1.
Quantum relativistic Toda chain - Pronko, G.; Sergeev, Sergei
Investigated is the quantum relativistic periodic Toda chain, to
each site of which the ultra-local Weyl algebra is associated.
Weyls $q$
we are considering here is restricted to be inside the
unit circle. Quantum Lax operators of the model are intertwined by
six-vertex $R$ -matrix. Both independent Baxters $Q$ -operators are constructed explicitly as
seria over local Weyl generators. The operator-valued Wronskian of $R$ -matrix. Both independent Baxters $Qs$
is also calculated.
2.
Quasi-definiteness of generalized Uvarov transforms of moment functionals - Kim, D. H.; Kwon, K. H.
When $\sigma$
is a quasi-definite moment functional with the
monic orthogonal polynomial system $\{P_{n}(x)\}_{n=0}^{\infty}$ , we consider a point masses perturbation $\tau$
of $\sigma$
given by $\tau :=\sigma +\lambda \sum_{l=1}^{m}\sum_{k=0}^{m_{l}}({(-1)^{k}u_{lk}}/{k!})\delta^{(k)}(x-c_{l})$ , where $\lambda,u_{lk}$ , and $c_l$ are
constants with $c_i\neq c_j$
for $i\neq j$ . That is, $\tau$
is a generalized Uvarov transform of
$\sigma$ satisfying $A(x)\tau = A(x)\sigma$ , where
$A(x) =\prod_{l=1}^{m}(x-c_{l})^{m_{l}+1}$ . We find necessary and
sufficient conditions for $\tau$
to be quasi-definite. We also
discuss various properties of monic orthogonal polynomial system
$\{R_{n}(x)\}_{n=0}^{\infty}$
relative to $\tau$
including
two examples.
3.
A multiplicity result for a quasilinear gradient elliptic system - Ahammou, Abdelaziz
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 $H$ , 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 Hernández.
4.
Mixed problem with integral conditions for a certain class of hyperbolic equations - Mesloub, Said; Bouziani, Abdelfatah
We study a mixed problem with purely integral conditions for a
class of two-dimensional second-order hyperbolic equations. We
prove the existence, uniqueness, and the continuous dependence
upon the data of a generalized solution. We use a functional
analysis method based on a priori estimate and on the density of
the range of the operator generated by the considered
problem.
5.
Matrix variate Kummer-Dirichlet distributions - Gupta, Arjun K.; Cardeño, Liliam; Nagar, Daya K.
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.
6.
A Laplace decomposition algorithm applied to a class of nonlinear differential equations - Khuri, Suheil A.
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.
7.
A new method for numerical solution of checkerboard fields - Berggren, Stein A.; Lukkassen, Dag; Meidell, Annette; Simula, Leon
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.
8.
Chains of KP, semi-infinite $1$-Toda lattice hierarchy and Kontsevich integral - Dickey, L. A.
There are well-known constructions of integrable systems that are
chains of infinitely many copies of the equations of the KP
hierarchy glued together with some additional variables, for
example, the modified KP hierarchy. Another interpretation of the
latter, in terms of infinite matrices, is called the $1$ -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...
9.
Abstract mechanical connection and abelian reconstruction for
almost Kähler manifolds - Pekarsky, Sergey; Marsden, Jerrold E.
When the phase space $P$
of a Hamiltonian
$G$ -system $(P,\omega,G,J,H)$
has an almost Kähler 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
$\mathcal{A}$ 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 $G$ . These
ideas are illustrated using the example of the resonant
three-wave interaction. Explicit formulas for the connection
one-form...
10.
Explicit solutions of generalized
nonlinear Boussinesq equations - Kaya, Do?an
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 noise terms
where sum of components vanishes in the limit.
11.
On the optimal exercise boundary for
an American put option - Alobaidi, Ghada; Mallier, Roland
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.
12.
Introduction to Grassmann manifolds and quantum computation - Fujii, Kazuyuki
Geometrical aspects of quantum computing are reviewed elementarily for nonexperts and/or graduate students who are interested in both geometry and quantum computation. We show how to treat Grassmann manifolds which are very important examples of manifolds in mathematics and physics. Some of their applications to quantum computation and its efficiency problems are shown. An interesting current topic of holonomic quantum computation is also covered. Also, some related advanced topics are discussed.
13.
An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods - Kim, Shinuk; Kreider, Kevin L.
Elastic wave propagation in weakly nonlinear elastic rods is considered in the time domain. The method of wave splitting is employed to formulate a standard scattering problem, forming the mathematical basis for both direct and inverse problems. A quasi-linear version of the Wendroff scheme (FDTD) is used to solve the direct problem. To solve the inverse problem, an asymptotic expansion is used for the wave field; this linearizes the order equations, allowing the use of standard numerical techniques. Analysis and numerical results are presented for three model inverse problems: (i) recovery of the nonlinear parameter in the stress-strain relation for...
14.
The quantum spheres and their embedding into quantum Minkowski space-time - Lagraa, M.
We recast the Podle? spheres in the noncommutative physics context by showing that they can be regarded as slices along the time coordinate of the different regions of the quantum Minkowski space-time. The investigation of the transformations of the quantum sphere states under the left coaction of the $\mathrm{SO}_{q}(3)$
group leads to a decomposition of the transformed Hilbert space states in terms of orthogonal subspaces exhibiting the periodicity of the quantum sphere states.
15.
Compatible flat metrics - Mokhov, Oleg I.
We solve the problem of description of nonsingular pairs of compatible flat metrics for the general $N$ -component case. The integrable nonlinear partial differential equations describing all nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics) are found and integrated. The integrating of these equations is based on reducing to a special nonlinear differential reduction of the Lamé equations and using the Zakharov method of differential reductions in the dressing method (a version of the inverse scattering method).
16.
Explicit summation of the constituent WKB series and new approximate wave functions - Kudryashov, Vladimir V.; Vanne, Yulian V.
The independent solutions of the one-dimensional Schrödinger equation are approximated by means of the explicit summation of the leading constituent WKB series. The continuous matching of the particular solutions gives the uniformly valid analytical approximation to the wave functions. A detailed numerical verification of the proposed approximation is performed for some exactly solvable problems arising from different kinds of potentials.
17.
Faster backtracking algorithms for the generation of symmetry-invariant
permutations - Moreno, Oscar; Ramírez, John; Bollman, Dorothy; Orozco, Edusmildo
A new backtracking algorithm is developed for generating classes of permutations, that are invariant under the group $G_4$
of rigid motions of the square generated by reflections about the horizontal and vertical axes. Special cases give a new algorithm for generating solutions of the classical $n$ -queens problem, as well as a new algorithm for generating Costas sequences, which are used in encoding radar and sonar signals. Parallel implementations of this latter algorithm have yielded new Costas
sequences for length $n$ , $19\le n\le 24$ .
18.
Mixed variational inequalities and economic equilibrium problems - Konnov, I. V.; Volotskaya, E. O.
We consider rather broad classes of general economic equilibrium problems and oligopolistic equilibrium problems which can be formulated as mixed variational inequality problems. Such problems involve a continuous mapping and a convex, but not necessarily differentiable function. We present existence and
uniqueness results of solutions under weakened $P$ -type assumptions on the cost mapping. They enable us to establish new results for the economic equilibrium problems under consideration.
19.
A Green?s function for a convertible bond using the Vasicek model - Mallier, R.; Deakin, A. S.
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?s function solution for the value of the convertible bond.
20.
Unit root testing in the presence of innovation variance breaks: a simple solution with increased power - Cook, Steven
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.
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