kac formula and its connections with classical analysis were
initiated in the now celebrated paper [6] of M. Kac. It soon became obvious that
the formula provides a powerful tool for solving partial differential equations by
running the Brownian motion process. K.L. Chung and K.M. Rao in [4] used it
to characterize solutions of the Schrödinger equation. In this paper we study
some properties of the Feynman‐Kac functional using the Brownian motion process. In particular, we are going to use it in connection with the gauge function
in order to obtain an energy formula similar to one obtained by G. Dal Maso and
U. Mosco in [5].
A sturm separation theorem for a linear 2nth order self‐adjoint differential equation
Authors: Fulton Charles T. , Wu Limin , Pruess Steven
Published: March 2007

For the 2nth order equation, (−1) nv(2n) + qv = 0, with q continuous, we obtain a Sturm Separation theorem, involving n + 1 solutions of the equation,
which is somewhat analogous to the classical result that the zeros of two linearly
independent solutions of the second order equation separate each other.
Tracking control of a flexible beam by nonlinear boundary feedback
Authors: Guo Bao-Zhu , Song Qian
Published: March 2007

This paper is concerned with tracking control of a dynamic model consisting
of a flexible beam rotated by a motor in a horizontal plane at the one end and a
tip body rigidly attached at the free end. The well‐posedness of the closed loop
systems considering the dissipative nonlinear boundary feedback is discussed and
the asymptotic stability about difference energy of the hybrid system is also investigated.
Extension of the method of quasilinearization for stochasticinitial value problems
Authors: Shahzad N. , McRae Farzana A.
Published: March 2007

In this paper we extend the method of quasilinearization to stochastic initial
value problems. Further we prove that the iterates converge uniformly almost
surely to the unique solution and the convergence is quadratic.
New generating functions for multivariate biorthogonalpolynomials on the N‐sphere
Authors: Exton Harold
Published: March 2007

Certain multivariate biorthogonal polynomials on the N‐sphere arise in
connection with quantum chromodynamics. These functions can be expressed in
terms of Lauricella functions of the first kind, and multi‐dimensional generating
functions for them are deduced by means of an extension of Bailey′s theorem.
Representation and prediction for locally harmonizable isotropic random fields
Authors: Swift Randall J.
Published: March 2007

The class of harmonizable fields is a natural extension of the class of stationary fields. This paper considers fields whose increments are harmonizable and isotropic. Spectral representations are obtained for locally harmonizable isotropic
fields. A linear least squares prediction for locally harmonizable isotropic fields is
considered.