bluuebunny/crossref_metadata_2025 huggingface dataset:
Weak infinitesimal generator for a stochastic partialdifferential equation with time delay
Authors: Chang Mou-Hsiung
Published: March 2007

In this paper, we consider the Markov solution process for a stochastic parabolic differential equation with time delay. Under the Lipschitz condition and
boundedness on the drift and diffusion coefficient, properties of the weak infinitesimal generator of the associated Markov operators are established. Actions of
the weak infinitesimal generator on the space of quasi‐tame functions are also
investigated.
Convergence of a random iteration scheme to a random fixed point
Authors: Choudhury Binayak S.
Published: March 2007

This paper discusses the convergence of random Ishikawa iteration scheme to
a random fixed point for a certain class of random operators.
Transformation formulas for terminating Saalschützian hypergeometric series of unit argument
Authors: Bühring Wolfgang
Published: March 2007

Transformation formulas for terminating Saalschützian hypergeometric series
of unit argument  p+1Fp(1) are presented. They generalize the Saalschützian
summation formula for  3F2(1). Formulas for p = 3, 4, 5 are obtained explicitly,
and a recurrence relation is proved by means of which the corresponding formulas
can also be derived for larger p. The Gaussian summation formula can be derived from the Saalschützian formula by a limiting process, and the same is true for
the corresponding generalized formulas. By comparison with generalized Gaussian summation formulas obtained earlier in a different way, two identities for finite sums involving terminating  3F2(1) series are found. They depend on four or
six independent parameters, respectively.
Razumikhin′s method in the qualitative theory of processes with delay
Authors: Myshkis Anatoly D.
Published: March 2007

B.S. Razumikhin′s concept in the qualitative theory of systems delay is
clarified and discussed. Various ways of improvements of stability conditions are
considered. The author shows that the guiding role of Lyapunov functions and
demonstrates Razumikhin′s method as a practical case of continuous version of
the mathematical induction. Several examples demonstrate the obtained results.
Nonnegative solutions to superlinear problems of generalized Gelfand type
Authors: O′Regan Donal
Published: March 2007

Existence of nonnegative solutions to superlinear second order problems of
the form y″ + μq(t)g(t, y) is discussed in this paper. Here μ ≥ 0 is a parameter.
An approach to the stochastic calculus in the non‐Gaussian case
Authors: Dorogovtsev Andrey A.
Published: March 2007

We introduce and study a class of operators of stochastic differentiation and
integration for non‐Gaussian processes. As an application, we establish an analog
of the Itô formula.
Nonlinear stochastic functional integral equations in the plane
Authors: Turo Jan
Published: March 2007

Local or global existence and uniqueness theorems for nonlinear stochastic
functional integral equations are proved. The proofs are based on the successive
approximations methods. The formulation includes retarded arguments and hereditary Volterra terms.
Strongly damped semilinear equations
Authors: Bahuguna D.
Published: March 2007

A class of strongly damped semilinear equations is studied by using the
theory of analytic semigroups. Conditions (on the nonlinear forcing term) are
given under which the existence and uniqueness of local and global classical
solutions are ensured.
Stable discretization methods with external approximation schemes
Authors: Verma Ram U.
Published: March 2007

We investigate the external approximation‐solvability of nonlinear equations‐ an upgrade of the external approximation scheme of Schumann and Zeidler [3]
in the context of the difference method for quasilinear elliptic differential equations.
Generalized Neumann and Kapteyn expansions
Authors: Exton Harold
Published: March 2007

Certain formal series of a most general nature are specialized so as to deduce
expansions in terms of a class of generalized hypergeometric functions. These
series generalize the Neumann and Kapteyn series in the theory of Bessel functions, and their convergence is investigated. An example of a succinct expansion
is also given.
Periodic solutions of quasi‐differential equations
Authors: Boucherif Abdelkader , García-Río Eduardo , Nieto Juan J.
Published: March 2007

Existence principles and theorems are established for the nonlinear problem
Lu = f(t, u) where is a quasi‐differential operator and f is a
Carathéodory function. We prove a maximum principle for the operator L and
then we show the validity of the upper and lower solution method as well as the
monotone iterative technique.
On the solution of the Liouville equation over a rectangle
Authors: Arthurs A. M. , Clegg J. , Nagar A. K.
Published: March 2007

Methods for integral equations are used to derive pointwise bounds for the
solution of a boundary value problem for the nonlinear Liouville partial differential equation over a rectangle. Several test calculations are performed and the
resulting solutions are more accurate than those obtained previously by other
methods.
Painleve analysis of a class of nonlinear diffusion equations
Authors: Chandrasekaran P. , Ramasami E. K.
Published: March 2007

We study the Painleve analysis for a class of nonlinear diffusion equations.
We find that in some cases it has only the conditional Painleve property and in
other cases, just the Painleve property. We also obtained special solutions.
Mean time for the development of large workloads and large queue lengths in the GI/G/1 queue
Authors: Knessl Charles , Tier Charles
Published: March 2007

