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hep-th/9301023
Reflection equation and link polynomials for arbitrary genus solid tori
The correspondence between the braid group on a solid torus of arbitrary genus and the algebra of Yang-Baxter and reflection equation operators is shown. A representation of this braid group in terms of $R$-matrices is given. The characteristic equation of the reflection equation matrix is considered as an additional s...
1993-01-08
2008-02-03
[ "hep-th", "math.QA" ]
C. Schwiebert
hep-th/9301021
Positive Energy Theorem and Supersymmetry in Exactly Solvable Quantum-Corrected 2D Dilaton-Gravity
Extending the work of Park and Strominger, we prove a positive energy theorem for the exactly solvable quantum-corrected 2D dilaton gravity theories. The positive energy functional we construct is shown to be unique (within a reasonably broad class of such functionals). For field configurations asymptotic to the LDV we...
1993-01-07
2009-10-22
[ "hep-th", "gr-qc" ]
Adel Bilal
hep-th/9301020
On the Mass of Two Dimensional Quantum Black Hole
For the two dimensional dilaton-coupled quantum gravity model, we give the local black hole mass, which is an analogue of what was first introduced by Fischler, Morgan and Polchinski in the four dimensional gravitational systems. We analyze the original CGHS model with this local mass and find that the local mass is de...
1993-01-07
2011-04-20
[ "hep-th" ]
Tsukasa TADA and Shozo UEHARA
hep-th/9301019
Gauge Theory of the String Geodesic Field
A relativistic string is usually represented by the Nambu-Goto action in terms of the extremal area of a 2-dimensional timelike submanifold of Minkowski space. Alternatively, a family of classical solutions of the string equation of motion can be globally described in terms of the associated geodesic field. In this pap...
1993-01-07
2009-10-22
[ "hep-th" ]
A.Aurilia, A.Smailagic, E.Spallucci
hep-th/9301018
Characters in Conformal Field Theories from Thermodynamic Bethe Ansatz
We propose a new $q$-series formula for a character of parafermion conformal field theories associated to arbitrary non-twisted affine Lie algebra $\widehat{g}$. We show its natural origin from a thermodynamic Bethe ansatz analysis including chemical potentials.
1993-01-07
2009-10-22
[ "hep-th" ]
A.Kuniba, T.Nakanishi and J.Suzuki
hep-th/9301016
Modular Invariant Partition Functions and Method of Shift Vector
Using shift vector method we obtain a large class of self-dual lattices of dimension $(l,l)$, which has a one to one correspondence with modular invariants of free bosonic theory compactified on co-root lattice of a rank $l$ Lie group. Then a large number of modular invariants of affine Lie algebras are derived explici...
1993-01-06
2009-10-22
[ "hep-th" ]
H.Arfaei and A.Shirzad
hep-th/9301017
Nonperturbative Solution of the Super-Virasoro Constraints
We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also obtain the nonperturbative solution of the super-Virasoro constraints in the doubl...
1993-01-06
2015-06-26
[ "hep-th" ]
K. Becker and M. Becker
hep-th/9301015
Effective action of gauged WZW model and exact string solutions
We suggest how to derive the exact (all order in $\a'$) expressions for the background fields for string solutions corresponding to gauged WZW models directly at the $2d$ field theory level. One is first to replace the classical gauged WZW action by the quantum effective one and then to integrate out the gauge field. W...
1993-01-06
2009-09-17
[ "hep-th" ]
A.A. Tseytlin
hep-th/9301012
A Solvable Model for Intersecting Loops
We show that some models with non-local (and non-localizable) interactions have a property, called quasi-locality, which allows for the definition of a transfer matrix. We give the Yang-Baxter equation as a sufficient condition for the existence of a family of commuting transfer matrices and solve them for a loop model...
1993-01-05
2007-05-23
[ "hep-th" ]
Bernard Nienhuis and Ronald Rietman
hep-th/9301006
Light-cone approach to random surfaces embedded in two dimensions
We review the recently proposed \lc\ quantization of the matrix model which is expected to have a critical point describing 2-d quantum gravity coupled to $c=2$ matter. In the $N\to\infty$ limit, we derive a linear Schroedinger equation for the free string spectrum. Numerical study of this equation suggests that the sp...
1993-01-05
2007-05-23
[ "hep-th" ]
K. Demeterfi and I. R. Klebanov
hep-th/9301014
Solitons and Instantons with(out) Supersymmetry
We give model-independent arguments, valid in nearly any number of spacetime dimensions, that topological solitons and instantons satisfy Bogomol'nyi-type bounds and, when these bounds are saturated, satisfy self-duality equations. In the supersymmetric case, we also show that, in spacetime dimensions greater than two,...
1993-01-05
2009-10-22
[ "hep-th", "hep-ph" ]
Zvonimir Hlousek and Donald Spector
hep-th/9301008
A Simple Method for Computing Soliton Statistics
I provide an extremely simple argument that the kink-type solitons in certain theories are fermionic. The argument is based on the Witten index, but can in fact be used to determine soliton statistics in non-supersymmetric theories as well.
