46,288 research outputs found
[Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]
We study the Hopf algebra structure and the highest weight representation of
a multiparameter version of . The commutation relations as well as
other Hopf algebra maps are explicitly given. We show that the multiparameter
universal matrix can be constructed directly as a quantum double
intertwiner, without using Reshetikhin's transformation. An interesting feature
automatically appears in the representation theory: it can be divided into two
types, one for generic , the other for being a root of unity. When
applying the representation theory to the multiparameter universal
matrix, the so called standard and nonstandard colored solutions of the Yang-Baxter equation is obtained.Comment: [14]pages, latex, no figure
Variational formulas of higher order mean curvatures
In this paper, we establish the first variational formula and its
Euler-Lagrange equation for the total -th mean curvature functional
of a submanifold in a general Riemannian manifold
for . As an example, we prove that closed
complex submanifolds in complex projective spaces are critical points of the
functional , called relatively -minimal submanifolds,
for all . At last, we discuss the relations between relatively -minimal
submanifolds and austere submanifolds in real space forms, as well as a special
variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201
A rescaled method for RBF approximation
In the recent paper [8], a new method to compute stable kernel-based
interpolants has been presented. This \textit{rescaled interpolation} method
combines the standard kernel interpolation with a properly defined rescaling
operation, which smooths the oscillations of the interpolant. Although
promising, this procedure lacks a systematic theoretical investigation. Through
our analysis, this novel method can be understood as standard kernel
interpolation by means of a properly rescaled kernel. This point of view allow
us to consider its error and stability properties
A rescaled method for RBF approximation
A new method to compute stable kernel-based interpolants
has been presented by the second and third authors. This rescaled interpolation method combines the
standard kernel interpolation with a properly defined rescaling operation, which
smooths the oscillations of the interpolant. Although promising, this procedure
lacks a systematic theoretical investigation.
Through our analysis, this novel method can be understood as standard
kernel interpolation by means of a properly rescaled kernel. This point of view
allow us to consider its error and stability properties.
First, we prove that the method is an instance of the Shepard\u2019s method,
when certain weight functions are used. In particular, the method can reproduce
constant functions.
Second, it is possible to define a modified set of cardinal functions strictly
related to the ones of the not-rescaled kernel. Through these functions, we
define a Lebesgue function for the rescaled interpolation process, and study its
maximum - the Lebesgue constant - in different settings.
Also, a preliminary theoretical result on the estimation of the interpolation
error is presented.
As an application, we couple our method with a partition of unity algorithm.
This setting seems to be the most promising, and we illustrate its behavior with
some experiments
Y(so(5)) symmtry of the nonlinear Schrdinger model with four-cmponents
The quantum nonlinear Schrdinger(NLS) model with four-component
fermions exhibits a symmetry when considered on an infintite
interval. The constructed generators of Yangian are proved to satisfy the
Drinfel'd formula and furthermore, the relation with the general form of
rational R-matrix given by Yang-Baxterization associated with algebraic
structure.Comment: 10 pages, no figure
A double bounded key identity for Goellnitz's (big) partition theorem
Given integers i,j,k,L,M, we establish a new double bounded q-series identity
from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon
for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the
identity yields a strong refinement of Goellnitz's theorem with a bound on the
parts given by L. This is the first time a bounded version of Goellnitz's (big)
theorem has been proved. This leads to new bounded versions of Jacobi's triple
product identity for theta functions and other fundamental identities.Comment: 17 pages, to appear in Proceedings of Gainesville 1999 Conference on
Symbolic Computation
Local U(1) symmetry in Y(so(5)) associated with Massless Thirring Model and its Bethe Ansatz
The Massless Thirring model associated with SO(5) is solved in terms of the
local U(1) symmetry. The local U(1) symmetry is related to q-deformation of
four-component field operators due to the nonlinear interaction for differently
internal degree of freedom. The Bethe ansatz wavefunction is also discussed. In
addition, the local U(1) symmetry in the Yangian associated with
SO(5)(Y(SO(5))) is explored.Comment: 10 pages, no figure
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