id
string | text
string | len_category
string | source
string |
|---|---|---|---|
math/0302153
|
Let $\tau$ be the primitive Dirichlet character of conductor 4, let $\chi$ be
the primitive even Dirichlet character of conductor 8 and let $k$ be an
integer. Then the $U_2$ operator acting on cuspidal overconvergent modular
forms of weight $2k+1$ and character $\tau$ has slopes in the arithmetic
progression ${2,4,...,2n,...}$, and the $U_2$ operator acting on cuspidal
overconvergent modular forms of weight $k$ and character $\chi \cdot \tau^k$
has slopes in the arithmetic progression ${1,2,...,n,...}$.
We then show that the characteristic polynomials of the Hecke operators $U_2$
and $T_p$ acting on the space of classical cusp forms of weight $k$ and
character either $\tau$ or $\chi\cdot\tau^k$ split completely over $\qtwo$.
|
lt256
|
arxiv_abstracts
|
math/0302154
|
We give an explicit description of all 168 quartic curves over the field of
two elements that are isomorphic to the Klein curve over an algebraic
extension. Some of the curves have been known for their small class number,
others for attaining the maximal number of rational points.
|
lt256
|
arxiv_abstracts
|
math/0302155
|
Let A be a set of nonnegative integers. For every nonnegative integer n and
positive integer h, let r_{A}(n,h) denote the number of representations of n in
the form n = a_1 + a_2 + ... + a_h, where a_1, a_2,..., a_h are elements of A
and a_1 \leq a_2 \leq ... \leq a_h. The infinite set A is called a basis of
order h if r_{A}(n,h) \geq 1 for every nonnegative integer n. Erdos and Turan
conjectured that limsup_{n\to\infty} r_A(n,2) = \infty for every basis A of
order 2. This paper introduces a new class of additive bases and a general
additive problem, a special case of which is the Erdos-Turan conjecture.
Konig's lemma on the existence of infinite paths in certain graphs is used to
prove that this general problem is equivalent to a related problem about finite
sets of nonnegative integers.
|
lt256
|
arxiv_abstracts
|
math/0302156
|
Colliot-Th{\'e}l{\`e}ne has determined the Chow group of zero-cycles on a
Ch{\^a}telet surface X defined over a finite extension K of the field of p-adic
numbers (p an odd prime) when X is split by an unramified extension of K. Using
similar techniques, we extend this calculation to the ramified case,
simplifying his result in the process. We also determine how this group changes
when we pass from K to a finite extension of K.
|
lt256
|
arxiv_abstracts
|
math/0302157
|
We determine the Chow group of zero-cycles on a rational surface X defined
over a finite extension K of the field of p-adic numbers (p a prime) when X is
split by an unramified extension of K.
|
lt256
|
arxiv_abstracts
|
math/0302158
|
A telegraphic survey of some of the standard results and conjectures about
the set $C({\bf Q})$ of rational points on a smooth projective absolutely
connected curve $C$ over ${\bf Q}$.
|
lt256
|
arxiv_abstracts
|
math/0302159
|
We prove an existence result for a class of Dirichlet boundary value problems
with discontinuous nonlinearity and involving a Leray-Lions operator. The proof
combines monotonicity methods for elliptic problems, variational inequality
techniques and basic tools related to monotone operators.
|
lt256
|
arxiv_abstracts
|
math/0302160
|
We construct solutions of the Cahn-Hilliard equation whose nodal set
converges to a given constant mean curvature hypersurface in a Riemannian
manifold.
|
lt256
|
arxiv_abstracts
|
math/0302161
|
We consider the crystalline realization of Deligne's 1-motives in positive
characteristics and prove a comparison theorem with the De Rham realization of
liftings to zero characteristic. We then show that one dimensional crystalline
cohomology of an algebraic variety, defined by universal cohomological descent
via de Jong's alterations, coincide with the crystalline realization of the
(cohomological) Picard 1-motive, over perfect fields.
|
lt256
|
arxiv_abstracts
|
math/0302162
|
Fractal measures of images of continuous maps from the set of p-adic numbers
Qp into complex plane C are analyzed. Examples of "anomalous" fractals, i.e.
the sets where the D-dimensional Hausdorff measures (HM) are trivial, i.e.
either zero, or sigma-infinite (D is the Hausdorff dimension (HD) of this set)
are presented. Using the Caratheodory construction, the generalized
scale-covariant HM (GHM) being non-trivial on such fractals are constructed. In
particular, we present an example of 0-fractal, the continuum with HD=0 and
nontrivial GHM invariant w.r.t. the group of all diffeomorphisms C. For
conformal transformations of domains in R^n, the formula for the change of
variables for GHM is obtained. The family of continuous maps Qp in C
continuously dependent on "complex dimension" d in C is obtained. This family
is such that: 1) if d=2(1), then the image of Qp is C (real axis in C); 2) the
fractal measures coincide with the images of the Haar measure in Qp, and at
d=2(1) they also coincide with the flat (linear) Lebesgue measure; 3) integrals
of entire functions over the fractal measures of images for any compact set in
Qp are holomorphic in d, similarly to the dimensional regularization method in
QFT.
|
256
|
arxiv_abstracts
|
math/0302163
|
In 1994, Matsuda and Okabe introduced the notion of semistar operation. This
concept extends the classical concept of star operation (cf. for instance,
Gilmer's book \cite{G}) and, hence, the related classical theory of ideal
systems based on the works by W. Krull, E. Noether, H. Pr\"{u}fer and P.
Lorenzen from 1930's. In \cite{FL1} and \cite{FL2} the current authors
investigated properties of the Kronecker function rings which arise from
arbitrary semistar operations on an integral domain $D$. In this paper we
extend that study and also generalize Kang's notion of a star Nagata ring
\cite{Kang:1987} and \cite{Kang:1989} to the semistar setting. Our principal
focuses are the similarities between the ideal structure of the Nagata and
Kronecker semistar rings and between the natural semistar operations that these
two types of function rings give rise to on $D$.
|
lt256
|
arxiv_abstracts
|
math/0302164
|
We consider the motion by curvature of a network of smooth curves with
multiple junctions in the plane, that is, the geometric gradient flow
associated to the length functional. Such a flow represents the evolution of a
two--dimensional multiphase system where the energy is simply the sum of the
lengths of the interfaces, in particular it is a possible model for the growth
of grain boundaries. Moreover, the motion of these networks of curves is the
simplest example of curvature flow for sets which are ``essentially'' non
regular. As a first step, in this paper we study in detail the case of three
curves in the plane concurring at a single triple junction and with the other
ends fixed. We show some results about the existence, uniqueness and, in
particular, the global regularity of the flow, following the line of analysis
carried on in the last years for the evolution by mean curvature of smooth
curves and hypersurfaces.