1993-01-05
2009-10-22
[ "hep-th", "cond-mat", "hep-ph" ]
Donald Spector
hep-th/9301009
Vertex operator algebras and operads
Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal to $0$, not just binary products. In this paper, a reformulation of the notion o...
1993-01-05
2008-02-03
[ "hep-th", "math.QA" ]
Yi-Zhi Huang and James Lepowsky
hep-th/9301013
Fermionic Determinant of the Massive Schwinger Model
A representation for the fermionic determinant of the massive Schwinger model, or $QED_2$, is obtained that makes a clean separation between the Schwinger model and its massive counterpart. From this it is shown that the index theorem for $QED_2$ follows from gauge invariance, that the Schwinger model's contribution to...
1993-01-05
2009-10-22
[ "hep-th" ]
M. P. Fry
hep-th/9301011
Characteristic Dynkin diagrams and W-algebras
We present a classification of characteristic Dynkin diagrams for the $A_N$, $B_N$, $C_N$ and $D_N$ algebras. This classification is related to the classification of \cw(\cg,\ck) algebras arising from non-Abelian Toda models, and we argue that it can give new insight on the structure of $W$ algebras.
1993-01-05
2009-10-22
[ "hep-th", "math.QA" ]
E. Ragoucy
hep-th/9301010
A New $N = 4$ Superconformal Algebra
It is shown that the previously known $N=3$ and $N=4$ superconformal algebras can be contracted consistently by singular scaling of some of the generators. For the later case, by a contraction which depends on the central term, we obtain a new $N=4$ superconformal algebra which contains an $SU(2)\times {U(1)}^4$ Kac-Mo...
1993-01-04
2015-06-26
[ "hep-th" ]
Abbas Ali and Alok Kumar
hep-th/9301004
Large Order Behaviour of 2D Gravity Coupled to $d<1$ Matter
We discuss the large order behaviour and Borel summability of the topological expansion of models of 2D gravity coupled to general $(p,q)$ conformal matter. In a previous work it was proven that at large order $k$ the string susceptibility had a generic $a^k\Gamma(2k-\ud)$ behaviour. Moreover the constant $a$, relevant...
1993-01-04
2010-11-01
[ "hep-th" ]
B. Eynard and J. Zinn-Justin
hep-th/9301005
Duality, Marginal Perturbations and Gauging
We study duality transformations for two-dimensional sigma models with abelian chiral isometries and prove that generic such transformations are equivalent to integrated marginal perturbations by bilinears in the chiral currents, thus confirming a recent conjecture by Hassan and Sen formulated in the context of Wess-Zu...
1993-01-04
2008-11-26
[ "hep-th" ]
M{\aa}ns Henningson and Chiara R. Nappi
hep-th/9301007
Integrability and Fusion Algebra for Quantum Mappings
We apply the fusion procedure to a quantum Yang-Baxter algebra associated with time-discrete integrable systems, notably integrable quantum mappings. We present a general construction of higher-order quantum invariants for these systems. As an important class of examples, we present the Yang-Baxter structure of the Gel...
1993-01-04
2009-10-22
[ "hep-th" ]
F.W. Nijhoff and H.W. Capel
hep-th/9301003
Summing Over Inequivalent Maps in the String Theory Interpretation of Two Dimensional QCD
Following some recent work by Gross, we consider the partition function for QCD on a two dimensional torus and study its stringiness. We present strong evidence that the free energy corresponds to a sum over branched surfaces with small handles mapped into the target space. The sum is modded out by all diffeomorphisms ...
1993-01-02
2009-10-22
[ "hep-th" ]
Joseph A. Minahan
hep-th/9301002
Scaling behavior of quantum four-geometries
We propose that large quantum fluctuations of the conformal factor drastically modify classical general relativity at cosmological distance scales, resulting in a scale invariant phase of quantum gravity in the far infrared. We derive scaling relations for the partition function and physical observables in this conform...
1993-01-02
2009-10-22
[ "hep-th", "gr-qc" ]
I. Antoniadis, P.O. Mazur and E. Mottola
hep-th/9301001
Gonihedric String and Asymptotic Freedom
Few natural basic principles allow to extend Feynman integral over the paths to an integral over the surfaces so, that they coincide at long time scale, that is when the surface degenerates into a single particle world line. In the first approximation the loop Green functions have perimeter behavior. That corresponds t...
1993-01-01
2015-06-26
[ "hep-th" ]
G.K.Savvidy and K.G.Savvidy
math/9307225
A counterexample to the rigidity conjecture for rings
An example is constructed of a local ring and a module of finite type and finite projective dimension over that ring such that the module is not rigid. This shows that the rigidity conjecture is false.