We consider the GI/G/1 queue described by either the workload U(t) (unfinished work) or the number of customers N(t) in the system. We compute the
mean time until U(t) reaches excess of the level K, and also the mean time until
N(t) reaches N0. For the M/G/1 and GI/M/1 models, we obtain exact contour
integral representations for these mean first passage times. We then compute the
mean times asymptotically, as K and N0 → ∞, by evaluating these contour integrals. For the general GI/G/1 model, we obtain asymptotic results by a singular
perturbation analysis of the appropriate backward Kolmogorov equation(s).
Numerical comparisons show that the asymptotic formulas are very accurate even
for moderate values of K and N0.
Stochastic analysis of the departure and quasi‐input processes in a versatile single‐server queue
Authors: Artalejo J. R. , Gomez-Corral A.
Published: March 2007

This paper is concerned with the stochastic analysis of the departure and
quasi‐input processes of a Markovian single‐server queue with negative exponential arrivals and repeated attempts. Our queueing system is characterized by the
phenomenon that a customer who finds the server busy upon arrival joins an
orbit of unsatisfied customers. The orbiting customers form a queue such that
only a customer selected according to a certain rule can reapply for service. The
intervals separating two successive repeated attempts are exponentially distributed with rate α + jμ, when the orbit size is j ≥ 1. Negative arrivals have the
effect of killing some customer in the orbit, if one is present, and they have no
effect otherwise. Since customers can leave the system without service, the structural form of type M/G/1 is not preserved. We study the Markov chain with
transitions occurring at epochs of service completions or negative arrivals. Then
we investigate the departure and quasi‐input processes.
A fixed‐size batch service queue with vacations
Authors: Lee Ho Woo , Lee Soon Seok , Chae K. C.
Published: March 2007

The paper deals with batch service queues with vacations in which customers
arrive according to a Poisson process. Decomposition method is used to derive
the queue length distributions both for single and multiple vacation cases. The
authors look at other decomposition techniques and discuss some related open problems.
Retrial queues with recurrent demand option
Authors: Farahmand K. , Smith N. H.
Published: March 2007

The object of this paper is to analyze the model of a queueing system in
which customers can call in only to request service: if the server is free, the customer enters service immediately. Otherwise, if the service system is occupied,
the customer joins a source of unsatisfied customers called the orbit. On completion of each service the recipient of service has an option of leaving the system
completely with probability 1 − p or returning to the orbit with probability p.
We consider two models characterized by the discipline governing the order of rerequests for service from the orbit. First, all the customers from the orbit apply
at a fixed rate. Secondly, customers from the orbit are discouraged and reduce
their rate of demand as more customers join the orbit. The arrival at and the demands from the orbit are both assumed to be according to the Poisson process.
However, the service times for both primary customers and customers from the
orbit are assumed to have a general distribution. We calculate several characteristic quantities of these queueing systems.
A characterization and moving average representation for stable harmonizable processes
Authors: Nikfar M. , Soltani A. Reza
Published: March 2007

In this paper we provide a characterization for symmetric α‐stable harmonizable processes for 1 < α ≤ 2. We also deal with the problem of obtaining a moving average representation for stable harmonizable processes discussed by Cambanis and Soltani [3], Makegan and Mandrekar [9], and Cambanis and Houdre
[2]. More precisely, we prove that if Z is an independently scattered countable
additive set function on the Borel field with values in a Banach space of jointly
symmetric α‐stable random variables, 1 < α ≤ 2, then there is a function
k ∈ L2(λ) (λ is the Lebesgue measure) and a certain symmetric‐α‐stable random
measure Y for which

urn:x-wiley:20903332:media:ista324107:ista324107-math-0001

,
if and only if Z(A) = 0 whenever λ(A) = 0. Our method is to view SαS processes with parameter space R as SαS processes whose parameter spaces are certain
Lβ spaces.
Solutions of initial value problems for a pair of linear firstorder ordinary differential systems with interface‐spatialconditions
Authors: Venkatesulu M. , Baruah Pallav Kumar
Published: March 2007

Solutions of initial value problems associated with a pair of ordinary differential systems (L1, L2) defined on two adjacent intervals I1 and I2 and satisfying
certain interface‐spatial conditions at the common end (interface) point are
studied.
Remarks on the life and research of Roland L. Dobrushin
Authors: Minlos R. A. , Pechersky E. A. , Suhov Yu. M.
Published: March 2007

The life and research work of Professor R.L. Dobrushin (1929‐1995) had a
profound influence on several areas of probability theory, information theory, and
mathematical physics. The paper contains a biographical note, a review of
Dobrushin′s results, and a list of his publications.
Differential inequalities for hysteresis systems
Authors: Chernorutskii Vladimir V. , Krasnosel′skii Mark A.
Published: March 2007

The theory of differential inequalities is extended to functional‐differential
equations with hysteresis nonlinearities. A key feature is the existence of a semiorder of the state space of nonlinearity and a special monotonicity of the righthand side of differential inequality.

This article is dedicated to the memory of Roland L. Dobrushin.
The failure rate in reliability: approximations and bounds
Authors: Cocozza-Thivent Christiane , Kalashnikov Vladimir
Published: March 2007

We consider models typical to the area of reliability, and a failure rate function for processes describing the dynamics of these models. Various approximations of the failure rate function are proposed and their accuracies are investigated. The basic case studied in the paper is a regenerative model. Some interesting particular cases (Markov, semi‐Markov, etc.) are considered. All proposed
estimates are stated in a tractable analytic form.