|
lt256
|
arxiv_abstracts
|
math/0302165
|
In connection to wavelet theory, we describe the peripheral spectrum of the
transfer operator. The solution involves the analysis of certain
representations of the algebra generated by two unitaries $U$ and $T$ that
satisfy the commutation relation $UTU^{-1}=T^N$.
|
lt256
|
arxiv_abstracts
|
math/0302166
|
We define the local trace function for subspaces of $\ltworn$ which are
invariant under integer translation. Our trace function contains the dimension
function and the spectral function defined by Bownik and Rzeszotnik and
completely characterizes the given translation invariant subspace. It has
properties such as positivity, additivity, monotony and some form of
continuity. It behaves nicely under dilations and modulations. We use the local
trace function to deduce, using short and simple arguments, some fundamental
facts about wavelets such as the characterizing equations, the equality between
the dimension function and the multiplicity function and some new relations
between scaling functions and wavelets.
|
lt256
|
arxiv_abstracts
|
math/0302167
|
Motivated by our study (elsewhere) of linear syzygies of homogeneous ideals
generated by quadrics and their restrictions to subvarieties of the ambient
projective space, we investigate in this note possible zero-dimensional
intersections of two Veronese surfaces in P^5.
The case of two Veronese surfaces in P^5 meeting in 10 simple points appears
also in work of Coble, Conner and Reye in relation to the 10 nodes of a quartic
symmetroid in P^3, and we provide here a modern account for some of their
results.
|
lt256
|
arxiv_abstracts
|
math/0302168
|
This paper has been withdrawn by the author due to a crucial error in Lemma
3.5.
|
lt256
|
arxiv_abstracts
|
math/0302169
|
Let F be a nonarchimedean local field, let D be a division algebra over F,
let GL(n) = GL(n,F). Let \nu denote Plancherel measure for GL(n). Each
component \Omega in the Bernstein variety \Omega(GL(n)) has several numerical
invariants attached to it. We provide explicit formulas for the Bernstein
component \nu_{\Omega} of Plancherel measure in terms of these invariants. We
also prove some new formal degree formulas, a transfer-of-measure formula for
GL(n), and a transfer-of-measure formula from GL(n,F) to GL(m,D).
|
lt256
|
arxiv_abstracts
|
math/0302170
|
Trigonometric degeneration of the Baxter-Belavin elliptic r matrix is
described by the degeneration of the twisted WZW model on elliptic curves. The
spaces of conformal blocks and conformal coinvariants of the degenerate model
are factorised into those of the orbifold WZW model.
|
lt256
|
arxiv_abstracts
|
math/0302171
|
The purpose of the present work is to describe a dequantization procedure for
topological modules over a deformed algebra. We define the characteristic
variety of a topological module as the common zeroes of the annihilator of the
representation obtained by setting the deformation parameter to zero. On the
other hand, the Poisson characteristic variety is defined as the common zeroes
of the ideal obtained by considering the annihilator of the deformed
representation, and only then setting the deformation parameter to zero. Using
Gabber's theorem, we show the involutivity of the characteristic variety. The
Poisson characteristic variety is indeed a Poisson subvariety of the underlying
Poisson manifold. We compute explicitly the characteristic variety in several
examples in the Poisson-linear case, including the dual of any exponential
solvable Lie algebra. In the nilpotent case, we show that any coadjoint orbit
appears as the Poisson characteristic variety of a well chosen topological
module.
|
lt256
|
arxiv_abstracts
|
math/0302172
|
We give a new and short proof of the Mallows-Sloane upper bound for self-dual
codes. We formulate a version of Greene's theorem for normalized weight
enumerators. We relate normalized rank-generating polynomials to two-variable
zeta functions. And we show that a self-dual code has the Clifford property,
but that the same property does not hold in general for formally self-dual
codes.
|
lt256
|
arxiv_abstracts
|
math/0302173
|
We describe singularities of the convex hull of a generic compact smooth
hypersurface in four-dimensional affine space up to diffeomorphisms. It turns
out there are only two new singularities (in comparison with the previous
dimension case) which appear at separate points of the boundary of the convex
hull and are not removed by a small perturbation of the original hypersurface.
The first singularity does not contain functional, but has at least nine
continuous number invariants. A normal form which does not contain invariants
at all is found for the second singularity.
|
lt256
|
arxiv_abstracts
|
math/0302174
|
We introduce a categorical framework for the study of representations of
$G_F$, where $G$ is a reductive group, and $\bF$ is a 2-dimensional local
field, i.e. $F=K((t))$, where $K$ is a local field. Our main result says that
the space of functions on $G_F$, which is an object of a suitable category of
representations of $G_F$ with the respect to the action of $G_F$ on itself by
left translations, becomes a representation of a certain central extension of
$G_F$, when we consider the action by right translations.
|
lt256
|
arxiv_abstracts
|
math/0302175
|
This paper contains a new proof of the classification of elements of prime
order in the Cremona group Bir(P^2), up to conjugation. In addition, we give
explicit geometric constructions of these Cremona transformations, and provide
a parameterization of their conjugacy classes. Analogous constructions in
higher dimensions are also discussed.
|
lt256
|
arxiv_abstracts
|
math/0302176
|
There are considered vector fields and quaternionic $\alpha$-hyperholomorphic
functions in a domain of $R^2$ which generalize the notion of solenoidal and
irrotational vector fields. There are established sufficient conditions for the
corresponding Cauchy-type integral along a closed Jordan rectifiable curve to
be continuously extended onto the closure of a domain. The
Sokhotski-Plemelj-type formulas are proved as well.
|
lt256
|
arxiv_abstracts
|
math/0302177
|
For a family X of k-subsets of the set 1,...,n, let |X| be the cardinality of
X and let Gamma(X,mu) be the expected maximum weight of a subset from X when
the weights of 1,...,n are chosen independently at random from a symmetric
probability distribution mu on R. We consider the inverse isoperimetric problem
of finding mu for which Gamma(X,mu) gives the best estimate of ln|X|. We prove
that the optimal choice of mu is the logistic distribution, in which case
Gamma(X,mu) provides an asymptotically tight estimate of ln|X| as k^{-1}ln|X|
grows. Since in many important cases Gamma(X,mu) can be easily computed, we
obtain computationally efficient approximation algorithms for a variety of
counting problems. Given mu, we describe families X of a given cardinality with
the minimum value of Gamma(X,mu), thus extending and sharpening various
isoperimetric inequalities in the Boolean cube.
