bluuebunny/crossref_metadata_2025 huggingface dataset:
On some inventory control problems with state‐dependent parameters
Authors: Abolnikov Lev
Published: March 2007

This article analyzes discrete Markov processes that arise in some
general control problems of a storage (or a dam) with an infinite
capacity. Employing a special “step‐wise” structure of the transition
matrices of these processes, the author obtains conditions for their
ergodicity and develops an implementable algorithm for finding the
generating function of the corresponding distributions. This algorithm
is applied to a dam with a multilevel state‐dependent control strategy,
according to which parameters of the input and output processes may
depend on the amount of the water in the dam. The method is
illustrated with a case of a single‐level control strategy where explicit
results are obtained.
Correlated random walks with stay
Authors: Lal Ram , Bhat U. Narayan
Published: March 2007

A random walk describes the movement of a particle in discrete
time, with the direction and the distance traversed in one step being
governed by a probability distribution. In a correlated random walk
(CRW) the movement follows a Markov chain and induces correlation
in the state of the walk at various epochs. Then, the walk can be
modelled as a bivariate Markov chain with the location of the particle
and the direction of movement as the two variables. In such random
walks, normally, the particle is not allowed to stay at one location from
one step to the next. In this paper we derive explicit results for the
following characteristics of the CRW when it is allowed to stay at the
same location, directly from its transition probability matrix: (i)
equilibrium solution and the fast passage probabilities for the CRW
restricted on one side, and (ii) equilibrium solution and first passage
characteristics for the CRW restricted on bath sides (i.e., with finite
state space).
Queues, random graphs and branching processes
Authors: Takács Lajos
Published: March 2007

In this paper it is shown that certain basic results of
queueing theory can be used successfully in solving various
problems of random graphs and branching processes.
Large level crossings of a random polynomial
Authors: Farahmand Kambiz
Published: March 2007

We know the expected number of times that a polynomial of degree
n with independent random real coefficients asymptotically crosses the
level K, when K is any real value such that (K2/n) → 0 as n → ∞.
The present paper shows that, when K is allowed to be large, this
expected number of crossings reduces to only one. The coefficients of
the polynomial are assumed to be normally distributed. It is shown
that it is sufficient to let K ≥ exp(nf) where f is any function of n
such that f → ∞ as n → ∞.
Classical variational basis for Schrödinger quantum theory
Authors: Gilson James G.
Published: March 2007

A two‐dimensional classical hyperspace fluid theory of the
vacuum which is an alternative to Schrödinger quantum theory involves
a “stirring” energy density. This energy density, like entropy density,
measures the local “disturbance” involved by the time evolution of a
state of the system. The stirring energy density is shown to be the local
source term for the rate of generation of action density with time. A
classical fluid action principle is solved using the “action” of this source
term without assuming quantum time evolution. Schrödinger quantum
theory is recovered from this new action principle which is then
discussed. Finally, the quantity made stationary by the variational
principle measures disturbance in the environment as an angular change
in the orientation of the whole system.
Renewal characterization of Markov modulated Poisson processes
Authors: Neuts Marcel F. , Sumita Ushio , Takahashi Yoshitaka
Published: March 2007

A Markov Modulated Poisson Process (MMPP) M(t) defined on a Markov
chain J(t) is a pure jump process where jumps of M(t) occur according to a
Poisson process with intensity λi whenever the Markov chain J(t) is in state i.
M(t) is called strongly renewal (SR) if M(t) is a renewal process for an arbitrary
initial probability vector of J(t) with full support on P = {i : λi > 0}. M(t) is
called weakly renewal (WR) if there exists an initial probability vector of J(t)
such that the resulting MMPP is a renewal process. The purpose of this paper
is to develop general characterization theorems for the class SR and some
sufficiency theorems for the class WR in terms of the first passage times of the
bivariate Markov chain [J(t), M(t)]. Relevance to the lumpability of J(t) is also
studied.
Markov chains with quasitoeplitz transition matrix
Authors: Dukhovny Alexander M.
Published: March 2007

This paper investigates a class of Markov chains which are frequently encountered in various applications (e.g. queueing systems,
dams and inventories) with feedback. Generating functions of transient and steady state probabilities are found by solving a special
Riemann boundary value problem on the unit circle. A criterion of
ergodicity is established.
Surface integrals approach to solution of some free boundary problems ‐ II
Authors: Malyshev Igor
Published: March 2007

This paper is a continuation of the publication [1] where integral equation
techniques were applied to the solution of a generalized Stefan problem. The
regularization of the corresponding system of nonlinear integral Volterra equations
offered here is quite different from that in [1], hence ‐ several new algorithms and
numerical experiments. For consistency and easy reference we start this paper with
sec.6.
Sharp conditions for the oscillation of delay difference equations
Authors: Ladas G. , Philos Ch. G. , Sficas Y. G.
Published: March 2007

Suppose that {pn} is a nonnegative sequence of real numbers
and let k be a positive integer. We prove that

urn:x-wiley:20903332:media:ista150178:ista150178-math-0001

is a sufficient condition for the oscillation of all solutions of the
delay difference equation

urn:x-wiley:20903332:media:ista150178:ista150178-math-0002

.
This result is sharp in that the lower bound kk/(k+1)k+1 in
the condition cannot be improved. Some results on difference
inequalities and the existence of positive solutions are also presented.
The square‐wave spectral density of a stationary renewal process
Authors: Neuts Marcel F. , Sitaraman H.
Published: March 2007