1993-07-01
2008-02-03
[ "math.AC" ]
Raymond C. Heitmann
math/9304212
Zariski Geometries
We characterize the Zariski topologies over an algebraically closed field in terms of general dimension-theoretic properties. Some applications are given to complex manifold and to strongly minimal sets.
1993-04-01
2016-09-06
[ "math.AG" ]
Ehud Hrushovski, Boris Zilber
math/9301213
Relative $K$-cycles and elliptic boundary conditions
In this paper, we discuss the following conjecture raised by Baum-Douglas: For any first-order elliptic differential operator $D$ on smooth manifold $M$ with boundary $\p M$, $D$ possesses an elliptic boundary condition if and only if $\partial [D]$ = 0 in $K_1(\partial M)$, where $[D]$ is the relative $K$-cycle in $K_...
1993-01-01
2008-02-03
[ "math.AP", "math.DG", "math.KT" ]
Guihua Gong
math/9301218
A new result for the porous medium equation derived from the Ricci flow
Given $\Bbb R^2, $ with a ``good'' complete metric, we show that the unique solution of the Ricci flow approaches a soliton at time infinity. Solitons are solutions of the Ricci flow, which move only by diffeomorphism. The Ricci flow on $\Bbb R^2$ is the limiting case of the porous medium equation when $m$ is zero. The...
1993-01-01
2008-02-03
[ "math.AP" ]
Lang-Fang Wu
math/9310228
Intersecting families of sets and the topology of cones in economics
Two classical problems in economics, the existence of a market equilibrium and the existence of social choice functions, are formalized here by the properties of a family of cones associated with the economy. It was recently established that a necessary and sufficient condition for solving the former is the nonempty in...
1993-10-01
2016-09-06
[ "math.AT", "math.OC" ]
Graciela Chichilnisky
math/9312211
Watson's basic analogue of Ramanujan's entry 40 and its generalization
We generalize Watson's $ q $-analogue of Ramanujan's Entry 40 continued fraction by deriving solutions to a $ {}_{10} \phi_9 $ series contiguous relation and applying Pincherle's theorem. Watson's result is recovered as a special terminating case, while a limit case yields a new continued fraction associated with an $ ...
1993-12-29
2008-02-03
[ "math.CA" ]
Dharma P. Gupta, David R. Masson
math/9312210
Solutions to the associated q-Askey-Wilson polynomial recurrence relation
A $\tphin$ contiguous relation is used to derive contiguous relations for a very-well-poised $\ephis$. These in turn yield solutions to the associated $q$-Askey-Wilson polynomial recurrence relation, expressions for the associated continued fraction, the weight function and a $q$-analogue of a generalized Dougall's the...
1993-12-29
2016-09-06
[ "math.CA" ]
Dharma P. Gupta, David R. Masson
math/9311210
From Schr\"odinger spectra to orthogonal polynomials, via a functional equation
The main difference between certain spectral problems for linear Schr\"odinger operators, e.g. the almost Mathieu equation, and three-term recurrence relations for orthogonal polynomials is that in the former the index ranges across $\ZZ$ and in the latter only across $\Zp$. We present a technique that, by a mixture of...
1993-11-17
2016-09-06
[ "math.CA" ]
Arieh Iserles
math/9311209
Some basic bilateral sums and integrals
By splitting the real line into intervals of unit length a doubly infinite integral of the form $\Int F(q^x)\,dx,\; 0<q<1$, can clearly be expressed as $\Integ \Sum F(q^{x+n})\,dx$, provided $F$ satisfies the appropriate conditions. This simple idea is used to prove Ramanujan's integral analogues of his \ph{1}{1} sum a...
1993-11-01
2016-09-06
[ "math.CA" ]
Mourad E. H. Ismail, Mizan Rahman
math/9310223
Asymptotic approximations for symmetric elliptic integrals
Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than the others, asymptotic approximations with error bounds are presented. In most c...
1993-10-07
2016-09-06
[ "math.CA" ]
Bille C. Carlson, John L. Gustafson
math/9310221
Diagonalization of certain integral operators II
We establish an integral representations of a right inverses of the Askey-Wilson finite difference operator in an $L^2$ space weighted by the weight function of the continuous $q$-Jacobi polynomials. We characterize the eigenvalues of this integral operator and prove a $q$-analog of the expansion of $e^{ixy}$ in Jacobi...
1993-10-05
2016-09-06
[ "math.CA" ]
Mourad E. H. Ismail, Mizan Rahman, Ruiming Zhang
math/9310222
Moments of Dirichlet splines and their applications to hypergeometric functions
Dirichlet averages of multivariate functions are employed for a derivation of basic recurrence formulas for the moments of multivariate Dirichlet splines. An algorithm for computing the moments of multivariate simplex splines is presented. Applications to hypergeometric functions of several variables are discussed.