|
lt256
|
arxiv_abstracts
|
math/0302178
|
We study $A_{\infty}$-structures extending the natural algebra structure on
the cohomology of $\oplus_n L^n$, where $L$ is a very ample line bundle on a
projective $d$-dimensional variety $X$ such that $H^i(X,L^n)=0$ for $0<i<d$ and
all $n$. We prove that there exists a unique such nontrivial
$A_{\infty}$-structure up to homotopy and rescaling. In the case when $X$ is a
curve we also compute the group of self-homotopies of this
$A_{\infty}$-structure.
|
lt256
|
arxiv_abstracts
|
math/0302179
|
We show that certain generating sets of Dykema and Radulescu for $L(F_r)$
have free Hausdorff dimension r and nondegenerate free Hausdorff r-entropy
|
lt256
|
arxiv_abstracts
|
math/0302180
|
For any $n>1$, we construct examples branched Galois coverings from $M$ to
the nth projective space ${\mathbb P}^n$ where $M$ is one of $({\mathbb
P}^1)^n$, ${\mathbb C}^n$ or $(B_1)^n$, and $B_1$ is the 1-ball. In terms of
orbifolds, this amounts to giving examples of orbifolds over ${\mathbb P}^n$
uniformized by $M$.We also discuss the related "orbifold braid groups".
|
lt256
|
arxiv_abstracts
|
math/0302181
|
We investigate projections to odometers (group rotations over adic groups) of
topological invertible dynamical systems with discrete time and compact
Hausdorff phase space.
For a dynamical system $(X, f)$ with a compact phase space we consider the
category of its projections onto odometers. We examine the connected partial
order relation on the class of all objects of a skeleton of this category. We
claim that this partially ordered class always have maximal elements and
characterize them. It is claimed also, that this class have a greatest element
and is isomorphic to some characteristic for the dynamical system $(X, f)$
subset of the set $\Sigma$ of ultranatural numbers if and only if the dynamical
system $(X, f)$ is indecomposable (the space $X$ could not be decomposed into
two proper disjoint closed invariant subsets).
|
lt256
|
arxiv_abstracts
|
math/0302182
|
It is well-known that an effective orbifold M (one for which the local
stabilizer groups act effectively) can be presented as a quotient of a smooth
manifold P by a locally free action of a compact lie group K. We use the
language of groupoids to provide a partial answer to the question of whether a
noneffective orbifold can be so presented. We also note some connections to
stacks and gerbes.
|
lt256
|
arxiv_abstracts
|
math/0302183
|
We present a new method for expressing Chaitin's random real, Omega, through
Diophantine equations. Where Chaitin's method causes a particular quantity to
express the bits of Omega by fluctuating between finite and infinite values, in
our method this quantity is always finite and the bits of Omega are expressed
in its fluctuations between odd and even values, allowing for some interesting
developments. We then use exponential Diophantine equations to simplify this
result and finally show how both methods can also be used to create polynomials
which express the bits of Omega in the number of positive values they assume.
|
lt256
|
arxiv_abstracts
|
math/0302184
|
On the rank of Jacobians over function fields.} Let $f:\mathcal{X}\to C$ be a
projective surface fibered over a curve and defined over a number field $k$. We
give an interpretation of the rank of the Mordell-Weil group over $k(C)$ of the
jacobian of the generic fibre (modulo the constant part) in terms of average of
the traces of Frobenius on the fibers of $f$. The results also give a
reinterpretation of the Tate conjecture for the surface $\mathcal{X}$ and
generalizes results of Nagao, Rosen-Silverman and Wazir.
|
lt256
|
arxiv_abstracts
|
math/0302185
|
We consider three probability measures on subsets of edges of a given finite
graph $G$, namely those which govern, respectively, a uniform forest, a uniform
spanning tree, and a uniform connected subgraph. A conjecture concerning the
negative association of two edges is reviewed for a uniform forest, and a
related conjecture is posed for a uniform connected subgraph. The former
conjecture is verified numerically for all graphs $G$ having eight or fewer
vertices, or having nine vertices and no more than eighteen edges, using a
certain computer algorithm which is summarised in this paper. Negative
association is known already to be valid for a uniform spanning tree. The three
cases of uniform forest, uniform spanning tree, and uniform connected subgraph
are special cases of a more general conjecture arising from the random-cluster
model of statistical mechanics.
|
lt256
|
arxiv_abstracts
|
math/0302186
|
The main aim of this paper is to describe the most adequate generalization of
the Cauchy-Riemann system fixing properties of classical functions in
octonionic case. An octonionic generalization of the Laplace transform is
introduced. Octonionic generalizations of the inversion transformation, the
gamma function and the Riemann zeta-function are given.
|
lt256
|
arxiv_abstracts
|
math/0302187
|
Let $G/K$ be an irreducible Hermitian symmetric spaces of compact type with
the standard homogeneous complex structure. Then the real symplectic manifold
$(T^*(G/K),\Omega)$ has the natural complex structure $J^-$. We construct all
$G$-invariant K\"ahler structures $(J,\Omega)$ on homogeneous domains in
$T^*(G/K)$ anticommuting with $J^-$. Each such a hypercomplex structure,
together with a suitable metric, defines a hyperk\"ahler structure. As an
application, we obtain a new proof of the Harish-Chandra and Moore theorem.
|
lt256
|
arxiv_abstracts
|
math/0302188
|
This paper has been withdrawn. The result anyway is still true for rational
double points Dn. (the cases of E6,E7,E8 are not solved yet).
|
lt256
|
arxiv_abstracts
|
math/0302189
|
Let p be a monic polynomial in one complex variable and K a measurable subset
of the complex plane. In terms of the area of K, we give an upper bound on the
area of the preimage of K under p and a lower bound on the area of the image of
K under p, (counted with multiplicity). Both bounds are sharp. The former
extends an inequality of Polya. The proof uses Carleman's isoperimetric
inequality for plane condensers. We include a summary of the necessary
potential theory.
|
lt256
|
arxiv_abstracts
|
math/0302190
|
These notes deal with metric spaces, Hausdorff measures and dimensions,
Lipschitz mappings, and related topics. The reader is assumed to have some
familiarity with basic analysis, which is also reviewed.
|
lt256
|
arxiv_abstracts
|
math/0302191
|
We show that PSL(2,Z[1/p]) admits a combing with bounded asynchronous width,
and use this combing to show that PSL(2,Z[1/p]) has an exponential Dehn
function. As a corollary, PSL(2,Z[1/p]) has solvable word problem and is not an
automatic group.