The power spectral density of a random square wave is a promising tool in the
qualitative study of stationary point processes. This is illustrated for renewal
processes and their superpositions.
Large scale singularly perturbed boundary value problems
Authors: Kathirkamanayagan M. , Ladde G. S.
Published: March 2007

In this paper an alternative approach to the method of asymptotic expansions for the study of a
singularly perturbed linear system with multiparameters and multiple time scales is developed. The
method consists of developing a linear non‐singular transformation that transforms an arbitrary
n—time scale system into a diagonal form. Furthermore, a dichotomy transformation is employed to
decompose the faster subsystems into stable and unstable modes. Fast, slow, stable and unstable
modes decomposition processes provide a modern technique to find an approximate solution of the
original system in terms of the solution of an auxiliary system. This method yields a constructive and
computationally attractive way to investigate the system.
Nonlinear second order system of Neumann boundary value problems at resonance
Authors: Gupta Chaitan P.
Published: March 2007

Let f : [0, π] × ℝN → ℝN, (N ≥ 1) satisfy Caratheodory conditions, e(x) ∈ L1([0, π]; ℝN).
This paper studies the system of nonlinear Neumann boundary value problems

,

.
This problem is at resonance since the associated linear boundary value problem

,

,
has λ = 0 as an eigenvalue. Asymptotic conditions on the nonlinearity f(t, x(t)) are offered to
give existence of solutions for the nonlinear systems. The methods apply to the corresponding
system of Lienard‐type periodic boundary value problems.
On a multi‐channel queue with state dependent input flow and interruptions
Authors: Dshalalow Jewgeni
Published: March 2007

This paper deals with a multi‐channel queueing system with a
finite waiting room but without losses. The latter is achieved by a
temporary interruption of the input flow activity until the waiting room
is ready to place a new customer. In addition, the input flow on its “busy
period” is non‐recurrent: It is state dependent and may be controlled over
relevant times of decision making. A similar model without interruptions
(i.e. with losses) was earlier studied by the author, where in particular,
major probability characteristics of the queueing process in equilibrium
were obtained. Now the author derives a simple explicit relation between
the two models allowing the given queue to inherit the results previously
obtained. New techniques for semi‐regenerative processes are used.
Monotone method for first order singular systems with boundary conditions
Authors: Uvah J. A. , Vatsala A. S.
Published: March 2007

Existence of maximal and minimal solutions are proved for the first
order singular systems with boundary conditions by combining the
method of upper and lower solutions and the monotone iterative
technique.
Applications of the penalty function method in constrained optimal control problems
Authors: Xing An-qing
Published: March 2007

This paper uses the penalty function method to solve constrained optimal control problems. Under suitable assumptions, we can solve a
constrained optimal control problem by solving a sequence of unconstrained
optimal control problems. In turn, the constrained solution to the main problem can be obtained as the limit of the solutions of the sequence. In using the
penalty function method to solve constrained optimal control problems, it is
usually assumed that each of the modified unconstrained optimal control problems has at least one solution. Here we establish an existence theorem for
those problems. Two numerical examples are presented to demonstrate the
findings.
Existence of positive solutions for neutral differential equations
Authors: Chuanxi Q. , Ladas G.
Published: March 2007

We establish sufficient conditions for the existence
of positive solutions of the neutral delay differential
equation

urn:x-wiley:20903332:media:ista898259:ista898259-math-0001

.
Two new algorithms for discrete boundary value problems
Authors: Agarwal Ravi P. , Nanda Tara R.
Published: March 2007

We propose two new methods of constructing the solutions of linear
multi‐point discrete boundary value problems. These methods are
applied to solve some continuous two‐point boundary value problems
which are known to be numerically unstable.
Asymptotic optimality of experimental designs in estimating a product of means
Authors: Rekab Kamel
Published: March 2007

In nonlinear estimation problems with linear models, one difficulty in obtaining
optimal designs is their dependence on the true value of the unknown parameters.
A Bayesian approach is adopted with the assumption the means are independent
apriori and have conjuguate prior distributions. The problem of designing an experiment to estimate the product of the means of two normal populations is considered.
The main results determine an asymptotic lower bound for the Bayes risk, and a
necessary and sufficient condition for any sequential procedure to achieve the bound.
On the theory of one‐sided models in spaces with arbitrary cones
Authors: Martynyuk A. A. , Obolensky A. Yu.
Published: March 2007

The paper presents a way of constructing quasimonotone nonautonomous
systems ensuring x‐stability of the nonautonomous system. There are
described extensions quasimonotone with respect to an arbitrary cone,
Perron condition and invariant surface stability under perturbations U‐stability on the set of non wandering points is proved to imply u‐stability
of quasimonotone nonlinear system and exponential u‐stability on
minimal attraction center provides u‐stability of the total systems
Examples are available.
Asymptotic approximations to the Bayes posterior risk
Authors: Zoubeidi Toufik
Published: March 2007

