The small amplitude-to-thread ratio helical configuration of a
vortex filament in the ideal fluid behaves exactly as de Broglie
wave. The complex-valued algebra of quantum mechanics finds a
simple mechanical interpretation in terms of differential
geometry of the space curve. The wave function takes the meaning
of the velocity, with which the helix rotates about the screw
axis. The helices differ in type of the screw&#8212;right- or
left-handed. Two kinds of the helical waves deflect in the
inhomogeneous fluid vorticity field in the same way as spin
particles in the Stern-Gerlach experiment.

Valery P. Dmitriyev

Mechanical analogy for the wave-particle: helix on a vortex filament

The Dickey-Fuller unit root test is known to suffer severe
oversizing in the presence of innovation variance breaks. In this
paper, forward and reverse Dickey-Fuller regressions are proposed
as a means of correcting this size distortion. The results of
Monte Carlo experimentation show such an approach to result in
both satisfactory size properties and increased power relative to
previously suggested solutions.

Steven  Cook

Unit root testing in the presence of innovation variance breaks: a simple solution with increased power

We consider a convertible security where the underlying stock
price obeys a lognormal random walk and the risk-free
rate is given by the Vasicek model. Using a Laplace transform in
time and a Mellin transform in the stock price, we derive a
Green&#8242;s function solution for the value of the convertible bond.

R.  Mallier

A. S. Deakin

A Green&#8242;s function for a convertible bond using the Vasicek model

The network flow optimization approach is offered for restoration
of gray-scale and color images corrupted by noise. The Ising
models are used as a statistical background of the proposed
method. We present the new multiresolution network flow minimum
cut algorithm, which is especially efficient in identification of
the maximum a posteriori (MAP) estimates of corrupted images. The
algorithm is able to compute the MAP estimates of large-size
images and can be used in a concurrent mode. We also consider the
problem of integer minimization of two functions,
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="bold">x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>&#955;</mml:mi><mml:msub><mml:mo>&#8721;</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&#8722;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:msub><mml:mo>&#8721;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mtext>&#8201;</mml:mtext><mml:mtext>&#8201;</mml:mtext><mml:msub><mml:mi>&#946;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&#8722;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math>
and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="bold">x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mo>&#8721;</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mtext>&#8201;</mml:mtext><mml:msub><mml:mi>&#955;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mtext>&#8201;</mml:mtext><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&#8722;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo></mml:mrow><mml:msub><mml:mo>&#8721;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mtext>&#8201;</mml:mtext><mml:mtext>&#8201;</mml:mtext><mml:msub><mml:mi>&#946;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mtext>&#8201;</mml:mtext><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&#8722;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:math>, with parameters
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>&#955;</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>&#955;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>&#946;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#62;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>
and vectors
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="bold">x</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mo>&#8230;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>,
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="bold">y</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mo>&#8230;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#8712;</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mo>&#8230;</mml:mo><mml:mo>,</mml:mo><mml:mi>L</mml:mi><mml:mo>&#8722;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>.
Those functions constitute the energy ones for the Ising model of
color and gray-scale images. In the case <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>L</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math>, they coincide,
determining the energy function of the Ising model of binary
images, and their minimization becomes equivalent to the network
flow minimum cut problem. The efficient integer minimization of
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="bold">x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:msub><mml:mi>U</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="bold">x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>
by the network flow
algorithms is described.

Boris A. Zalesky

Network flow optimization for restoration of images

We study the class of the free relativistic covariant equations
generated by the fractional powers of the d&#8242;Alembertian operator
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mo>&#9633;</mml:mo><mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>. The equations corresponding to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>2</mml:mn></mml:math>
(Klein-Gordon and Dirac equations) are local in their nature, but
the multicomponent equations for arbitrary <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#62;</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>
are nonlocal. We
show the representation of the generalized algebra of Pauli and
Dirac matrices and how these matrices are related to the algebra
of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtext>SU</mml:mtext><mml:mtext>&#8201;</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>
group. The corresponding representations of the
Poincar&#233; group and further symmetry transformations on the
obtained equations are discussed. The construction of the related
Green functions is suggested.

Petr  Z&#225;vada

Relativistic wave equations with fractional derivatives and
pseudodifferential operators

We consider a kinetic-theory treatment of the cylindrical unsteady heat transfer. A model kinetic equation of the BGK (Bhatnager-Gross-Krook) type is solved using the method of moments with a two-sided distribution function. We study the relations between the different macroscopic properties of the gas as the temperature, density, and heat flux with both the radial distance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>r</mml:mi></mml:math> and the time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi></mml:math>. Also we study the problem from the viewpoint of irreversible thermodynamics and estimate the entropy, entropy production, entropy flux, thermodynamic forces, kinetic coefficients, the change in internal energy, and verify Onsager&#8242;s relation for nonequilibrium thermodynamic properties of the system.

A. M. Abourabia

M. A. Mahmoud

W. S. Abdel Kareem

Unsteady heat transfer of a monatomic gas between two coaxial circular cylinders

We consider a mathematical model which describes the contact
between a deformable body and an obstacle, the so-called
foundation. The body is assumed to have a viscoelastic behavior
that we model with the Kelvin-Voigt constitutive law. The contact
is frictionless and  is modeled with the well-known Signorini
condition in a form with a zero gap function. We present
two alternative yet equivalent weak formulations of the problem
and establish existence and uniqueness results for both
formulations. The proofs are based on a general result on
evolution equations with maximal monotone operators. We then
study a semi-discrete numerical scheme for the problem, in terms
of displacements. The numerical scheme has a unique solution. We
show the convergence of the scheme under the basic solution
regularity. Under appropriate regularity assumptions on the
solution, we also provide optimal order error estimates.

Mikäel Barboteu

Weimin Han

Mircea Sofonea

A frictionless contact problem for viscoelastic materials

About this journal

Journal of Applied Mathematics publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.

Journal profile

Meet the editorial board

Chief Editor, Professor Theodore E. Simos, is based at Ulyanovsk State Technical University, Russia. His main research interest is the numerical analysis of differential equations.

Editor spotlight

Submit your proposal

Do you think there is an emerging area of research that really needs to be highlighted? Or an existing research area that has been overlooked or would benefit from deeper investigation? Raise the profile of a research area by leading a Special Issue.

Special Issues

Author guidelines

Editorial board

Databases and indexing

Journal of Applied Mathematics - Table of contents 2002

title

Journal of Applied Mathematics publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.

Journal of Applied Mathematics