|
lt256
|
arxiv_abstracts
|
math/0302192
|
Although it is important both in theory as well as in applications, a theory
of Birkhoff interpolation with main emphasis on the shape of the set of nodes
is still missing. Although we will consider various shapes (e.g. we find all
the shapes for which the associated Lagrange problem has unique solution), we
concentrate on one of the simplest shapes:``rectangular'' (also called
"cartesian grids"). The ultimate goal is to obtain a geometrical understanding
of the solvability. We partially achieve this by describing several regularity
criteria, which we illustrate by many examples. At the end we discuss several
conjectures which, we think, are important in understanding the behaviour of
Birkhoff interpolation schemes in higer dimensions. Although we prove these
conjectures in many unrelated cases, we believe that a ``complete proof''
requires new ideas which go beyond the usual methods in interpolation theory
(and may reach areas such as algebraic geometry or algebraic topology).
|
lt256
|
arxiv_abstracts
|
math/0302193
|
The following problem originated from a question due to Paul Turan. Suppose
$\Omega$ is a convex body in Euclidean space $\RR^d$ or in $\TT^d$, which is
symmetric about the origin. Over all positive definite functions supported in
$\Omega$, and with normalized value 1 at the origin, what is the largest
possible value of their integral? From this Arestov, Berdysheva and Berens
arrived to pose the analogous pointwise extremal problem for intervals in
$\RR$. That is, under the same conditions and normalizations, and for any
particular point $z\in\Omega$, the supremum of possible function values at $z$
is to be found. However, it turns out that the problem for the real line has
already been solved by Boas and Kac, who gave several proofs and also mentioned
possible extensions to $\RR^d$ and non-convex domains as well.
We present another approach to the problem, giving the solution in $\RR^d$
and for several cases in $\TT^d$. In fact, we elaborate on the fact that the
problem is essentially one-dimensional, and investigate non-convex open domains
as well. We show that the extremal problems are equivalent to more familiar
ones over trigonometric polynomials, and thus find the extremal values for a
few cases. An analysis of the relation of the problem for the space $\RR^d$ to
that for the torus $\TT^d$ is given, showing that the former case is just the
limiting case of the latter. Thus the hiearachy of difficulty is established,
so that trigonometric polynomial extremal problems gain recognition again.
|
256
|
arxiv_abstracts
|
math/0302194
|
Here are studied pairs of transversal foliations with singularities, defined
on the Elliptic region (where the Gaussian curvature $\mathcal K$ is positive)
of an oriented surface immersed in $\mathbb R^3$. The leaves of the foliations
are the lines of geometric mean curvature, along which the normal curvature is
given by $\sqrt {\mathcal K}$, which is the geometric mean curvature of the
principal curvatures $ k_1, k_2$ of the immersion. The singularities of the
foliations are the umbilic points and parabolic curves}, where $ k_1 = k_2$ and
${\mathcal K} = 0$, respectively. Here are determined the structurally stable
patterns of geometric mean curvature lines near the umbilic points, parabolic
curves and geometric mean curvature cycles, the periodic leaves of the
foliations. The genericity of these patterns is established. This provides the
three essential local ingredients to establish sufficient conditions, likely to
be also necessary, for Geometric Mean Curvature Structural Stability. This
study, outlined at the end of the paper, is a natural analog and complement for
the Arithmetic Mean Curvature and Asymptotic Structural Stability of immersed
surfaces studied previously by the authors.
|
256
|
arxiv_abstracts
|
math/0302195
|
We developed a non-parametric method of Information Decomposition (ID) of a
content of any symbolical sequence. The method is based on the calculation of
Shannon mutual information between analyzed and artificial symbolical
sequences, and allows the revealing of latent periodicity in any symbolical
sequence. We show the stability of the ID method in the case of a large number
of random letter changes in an analyzed symbolic sequence. We demonstrate the
possibilities of the method, analyzing both poems, and DNA and protein
sequences. In DNA and protein sequences we show the existence of many DNA and
amino acid sequences with different types and lengths of latent periodicity.
The possible origin of latent periodicity for different symbolical sequences is
discussed.
|
lt256
|
arxiv_abstracts
|
math/0302196
|
Consider oriented surfaces immersed in $\mathbb R^3.$ Associated to them,
here are studied pairs of transversal foliations with singularities, defined on
the Elliptic region, where the Gaussian curvature $\mathcal K$, given by the
product of the principal curvatures $k_1, k_2$ is positive. The leaves of the
foliations are the lines of harmonic mean curvature, also called characteristic
or diagonal lines, along which the normal curvature of the immersion is given
by ${\mathcal K}/{\mathcal H}$, where $ {\mathcal H}=({k_1}+k_2)/2$ is the
arithmetic mean curvature. That is, ${\mathcal K}/{\mathcal H}=((1/{k_1} +
1/{k_2})/2)^{-1}$ is the harmonic mean of the principal curvatures $k_1, k_2$
of the immersion. The singularities of the foliations are the umbilic points
and parabolic curves, where $k_1 = k_2$ and ${\mathcal K} = 0$, respectively.
Here are determined the structurally stable patterns of harmonic mean curvature
lines near the umbilic points, parabolic curves and harmonic mean curvature
cycles, the periodic leaves of the foliations. The genericity of these patterns
is established. This provides the three essential local ingredients to
establish sufficient conditions, likely to be also necessary, for Harmonic Mean
Curvature Structural Stability of immersed surfaces. This study, outlined
towards the end of the paper, is a natural analog and complement for that
carried out previously by the authors for the Arithmetic Mean Curvature and the
Asymptotic Structural Stability of immersed surfaces.
|
256
|
arxiv_abstracts
|
math/0302197
|
In this paper, we study the discrete cubic nonlinear Schroedinger lattice
under Hamiltonian perturbations. First we develop a complete isospectral theory
relevant to the hyperbolic structures of the lattice without perturbations. In
particular, Backlund-Darboux transformations are utilized to generate
heteroclinic orbits and Melnikov vectors. Then we give coordinate-expressions
for persistent invariant manifolds and Fenichel fibers for the perturbed
lattice. Finally based upon the above machinery, existence of codimension 2
transversal homoclinic tubes is established through a Melnikov type calculation
and an implicit function argument. We also discuss symbolic dynamics of
invariant tubes each of which consists of a doubly infinite sequence of curve
segments when the lattice is four dimensional. Structures inside the asymptotic
manifolds of the transversal homoclinic tubes are studied, special orbits, in
particular homoclinic orbits and heteroclinic orbits when the lattice is four
dimensional, are studied.
|
lt256
|
arxiv_abstracts
|
math/0302198
|
For a general evolution equation with a Silnikov homoclinic orbit, Smale
horseshoes are constructed.
|
lt256
|
arxiv_abstracts
|
math/0302199
|
The global regularity for the viscous Boussinesq equations is proved.
|
lt256
|
arxiv_abstracts
|
math/0302200
|
Recently, the author and collaborators have developed a systematic program
for proving the existence of homoclinic orbits in partial differential
equations. Two typical forms of homoclinic orbits thus obtained are: (1).
transversal homoclinic orbits, (2). Silnikov homoclinic orbits. Around the
transversal homoclinic orbits in infinite dimensional autonomous systems, the
author was able to prove the existence of chaos through a shadowing lemma.