Suppose that, given ω = (ω1, ω2) ∈ ℜ2, X1, X2, … and
Y1, Y2, … are independent random variables and their respective
distribution functions and belong to a one parameter
exponential family of distributions. We derive approximations
to the posterior probabilities of ω lying in closed convex subsets
of the parameter space under a general prior density. Using
this, we then approximate the Bayes posterior risk for testing
the hypotheses H0 : ω ∈ Ω1 versus H1 : ω ∈ Ω2 using a zero‐one
loss function, where Ω1 and Ω2 are disjoint closed convex subsets
of the parameter space.
Error bounds for two even degree tridiagonal splines
Authors: Howell Gary W.
Published: March 2007

We study a C(1) parabolic and a C(2) quartic spline which are determined by
solution of a tridiagonal matrix and which interpolate subinterval midpoints. In
contrast to the cubic C(2) spline, both of these algorithms converge to any continuous
function as the length of the largest subinterval goes to zero, regardless of “mesh ratios”.
For parabolic splines, this convergence property was discovered by Marsden [1974]. The
quartic spline introduced here achieves this convergence by choosing the second
derivative zero at the breakpoints. Many of Marsden′s bounds are substantially
tightened here. We show that for functions of two or fewer coninuous derivatives the
quartic spline is shown to give yet better bounds. Several of the bounds given here are
optimal.
Markov chains with quasitoeplitz transition matrix: applications
Authors: Dukhovny A. M.
Published: March 2007

Application problems are investigated for the Markov chains with quasitoeplitz
transition matrix. Generating functions of transient and steady state probabilities, first
zero hitting probabilities and mean times are found for various particular cases,
corresponding to some known patterns of feedback ( “warm‐up,” “switch at threshold”
etc.), Level depending dams and queue‐depending queueing systems of both M/G/1 and
MI/G/1 types with arbitrary random sizes of arriving and departing groups are studied.
Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation uxt = F(x, t, u, ux)
Authors: Byszewski L.
Published: March 2007

The aim of the paper is to give two theorems about
existence and uniqueness of continuous solutions for hyperbolic
nonlinear differential problems with nonlocal conditions in
bounded and unbounded domains. The results obtained in this
paper can be applied in the theory of elasticity with better effect than analogous known results with classical initial conditions.
On some perturbation techniques for quasi‐linear parabolic equations
Authors: Malyshev Igor
Published: March 2007

We study a nonhomogeneous quasi‐linear parabolic equation and introduce a
method that allows us to find the solution of a nonlinear boundary value problem
in “explicit” form. This task is accomplished by perturbing the original equation
with a source function, which is then found as a solution of some nonlinear
operator equation.
On a Volterra Stieltjes integral equation
Authors: Vaz P. T. , Deo S. G.
Published: March 2007

The paper deals with a study of linear Volterra integral equations involving
Lebesgue‐Stieltjes integrals in two independent variables. The authors prove an
existence theorem using the Banach fixed‐point principle. An explicit example is
also considered.
Difference equations of Volterra type and extension of Lyapunov′s method
Authors: Zouyousefain M.
Published: March 2007

In this paper, the stability properties of nonlinear difference equations of
Volterra type is discussed. For this purpose some comparison Theorems are developed,
then using these results the stability of the nonlinear difference equations of Volterra
type is investigated.
Rothe′s method to semilinear hyperbolic integrodifferential equations
Authors: Bahaguna D. , Pani A. K. , Raghavendra V.
Published: March 2007

In this paper we consider an application of Rothe′s method to abstract
semi‐linear hyperbolic integrodifferential equations in Hilbert spaces. With the
aid of Rothe′s method we establish the existence of a unique strong solution.
On a probability problem connected with Railway traffic
Authors: Takács Lajos
Published: March 2007

Let Fn(x) and Gn(x) be the empirical distribution functions of two
independent samples, each of size n, in the case where the elements of the
samples are independent random variables, each having the same continuous
distribution function V(x) over the interval (0, 1). Define a statistic θn by

urn:x-wiley:20903332:media:ista363025:ista363025-math-0001

.
In this paper the limits of (r = 0, 1, 2, …) and
are determined for n → ∞. The problem of finding the asymptotic behavior of
the moments and the distribution of θn as n → ∞ has arisen in a study of the
fluctuations of the inventory of locomotives in a randomly chosen railway
depot.
The computation of stationary distributions of Markov chains through perturbations
Authors: Hunter Jeffery J.
Published: March 2007

An algorithmic procedure for the determination of the stationary
distribution of a finite, m‐state, irreducible Markov chain, that does not
require the use of methods for solving systems of linear equations, is presented.
The technique is based upon a succession of m, rank one, perturbations of the
trivial doubly stochastic matrix whose known steady state vector is updated at
each stage to yield the required stationary probability vector.
Stability of Volterra system with impulsive effect
Authors: Rao M. Ramamohana , Sivasundaram S.
Published: March 2007

Sufficient conditions for uniform stability and uniform asymptotic
stability of impulsive integrodifferential equations are investigated by
constructing a suitable piecewise continuous Lyapunov‐like functionals without
the decresent property. A result which establishes no pulse phenomena in the
given system is also discussed.
Existence of periodic solutions of impulsive differential systems
Authors: Erbe L. H. , Liu Xinzhi
Published: March 2007