This article is dedicated to the memory of Roland L. Dobrushin.
Balls left empty by a critical branching Wiener process
Authors: Révész Pál
Published: March 2007

At time t = 0 we have a Poisson random field on ℝd. Each particle executes
a critical branching Wiener process starting from its position at time t = 0. Let
RT be the radius of the largest ball around the origin of ℝd which does not
contain any particle at time T. Our goal is to characterize the properties of the
stochastic process {RT, T ≥ 0}.

This article is dedicated to the memory of Professor Roland L. Dobrushin.
The failure rate in reliability: numerical treatment
Authors: Cocozza-Thivent Christiane , Kalashnikov Vladimir
Published: March 2007

This paper contains approximations and bounds of failure rate functions of
redundant systems. We illustrate properties of these bounds and their
accuracy.
Stochastic approximation‐solvability of linear random equations involving numerical ranges
Authors: Verma Ram U.
Published: March 2007

The random (or stochastic) approximation‐solvability, based on a projection scheme, of linear random operator equations involving the theory of
the numerical range of a bounded linear random operator is considered.
The obtained results generalize results with regard to the deterministic
approximation‐solvability of linear operator equations using the Galerkin
convergence method.
Terminal value problems of impulsive integro‐differential equations in Banach spaces
Authors: Guo Dajun
Published: March 2007

This paper uses cone theory and the monotone iterative technique to
investigate the existence of minimal nonnegative solutions of terminal
value problems for first order nonlinear impulsive integro‐differential
equations of mixed type in a Banach space.
Integral inequalities of Gronwall type for piecewise continuous functions
Authors: Bainov Drumi D. , Hristova Snezhana G.
Published: March 2007

In this paper we generalize the integral inequality of Gronwall and study
the continuous dependence of the solution of the initial value problem for
nonlinear impulsive integro‐differential equations of Volterra type on the
initial conditions.
Random fixed points of non‐self maps and random approximations
Authors: Beg Ismat
Published: March 2007

In this paper we prove random fixed point theorems in reflexive Banach
spaces for nonexpansive random operators satisfying inward or Leray‐Schauder condition and establish a random approximation theorem.
On the setwise convergence of sequences of measures
Authors: Lasserre Jean B.
Published: March 2007

We consider a sequence {μn} of (nonnegative) measures on a general measurable space (X, ℬ). We establish sufficient conditions for setwise convergence and convergence in total variation.
Random vector variational inequalities and random noncooperative vector equilibrium
Authors: Lee Gue Myung , Lee Byung Soo , Chang Shih-Sen
Published: March 2007

In this paper, we prove some existence theorems for random vector variational inequalities and an existence theorem for the random noncooperative vector equilibrium under suitable assumptions.
Functional differential equations with nonlocal initial conditions
Authors: Aizicovici Sergiu , Gao Yun
Published: March 2007

We study the existence, uniqueness, asymptotic properties, and continuous
dependence upon data of solutions to a class of abstract nonlocal Cauchy
problems. The approach we use is based on the theory of m‐accretive
operators and related evolution equations in Banach spaces.
Reaction diffusion equations and quadratic convergence
Authors: Vatsala A. S. , Mahrous Mohamed A. , Alkahby Hadi Yahya
Published: March 2007

In this paper, the method of generalized quasilinearization has been extended to reaction diffusion equations. The extension includes earlier known results as special cases. The earlier results developed are when (i) the right‐hand side function is the sum of a convex and concave function, and (ii)
the right‐hand function can be made convex by adding a convex function.
In our present result, if the monotone iterates are mildly nonlinear, we
establish the quadratic convergence as in the quasilinearization method. If
the iterates are totally linear then the iterates converge semi‐quadratically.
An iterative algorithm on fixed points of relaxed Lipschitz operators
Authors: Verma Ram U.
Published: March 2007

Fixed points of Lipschitzian relaxed Lipschitz operators based on a generalized iterative algorithm are approximated.
New generalizations of the Poisson Kernel
Authors: Haruki Hiroshi , Rassias Themistocles M.
Published: March 2007

The purpose of this paper is to give new generalizations of the Poisson
Kernel in two dimensions and discuss integral formulas for them. This
paper concludes with an open problem.
A new criterion for close‐to‐convexity of partial sums of certain hypergeometric functions
Authors: Jahangiri Massoud
Published: March 2007

We consider the partial sums of certain hypergeometric functions and
establish conditions imposed on the locations of zeros of those polynomials
in order to be close‐to‐convex in the open unit disk.
A strong law of large numbers for 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 a strong law of large numbers for the
spherical average of a harmonizable isotropic random field.
Quasi‐retractive representation of solution sets to stochastic inclusions
Authors: Kisielewicz Michal
Published: March 2007

Continuous dependence and retraction properties of solution sets to
stochastic inclusions are considered.
Stability of stationary and periodic solutions equations in Banach space
Authors: Dorogovtsev A. Ya.
Published: March 2007

Linear difference and differential equations with operator coefficients and
random stationary (periodic) input are considered. Conditions are presented for the mean stability of stationary (periodic) solutions under small perturbation of the coefficients.
Real zeros of a random polynomial with Legendre elements
Authors: Farahmand K.
Published: March 2007