Around the Silnikov homoclinic orbits, the author was able to prove the
existence of chaos through a horseshoe construction.
Very recently, there has been a breakthrough by the author in finding Lax
pairs for Euler equations of incompressible inviscid fluids. Further results
have been obtained by the author and collaborators.
|
lt256
|
arxiv_abstracts
|
math/0302201
|
Let \alpha be an automorphism of the totally disconnected group G. The
compact open subgroup, V, if G is tidy for \alpha if [\alpha(V') :
\alpha(V')\cap V'] is minimised at V, where V' ranges over all compact open
subgroups of G. Identifying a subgroup tidy for \alpha is analogous to
identifying a basis which puts a linear transformation into Jordan canonical
form. This analogy is developed here by showing that commuting automorphisms
have a common tidy subgroup of G and, conversely, that a group H of
automorphisms having a common tidy subgroup V is abelian modulo the
automorphisms which leave V invariant. Certain subgroups of G are the analogues
of eigenspaces and corresponding real characters of H the analogues of
eigenvalues.
|
lt256
|
arxiv_abstracts
|
math/0302202
|
We study the distribution of the number of permutations with a given periodic
up-down sequence w.r.t. the last entry, find exponential generating functions
and prove asymptotic formulas for this distribution.
|
lt256
|
arxiv_abstracts
|
math/0302203
|
We prove a convolution formula for the conjugacy classes in symmetric groups
conjectured by the second author. A combinatorial interpretation of
coefficients is provided. As a main tool we introduce new semigroup of partial
permutations. We describe its structure, representations, and characters. We
also discuss filtrations on the subalgebra of invariants in the semigroup
algebra.
|
lt256
|
arxiv_abstracts
|
math/0302204
|
We prove that the nilpotent commuting variety of a reductive Lie algebra over
an algebraically closed field of good characteristic is equidimensional. In
characteristic zero, this confirms a conjecture of Vladimir Baranovsky. As a
by-product, we obtain tat the punctual (local) Hilbert scheme parametrising the
ideals of colength $n$ in $k[[X,Y]]$ is irreducible over any algebraically
closed field $k$.
|
lt256
|
arxiv_abstracts
|
math/0302205
|
We show that it is natural to consider the energy-momentum tensor associated
with a spinor field as the second fundamental form of an isommetric immersion.
In particular we give a generalization of the warped product construction over
a Riemannian manifold leading to this interpretation. Special sections of the
spinor bundle, generalizing the notion of Killing spinor, are studied. First
applications of such a construction are then given.
|
lt256
|
arxiv_abstracts
|
math/0302206
|
We introduce a combinatorial version of Stallings-Bestvina-Feighn-Dunwoody
folding sequences. We then show how they are useful in analyzing the
solvability of the uniform subgroup membership problem for fundamental groups
of graphs of groups. Applications include coherent right-angled Artin groups
and coherent solvable groups.
|
lt256
|
arxiv_abstracts
|
math/0302207
|
Parabolic triples of the form $(E_*,\theta,\sigma)$ are considered, where
$(E_*,\theta)$ is a parabolic Higgs bundle on a given compact Riemann surface
$X$ with parabolic structure on a fixed divisor $S$, and $\sigma$ is a nonzero
section of the underlying vector bundle. Sending such a triple to the Higgs
bundle $(E_*,\theta)$ a map from the moduli space of stable parabolic triples
to the moduli space of stable parabolic Higgs bundles is obtained. The pull
back, by this map, of the symplectic form on the moduli space of stable
parabolic Higgs bundles will be denoted by $\text{d}\Omega'$. On the other
hand, there is a map from the moduli space of stable parabolic triples to a
Hilbert scheme $\text{Hilb}^\delta(Z)$, where $Z$ denotes the total space of
the line bundle $K_X\otimes{\mathcal O}_X(S)$, that sends a triple
$(E_*,\theta,\sigma)$ to the divisor defined by the section $\sigma$ on the
spectral curve corresponding to the parabolic Higgs bundle $(E_*,\theta)$.
Using this map and a meromorphic one--form on $\text{Hilb}^\delta(Z)$, a
natural two--form on the moduli space of stable parabolic triples is
constructed. It is shown here that this form coincides with the above mentioned
form $\text{d}\Omega'$.
|
256
|
arxiv_abstracts
|
math/0302208
|
We give the first part of a proof of Thurston's Ending Lamination conjecture.
In this part we show how to construct from the end invariants of a Kleinian
surface group a ``Lipschitz model'' for the thick part of the corresponding
hyperbolic manifold. This enables us to describe the topological structure of
the thick part, and to give a-priori geometric bounds.
|
lt256
|
arxiv_abstracts
|
math/0302209
|
Let X be a smooth projective connected curve of genus $g \ge 2$ and let I be
a finite set of points of X. Fix a parabolic structure on I for rank r vector
bundles on X. Let $M^{par}$ denote the moduli space of parabolic semistable
bundles and let $L^{par}$ denote the parabolic determinant bundle. In this
paper we show that the n-th tensor power line bundle ${L^{par}}^n$ on the
moduli space $M^{par}$ is globally generated, as soon as the integer n is such
that $n \ge [\frac{r^2}{4}]$. In order to get this bound, we construct a
parabolic analogue of the Quot scheme and extend the result of Popa and Roth on
the estimate of its dimension.
|
lt256
|
arxiv_abstracts
|
math/0302210
|
The aim of these notes is to generalize Laumon's construction [18] of
automorphic sheaves corresponding to local systems on a smooth, projective
curve $C$ to the case of local systems with indecomposable unipotent
ramification at a finite set of points. To this end we need an extension of the
notion of parabolic structure on vector bundles to coherent sheaves. Once we
have defined this, a lot of arguments from the article "On the geometric
Langlands conjecture" by Frenkel, Gaitsgory and Vilonen [10] carry over to our
situation. We show that our sheaves descend to the moduli space of parabolic
bundles if the rank is $\leq 3$ and that the general case can be deduced form a
generalization of the vanishing conjecture of [10].
|
lt256
|
arxiv_abstracts
|
math/0302211
|
Various equivariant intersection numbers on Hilbert schemes of points on the
affine plane are computed, some of which are organized into tau-functions of
2-Toda hierarchies. A correspondence between the equivariant intersection on
Hilbert schemes and stationary Gromov-Witten theory is established.
