William A. Denig

M. Ishaq Zahid

QPACK - software for queueing system analysis

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

Igor  Malyshev

Hedley  Morris

Vladimir  Naroditsky

Leonid  Romanyuk

Surface integrals approach to solution of some free boundary problems

A two-dimensional classical hyperspace fluid theory of the 
vacuum which is an alternative to Schr&#246;dinger quantum theory involves 
a &#147;stirring&#148; energy density. This energy density, like entropy density, 
measures the local &#147;disturbance&#148; 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 &#147;action&#148; of this source 
term without assuming quantum time evolution. Schr&#246;dinger 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.

James G. Gilson

Classical variational basis for Schr&#246;dinger quantum theory

The propagation of edge waves in a thinly layered laminated 
medium with stress couples under initial stresses is examined. Based 
upon an approximate representation of a laminated medium by an 
equivalent anisotropic continuum with average initial and couple 
stresses, an explicit form of frequency equation is obtained to derive the 
phase velocity of edge waves. Edge waves exist under certain 
conditions. The inclusion of couple stresses increases the velocity of 
wave propagation. For a specific compression, the presence of couple 
stresses increases the velocity of wave propagation with the increase of 
wave number, whereas the reverse is the case when there is no couple 
stress. Numerical computation is performed with graphical 
representations. Several special cases are also examined.

Lokenath Debnath

Pijush Pal Roy

Propagation of edge waves in a thinly layered laminated medium with stress couples under initial stresses

We know the expected number of times that a polynomial of degree 
<mml:math alttext="$n$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math> with independent random real coefficients asymptotically crosses the
level <mml:math alttext="$K$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi></mml:math>, when <mml:math alttext="$K$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi></mml:math> is any real value such that <mml:math alttext="$\left( {{{K^2 } \mathord{\left/  {\vphantom {{K^2 } n}} \right.  \kern-\nulldelimiterspace} n}} \right) \to 0$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:msup><mml:mi>K</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#8594;</mml:mo><mml:mn>0</mml:mn></mml:math> as <mml:math alttext="$n \to \infty $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi><mml:mo>&#8594;</mml:mo><mml:mi>&#8734;</mml:mi></mml:math>. 
The present paper shows that, when <mml:math alttext="$K$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi></mml:math> is allowed to be large, this 
expected number of crossings reduces to only one. The coefficients of 
the polynomial are assumed to be normally distributed. It is shown 
that it is sufficient to let <mml:math alttext="$K \geqslant \exp \left( {nf} \right)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi><mml:mo>&#8805;</mml:mo><mml:mo>exp</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mi>f</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math> where <mml:math alttext="$f$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi></mml:math> is any function of <mml:math alttext="$n$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math> 
such that <mml:math alttext="$f \to \infty $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi><mml:mo>&#8594;</mml:mo><mml:mi>&#8734;</mml:mi></mml:math> as <mml:math alttext="$n \to \infty $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi><mml:mo>&#8594;</mml:mo><mml:mi>&#8734;</mml:mi></mml:math>.

Kambiz  Farahmand

Large level crossings of a random polynomial

James  Caristi

The simulation language SIMAN on microcomputers and mainframes

This paper examines a doubly controlled process of servicing 
machines. The classical system treated by Takács is equipped with 
<mml:math alttext="$m + 1$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math> unreliable machines served by one repairman. In the present 
modification of this model, the failure rates and the repair time may be 
controlled with respect to the state of the system. The process 
describing the number of intact machines is considered. To derive its 
steady state distribution in the form of a simple explicit formula, the 
author introduces an auxiliary model with <mml:math alttext="$m$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>m</mml:mi></mml:math> unreliable machines and a 
single repairman who keeps working even when all machines are intact. 
This result is based on a duality principle applied to the process above.

Jewgeni Dshalalow

On a duality principle in processes of servicing machines with double control

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.

Lajos Takács

Queues, random graphs and branching processes

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).

Ram  Lal

U. Narayan Bhat

Correlated random walks with stay

Integer and digital spaces are playing a significant role in digital image 
processing, computer graphics, computer tomography, robot vision, 
and many other fields dealing with finitely or countable many objects. 
It is proven here that every finite <mml:math alttext="$T_0 $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>T</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>-space is a quotient space of a
subspace of some simplex, i.e. of some subspace of a Euclidean space. 
Thus finite and digital spaces can be considered as abstract simplicial 
structures of subspaces of Euclidean spaces. Primitive subspaces of 
finite, digital, and integer spaces are introduced. They prove to be 
useful in the investigation of connectedness structure, which can be 
represented as a poset, and also in consideration of the dimension of 
finite spaces. Essentially <mml:math alttext="$T_0 $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>T</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>-spaces and finitely connected and
primitively path connected spaces are discussed.

Efim  Khalimsky

Finite, primitive and euclidean spaces

A study is made of the propagation of Rayleigh waves in a thinly layered 
laminated thermoelastic medium under deviatoric, hydrostatic, and couple 
stresses. The frequency equation of the Rayleigh waves is obtained. The 
phase velocity of the Rayleigh waves depends on the initial stress, deviatoric 
stress, and the couple stress. The laminated medium is first replaced by an 
equivalent anisotropic thermoelastic continuum. The corresponding 
thermoelastic coefficients (after deformation) are derived in terms of initially 
isotropic thermoelastic coefficients (before deformation) of individual layers. 
Several particular cases are discussed for the determination of the 
displacement fields with or without the effect of the couple stress.

On Rayleigh waves in a thinly layered laminated thermoelastic medium with stress couples under initial stresses

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International Journal of Stochastic Analysis - Table of contents 1988

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International Journal of Stochastic Analysis