In this paper, the existence of periodic solutions of impulsive
differential systems is considered. Since the solutions of such a system
are peicewise continuous, it is necessary to introduce piecewise
continuous Lyapunov functions. By means of such functions, together
with the comparison principle, some sufficient conditions for the
existence of periodic solutions of impulsive differential systems are
established.
On the distribution of the number of vertices in layers of random trees
Authors: Takács Lajos
Published: March 2007

Denote by Sn the set of all distinct rooted trees with n labeled
vertices. A tree is chosen at random in the set Sn, assuming that all the
possible nn−1 choices are equally probable. Define τn(m) as the number
of vertices in layer m, that is, the number of vertices at a distance m
from the root of the tree. The distance of a vertex from the root is the
number of edges in the path from the vertex to the root. This paper is
concerned with the distribution and the moments of τn(m) and their
asymptotic behavior in the case where , 0 < α < ∞ and n → ∞.
In addition, more random trees, branching processes, the Bernoulli
excursion and the Brownian excursion are also considered.
A single‐server queue with random accumulation level
Authors: Dshalalow Jewgeni H.
Published: March 2007

The author studies the queueing process in a single‐server bulk queueing system. Upon completion of a previous service, the server can take a group
of random size from customers that are available. Or, the server can wait until
the queue attains a desired level.
The author establishes an ergodicity criterion for both the queueing
process with continuous time parameter and the imbedded process. Under this
criterion, the author obtains explicit formulas for the stationary distributions
of both processes by using semi‐regenerative techniques.
Stability of solutions of a nonstandard ordinary differentialsystem by Lyapunov′s second method
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 y′ = f(t, y, y′), y(t0) = y0 under certain natural hypotheses on f. In this paper,
we studied the stability of solutions of a nonstandard first order ordinary
differential system.
Oscillations in linear difference equations with variablecoefficients
Authors: Philos Ch. G. , Purnaras I. K.
Published: March 2007

A class of linear difference equations with variable coefficients is
considered. Sufficient conditions and necessary conditions for the oscillation of
the solutions are established. In the special cases where the coefficients are
constant or periodic the conditions become both necessary and sufficient.
On a counterexample of Garofalo ‐ Lin for a unique continuation of Schrödinger equation
Authors: Lee Will Y.
Published: March 2007

Garofalo and Lin have given a counterexample for which
unique continuation fails for the Schrödinger equation

urn:x-wiley:20903332:media:ista503207:ista503207-math-0001

.

Their counterexample consists of a Bessel function of the third
kind Kv(|x|) with the restriction that v cannot be an integer. In this
note we have removed the restriction.
Conditional limit theorems for branching processes
Authors: Takács Lajos
Published: March 2007

Let [ξ(m), m = 0, 1, 2, …] be a branching process in which each
individual reproduces independently of the others and has probability pj(j = 0, 1, 2, …) of giving rise to j descendants in the following generation.
The random variable ξ(m) is the number of individuals in the mth
generation. It is assumed that P{ξ(0) = 1} = 1. Denote by ρ the total
progeny, μ, the time of extinction, and τ, the total number of ancestors
of all the individuals in the process. This paper deals with the
distributions of the random variables ξ(m), μ and τ under the condition
that ρ = n and determines the asymptotic behavior of these distributions
in the case where n → ∞ and m → ∞ in such a way that tends to a
finite positive limit.
Error estimates for the semidiscrete finite element approximation of linear nonlocal parabolic equations
Authors: Jackson Dennis E.
Published: March 2007

Existence and uniqueness are proved for nonlocal (in time) for
solutions of linear parabolic partial differential equations. Instead of an
initial condition, there is a relation connecting the initial value to values
of the solution at other times. L2 error estimates are obtained for the
semidiscrete approximation of the problem using finite elements in the
space variables.
Existence of a solution of a Fourier nonlocal quasilinear parabolic problem
Authors: Byszewski Ludwik
Published: March 2007

The aim of this paper is to give a theorem about the existence
of a classical solution of a Fourier third nonlocal quasilinear parabolic
problem. To prove this theorem, Schauder′s theorem is used. The paper
is a continuation of papers [1]‐[8] and the generalizations of some results
from [9]‐[11]. The theorem established in this paper can be applied to
describe some phenomena in the theories of diffusion and heat conduction
with better effects than the analogous classical theorem about the
existence of a solution of the Fourier third quasilinear parabolic problem.
On the unsteady flow of two visco‐elastic fluids between two inclined porous plates
Authors: Sengupta P. R. , Ray T. K. , Debnath L.
Published: March 2007

This study is concerned with both hydrodynamic and
hydromagnetic unsteady slow flows of two immiscible visco‐elastic fluids
of Rivlin‐Ericksen type between two porous parallel nonconducting plates
inclined at a certain angle to the horizontal. The exact solutions for the
velocity fields, skin frictions, and the interface velocity distributions are
found for both fluid models. Numerical results are presented in graphs.
A comparison is made between the hydrodynamic and hydromagnetic
velocity profiles. It is shown that the velocity is diminished due to the
presence of a transverse magnetic field.
Generalized two point boundary value problems. existence and uniqueness
Authors: Murty K. N. , Sivasundaram S.
Published: March 2007