|
lt256
|
arxiv_abstracts
|
math/0302212
|
For a sample set of 1024 values, the FFT is 102.4 times faster than the
discrete Fourier transform (DFT). The basis for this remarkable speed advantage
is the `bit-reversal' scheme of the Cooley-Tukey algorithm. Eliminating the
burden of `degeneracy' by this means is readily understood using vector
graphics.
|
lt256
|
arxiv_abstracts
|
math/0302213
|
We give factorizations for weighted spanning tree enumerators of Cartesian
products of complete graphs, keeping track of fine weights related to degree
sequences and edge directions. Our methods combine Kirchhoff's Matrix-Tree
Theorem with the technique of identification of factors.
|
lt256
|
arxiv_abstracts
|
math/0302214
|
We describe numerical calculations which examine the Phillips-Sarnak
conjecture concerning the disappearance of cusp forms on a noncompact finite
volume Riemann surface $S$ under deformation of the surface. Our calculations
indicate that if the Teichmuller space of $S$ is not trivial then each cusp
form has a set of deformations under which either the cusp form remains a cusp
form, or else it dissolves into a resonance whose constant term is uniformly a
factor of $10^{8}$ smaller than a typical Fourier coefficient of the form. We
give explicit examples of those deformations in several cases.
|
lt256
|
arxiv_abstracts
|
math/0302215
|
We call a smooth function of one variable a degree n pseudopolynomial if its
n-th derivative has no (real) zeros. An n pseudopolynomial is called hyperbolic
if it has exactly n simple zeros. In this short note we describe the necessary
and sufficient conditions on the arrangements of 6 points consisting of 3 zeros
of pseudopolynomials of degree 3, two zeros of their 1st derivatives and 1 zero
of their second derivatives. Besides the standard Rolle's inequalities the
restrictions include additional quadratic inequalities of geometric origin.
This text is an easy reading accessible for undergraduates. We formulated
also two questions not solved yet.
|
lt256
|
arxiv_abstracts
|
math/0302216
|
We prove that $$\int_0^1\frac{-\log f(x)}xdx=\frac{\pi^2}{3ab}$$ where $f(x)$
is the decreasing function that satisfies $f^a-f^b=x^a-x^b$, for $0<a<b$. When
$a$ is an integer and $b=a+1$ we deduce several combinatorial results. These
include an asymptotic formula for the number of integer partitions not having
$a$ consecutive parts, and a formula for the metastability thresholds of a
class of threshold growth cellular automaton models related to bootstrap
percolation.
|
lt256
|
arxiv_abstracts
|
math/0302217
|
We show that Ozawa's recent results on solid von Neumann algebras imply that
there are free Araki-Woods factors, which fail to have free absorption. We also
show that a free Araki-Woods factors $\Gamma (\mu, n)$ associated to a measure
and a multiplicity function $n$ may non-trivially depend on the multiplicity
function.
|
lt256
|
arxiv_abstracts
|
math/0302218
|
In this paper, we show that if G is a finite p-group (p prime) acting by
automorphisms on a $\delta$-hyperbolic Poincare Duality group, then the fixed
subgroup is a Poincare Duality group over Z/p. We also provide examples to show
that the fixed subgroup might not even be a Duality group over Z.
|
lt256
|
arxiv_abstracts
|
math/0302219
|
Let M be a compact locally conformal hyperkaehler manifold. We prove a
version of Kodaira-Nakano vanishing theorem for M. This is used to show that M
admits no holomorphic differential forms, and the cohomology of the structure
sheaf $H^i(O_M)$ vanishes for i>1. We also prove that the first Betti number of
M is 1. This leads to a structure theorem for locally conformally hyperkaehler
manifolds, describing them in terms of 3-Sasakian geometry. Similar results are
proven for compact Einstein-Weyl locally conformal Kaehler manifolds.
|
lt256
|
arxiv_abstracts
|
math/0302220
|
We characterize co-Hopfian finitely generated torsion free nilpotent groups
in terms of their Lie algebra automorphisms, and construct many examples of
such groups.
|
lt256
|
arxiv_abstracts
|
math/0302221
|
We prove a result on equivariant deformations of flat bundles, and as a
corollary, we obtain two ``splitting in a finite cover'' theorems for isometric
group actions on Riemannian manifolds with infinite fundamental groups, where
the manifolds are either compact of nonnegative Ricci curvature, or complete of
nonnegative sectional curvature.
|
lt256
|
arxiv_abstracts
|
math/0302222
|
Z.-J. Ruan has shown that several amenability conditions are all equivalent
in the case of discrete Kac algebras. In this paper, we extend this work to the
case of discrete quantum groups. That is, we show that a discrete quantum
group, where we do not assume its unimodularity, has an invariant mean if and
only if it is strongly Voiculescu amenable.
|
lt256
|
arxiv_abstracts
|
math/0302223
|
It is well known that a domain without proper strongly divisorial ideals is
completely integrally closed. In this paper we show that a domain without {\em
prime} strongly divisorial ideals is not necessarily completely integrally
closed, although this property holds under some additional assumptions.
|
lt256
|
arxiv_abstracts
|
math/0302224
|
Two plane analytic branches are topologically equivalent if and only if they
have the same multiplicity sequence. We show that having same semigroup is
equivalent to having same multiplicity sequence, we calculate the semigroup
from a parametrization, and we characterize semigroups for plane branches.
These results are known, but the proofs are new. Furthermore we characterize
multiplicity sequences of plane branches, and we prove that the associated
graded ring, with respect to the values, of a plane branch is a complete
intersection.
|
lt256
|
arxiv_abstracts
|
math/0302225
|
We prove the existence of a finite set of moves sufficient to relate any two
representations of the same 3-manifold as a 4-fold simple branched covering of
S^3. We also prove a stabilization result: after adding a fifth trivial sheet
two local moves suffice. These results are analogous to results of Piergallini
in degree 3 and can be viewed as a second step in a program to establish
similar results for arbitrary degree coverings of S^3.
|
lt256
|
arxiv_abstracts
|
math/0302226
|
We show the non-vanishing of cohomology groups of sufficiently small
congruence lattices in $SL(1,D)$, where $D$ is a quaternion division algebras
defined over a number field $E$ contained inside a solvable extension of a
totally real number field.