Let be a sequence of normalized Legendre polynomials orthogonal with respect to the interval (−1, 1). The asymptotic
estimate of the expected number of real zeros of the random polynomial
where gj, j = 1, 2, …, n are independent
identically and normally distributed random variables with mean zero and
variance one is known. The present paper considers the case when the
means and variances of the coefficients are not all necessarily equal. It is
shown that in general this expected number of real zeros is only dependent
on variances and is independent of the means.
On a mild solution of a semilinear functional‐differential evolution nonlocal problem
Authors: Byszewski Ludwik , Akca Haydar
Published: March 2007

The existence, uniqueness, and continuous dependence of a mild solution of
a nonlocal Cauchy problem for a semilinear functional‐differential evolution equation in a general Banach space are studied. Methods of a C0
semigroup of operators and the Banach contraction theorem are applied.
The result obtained herein is a generalization and continuation of those reported in references [2‐8].
Existence of solutions of nonlinear integrodifferential equation with nonlocal condition
Authors: Balachandran K. , Chandrasekaran M.
Published: March 2007

In this paper we prove the existence and uniqueness of local and global
solutions of a nonlocal Cauchy problem for a class of integrodifferential
equation. The method of semigroups and the contraction mapping principle are used to establish the results.
Generalized nonlinear variational inequality problems involving multivalued mappings
Authors: Verma Ram U.
Published: March 2007

The solvability of a class of generalized nonlinear variational inequality
problems involving multivalued, strongly monotone and strongly Lipschitz
(a special type) operators, which are closely associated with generalized
nonlinear complementarily problems, is discussed.
Two parallel finite queues with simultaneous services and Markovian arrivals
Authors: Chakravarthy S. R. , Thiagarajan S.
Published: March 2007

In this paper, we consider a finite capacity single server queueing model
with two buffers, A and B, of sizes K and N respectively. Messages arrive
one at a time according to a Markovian arrival process. Messages that arrive at buffer A are of a different type from the messages that arrive at
buffer B. Messages are processed according to the following rules: 1. When
buffer A(B) has a message and buffer B(A) is empty, then one message
from A(B) is processed by the server. 2. When both buffers, A and B, have
messages, then two messages, one from A and one from B, are processed simultaneously by the server. The service times are assumed to be exponentially distributed with parameters that may depend on the type of service.
This queueing model is studied as a Markov process with a large state
space and efficient algorithmic procedures for computing various system
performance measures are given. Some numerical examples are discussed.
The MAP, M/G1, G2/1 queue with preemptive priority
Authors: Choi Bong Dae , Hwang Gang Uk
Published: March 2007

We consider the MAP, M/G1, G2/1 queue with preemptive resume priority, where low priority customers arrive to the system according to a Markovian arrival process (MAP) and high priority customers according to a
Poisson process. The service time density function of low (respectively:
high) priority customers is g1(x) (respectively: g2(x)). We use the supplementary variable method with Extended Laplace Transforms to obtain the
joint transform of the number of customers in each priority queue, as well
as the remaining service time for the customer in service in the steady
state. We also derive the probability generating function for the number
of customers of low (respectively, high) priority in the system just after
the service completion epochs for customers of low (respectively, high)
priority.
Impulse control in Kalman‐like filtering problems
Authors: Basin Michael V. , Pinsky Mark A.
Published: March 2007

This paper develops the impulse control approach to the observation process in Kalman‐like filtering problems, which is based on impulsive modeling of the transition matrix in an observation equation. The impulse control generates the jumps of the estimate variance from its current position
down to zero and, as a result, enables us to obtain the filtering equations
for the Kalman estimate with zero variance for all post‐jump time
moments. The filtering equations for the estimates with zero variances are
obtained in the conventional linear filtering problem and in the case of
scalar nonlinear state and nonlinear observation equations.
The stationary G/G/s queue
Authors: Gall Pierre Le
Published: March 2007

The distribution of the queueing delay in the stationary G/G/s queue is
given with an application to the GI/G/s queue and to the M/G/s queue.
On the approximation of an integral by a sum of random variables
Authors: Einmahl John H. J. , Van Zuijlen Martien C. A.
Published: March 2007

We approximate the integral of a smooth function on [0, 1], where values
are only known at n random points (i.e., a random sample from the uniform‐(0, 1) distribution), and at 0 and 1. Our approximations are based
on the trapezoidal rule and Simpson′s rule (generalized to the non‐equidistant case), respectively. In the first case, we obtain an n2‐rate of
convergence with a degenerate limiting distribution; in the second case, the
rate of con‐vergence is as fast as n3½, whereas the limiting distribution is
Gaussian then.
A system of functional‐differential equations associated with the optimal detection problem for jump‐times of a Poisson process
Authors: Donchev Doncho S.
Published: March 2007

The value function in the optimal detection problem for jump‐times of a
Poisson process satisfies a special system of functional‐differential equations. In this paper, we investigate the system and prove the existence
and uniqueness of its solution.
On Ryszard Syski
Authors: Cohen J. W.
Published: March 2007

This is a brief account on Ryszard Syski′s scientific contributions and his
collaboration with the author.
Monotone measures of ergodicity for Markov chains
Authors: Keilson J. , Vasicek O. A.
Published: March 2007