1993-10-05
2025-10-20
[ "math.CA", "cs.NA", "math.NA" ]
Edward Neuman, Patrick J. Van Fleet
math/9310219
A right inverse of the Askey-Wilson operator
We establish an integral representation of a right inverse of the Askey-Wilson finite difference operator on $L^2$ with weight $(1-x^2)^{-1/2}$. The kernel of this integral operator is $\vartheta'_4/\vartheta_4$ and is the Riemann mapping function that maps the open unit disc conformally onto the interior of an ellipse...
1993-10-05
2009-09-25
[ "math.CA" ]
B. Malcolm Brown, Mourad E. H. Ismail
math/9310220
Orthogonal matrix polynomials and higher order recurrence relations
It is well-known that orthogonal polynomials on the real line satisfy a three-term recurrence relation and conversely every system of polynomials satisfying a three-term recurrence relation is orthogonal with respect to some positive Borel measure on the real line. In this paper we extend this result and show that ever...
1993-10-05
2016-09-06
[ "math.CA" ]
Antonio J. Dur\'an, Walter Van Assche
math/9309213
Uniform multi-parameter limit transitions in the Askey tableau
Extended abstract for the Proceedings of the Conference ``Modern developments in complex analysis and related topics'' (on the occasion of the 70th birthday of prof.\ dr.\ J. Korevaar), University of Amsterdam, January 27--29, 1993.
1993-09-28
2016-09-06
[ "math.CA" ]
Tom H. Koornwinder
math/9308209
Astrophysical thermonuclear functions
Stars are gravitationally stabilized fusion reactors changing their chemical composition while transforming light atomic nuclei into heavy ones. The atomic nuclei are supposed to be in thermal equilibrium with the ambient plasma. The majority of reactions among nuclei leading to a nuclear transformation are inhibited b...
1993-08-23
2016-09-06
[ "math.CA", "astro-ph" ]
William J. Anderson, Hans J. Haubold, Arak Mathai Mathai
math/9307224
Generalized Hermite polynomials and the Bose-like oscillator calculus
This paper studies a suitably normalized set of generalized Hermite polynomials and sets down a relevant Mehler formula, Rodrigues formula, and generalized translation operator. Weighted generalized Hermite polynomials are the eigenfunctions of a generalized Fourier transform which satisfies an F. and M. Riesz theorem ...
1993-07-25
2016-09-06
[ "math.CA" ]
Marvin Rosenblum
math/9307223
Gauss-type quadrature rules for rational functions
When integrating functions that have poles outside the interval of integration, but are regular otherwise, it is suggested that the quadrature rule in question ought to integrate exactly not only polynomials (if any), but also suitable rational functions. The latter are to be chosen so as to match the most important po...
1993-07-20
2025-10-20
[ "math.CA", "cs.NA", "math.NA" ]
Walter Gautschi
math/9307222
Applications of generalized special functions in stellar astrophysics
This article gives an brief outline of the applications of generalized special functions such as generalized hypergeometric functions, G-functions and H-functions into the general area of nuclear energy generation and reaction rate theory such as the energy generation in a simple stellar model and nuclear reaction rate...
1993-07-14
2016-09-06
[ "math.CA", "astro-ph" ]
Hans J. Haubold, Arak Mathai Mathai
math/9307206
The q-harmonic oscillator and an analog of the Charlier polynomials
A model of a q-harmonic oscillator based on q-Charlier polynomials of Al-Salam and Carlitz is discussed. Simple explicit realization of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation are found. A connection of the kernel of this transform with biorthogonal rationa...
1993-07-09
2009-10-22
[ "math.CA", "math.QA" ]
Richard A. Askey, Serge\u{\i} K. Suslov
math/9307220
The impact of Stieltjes' work on continued fractions and orthogonal polynomials
Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials.
1993-07-09
2013-10-16
[ "math.CA" ]
Walter Van Assche
math/9307212
Algorithm xxx --- ORTHPOL: A package of routines for generating orthogonal polynomials and Gauss-type quadrature rules
A collection of subroutines and examples of their uses, as well as the underlying numerical methods, are described for generating orthogonal polynomials relative to arbitrary weight functions. The object of these routines is to produce the coefficients in the three-term recurrence relation satisfied by the orthogonal p...
1993-07-09
2025-10-20
[ "math.CA", "cs.NA", "math.NA" ]
Walter Gautschi
math/9307213
Some integrals involving Bessel functions
A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection ...
1993-07-09
2016-09-06
[ "math.CA" ]
M. Lawrence Glasser, Emilio Montaldi
math/9307214
Computational aspects of the gravitational instability problem for a multicomponent cosmological medium
The paper presents results for deriving closed-form analytic solutions of the evolution of inhomogeneities in a homogeneous spatially flat multicomponent cosmological model. Mathematical methods to derive computable forms of the perturbations are outlined.
1993-07-09
2016-09-06
[ "math.CA", "astro-ph" ]
Hans J. Haubold, Arak Mathai Mathai
math/9307218
Painlev\'e-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials.
