In this paper, a numerical Laplace transform algorithm which is
based on the decomposition method is introduced for the
approximate solution of a class of nonlinear differential
equations. The technique is described and illustrated with some
numerical examples. The results assert that this scheme is
rapidly convergent and quite accurate by which it approximates
the solution using only few terms of its iterative scheme.

Suheil A.   Khuri

A Laplace decomposition algorithm applied to a class of nonlinear differential equations

The multivariate Kummer-Beta and multivariate Kummer-Gamma
families of distributions have been proposed and studied recently
by Ng and Kotz. These distributions are extensions of Kummer-Beta
and Kummer-Gamma distributions.  In this article we propose and
study matrix variate generalizations of multivariate Kummer-Beta
and multivariate Kummer-Gamma families of distributions.

Arjun K. Gupta

Liliam Cardeño

Daya K. Nagar

Matrix variate Kummer-Dirichlet distributions

The aim of this work is to establish the existence of infinitely
many solutions to gradient elliptic system problem, placing only
conditions on a potential function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>H</mml:mi></mml:math>, associated to the problem,
which is assumed to have an oscillatory behaviour at infinity. The
method used in this paper is a shooting technique combined with
an elementary variational argument. We are concerned with the
existence of upper and lower solutions in the sense of Hern&#225;ndez.

Abdelaziz  Ahammou

A multiplicity result for a quasilinear gradient elliptic system

When <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>σ</mml:mi></mml:math>
is a quasi-definite moment functional with the
monic orthogonal polynomial system <mml:math id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mtext> </mml:mtext><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mtext> </mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mi>∞</mml:mi></mml:msubsup></mml:mrow></mml:math>, we consider a point masses perturbation <mml:math id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>τ</mml:mi></mml:math>
of <mml:math id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>σ</mml:mi></mml:math>
given by <mml:math id="E5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>τ</mml:mi><mml:mo>:</mml:mo><mml:mo>=</mml:mo><mml:mi>σ</mml:mi><mml:mo>+</mml:mo><mml:mi>λ</mml:mi><mml:msubsup><mml:mi>Σ</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mtext> </mml:mtext><mml:mi>m</mml:mi></mml:mrow></mml:msubsup><mml:msubsup><mml:mi>Σ</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mtext> </mml:mtext><mml:msub><mml:mi>m</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mi>k</mml:mi></mml:msup><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>!</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mi>δ</mml:mi><mml:mrow><mml:mtext> </mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mtext> </mml:mtext><mml:mo>−</mml:mo><mml:mtext> </mml:mtext><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mtext> </mml:mtext><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>, where <mml:math id="E6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>λ</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>, and <mml:math id="E7" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></mml:math> are
constants with <mml:math id="E8" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>≠</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math>
for <mml:math id="E9" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>i</mml:mi><mml:mo>≠</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:math>. That is, <mml:math id="E10" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>τ</mml:mi></mml:math>
is a generalized Uvarov transform of 
<mml:math id="E11" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>σ</mml:mi></mml:math> satisfying <mml:math id="E12" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>A</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mtext> </mml:mtext><mml:mi>τ</mml:mi><mml:mo>=</mml:mo><mml:mi>A</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mtext> </mml:mtext><mml:mi>σ</mml:mi></mml:mrow></mml:math>, where
<mml:math id="E13" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>A</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∏</mml:mo><mml:mrow><mml:mi>l</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:msubsup><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>c</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>l</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>. We find necessary and
sufficient conditions for <mml:math id="E14" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>τ</mml:mi></mml:math>
to be quasi-definite. We also
discuss various properties of monic orthogonal polynomial system
<mml:math id="E15" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mtext> </mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mi>∞</mml:mi></mml:msubsup></mml:mrow></mml:math>
relative to <mml:math id="E16" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>τ</mml:mi></mml:math>
including
two examples.