The following paper, first written in 1974, was never published other than
as part of an internal research series. Its lack of publication is unrelated
to the merits of the paper and the paper is of current importance by virtue
of its relation to the relaxation time. A systematic discussion is provided
of the approach of a finite Markov chain to ergodicity by proving the
monotonicity of an important set of norms, each measures of egodicity,
whether or not time reversibility is present. The paper is of particular
interest because the discussion of the relaxation time of a finite Markov
chain [2] has only been clean for time reversible chains, a small subset of
the chains of interest. This restriction is not present here. Indeed, a new
relaxation time quoted quantifies the relaxation time for all finite ergodic
chains (cf. the discussion of Q1(t) below Equation (1.7)]. This relaxation
time was developed by Keilson with A. Roy in his thesis [6], yet to be
published.
Filtering with a limiter
Authors: Liptser R. , Muzhikanov P.
Published: March 2007

We consider a filtering problem for a Gaussian diffusion process observed
via discrete‐time samples corrupted by a non‐Gaussian white noise. Combining the Goggin′s result [2] on weak convergence for conditional expectation with diffusion approximation when a sampling step goes to zero we
construct an asymptotic optimal filter. Our filter uses centered observations passed through a limiter. Being asymptotically equivalent to a similar filter without centering, it yields a better filtering accuracy in a prelimit case.
Elementary methods for failure due to a sequence of Markovian events
Authors: Gani J.
Published: March 2007

This paper is concerned with elementary methods for evaluating the distribution of the time to system failure, following a particular sequence of
events from a Markov chain. After discussing a simple example in which
a specific sequence from a two‐state Markov chain leads to failure, the
method is generalized to a sequence from a (k > 2)‐state chain. The expectation and variance of the time T to failure can be obtained from the
probability generating function (p.g.f.) of T. The method can be extended
to the case of continuous time.
Analysis of a multi‐server queueing model of ABR
Authors: Núñez-Queija R. , Boxma O. J.
Published: March 2007

In this paper we present a queueing model for the performance analysis of
Available Bit Rate (ABR) traffic in Asynchronous Transfer Mode (ATM)
networks. We consider a multi‐channel service station with two types of
customers, denoted by high priority and low priority customers. In principle, high priority customers have preemptive priority over low priority
customers, except on a fixed number of channels that are reserved for low
priority traffic. The arrivals occur according to two independent Poisson
processes, and service times are assumed to be exponentially distributed.
Each high priority customer requires a single server, whereas low priority
customers are served in processor sharing fashion. We derive the joint distribution of the numbers of customers (of both types) in the system in
steady state. Numerical results illustrate the effect of high priority traffic
on the service performance of low priority traffic.
Stabilization of nonlinear systems by similarity transformations
Authors: Zuber Irina E.
Published: March 2007

For a system , u(x) = s∗(x)x, x ∈ ℝn, where the pair
(A(x), b(x)) is given, we obtain the feedback vector s(x) to stabilize the
corresponding closed loop system. For an arbitrarily chosen constant
vector g, a sufficient condition of the existence and an explicit form of a
similarity transformation T(A(x), b(x), g) is established. The latter
transforms matrix A(x) into the Frobenius matrix, vector b(x) into g, and
an unknown feedback vector s(x) into the first unit vector. The boundaries
of are determined by the boundaries of , . The stabilization of the transformed system is subject to the
choice of the constant vector g.
A stochastic inventory model with perishable and aging items
Authors: Aggoun Lakhdar , Benkherouf Lakdere , Tadj Lotfi
Published: March 2007

In this paper, we propose a single‐product, discrete time inventory model
for perishable items. Inventory levels are reviewed periodically and units
in stock have a maximum lifetime of M periods. It is assumed that the
dynamics of the inventory level is driven by a parameter process (reflecting perishability) and demands. By observing the history of the inventory
level we obtain the conditional distribution of the perishability parameter
by using the change of measure techniques. A special case is also presented.
A queueing system with queue length dependent service times, with applications to cell discarding in ATM networks
Authors: Choi Doo Il , Knessl Charles , Tier Charles
Published: March 2007

A queueing system (M/G1, G2/1/K) is considered in which the service time
of a customer entering service depends on whether the queue length, N(t),
is above or below a threshold L. The arrival process is Poisson, and the
general service times S1 and S2 depend on whether the queue length at the
time service is initiated is <L or ≥L, respectively. Balance equations
are given for the stationary probabilities of the Markov process (N(t), X(t)), where X(t) is the remaining service time of the customer currently
in service. Exact solutions for the stationary probabilities are constructed
for both infinite and finite capacity systems. Asymptotic approximations
of the solutions are given, which yield simple formulas for performance
measures such as loss rates and tail probabilities. The numerical accuracy
of the asymptotic results is tested.
Linear filtering with fractional Brownian motion in the signal and observation processes
Authors: Kleptsyna M. L. , Kloeden P. E. , Anh V. V.
Published: March 2007

Integral equations for the mean‐square estimate are obtained for the linear
filtering problem, in which the noise generating the signal is a fractional
Brownian motion with Hurst index h ∈ (3/4, 1) and the noise in the observation process includes a fractional Brownian motion as well as a Wiener
process.
In memoriam: Julian Keilson (November 19, 1924 ‐ March 8, 1999)
Authors: Syski Ryszard
Published: March 2007