An algorithm is presented for finding the pseudo‐inverse of a
rectangular matrix. Using this algorithm as a tool, existence and
uniqueness of solutions to two point boundary value problems associated
with general first order matrix differential equations are established.
Extremal solutions to a class of multivalued integral equations in Banach space
Authors: Aizicovici Sergiu , Papageorgiou Nikolaos S.
Published: March 2007

We consider a nonlinear Volterra integral inclusion in a Banach
space. We establish the existence of extremal integral solutions, and we
show that they are dense in the solution set of the original equation. As
an important application, we obtain a “bang‐bang” theorem for a class of
nonlinear, infinite dimensional control systems.
Admissible relaxation in optimal control problems for infinite dimensional uncertain systems
Authors: Ahmed N. U. , Xiang X.
Published: March 2007

In this paper we present a result on admissible relaxation for a
class of systems governed by an uncertain evolution equation on Banach
space. We show that the set of original trajectories is dense in the set of
relaxed trajectories and that under certain assumptions the relaxed
system is equivalent to the original system.
Existence of solutions of functional differential inclusions
Authors: Anguraj A. , Balachandran K.
Published: March 2007

We prove the existence of solutions of a functional differential
inclusion. By using the variation of parameters formula we convert the
functional differential inclusion into an integral inclusion and prove the
existence of a fixed point of the set‐valued mapping with the help of the
Kakutani‐Bohnenblust‐Karlin fixed point theorem.
Existence of solution to transpiration control problem
Authors: Zhu Guanstian , Wu Jingang , Liang Benzhong , Ji Xinhua , Yang Xueshi
Published: March 2007

Transpiration control can avoid change of the shape of a high‐speed vehicle resulting from ablation of the nose, therefore also can avoid
the change of the performance of Aerodynamics. Hence it is of practical
importance. A set of mathematical equations and their boundary
conditions are founded and justified by an example of non‐ablation
calculation in reference [1]. In [2], the ablation model is studied by the
method of finite differences, the applicable margin of the equations is
estimated through numerical calculation, and the dynamic responses of
control parameters are analyzed numerically. In this paper we prove
that the solution to transpiration control problem given in [1] exists
uniquely under the assumption that the given conditions (i.e. given
functions) are continuous.
Note on the inequalities of J. Kazdan
Authors: Lee Will Y.
Published: March 2007

In this note, we prove the Kazdan′s inequalities without using
what is called the Heisenberg uncertainty principle. Instead we prove it
using Garofalo‐Lin inequality among other things.
Nonlinear impulsive Volterra integral equations in Banach spaces and applications
Authors: Guo Dajun
Published: March 2007

In this paper, we first extend results on the existence of maximal
solutions for nonlinear Volterra integral equations in Banach spaces to
impulsive Volterra integral equations. Then, we give some applications
to initial value problems for first order impulsive differential equations in
Banach spaces. The results are demonstrated by means of an example of
an infinite system for impulsive differential equations.
Positive solutions of integrodifferential equations
Authors: Philos Ch. G.
Published: March 2007

Integrodifferential equations of the forms

urn:x-wiley:20903332:media:ista345783:ista345783-math-0001

are considered, where K ∈ C([0, ∞), [0, ∞)), p ∈ C([0, ∞), [0, ∞)) and
q ∈ C((−∞, ∞), [0, ∞)). Necessary conditions and also sufficient
conditions for the existence of positive solutions are established.
Constructive method for solving a nonlinear singularly perturbed system of differential equations in critical case
Authors: Slavova Angela
Published: March 2007

A singularly, perturbed system of differential equations with
degenerate matrix at the derivative is considered. The existence and
construction of the periodic solutions are investigated in critical case.
For the analysis of these algorithms the apparatus of Lyapunov′s finite
majorizing equations is used. An implementation of this method is given
in two examples.
Dynamic properties of cellular neural networks
Authors: Slavova Angela
Published: March 2007

Dynamic behavior of a new class of information‐processing
systems called Cellular Neural Networks is investigated. In this paper we
introduce a small parameter in the state equation of a cellular neural
network and we seek for periodic phenomena. New approach is used for
proving stability of a cellular neural network by constructing Lyapunov′s
majorizing equations. This algorithm is helpful for finding a map from
initial continuous state space of a cellular neural network into discrete
output. A comparison between cellular neural networks and cellular
automata is made.
Limit distributions for queues and random rooted trees
Authors: Takács Lajos
Published: March 2007

In this paper several limit theorems are proved for the
fluctuations of the queue size during the initial busy period of a queuing
process with one server. These theorems are used to find the solutions of
various problems connected with the heights and widths of random
rooted trees.
Properties of solution set of stochastic inclusions
Authors: Kisielewicz Michał
Published: March 2007

The properties of the solution set of stochastic inclusions are
investigated. They are equivalent to properties of fixed points sets of
appropriately defined set‐valued mappings.
Random fixed points and approximations in random convex metric spaces
Authors: Beg Ismat , Shahzad Naseer
Published: March 2007