Recurrence coefficients of semi-classical orthogonal polynomials (orthogonal polynomials related to a weight function $w$ such that $w'/w$ is a rational function) are shown to be solutions of non linear differential equations with respect to a well-chosen parameter, according to principles established by D. G. Chudnovs...
1993-07-09
2016-09-06
[ "math.CA" ]
Alphonse P. Magnus
math/9307209
A high-school algebra wallet-sized proof, of the Bieberbach conjecture After L. Weinstein]
Weinstein's[2] brilliant short proof of de Branges'[1] theorem can be made yet much shorter(modulo routine calculations), completely elementary (modulo L\"owner theory), self contained(no need for the esoteric Legendre polynomials' addition theorem), and motivated(ditto), as follows.
1993-07-09
2016-09-06
[ "math.CA" ]
Shalosh B. Ekhad, Doron Zeilberger
math/9307208
The combinatorics of q-Charlier polynomials
We describe various aspects of the Al-Salam-Carlitz $q$-Charlier polynomials. These include combinatorial descriptions of the moments, the orthogonality relation, and the linearization coefficients.
1993-07-09
2016-09-06
[ "math.CA", "math.CO" ]
Anne de M\'edicis, Dennis W. Stanton, Dennis E. White
math/9307210
Using sums of squares to prove that certain entire functions have only real zeros
It is shown how sums of squares of real valued functions can be used to give new proofs of the reality of the zeros of the Bessel functions $J_\alpha (z)$ when $\alpha \ge -1,$ confluent hypergeometric functions ${}_0F_1(c\/; z)$ when $c>0$ or $0>c>-1$, Laguerre polynomials $L_n^\alpha(z)$ when $\alpha \ge -2,$ and Jac...
1993-07-09
2016-09-06
[ "math.CA" ]
George Gasper Jr
math/9307221
Quadrature formulas based on rational interpolation
We consider quadrature formulas based on interpolation using the basis functions $1/(1+t_kx)$ $(k=1,2,3,\ldots)$ on $[-1,1]$, where $t_k$ are parameters on the interval $(-1,1)$. We investigate two types of quadratures: quadrature formulas of maximum accuracy which correctly integrate as many basis functions as possibl...
1993-07-09
2025-10-20
[ "math.CA", "cs.NA", "math.NA" ]
Walter Van Assche, Ingrid Vanherwegen
math/9307215
Polynomial interpolation and Gaussian quadrature for matrix valued functions
The techniques for polynomial interpolation and Gaussian quadrature are generalized to matrix-valued functions. It is shown how the zeros and rootvectors of matrix orthonormal polynomials can be used to get a quadrature formula with the highest degree of precision.
1993-07-09
2025-10-20
[ "math.CA", "cs.NA", "math.NA" ]
Walter Van Assche, Ann Sinap
math/9307207
The q-harmonic oscillator and the Al-Salam and Carlitz polynomials
One more model of a q-harmonic oscillator based on the q-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of...
1993-07-09
2016-09-06
[ "math.CA", "math.QA" ]
Richard A. Askey, Serge\u{\i} K. Suslov
math/9307211
On necessary multiplier conditions for Laguerre expansions
The necessary multiplier conditions for Laguerre expansions derived in Gasper and Trebels \cite{laguerre} are supplemented and modified. This allows us to place Markett's Cohen type inequality \cite{cohen} (up to the $\log $--case) in the general framework of necessary conditions.
1993-07-09
2016-09-06
[ "math.CA" ]
George Gasper Jr, Walter Trebels
math/9307216
Jacobi polynomials of type BC, Jack polynomials, limit transitions and O(\infty)
This is an extended abstract of a lecture held at the Conference ``Fourier and Radon transformations on symmetric spaces'' in honor of Professor S. Helgason's 65th birthday, Roskilde, Denmark, Sept. 10--12, 1992.
1993-07-09
2008-02-03
[ "math.CA" ]
Tom H. Koornwinder
math/9307205
An analog of the Fourier transformation for a q-harmonic oscillator
A q-version of the Fourier transformation and some of its properties are discussed.
1993-07-09
2009-09-25
[ "math.CA", "math.QA" ]
Richard A. Askey, Natig M. Atakishiyev, Serge\u{\i} K. Suslov
math/9307219
Specializations of generalized Laguerre polynomials
Three specializations of a set of orthogonal polynomials with ``8 different q's'' are given. The polynomials are identified as $q$-analogues of Laguerre polynomials, and the combinatorial interpretation of the moments give infinitely many new Mahonian statistics on permutations.
1993-07-09
2009-09-25
[ "math.CA", "math.CO" ]
Rodica Simion, Dennis W. Stanton
math/9307217
Some results on co-recursive associated Laguerre and Jacobi polynomials
We present results on co-recursive associated Laguerre and Jacobi polynomials which are of interest for the solution of the Chapman-Kolmogorov equations of some birth and death processes with or without absorption. Explicit forms, generating functions, and absolutely continuous part of the spectral measures are given. ...