This is a brief biographical account on late Julian Keilson, his scientific
contributions, and his collaboration with the author.
Existence of moments of increasing predictable processes associated with one‐ and two‐parameter potentials
Authors: Mishura Yu. , Oltsik Ya.
Published: March 2007

The criterion and sufficient condition for the existence of moments of one‐parameter increasing predictable processes is presented in terms of an associated potential. The estimates of moments of special functional connected with two‐parameter increasing predictable processes are given in the
case when the associated potential is bounded. The application of these
estimates to the local time for purely discontinuous strong martingales in
the plane is also presented.
Exact solution of the Bellman equation for a β‐discounted reward in a two‐armed bandit with switching arms
Authors: Donchev Doncho S.
Published: March 2007

We consider the symmetric Poissonian two‐armed bandit problem. For
the case of switching arms, only one of which creates reward, we solve explicitly the Bellman equation for a β‐discounted reward and prove that a
myopic policy is optimal.
An application of a noncompactness technique to an investigation of the existence of solutions to a nonlocal multivalued Darboux problem
Authors: Byszewski Ludwik , Papageorgiou Nikolaos S.
Published: March 2007

The aim of the paper is to prove two theorems on the existence of solutions to a nonlocal multivalued Darboux problem. The first theorem concerns the case when the orientor field is convex valued. The second
theorem concerns the case when the orientor field is nonconvex valued. A
compactness type condition involving the ball measure of noncompactness
is applied.
Sensitivity analysis for variational inclusions by Wiener‐Hopf equation techniques
Authors: Moudafi Abdellatif , Noor Muhammad Aslam
Published: March 2007

In this paper, we extend the sensitivity analysis framework developed recently for variational inequalities by Noor and Yen to variational inclusions relying on Wiener‐Hopf equation techniques. We prove the continuity and the Lipschitz continuity of the locally unique solution to parametric
variational inclusions without assuming differentiability of the given data.
Controllability of second order semilinear ordinary differential systems in Banach spaces
Authors: Balachandran K. , Anthoni S. Marshal
Published: March 2007

Sufficient conditions for controllability of semilinear second order ordinary
differential systems in Banach spaces are established using the theory of
strongly continuous cosine families. The results obtained are based on the
Schaefer theorem.
Transient analysis of a queue with queue‐length dependent MAP and its application to SS7 network
Authors: Choi Bong Dae , Choi Sung Ho , Sung Dan Keun , Lee Tae-Hee , Song Kyu-Seog
Published: March 2007

We analyze the transient behavior of a Markovian arrival queue with congestion control based on a double of thresholds, where the arrival process
is a queue‐length dependent Markovian arrival process. We consider
Markov chain embedded at arrival epochs and derive the one‐step transition probabilities. From these results, we obtain the mean delay and the
loss probability of the nth arrival packet. Before we study this complex
model, first we give a transient analysis of an MAP/M/1 queueing system
without congestion control at arrival epochs. We apply our result to a
signaling system No. 7 network with a congestion control based on thresholds.
Multi‐dimensional quasitoeplitz Markov chains
Authors: Dudin Alexander N. , Klimenok Valentina I.
Published: March 2007

This paper deals with multi‐dimensional quasitoeplitz Markov chains. We establish a sufficient equilibrium condition and derive a functional matrix equation for the corresponding vector‐generating function, whose solution is given algorithmically. The results are demonstrated in the form of examples and applications in queues with BMAP‐input, which operate in synchronous random environment.
The stationary local sojourn time in single server tandem queues with renewal input
Authors: Gall Pierre Le
Published: March 2007

We start from an earlier paper evaluating the overall sojourn time to derive the local sojourn time in stationary regime, in a single server tandem
queue of (m + 1) stages with renewal input. The successive service times
of a customer may or may not be mutually dependent, and are governed
by a general distribution which may be different at each sage.
Phototransformation of three herbicides: chlorbufam, isoproturon, and chlorotoluron. Influence of irradiation on toxicity
Authors: Tixier C. , Meunier L. , Bonnemoy F. , Boule P.
Published: March 2007

The direct phototransformations in aqueous solution of chlorbufam (I), chlorotoluron (II), and
isoproturon (III) are compared.

With I and II photohydrolysis (substitution of chlorine atom with formation of the corresponding hydroxylated
derivative) is initially almost quantitative. It does not depend on irradiation wavelength in the range
250–300 nm. In contrast with III the main reaction is a free radical rearrangement, the reaction being more
efficient at 254nm than at wavelengths longer than 270 nm.

Compounds II and III were also irradiated on sand in the absence of water. Several photoproducts were
identified, they result from elimination or oxidation of methyl groups of urea moiety.

The toxicity of photoproducts was determined using the standard Microtox® test (toxicity on the bacterium
Vibrio fischeri). Photohydrolysis of I and II does not change much the toxicity of solutions whereas
the oxidation, or at a lower scale the elimination of methyl group on the urea moiety, dramatically increases
the toxicity.
Electron transfer reaction and demetalation of phthalocyanines
Authors: Kossanyi Jean , Chahraoui Driss
Published: March 2007

An electron‐transfer reaction takes place in the ground state between phthalocyanines (as
electron‐donors) and pyrylium cations (as electron‐acceptors) in polar solvents, reaction which leads to the
phthalocyanine radical‐cations as evidenced by its absorption spectra identical to the one of the species
formed by electrochemical oxidation.