Some random fixed point theorems in random convex metric
spaces are obtained. Results regarding random best approximation on
random convex metric spaces are also proved.
On applications of Little′s formula
Authors: Dshalalow Jewgeni H.
Published: March 2007

In classical Little′s formula L = λW used in queueing, the parameter λ
serves as the intensity of the input process. In various applications this
parameter may not be known. The author discusses important classes of modulated input processes, where this parameter can be found.
Scientific word, Version 1.0
Authors: Köksal Semen
Published: March 2007

Scientific Word is the first fully integrated mathematical word
processor in the Windows 3.1 environment, which uses the TEX typesetting language for output. It runs as a Microsoft Windows application
program and has two‐way interface to TEX. The Scientific Word is an
object‐oriented WYSIWYG word processor for virtually all users who
need typesetting scientific books, manuals and papers. It includes automatic equation numbering, spell checking, and LATEX and DVI previewer.
On second order discontinuous differential equations in Banach spaces
Authors: Heikkilä S. , Leela S.
Published: March 2007

In this paper we study a second order semilinear initial value
problem (IVP), where the linear operator in the differential equation is
the infinitesimal generator of a strongly continuous cosine family in a
Banach space E. We shall first prove existence, uniqueness and
estimation results for weak solutions of the IVP with Carathéodory type
of nonlinearity, by using a comparison method. The existence of the
extremal mild solutions of the IVP is then studied when E is an ordered
Banach space. We shall also discuss the dependence of these solutions on
the data. A characteristic feature of the results concerning extremal
solutions is that the nonlinearity is not assumed to be continuous in any
of its arguments. Moreover, no compactness conditions are assumed. The
obtained results are then applied to a second order partial differential
equation of hyperbolic type.
On revelation transforms that characterize probability distributions
Authors: Chukova S. , Dimitrov B. , Dion J.-P.
Published: March 2007

A characterization of exponential, geometric and of distributions
with almost‐lack‐of‐memory property, based on the “revelation transform
of probability distributions” and “relevation of random variables” is
discussed. Known characterizations of the exponential distribution on
the base of relevation transforms given by Grosswald et al. [4], and Lau
and Rao [7] are obtained under weakened conditions and the proofs are simplified. A characterization the class of almost‐lack‐of‐memory distributions through the relevation is specified.
A bulk queueing system under N‐policy with bilevel service delay discipline and start‐up time
Authors: Muh David C. R.
Published: March 2007

The author studies the queueing process in a single‐server, bulk
arrival and batch service queueing system with a compound Poisson
input, bilevel service delay discipline, start‐up time, and a fixed
accumulation level with control operating policy. It is assumed that when
the queue length falls below a predefined level r(≥1), the system, with
server capacity R, immediately stops service until the queue length
reaches or exceeds the second predefined accumulation level N(≥r).
Two cases, with N ≤ R and N ≥ R, are studied.

The author finds explicitly the probability generating function of
the stationary distribution of the queueing process and gives numerical
examples.
On invariant measures of nonlinear Markov processes
Authors: Ahmed N. U. , Ding Xinhong
Published: March 2007

We consider a nonlinear (in the sense of McKean) Markov
process described by a stochastic differential equations in Rd. We prove
the existence and uniqueness of invariant measures of such process.
Anti‐periodic traveling wave solutions to a class of higher‐order Kadomtsev‐Petviashvili‐Burgers equations
Authors: Aizicovici Sergiu , Gao Yun , Wen Shih-Liang
Published: March 2007

We discuss the existence, uniqueness, and continuous dependence
on data, of anti‐periodic traveling wave solutions to higher order two‐dimensional equations of Korteweg‐deVries type.
Initial value problems for integro‐differential equations of Volterra type in Banach spaces
Authors: Guo Dajun
Published: March 2007

This paper investigates the extremal solutions of initial value
problems for first order integro‐differential equations of Volterra type in
Banach spaces by means of establishing a comparison result.
The method of lower and upper solutions for nth‐order periodic boundary value problems
Authors: Cabada Alberto
Published: March 2007

In this paper we develop the monotone method in the presence of
lower and upper solutions for the problem

urn:x-wiley:20903332:media:ista737583:ista737583-math-0001

where f is a Carathéodory function. We obtain sufficient conditions for
f to guarantee the existence and approximation of solutions between a
lower solution α and an upper solution β for n ≥ 3 with either α ≤ β or
α ≥ β.