D. H. Kim

K. H. Kwon

Quasi-definiteness of generalized Uvarov transforms of moment functionals

Investigated is the quantum relativistic periodic Toda chain, to
each site of which the ultra-local Weyl algebra is associated.
Weyl’s <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>
we are considering here is restricted to be inside the
unit circle. Quantum Lax operators of the model are intertwined by
six-vertex <mml:math id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math>-matrix. Both independent Baxter’s <mml:math id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Q</mml:mi></mml:math>-operators are constructed explicitly as 
seria over local Weyl generators. The operator-valued Wronskian of <mml:math id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math>-matrix. Both independent Baxter’s <mml:math id="E5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Q</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:math>
is also calculated.

G. Pronko

Sergei Sergeev

Quantum relativistic Toda chain

An American put option is a derivative financial instrument that
gives its holder the right but not the obligation to sell an
underlying security at a pre-determined price. American options
may be exercised at any time prior to expiry at the discretion of
the holder, and the decision as to whether or not to exercise
leads to a free boundary problem. In this paper, we examine the
behavior of the free boundary close to expiry. Working directly
with the underlying PDE, by using asymptotic expansions, we are
able to deduce this behavior of the boundary in this limit.

Ghada  Alobaidi

Roland  Mallier

On the optimal exercise boundary for an American put option

By considering the Adomian decomposition scheme, we
solve a generalized Boussinesq equation. The method does not need
linearization or weak nonlinearly assumptions. By using this
scheme, the solutions are calculated in the form of a convergent
power series with easily computable components. The decomposition
series analytic solution of the problem is quickly obtained by
observing the existence of the self-canceling &#x201C;noise&#x201D; terms
where sum of components vanishes in the limit.

Do&#x11F;an Kaya

Explicit solutions of generalized nonlinear Boussinesq equations

There are well-known constructions of integrable systems that are
chains of infinitely many copies of the equations of the KP
hierarchy &#8220;glued&#8221; together with some additional variables, for
example, the modified KP hierarchy. Another interpretation of the
latter, in terms of infinite matrices, is called the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn></mml:math>-Toda
lattice hierarchy. One way infinite reduction of this hierarchy
has all the solutions in the form of sequences of expanding
Wronskians. We define another chain of the KP equations, also
with solutions of the Wronsksian type, that is characterized by
the property to stabilize with respect to a gradation. Under some
constraints imposed, the tau functions of the chain are the tau
functions associated with the Kontsevich integrals.

L. A. Dickey

Chains of KP, semi-infinite <svg style="vertical-align:-0.0pt" height="10.9125" version="1.1" viewBox="0 0 8.2875004 10.9125" width="8.2875004" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" /></g></svg>-Toda lattice hierarchy and Kontsevich integral

We consider a generalized version of the standard checkerboard
and discuss the difficulties of finding the corresponding field
by standard numerical treatment. A new numerical method is
presented which converges independently of the local
conductivities.

Stein A. Berggren

Dag Lukkassen

Annette Meidell

Leon Simula

A new method for numerical solution of checkerboard fields

When the phase space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi></mml:math>
of a Hamiltonian 
				<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math>-system <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>P</mml:mi><mml:mo>,</mml:mo><mml:mi>&#969;</mml:mi><mml:mo>,</mml:mo><mml:mi>G</mml:mi><mml:mo>,</mml:mo><mml:mi>J</mml:mi><mml:mo>,</mml:mo><mml:mi>H</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>
has an almost K&#228;hler structure a preferred
connection, called abstract mechanical connection, can
be defined by declaring horizontal spaces at each point to be
metric orthogonal to the tangent to the group orbit. Explicit
formulas for the corresponding connection one-form
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#119964;</mml:mi></mml:math> are derived in terms of the momentum map,
symplectic and complex structures. Such connection can play the
role of the reconstruction connection (due to the work of A.
Blaom), thus
significantly simplifying computations of the corresponding
dynamic and geometric phases for an Abelian group <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math>. These
ideas are illustrated using the example of the resonant
three-wave interaction. Explicit formulas for the connection
one-form and the phases are given together with some new results
on the symmetry reduction of the Poisson structure.

Sergey  Pekarsky

Jerrold E. Marsden

Abstract mechanical connection and abelian reconstruction for
almost K&#228;hler manifolds

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

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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.

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Journal of Applied Mathematics - Table of contents 2001

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