The fluorescence emission of the phthalocyanines is quenched by electron‐acceptors (principally quinones).
The free energy change ΔGCT of the electron‐transfer reaction has been evaluated for each electron acceptor
with a solvation energy of 0.14 eV in the case of dimethylformamide and 1.2 eV in that of dichloromethane.
The rate constant of the quenching of the phthalocyanines singlet excited state by a series of electronacceptors
is found to be of the order of 1.2 − 1.5 × 1010L · mol-1s-1.

Metalated phthalocyanines are demetalated in the dark by hydroxy‐anthraquinones with a rate constant
of the order of 10−2L · mol-1s-1 at 292K and which increases (up to 7 × 10−2L · mol-1s-1 at 349 K) with
temperature. The activation energy of the demetalation reaction has been determined to be ca 30 kJ · mol-1 for 1,4‐dihydroxyanthraquinone and 35 kJ · mol-1 for 1,2,4‐trihydroxyanthraquinone.
Fluorescence and photostability studies of anthracene‐9‐carboxylic acid in different media
Authors: Abdel-Mottaleb M. S. A. , Galal H. R. , Dessouky A. F. M. , El-Naggar M. , Mekkawi D. , Ali S. S. , Attya G. M.
Published: March 2007

Electronic absorption and fluorescence spectra of anthracene‐9‐carboxylic acid (ANCA) were
studied in different homogeneous solvents, binary protic/aprotic solvent mixtures and in heterogeneous
solutions of the cationic cetyltrimethyl ammonium bromide (CTAB) micelle. Different chemical species of
ANCA were identified spectroscopically in different media. The results are discussed on the basis of a mechanism
that involves two equilibria: acid‐base equilibrium and monomer‐dimer equilibrium. These equilibria
were found to be very sensitive to the nature of the medium and the concentration of ANCA.

Moreover, while it is photostable in most solvents studied, the ANCA was found to be photolabile in aqueous
media of different pHs. The acid‐base catalyzed photodegradation rate was studied by following up
absorption and/or fluorescence intensities as a function of illumination dose. The determined rate of the
photochemical degradation of ANCA depends on the nature of the medium. The first order degradation rate
constant is remarkably enhanced in heterogeneous medium of CTAB. As expected, the determined activation
energy is low (∼ 3.2 kJ. mol-1). This result favors photooxidation process. Anthraquinone was the main photodegradation
product obtained via9, 9′‐dicarboxylic head‐to‐head dimer of anthracene that was identified
by GC‐Mass technique.
Photostability and photostabilizing effect of humic acids
Authors: Mekkaoui M. , Elazzouzi M. , Bouhaouss A. , Ferhat M. , Chovelon J. M. , Meallier P.
Published: March 2007

The photolysis of Humic Acids (HA) extracted from Moroccan soil in water under simulated
sunlight method has been studied. The photochemical degradation of HA in concentration (30 mg/L) has
been followed by TOC (Total Organic Carbon) and E4/E6 ratio (The E4/E6 value widely used to characterize
humic acids is the ratio of absorption intensities at 465 and 665 nm). HA were found photostable after 24 h of
irradiation exposure and produce a screen effect on photochemical degradation of TRB (Tribenuron‐methyl)
and IMAZ (Imazapyr) herbicides.
Photocatalytic degradation of aqueous tetrahydrofuran, 1,4‐dioxane, and their mixture with TiO2
Authors: Mehrvar Mehrab , Anderson William A. , Moo-Young Murray
Published: March 2007

Photocatalytic degradation of tetrahydrofuran, 1,4‐dioxane, and their mixture in a slurry photoreactor
was studied. Using both GC/MS and ion chromatography (IC) methods, possible intermediates were
detected and the reaction mechanism pathways for both compounds were proposed. Kinetic models were
developed and the kinetic parameters were estimated using a statistical method of non‐linear parameter estimation
in which all experimental data were utilized. It was shown that tetrahydrofuran was disappeared via
direct oxidation as well as hydroxyl radical attack. A modified Langmuir‐Hinshelwood described the degradation
behavior of tetrahydrofuran and the binary system. 1,4‐Dioxane obeyed a simple Langmuir‐Hinshelwood
kinetic form in the single compound system.
Artificial molecular‐level machines with [Ru(bpy)3]2+ as a “light‐fueled motor”
Authors: Ballardini Roberto , Balzani Vincenzo , Credi Alberto , Gandolfi Maria Teresa , Venturi Margherita
Published: March 2007

A molecular‐level machine is an assembly of a discrete number of molecular components (that is,
a supramolecular structure) designed to perform mechanical‐like movements (output) as a consequence of
appropriate external stimuli (input). Like macroscopic machines, molecular‐level machines are characterized
by (i) the kind of energy input supplied to make them work, (ii) the kind of movement performed by their components,
(iii) the way in which their operation can be controlled and monitored, (iv) the possibility to repeat
the operation at will and establish a cyclic process, (v) the time scale needed to complete a cycle of operation,
and (vi) the function performed. The most convenient way to supply energy to an artificial molecular‐level
machine is through a photochemical reaction. (bpy = 2, 2′‐bipyridine) can be used as a photosensitizer
to power mechanical movements in machines based on pseudorotaxanes, rotaxanes and catenanes.
Besides being used as an external photosensitizer, can be incorporated in one of the machine
components as a “light‐fueled” motor. Three types of photochemically driven piston/cylinder systems and
a photocontrollable molecular abacus are described. Other kinds of more sophisticated molecular‐level machines
based on rotaxanes and catenanes are proposed. The extension of the concept of machine to the
molecular level is important not only for the sake of basic research, but also for the growth of nanoscience
and the development of nanotechnology.
Photoinduced charge separation and recombination under distance, orientation, and spin controlled conditions
Authors: Verhoeven Jan W. , Paddon-Row Michael N.
Published: March 2007

