317 research outputs found
Position Dependent Mass Schroedinger Equation and Isospectral Potentials : Intertwining Operator approach
Here we have studied first and second-order intertwining approach to generate
isospectral partner potentials of position-dependent (effective) mass
Schroedinger equation. The second-order intertwiner is constructed directly by
taking it as second order linear differential operator with position depndent
coefficients and the system of equations arising from the intertwining
relationship is solved for the coefficients by taking an ansatz. A complete
scheme for obtaining general solution is obtained which is valid for any
arbitrary potential and mass function. The proposed technique allows us to
generate isospectral potentials with the following spectral modifications: (i)
to add new bound state(s), (ii) to remove bound state(s) and (iii) to leave the
spectrum unaffected. To explain our findings with the help of an illustration,
we have used point canonical transformation (PCT) to obtain the general
solution of the position dependent mass Schrodinger equation corresponding to a
potential and mass function. It is shown that our results are consistent with
the formulation of type A N-fold supersymmetry [14,18] for the particular case
N = 1 and N = 2 respectively.Comment: Some references have been adde
A new family of shape invariantly deformed Darboux-P\"oschl-Teller potentials with continuous \ell
We present a new family of shape invariant potentials which could be called a
``continuous \ell version" of the potentials corresponding to the exceptional
(X_{\ell}) J1 Jacobi polynomials constructed recently by the present authors.
In a certain limit, it reduces to a continuous \ell family of shape invariant
potentials related to the exceptional (X_{\ell}) L1 Laguerre polynomials. The
latter was known as one example of the `conditionally exactly solvable
potentials' on a half line.Comment: 19 pages. Sec.5(Summary and Comments): one sentence added in the
first paragraph, several sentences modified in the last paragraph.
References: one reference ([25]) adde
Darboux transformation and multi-soliton solutions of Two-Boson hierarchy
We study Darboux transformations for the two boson (TB) hierarchy both in the
scalar as well as in the matrix descriptions of the linear equation. While
Darboux transformations have been extensively studied for integrable models
based on within the AKNS framework, this model is based on
. The connection between the scalar and the matrix
descriptions in this case implies that the generic Darboux matrix for the TB
hierarchy has a different structure from that in the models based on
studied thus far. The conventional Darboux transformation is shown to be quite
restricted in this model. We construct a modified Darboux transformation which
has a much richer structure and which also allows for multi-soliton solutions
to be written in terms of Wronskians. Using the modified Darboux
transformations, we explicitly construct one soliton/kink solutions for the
model.Comment:
Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials
A geometric approach is used to study a family of higher-order nonlinear Abel
equations. The inverse problem of the Lagrangian dynamics is studied in the
particular case of the second-order Abel equation and the existence of two
alternative Lagrangian formulations is proved, both Lagrangians being of a
non-natural class (neither potential nor kinetic term). These higher-order Abel
equations are studied by means of their Darboux polynomials and Jacobi
multipliers. In all the cases a family of constants of the motion is explicitly
obtained. The general n-dimensional case is also studied
G´en´etique Clinique dans le Service de P´ediatrie et de G´en´etique M´edicale du Centre National Hospitalier et Universitaire de Cotonou : Etat des Lieux et Perspectives
Il s’agissait d’une ´etude r´etrospective descriptive portant sur les patients rec¸us en consultation de g´en´etique m´edicale de Septembre 2004 `a Aoˆut 2007. Les patients b´en´eficiaient des examens dysmorphologique et physique, des bilans cytog´en´etiques et/ou mol´eculaires, des interventions th´erapeutiques et un suivi `a long terme. Les variables ´etudi´ees ´etaient les donn´ees sociod´emographiques et cliniques. Soixante et seize patients ont ´et´e rec¸us durant la p´eriode avec une pr´edominance masculine (57,89%). Les motifs de consultation ´etaient domin´es par le retard psychomoteur (38,15%), la dysmorphie faciale (30,26%) et les malformations (19,73%). Les principales malformations portaient sur les extr´emit´es et la face. Les pathologies confirm´ees comprenaient des aberrations chromosomiques (46,05%) avec une pr´edominance de la trisomie 21 et des maladies monog´eniques (7,89%). Le rendement de nos recherches pourrait ˆetre am´elior´e par l’acc`es `a la technique FISH. C’est une exp´erience quasi unique en Afrique de l’ouest et permet d’apporter des r´eponses aux personnes souffrant d’affections h´er´editaires.Mots Cl´es g´en´etique clinique ; retard psychomoteur ; dysmorphie ; malformation ; aberration chromosomique ; maladie monog´eniqu