1993-07-09
2016-09-06
[ "math.CA" ]
Jean Letessier
math/9307204
Associated Stieltjes-Carlitz polynomials and a generalization of Heun's differential equation.
The generating function of Stieltjes-Carlitz polynomials is a solution of Heun's differential equation and using this relation Carlitz was the first to get exact closed forms for some Heun functions. Similarly the associated Stieltjes-Carlitz polynomials lead to a new differential equation which we call associated Heun...
1993-07-08
2016-09-06
[ "math.CA" ]
Galliano Valent
math/9307203
On weighted transplantation and multipliers for Laguerre expansions
Using the standard square--function method (based on the Poisson semigroup), multiplier conditions of H\"ormander type are derived for Laguerre expansions in $L^p$--spaces with power weights in the $A_p$-range; this result can be interpreted as an ``upper end point'' multiplier criterion which is fairly good for $p$ ne...
1993-07-08
2016-09-06
[ "math.CA" ]
Krzysztof Stempak, Walter Trebels
math/9301217
Best uniform rational approximation of $x^\alpha$ on $[0,1]$
A strong error estimate for the uniform rational approximation of $x^\alpha$ on $[0,1]$ is given, and its proof is sketched. Let $E_{nn}(x^\alpha,[0,1])$ denote the minimal approximation error in the uniform norm. Then it is shown that $$\lim_{n\to\infty}e^{2\pi\sqrt{\alpha n}}E_{nn}(x^\alpha,[0,1]) = 4^{1+\alpha}|\sin...
1993-01-01
2008-02-03
[ "math.CA" ]
Herbert Stahl
math/9301215
Singularities of the Radon transform
Singularities of the Radon transform of a piecewise smooth function $f(x)$, $x\in R^n$, $n\geq 2$, are calculated. If the singularities of the Radon transform are known, then the equations of the surfaces of discontinuity of $f(x)$ are calculated by applying the Legendre transform to the functions, which appear in the ...
1993-01-01
2008-02-03
[ "math.CA" ]
Alexander G. Ramm, Alexander I. Zaslavsky
math/9312214
The sandwich theorem
This report contains expository notes about a function $\vartheta(G)$ that is popularly known as the Lov\'asz number of a graph~$G$. There are many ways to define $\vartheta(G)$, and the surprising variety of different characterizations indicates in itself that $\vartheta(G)$ should be interesting. But the most interes...
1993-12-06
2008-02-03
[ "math.CO" ]
Donald E. Knuth
math/9310232
The Dinitz problem solved for rectangles
The Dinitz conjecture states that, for each $n$ and for every collection of $n$-element sets $S_{ij}$, an $n\times n$ partial latin square can be found with the $(i,j)$\<th entry taken from $S_{ij}$. The analogous statement for $(n-1)\times n$ rectangles is proven here. The proof uses a recent result by Alon and Tarsi ...
1993-10-01
2009-09-25
[ "math.CO" ]
Jeannette C. M. Janssen
math/9310227
A linear construction for certain Kerdock and Preparata codes
The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre\- parata codes are shown to be linear over $\ZZ_4$, the integers $\bmod~4$. The Kerdock and Preparata codes are duals over $\ZZ_4$, and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over $\ZZ_4$. This provides a simp...
1993-10-01
2009-09-25
[ "math.CO", "cs.IT", "math.IT" ]
A. R. Calderbank, A. Roger Hammons Jr., P. Vijay Kumar, N. J. A. Sloane, Patrick Sol\'e
math/9309212
Combinatorial Proofs of Capelli's and Turnbull's Identities from Classical Invariant Theory
Capelli's and Turnbull's classical identities are given elegant combinatorial proofs.
1993-09-21
2008-02-03
[ "math.CO" ]
Dominique Foata (University of Strasbourg) and Doron Zeilberger (Temple University)
math/9307202
Chu's 1303 Identity Implies Bombieri's 1990 Norm-Inequality [via an Identity of Beauzamy and D\'egot]
The Vandermonde-Chu Binomial Coefficients Identity is shown to imply Bombieri's deep norm inequalities, via identities of Beauzamy-D\'egot, and Reznick.
1993-07-02
2008-02-03
[ "math.CO" ]
Doron Zeilberger (Temple University)
math/9306213
A WZ proof of Ramanujan's Formula for Pi
Ramanujan's series for Pi, that appeared in his famous letter to Hardy, is given a one-line WZ proof.
1993-06-03
2008-02-03
[ "math.CO" ]
Shalosh B. Ekhad (Temple University) and Doron Zeilberger (Temple University)
math/9301202
Theorems for a Price: Tomorrow's Semi-Rigorous Mathematical Culture
The future of mathematics is described, by using the WZ algorithmic proof theory as a parable.