Great efforts have been made to mimic the efficient photoinduced charge separation and concomitant
energy storage of natural photosynthetic systems via artificial (supra) molecular constructs as well
as to design molecules with potential use for application in molecular electronic circuits. Close packing
of such molecules introduces the problem of short‐circuiting and cross talk between the separate molecular
components. In the present paper the limits will be investigated to which such short‐circuiting can be
prevented by the use of saturated hydrocarbon (alkane) type insulating structures. Furthermore, as will be
shown, several typically molecular scale operating principles such as orbital symmetry and spin multiplicity
control can allow the realisation of systems in which fast and efficient charge separation is combined
with very slow charge recombination even when the distance between the D(onor) and A(cceptor) moieties
is very small.
Design and development of second‐generation titanium oxide photocatalysts to better our environment—approaches in realizing the use of visible light
Authors: Anpo Masakazu , Takeuchi Masato
Published: March 2007

The design and development of second‐generation titanium oxide photocatalysts which absorb
UV‐visible light and work as efficient photocatalysts under irradiation of light in the UV‐visible light
regions were successfuly carriedout by applying advancedmetal ion‐implantation techniques. Titanium oxide
catalysts were implanted with various transition‐metal ions by a high‐voltage acceleration technique,
then calcined in O2 at around 723–823 K to produce photocatalysts capable of absorbing visible light, the
extent of such redshift depending on the kind and amount of metal ion implanted. The transition‐metal ion implanted titanium
oxide photocatalysts, specifically using V, Mn, or Cr ions, were successful in carring out
various photocatalytic reactions such as the decomposition of NOX and the reaction involving the decomposition of H2O at 295 K, significantly under irradiation with visible light longer than 450 nm. In outdoor field
reactivity tests, these V or Cr ion‐implanted titanium oxide photocatalysts showed four to three times higher
photocatalytic reactivity for those photocatalytic reactions under solar beam irradiation, as compared with
the original unimplanted titanium oxide photocatalyst. The advantages and possibilities of utilizing such
second‐generation titanium oxide photocatalysts are the only way to address environmental pollution on a
large andglobal scale.
Photoelectrochemical solar cells using [(dcbH2)2RuLL ],L, L′ = substituted pyridines, as nanocrystalline TiO2 sensitizers
Authors: Garcia Christian Graziani , Iha Neyde Yukie Murakami
Published: March 2007

The development of thin‐layer transparent solar cells based on dye sensitization of nanocrystalline
n‐type TiO2 undertaken at the Laboratory of Inorganic Photochemistry and Energy Conversion
at the Chemistry Institute of Universidade de São Paulo is presented. Compounds of the formula cis‐
,
L, L′ = substituted pyridines, as nanocrystalline TiO2, ‐bipyridine and L, L′ = substituted pyridines, have been successfully
employed as molecular sensitizers in photoelectrochemical solar cells based on dye‐sensitization
of n‐TiO2. This regenerative solar cell consists of a TCO glass with a dye‐sensitized TiO2 semiconductor film as a photoanode, I2/LiI solution in acetonitrile as a redox mediator and a transparent Pt coated TCO glass
as a counter electrode. Efficient conversion of visible light into electricity was achieved with IPCE (Incident
Photon‐to‐Current Conversion Efficiency) as high as 50% between 400 and 550 nm.
Role of photochemical and microbial degradation of phenol in water
Authors: Tchaikovskaya O. , Sokolova I. , Kondratieva L. , Karetnikova E.
Published: March 2007

The present work is aimed at spectroscopic and luminescent investigations of the microbial
cleavage efficiency of phenol in the water solution upon expose to UV light. With increasing time of irradiation
of phenol in the saline solution,the absorption intensity increases throughout the spectrum. The efficiency
of photoalteration of phenol in the saline solution is higher compared to that in water. The results obtained
have shown that the efficiency of complex photobiological phenol destruction increases sharply compared
to the photochemical or microbial destruction.
Influence of cyclodextrins on the photostability of selected drug molecules in solution and the solid‐state
Authors: Glass B. D. , Brown M. E. , Daya S. , Worthington M. S. , Drummond P. , Antunes E. , Lebete M. , Anoopkumar-Dukie S. , Maharaj D.
Published: March 2007

The photostability of selected drug molecules, including furosemide, prochlorperazine, diclofenac,
piroxicam, midazolam and nifedipine was studied, the kinetics of photodegradation, identification
of the photodegradants investigated and mechanisms of photodegradation proposed. Selected cyclodextrins
altered the photodegradation profiles of diclofenac, piroxicam, midazolam and nifedipine by either accelerating
or retarding the rate of photodegradation and generating novel photodegradants.