As a corollary, we obtain new examples of compact, arithmetic, hyperbolic
three manifolds, with non-torsion first homology group, confirming a conjecture
of Thurston. The proof uses the characterisation of the image of solvable base
change by the author, and the construction of cusp forms with non-zero cusp
cohomology by Labesse and Schwermer.
|
lt256
|
arxiv_abstracts
|
math/0302227
|
The theory of weak solutions for nonlinear conservation laws is now well
developed in the case of scalar equations [3] and for one-dimensional
hyperbolic systems [1, 2]. For systems in several space dimensions, however,
even the global existence of solutions to the Cauchy problem remains a
challenging open question. In this note we construct a conterexample showing
that, even for a simple class of hyperbolic systems, in two space dimensions
the Cauchy problem can be ill posed.
|
lt256
|
arxiv_abstracts
|
math/0302228
|
Consider a stack of books, containing both white and black books. Suppose
that we want to sort them out, putting the white books on the right, and the
black books on the left (fig.~1). This will be done by a finite sequence of
elementary transpositions. In other words, if we have a stack of all black
books of length $a$ followed by a stack of all white books of length $b$, we
are allowed to reverse their order at the cost of $a+b$. We are interested in a
lower bound on the total cost of the rearrangement.
|
lt256
|
arxiv_abstracts
|
math/0302229
|
The purpose of this paper is to study finite-dimensional Lie algebras over a
field k of characteristic zero which admit a commutative polarization (CP).
Among the many results and examples, it is shown that, if k is algebraically
closed, the nilradical N of a parabolic subalgebra in A_n and C_n has such a
CP. Using this fact a simple closed formula is derived for the index of N.
|
lt256
|
arxiv_abstracts
|
math/0302230
|
We study different notions of slope of a vector bundle over a smooth
projective curve with respect to ampleness and affineness in order to apply
this to tight closure problems. This method gives new degree estimates from
above and from below for the tight closure of a homogeneous $R_+$-primary ideal
in a two-dimensional normal standard-graded algebra $R$ in terms of the minimal
and the maximal slope of the sheaf of relations for some ideal generators. If
moreover this sheaf of relations is semistable, then both degree estimates
coincide and we get a vanishing type theorem.
|
lt256
|
arxiv_abstracts
|
math/0302231
|
We consider dynamical systems arising from substitutions over a finite
alphabet. We prove that such a system is linearly repetitive if and only if it
is minimal. Based on this characterization we extend various results from
primitive substitutions to minimal substitutions. This includes applications to
random Schr\"odinger operators and to number theory.
|
lt256
|
arxiv_abstracts
|
math/0302232
|
Let X = G/H be a reductive symmetric space and K a maximal compact subgroup
of G. The image under the Fourier transform of the space of K-finite compactly
supported smooth functions on X is characterized.
|
lt256
|
arxiv_abstracts
|
math/0302233
|
We study complements of hypersurfaces in schemes with respect to the property
being affine.
|
lt256
|
arxiv_abstracts
|
math/0302234
|
The existence and continuity for the Calderon projector of the perturbed odd
signature operator on a 3-manifold is established. As an application we give a
new proof of a result of Taubes relating the mod 2 spectral flow of a family of
operators on a homology 3-sphere with the difference in local intersection
numbers of the character varieties coming from a Heegard decomposition.
|
lt256
|
arxiv_abstracts
|
math/0302235
|
We provide the set of filters (saturated submonoids) in a commutative monoid
with a topology (like the spectrum of a ring) and study the resulting spaces.
|
lt256
|
arxiv_abstracts
|
math/0302236
|
The Hard Lefschetz theorem for intersection cohomology of nonrational
polytopes was recently proved by K. Karu [Ka]. This theorem implies the
conjecture of R. Stanley on the unimodularity of the generalized $h$-vector. In
this paper we strengthen Karu's theorem by introducing a canonical bilinear
form $(\cdot ,\cdot)_{\Phi}$ on the intersection cohomology $IH(\Phi)$ of a
complete fan $\Phi$ and proving the Hodge-Riemann bilinear relations for
$(\cdot ,\cdot)_{\Phi}$.
|
lt256
|
arxiv_abstracts
|
math/0302237
|
In this paper we study the behavior of the solution to the dbar-Neumann
problem for (0,1)-forms on a bi-disc in C^2. We show singularities which arise
at the distinguished boundary are of logarithmic and arctangent type.
|
lt256
|
arxiv_abstracts
|
math/0302238
|
Several authors have proved Lefschetz type formulae for the local Euler
obstruction. In particular, a result of this type is proved in [BLS].The
formula proved in that paper turns out to be equivalent to saying that the
local Euler obstruction, as a constructible function, satisfies the local Euler
condition (in bivariant theory) with respect to general linear forms.
The purpose of this work is to understand what prevents the local Euler
obstruction of satisfying the local Euler condition with respect to functions
which are singular at the considered point. This is measured by an invariant
(or ``defect'') of such functions that we define below. We give an
interpretation of this defect in terms of vanishing cycles, which allows us to
calculate it algebraically. When the function has an isolated singularity, our
invariant can be defined geometrically, via obstruction theory. We notice that
this invariant unifies the usual concepts of {\it the Milnor number} of a
function and of the {\it local Euler obstruction} of an analytic set.
|
256
|
arxiv_abstracts
|
math/0302239
|
If B is an infinite subset of omega and X is a topological group, let C^X_B
be the set of all x in X such that <x^n : n in B> converges to 1. If F is a
filter of infinite sets, let D^X_F be the union of all the C^X_B for B in F.
The C^X_B and D^X_F are subgroups of X when X is abelian. In the circle group
T, it is known that C^X_B always has measure 0. We show that there is a filter
F such that D^T_F has measure 0 but is not contained in any C^X_B. There is
another filter G such that D^X_G = T. We also describe the relationship between
D^T_F and the D^X_F for arbitrary compact groups X.
|
lt256
|
arxiv_abstracts
|
math/0302240
|
We prove several unique prime factorization results for tensor products of
type II_1 factors coming from groups that can be realized either as subgroups
of hyperbolic groups or as discrete subgroups of connected Lie groups of real
rank 1. In particular, we show that if $R \otimes LF_{r_1} \otimes ... \otimes
LF_{r_m}$ is isomorphic to a subfactor in $R \otimes LF_{s_1} \otimes >...