1993-01-03
2008-02-03
[ "math.CO" ]
Doron Zeilberger (Temple University)
math/9301216
Linkless embeddings of graphs in $3$-space
We announce results about flat (linkless) embeddings of graphs in 3-space. A piecewise-linear embedding of a graph in 3-space is called {\it flat} if every circuit of the graph bounds a disk disjoint from the rest of the graph. We have shown: (i) An embedding is flat if and only if the fundamental group of the comple...
1993-01-01
2016-09-06
[ "math.CO", "math.GT" ]
Neil Robertson, Paul Seymour, Robin Thomas
math/9312202
Regularity And Extremality Of Quasiconformal Homeomorphisms On CR 3-Manifolds
This paper first studies the regularity of conformal homeomorphisms on smooth locally embeddable strongly pseudoconvex CR manifolds. Then moduli of curve families are used to estimate the maximal dilatations of quasiconformal homeomorphisms. On certain CR 3-manifolds, namely, CR circle bundles over flat tori, extremal ...
1993-12-30
2009-09-25
[ "math.CV" ]
Puqi Tang
math/9312201
Quasiconformal Homeomorphisms on CR 3-Manifolds With Symmetries
An extremal quasiconformal homeomorphisms in a class of homeomorphisms between two CR 3-manifolds is an one which has the least conformal distortion among this class. This paper studies extremal quasiconformal homeomorphisms between CR 3-manifolds which admit transversal CR circle actions. Equivariant $K$-quasiconforma...
1993-12-30
2008-02-03
[ "math.CV" ]
Puqi Tang
math/9310201
Complex Finsler metrics
In this paper we describe an approach to complex Finsler metrics suitable to deal with global questions, and stressing the similarities between hermitian and complex Finsler metrics. Let $F$ be a smooth complex Finsler metric on a complex manifold $M$, and assume that the indicatrices of $F$ are strongly pseudoconvex -...
1993-10-31
2016-09-06
[ "math.CV" ]
Marco Abate and Giorgio Patrizio
math/9309201
Complexity of the classical kernel functions of potential theory
We show that the Bergman, Szego, and Poisson kernels associated to a finitely connected domain in the plane are all composed of finitely many easily computed functions of one variable. The new formulas give rise to new methods for computing the Bergman and Szeg\H o kernels in which all integrals used in the computation...
1993-09-30
2008-02-03
[ "math.CV" ]
Steven R. Bell
math/9309202
Moduli of bounded holomorphic functions in the ball
We prove that there is a continuous non-negative function $g$ on the unit sphere in $\cd$, $d \geq 2$, whose logarithm is integrable with respect to Lebesgue measure, and which vanishes at only one point, but such that no non-zero bounded analytic function $m$ in the unit ball, with boundary values $m^\star$, has $|m^\...
1993-09-30
2009-09-25
[ "math.CV" ]
B. Korenblum and J. McCarthy
math/9310231
Stokes' theorem for nonsmooth chains
Much of the vast literature on the integral during the last two centuries concerns extending the class of integrable functions. In contrast, our viewpoint is akin to that taken by Hassler Whitney [{\it Geometric integration theory}, Princeton Univ. Press, Princeton, NJ, 1957] and by geometric measure theorists because ...
1993-10-01
2016-09-06
[ "math.DG", "math.CA" ]
Jenny Harrison
math/9309214
Differential geometry of $\frak g$-manifolds
An action of a Lie algebra $\frak g$ on a manifold $M$ is just a Lie algebra homomorphism $\zeta:\frak g\to \frak X(M)$. We define orbits for such an action. In general the space of orbits $M/\frak g$ is not a manifold and even has a bad topology. Nevertheless for a $\frak g$-manifold with equidimensional orbits we tre...
1993-09-01
2016-09-06
[ "math.DG" ]
Dimitri Alekseevsky, Peter W. Michor
math/9307226
Adding handles to the helicoid
There exist two new embedded minimal surfaces, asymptotic to the helicoid. One is periodic, with quotient (by orientation-preserving translations) of genus one. The other is nonperiodic of genus one.
1993-07-01
2008-02-03
[ "math.DG" ]
David A. Hoffman
math/9306216
The geometry of symplectic energy
In this paper we consider a geometric variant of Hofer's symplectic energy, which was first considered by Eliashberg and Hofer in connection with their study of the extent to which the interior of a region in a symplectic manifold determines its boundary. We prove, by a simple geometric argument, that both versions of ...
1993-06-12
2008-02-03
[ "math.DG", "math.SG" ]
Fran\c{c}ois Lalonde, Dusa McDuff
math/9311213
Teichm\"uller space of Fibonacci maps
According to Sullivan, a space ${\cal E}$ of unimodal maps with the same combinatorics (modulo smooth conjugacy) should be treated as an infinitely-dimensional Teichm\"{u}ller space. This is a basic idea in Sullivan's approach to the Renormalization Conjecture. One of its principle ingredients is to supply ${\cal E}$ w...