For this, we study some maximum principles for the operator
Lu ≡ u(n) + Mu. Furthermore, we obtain a generalization of the method of mixed monotonicity considering f and u as vectorial functions.
Delay differential systems with discontinuous initial data and existence and uniqueness theorems for systems with impulse and delay
Authors: Krishna S. V. , Anokhin A. V.
Published: March 2007

The main purpose of this paper is to discuss some qualitative
aspects of differential equations with delays and impulses. Such systems
are encountered in modeling the dynamics of prices and cultured
populations. However, any such discussion has to be based on some
existence and uniqueness results for delay equations with discontinuous
initial data. This is the content of the first part of the paper. For an
impulsive system, we observe a phenomenon of existence of infinite
number of solutions subject to impulses arbitrarily close to a fixed time.
Conditions, when such solutions exist and when they do not, are
discussed.
Inclusion relations between classes of hypergeometric functions
Authors: Ahuja O. P. , Jahangiri M.
Published: March 2007

The use of hypergeometric functions in univalent function theory
received special attention after the surprising application of such
functions by de Branges in the proof of the 70‐year old Bieberbach
Conjecture. In this paper we consider certain classes of analytic functions
and examine the distortion and containment properties of generalized
hypergeometric functions under some operators in these classes.
Some performance measures for vacation models with a batch Markovian arrival process
Authors: Matendo Sadrac K.
Published: March 2007

We consider a single server infinite capacity queueing system, where
the arrival process is a batch Markovian arrival process (BMAP).
Particular BMAPs are the batch Poisson arrival process, the Markovian
arrival process (MAP), many batch arrival processes with correlated
interarrival times and batch sizes, and superpositions of these processes.
We note that the MAP includes phase‐type (PH) renewal processes and
non‐renewal processes such as the Markov modulated Poisson process
(MMPP).

The server applies Kella′s vacation scheme, i.e., a vacation policy
where the decision of whether to take a new vacation or not, when the
system is empty, depends on the number of vacations already taken in
the current inactive phase. This exhaustive service discipline includes the
single vacation T‐policy, T(SV), and the multiple vacation T‐policy,
T(MV). The service times are i.i.d. random variables, independent of
the interarrival times and the vacation durations. Some important
performance measures such as the distribution functions and means of
the virtual and the actual waiting times are given. Finally, a numerical
example is presented.
Laws of large numbers for L‐statistics
Authors: Norvaiša Rimas
Published: March 2007

Consider Ln = n−1∑1≤i≤ncnig(Xn:i) for order statistics Xn:i
and let for some (Lebesgue) λ‐summable over (0, 1)
function J. Sufficient as well as necessary conditions for to hold almost surely and in probability are given. Superposition
(or Nemytskii) operators have been used to derive the laws of large
numbers for L‐statistics from the laws of large numbers in quasi‐Banach
function spaces for the empirical distribution functions based on
X1, …, Xn.
Random approximations and random fixed point theorems
Authors: Beg Ismat , Shahzad Naseer
Published: March 2007

Some results regarding random best approximation are proved. As applications, several random fixed point theorems are obtained.
Existence theorem for nonconvex stochastic inclusions
Authors: Kisielewicz Michał
Published: March 2007

An existence theorem for stochastic inclusions with nonanticipative nonconvex‐valued right‐hand sides is proved.
A finite capacity queue with Markovian arrivals and two servers with group services
Authors: Chakravarthy S. , Alfa Attahiru Sule
Published: March 2007

In this paper we consider a finite capacity queuing system in which arrivals
are governed by a Markovian arrival process. The system is attended by two
exponential servers, who offer services in groups of varying sizes. The service
rates may depend on the number of customers in service. Using Markov theory,
we study this finite capacity queuing model in detail by obtaining numerically
stable expressions for (a) the steady‐state queue length densities at arrivals and
at arbitrary time points; (b) the Laplace‐Stieltjes transform of the stationary
waiting time distribution of an admitted customer at points of arrivals. The
stationary waiting time distribution is shown to be of phase type when the
interarrival times are of phase type. Efficient algorithmic procedures for
computing the steady‐state queue length densities and other system performance
measures are discussed. A conjecture on the nature of the mean waiting time is
proposed. Some illustrative numerical examples are presented.
Initial and boundary value problems for functional integro‐differential equations
Authors: Ntouyas S. K. , Tsamatos P. Ch.
Published: March 2007

In this paper, we study initial and boundary value problems for functional
integro‐differential equations, by using the Leray‐Schauder Alternative.
Lajos Takács and his work
Authors: Dshalalow Jewgeni H. , Syski Ryszard
Published: March 2007

This paper, written in honor of the 70th birthday of Lajos Takács, addresses
his life and work, and includes some personal observations and appreciation of his
contributions. In particular, it includes a short biography, an informal discussion
of some of his major research areas (queueing, fluctuations, waiting time processes, and random rooted trees), and an account of the relationship of his work to
that of Félix Pollaczek.
On transformations of Wiener space
Authors: Skorokhod Anatoli V.
Published: March 2007

We consider transformations of the form

urn:x-wiley:20903332:media:ista584613:ista584613-math-0001

on the space C of all continuous functions x = xt : [0, 1] → ℝ, x0 = 0, where a(s, x)
is a measurable function [0, 1] × C → ℝ which is ‐measurable for a fixed s and
is the σ‐algebra generated by {xu, u ≤ t}. It is supposed that Ta maps the
Wiener measure μ0 on into a measure μa which is equivalent with respect
to μ0. We study some conditions of invertibility of such transformations. We
also consider stochastic differential equations of the form

urn:x-wiley:20903332:media:ista584613:ista584613-math-0005

where w(t) is a Wiener process. We prove that this equation has a unique strong
solution if and only if it has a unique weak solution.
Busy period analysis, rare events and transient behavior in fluid flow models
Authors: Asmussen Søren
Published: March 2007