\otimes LF_{s_n}$, for some $2\leq r_i, s_j \leq \infty$, then $m\le n$.
|
lt256
|
arxiv_abstracts
|
math/0302241
|
Let $(R, {\mathfrak m})$ be a Noetherian local ring and let $I$ be an
$R$-ideal. Inspired by the work of H\"ubl and Huneke, we look for conditions
that guarantee the Cohen-Macaulayness of the special fiber ring ${\mathcal
F}={\mathcal R}/{\mathfrak m}{\mathcal R}$ of $I$, where ${\mathcal R}$ denotes
the Rees algebra of $I$. Our key idea is to require `good' intersection
properties as well as `few' homogeneous generating relations in low degrees. In
particular, if $I$ is a strongly Cohen-Macaulay $R$-ideal with $G_{\ell}$ and
the expected reduction number, we conclude that ${\mathcal F}$ is always
Cohen-Macaulay. We also obtain a characterization of the Cohen-Macaulayness of
${\mathcal R}/K{\mathcal R}$ for any ${\mathfrak m}$-primary ideal $K$: This
result recovers a well-known criterion of Valabrega and Valla whenever $K=I$.
Furthermore, we study the relationship among the Cohen-Macaulay property of the
special fiber ring ${\mathcal F}$ and the one of the Rees algebra ${\mathcal
R}$ and the associated graded ring ${\mathcal G}$ of $I$. Finally, we focus on
the integral closedness of ${\mathfrak m}I$. The latter question is motivated
by the theory of evolutions.
|
256
|
arxiv_abstracts
|
math/0302242
|
Let f be a smooth map between unit spheres of possibly different dimensions.
We prove the global existence and convergence of the mean curvature flow of the
graph of f under various conditions. A corollary is that any area-decreasing
map between unit spheres (of possibly different dimensions) is homotopic to a
constant map.
|
lt256
|
arxiv_abstracts
|
math/0302243
|
We consider the problem of computing upper and lower bounds on the price of a
European basket call option, given prices on other similar baskets. Although
this problem is very hard to solve exactly in the general case, we show that in
some instances the upper and lower bounds can be computed via simple
closed-form expressions, or linear programs. We also introduce an efficient
linear programming relaxation of the general problem based on an integral
transform interpretation of the call price function. We show that this
relaxation is tight in some of the special cases examined before.
|
lt256
|
arxiv_abstracts
|
math/0302244
|
In the Friedmann Model of the universe, cosmologists assume that spacelike
slices of the universe are Riemannian manifolds of constant sectional
curvature. This assumption is justified via Schur's Theorem by stating that the
spacelike universe is locally isotropic. Here we define a Riemannian manifold
as almost locally isotropic in a sense which allows both weak gravitational
lensing in all directions and strong gravitational lensing in localized angular
regions at most points. We then prove that such a manifold is Gromov Hausdorff
close to a length space $Y$ which is a collection of space forms joined at
discrete points. Within the paper we define a concept we call an "exponential
length space" and prove that if such a space is locally isotropic then it is a
space form.
|
lt256
|
arxiv_abstracts
|
math/0302245
|
The following discourse is inspired by the works on hyperbolic groups of
Epstein, and Neumann/Reeves. Epstein showed that geometrically finite
hyperbolic groups are biautomatic. Neumann/Reeves showed that virtually central
extensions of word hyperbolic groups are biautomatic. We prove the following
generalisation:
Theorem. Let H be a geometrically finite hyperbolic group. Let sigma in
H^2(H) and suppose that sigma restricted to P is zero for any parabolic
subgroup P of H. Then the extension of H by sigma is biautomatic.
We also prove another generalisation of the result of Epstein.
Theorem. Let G be hyperbolic relative to H, with the bounded coset
penetration property. Let H be a biautomatic group with a prefix-closed normal
form. Then G is biautomatic.
Based on these two results, it seems reasonable to conjecture the following
(which the author believes can be proven with a simple generalisation of the
argument in Section 1): Let G be hyperbolic relative to H, where H has a
prefixed closed biautomatic structure. Let sigma in H^2(G) and suppose that
sigma restricted to H is zero. Then the extension of G by sigma is biautomatic.
|
256
|
arxiv_abstracts
|
math/0302246
|
Let $R$ be a Cohen-Macaulay local ring with maximal ideal $\max$. In this
paper we present a procedure for computing the Ratllif-Rush closure of a
$\max-$primary ideal $I \subset R$.
|
lt256
|
arxiv_abstracts
|
math/0302247
|
We continue the study of scattering theory for the system consisting of a
Schr"odinger equation and a wave equation with a Yukawa type coupling in space
dimension 3. In a previous paper we proved the existence of modified wave
operators for that system with no size restriction on the data and we
determined the asymptotic behaviour in time of solutions in the range of the
wave operators, under a support condition on the asymptotic state required by
the different propagation properties of the wave and Schr"odinger
equations.Here we eliminate that condition by using an improved asymptotic form
for the solutions.
|
lt256
|
arxiv_abstracts
|
math/0302248
|
In this survey article we will consider universal lower bounds on the volume
of a Riemannian manifold, given in terms of the volume of lower dimensional
objects (primarily the lengths of geodesics). By `universal' we mean without
curvature assumptions. The restriction to results with no (or only minimal)
curvature assumptions, although somewhat arbitrary, allows the survey to be
reasonably short. Although, even in this limited case the authors have left out
many interesting results.
|
lt256
|
arxiv_abstracts
|
math/0302249
|
One investigates the Hitchin systems over "large limit" curves.
|
lt256
|
arxiv_abstracts
|
math/0302250
|
Prompted by an example arising in critical percolation, we study some
reflected Brownian motions in symmetric planar domains and show that they are
intertwined with one-dimensional diffusions. In the case of a wedge, the
reflected Brownian motion is intertwined with the 3-dimensional Bessel process.
This implies some simple hitting distributions and sheds some light on the
formula proposed by Watts for double-crossing probabilities in critical
percolation.
|
lt256
|
arxiv_abstracts
|
math/0302251
|
An explicit bilinear generating function for Meixner-Pollaczek polynomials is
proved. This formula involves continuous dual Hahn polynomials,
Meixner-Pollaczek functions, and non-polynomial $_3F_2$-hypergeometric
functions that we consider as continuous Hahn functions. An integral transform
pair with continuous Hahn functions as kernels is also proved. These results
have an interpretation for the tensor product decomposition of a positive and a
negative discrete series representation of $\su(1,1)$ with respect to
hyperbolic bases, where the Clebsch-Gordan coefficients are continuous Hahn
functions.
|
lt256
|
arxiv_abstracts
|
math/0302252
|
Given a finite alphabet X and an ordering on the letters, the map \sigma
sends each monomial on X to the word that is the ordered product of the letter
powers in the monomial. Motivated by a question on Groebner bases, we
characterize ideals I in the free commutative monoid (in terms of a generating
set) such that the ideal <\sigma(I)> generated by \sigma(I) in the free monoid
is finitely generated. Whether there exists an ordering such that <\sigma(I)>
is finitely generated turns out to be NP-complete. The latter problem is
closely related to the recognition problem for comparability graphs.
|
lt256
|
arxiv_abstracts
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.