An extended scaling analysis of the S=1/2 Ising ferromagnet on the simple cubic lattice
It is often assumed that for treating numerical (or experimental) data on
continuous transitions the formal analysis derived from the Renormalization
Group Theory can only be applied over a narrow temperature range, the "critical
region"; outside this region correction terms proliferate rendering attempts to
apply the formalism hopeless. This pessimistic conclusion follows largely from
a choice of scaling variables and scaling expressions which is traditional but
which is very inefficient for data covering wide temperature ranges. An
alternative "extended caling" approach can be made where the choice of scaling
variables and scaling expressions is rationalized in the light of well
established high temperature series expansion developments. We present the
extended scaling approach in detail, and outline the numerical technique used
to study the 3d Ising model. After a discussion of the exact expressions for
the historic 1d Ising spin chain model as an illustration, an exhaustive
analysis of high quality numerical data on the canonical simple cubic lattice
3d Ising model is given. It is shown that in both models, with appropriate
scaling variables and scaling expressions (in which leading correction terms
are taken into account where necessary), critical behavior extends from Tc up
to infinite temperature.Comment: 16 pages, 17 figure
Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations
An alternative derivation is presented of the infinitely many exceptional
Wilson and Askey-Wilson polynomials, which were introduced by the present
authors in 2009. Darboux-Crum transformations intertwining the discrete quantum
mechanical systems of the original and the exceptional polynomials play an
important role. Infinitely many continuous Hahn polynomials are derived in the
same manner. The present method provides a simple proof of the shape invariance
of these systems as in the corresponding cases of the exceptional Laguerre and
Jacobi polynomials.Comment: 24 pages. Comments and references added. To appear in J.Phys.
Generalized isothermic lattices
We study multidimensional quadrilateral lattices satisfying simultaneously
two integrable constraints: a quadratic constraint and the projective Moutard
constraint. When the lattice is two dimensional and the quadric under
consideration is the Moebius sphere one obtains, after the stereographic
projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by
an algebraic constraint imposed on the (complex) cross-ratio of the circular
lattice. We derive the analogous condition for our generalized isthermic
lattices using Steiner's projective structure of conics and we present basic
geometric constructions which encode integrability of the lattice. In
particular, we introduce the Darboux transformation of the generalized
isothermic lattice and we derive the corresponding Bianchi permutability
principle. Finally, we study two dimensional generalized isothermic lattices,
in particular geometry of their initial boundary value problem.Comment: 19 pages, 11 figures; v2. some typos corrected; v3. new references
added, higlighted similarities and differences with recent papers on the
subjec
Darboux transformations for a 6-point scheme
We introduce (binary) Darboux transformation for general differential
equation of the second order in two independent variables. We present a
discrete version of the transformation for a 6-point difference scheme. The
scheme is appropriate to solving a hyperbolic type initial-boundary value
problem. We discuss several reductions and specifications of the
transformations as well as construction of other Darboux covariant schemes by
means of existing ones. In particular we introduce a 10-point scheme which can
be regarded as the discretization of self-adjoint hyperbolic equation
On the action principle for a system of differential equations
We consider the problem of constructing an action functional for physical
systems whose classical equations of motion cannot be directly identified with
Euler-Lagrange equations for an action principle. Two ways of action principle
construction are presented. From simple consideration, we derive necessary and
sufficient conditions for the existence of a multiplier matrix which can endow
a prescribed set of second-order differential equations with the structure of
Euler-Lagrange equations. An explicit form of the action is constructed in case
if such a multiplier exists. If a given set of differential equations cannot be
derived from an action principle, one can reformulate such a set in an
equivalent first-order form which can always be treated as the Euler-Lagrange
equations of a certain action. We construct such an action explicitly. There
exists an ambiguity (not reduced to a total time derivative) in associating a
Lagrange function with a given set of equations. We present a complete
description of this ambiguity. The general procedure is illustrated by several
examples.Comment: 10 page
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