We consider a process on E × [0, ∞), such that {Jt} is a
Markov process with finite state space E, and {Vt} has a linear drift ri on
intervals where Jt = i and reflection at 0. Such a process arises as a fluid flow
model of current interest in telecommunications engineering for the purpose of
modeling ATM technology. We compute the mean of the busy period and
related first passage times, show that the probability of buffer overflow within a
busy cycle is approximately exponential, and give conditioned limit theorems for
the busy cycle with implications for quick simulation. Further, various
inequalities and approximations for transient behavior are given. Also explicit
expressions for the Laplace transform of the busy period are found.
Mathematically, the key tool is first passage probabilities and exponential change
of measure for Markov additive processes.
Large deviations for tandem queueing systems
Authors: Dobrushin Roland L. , Pechersky Eugene A.
Published: March 2007

The crude asymptotics of the large delay probability in a tandem queueing
system is considered. The main result states that one of the two channels in the
tandem system defines the crude asymptotics. The constant that determines the
crude asymptotics is given. The results obtained are based on the large deviation
principle for random processes with independent increments on an infinite
interval recently established by the authors.
A new simulation estimator of system reliability
Authors: Ross Sheldon M.
Published: March 2007

A basic identity is proven and applied to obtain new simulation estimators
concerning (a) system reliability, (b) a multi‐valued system. We show that the
variance of this new estimator is often of the order α2 when the usual raw
estimator has variance of the order α and α is small. We also indicate how this
estimator can be combined with standard variance reduction techniques of
antithetic variables, stratified sampling and importance sampling.
asymptotics for open‐loop window flow control
Authors: Berger Arthur W. , Whitt Ward
Published: March 2007

An open‐loop window flow‐control scheme regulates the flow into a system
by allowing at most a specified window size W of flow in any interval of length
L. The sliding window considers all subintervals of length L, while the jumping window considers consecutive disjoint intervals of length L. To better understand
how these window control schemes perform for stationary sources, we describe for
a large class of stochastic input processes the asymptotic behavior of the maximum flow in such window intervals over a time interval [0, T] as T and Lget
large, with T substantially bigger than L. We use strong approximations to
show that when T ≫ L ≫ logT an invariance principle holds, so that the
asymptotic behavior depends on the stochastic input process only via its rate and
asymptotic variability parameters. In considerable generality, the sliding and
jumping windows are asymptotically equivalent. We also develop an approximate relation between the two maximum window sizes. We apply the asymptotic results to develop approximations for the means and standard deviations of
the two maximum window contents. We apply computer simulation to evaluate
and refine these approximations.
Regeneration and general Markov chains
Authors: Kalashnikov Vladimir V.
Published: March 2007

Ergodicity, continuity, finite approximations and rare visits of
general Markov chains are investigated. The obtained results permit
further quantitative analysis of characteristics, such as, rates of
convergence, continuity (measured as a distance between perturbed and
non‐perturbed characteristics), deviations between Markov chains, accuracy of approximations and bounds on the distribution function of the
first visit time to a chosen subset, etc. The underlying techniques use the
embedding of the general Markov chain into a wide sense regenerative
process with the help of splitting construction.
On the calculation of steady‐state loss probabilities in the GI/G/2/0 queue
Authors: Kovalenko Igor N. , Atkinson J. Ben
Published: March 2007

This paper considers methods for calculating the steady‐state loss probability
in the GI/G/2/0 queue. A previous study analyzed this queue in discrete time
and this led to an efficient, numerical approximation scheme for continuous‐time
systems. The primary aim of the present work is to provide an alternative approach by analyzing the GI/ME/2/0 queue; i.e., assuming that the service time
can be represented by a matrix‐exponential distribution. An efficient computational scheme based on this method is developed and some numerical examples
are studied. Some comparisons are made with the discrete‐time approach, and
the two methods are seen to be complementary.
A further study of an approximation for last‐exit and first‐passage probabilities of a random walk
Authors: Daley D. J. , Servi L. D.
Published: March 2007

Identities between first‐passage or last‐exit probabilities and unrestricted transition probabilities that hold for left‐ or right‐continuous lattice‐valued random
walks form the basis of an intuitively based approximation that is demonstrated
by computation to hold for certain random walks without either the left‐ or
right‐continuity properties. The argument centers on the use of ladder variables;
the identities are known to hold asymptotically from work of Iglehart leading to
Brownian meanders.
Sample‐path stability conditions for multiserver input‐output processes
Authors: El-Taha Muhammad , Stidham Shaler
Published: March 2007

We extend our studies of sample‐path stability to multiserver input‐output processes with conditional output rates that may depend on the
state of the system and other auxiliary processes. Our results include processes with countable as well as uncountable state spaces. We establish
rate stability conditions for busy period durations as well as the input
during busy periods. In addition, stability conditions for multiserver queues with possibly heterogeneous servers are given for the workload, attained service, and queue length processes. The stability conditions can be
checked from parameters of primary processes, and thus can be verified a
priori. Under the rate stability conditions, we provide stable versions of
Little′s formula for single server as well as multiserver queues. Our approach leads to extensions of previously known results. Since our results
are valid pathwise, non‐stationary as well as stationary processes are covered.