1993-11-27
2016-09-06
[ "math.DS" ]
Mikhail Lyubich
math/9310235
A monotonicity conjecture for real cubic maps
This is an outline of work in progress. We study the conjecture that the topological entropy of a real cubic map depends ``monotonely'' on its parameters, in the sense that each locus of constant entropy in parameter space is a connected set. This material will be presented in more detail in a later paper.
1993-10-30
2016-09-06
[ "math.DS" ]
Silvina P. Dawson, Roza Galeeva, John W. Milnor, Charles Tresser
math/9310226
Iteration of meromorphic functions
This paper attempts to describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions. The reader is not expected to be familiar with the iteration theory of rational functions. On the other hand, some aspects where the transcendental ca...
1993-10-01
2018-01-08
[ "math.DS", "math.CV" ]
Walter Bergweiler
math/9309215
Geometry of quadratic polynomials: moduli, rigidity and local connectivity
A while ago MLC (the conjecture that the Mandelbrot set is locally connected) was proven for quasi-hyperbolic points by Douady and Hubbard, and for boundaries of hyperbolic components by Yoccoz. More recently Yoccoz proved MLC for all at most finitely renormalizable parameter values. One of our goals is to prove MLC fo...
1993-09-04
2016-09-06
[ "math.DS" ]
Mikhail Lyubich
math/9308223
Induced expansion for quadratic polynomials
We prove that non-hyperbolic non-renormalizable quadratic polynomials are expansion inducing. For renormalizable polynomials a counterpart of this statement is that in the case of unbounded combinatorics renormalized mappings become almost quadratic. Technically, this follows from the decay of the box geometry. Specifi...
1993-08-07
2016-09-06
[ "math.DS" ]
Jacek Graczyk, Grzegorz Swiatek
math/9307235
On postcritically finite polynomials, part 2: Hubbard trees
We provide an effective classification of postcritically finite polynomials as dynamical systems by means of Hubbard Trees. This can be viewed as an application of the results developed in part 1 (Stony Brook IMS 1993/5).
1993-07-10
2009-09-25
[ "math.DS" ]
Alfredo Poirier
math/9305207
On postcritically finite polynomials, part 1: critical portraits
We extend the work of Bielefeld, Fisher and Hubbard on Critical Portraits to the case of arbitrary postcritically finite polynomials. This determines an effective classification of postcritically finite polynomials as dynamical systems. This paper is the first in a series of two based on the author's thesis, which deal...
1993-05-15
2009-09-25
[ "math.DS" ]
Alfredo Poirier
math/9304217
Density of periodic sources in the boundary of a basin of attraction for iteration of holomorphic maps, geometric coding trees technique
We prove that if A is the basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, then periodic points in the boundary of A are dense in this boundary. To prove this in the non simply- connected or parabolic situations we prove a more abstract, geometric cod...
1993-04-17
2008-02-03
[ "math.DS" ]
Feliks Przytycki, Anna Zdunik
math/9303209
Accessability of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps
We prove that if A is the basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, if $A$ is completely invariant (i.e. $f^{-1}(A)=A$), and if $\mu$ is an arbitrary $f$-invariant measure with positive Lyapunov exponents on the boundary of $A$, then $\mu$-almo...
1993-03-20
2016-09-06
[ "math.DS" ]
Feliks Przytycki
math/9301220
Distribution of periodic points of polynomial diffeomorphisms of C^2
This paper deals with the dynamics of a simple family of holomorphic diffeomorphisms of $\C^2$: the polynomial automorphisms. This family of maps has been studied by a number of authors. We refer to [BLS] for a general introduction to this class of dynamical systems. An interesting object from the point of view of pote...
1993-01-23
2016-09-06
[ "math.DS" ]
Eric Bedford, Mikhail Lyubich, John Smillie
math/9312208
Proportional subspaces of spaces with unconditional basis have good volume properties
A generalization of Lozanovskii's result is proved. Let E be $k$-dimensional subspace of an $n$-dimensional Banach space with unconditional basis. Then there exist $x_1,..,x_k \subset E$ such that $B_E \p \subset \p absconv\{x_1,..,x_k\}$ and \[ \kla \frac{{\rm vol}(absconv\{x_1,..,x_k\})}{{\rm vol}(B_E)} \mer^{\frac{1...
1993-12-29
2016-09-06
[ "math.FA" ]
Marius Junge
math/9312209
On Functions of Finite Baire Index
It is proved that every function of finite Baire index on a separable metric space $K$ is a $D$-function, i.e., a difference of bounded semi-continuous functions on $K$. In fact it is a strong $D$-function, meaning it can be approximated arbitrarily closely in $D$-norm, by simple $D$-functions. It is shown that if the ...
1993-12-29
2009-09-25
[ "math.FA" ]
Fouad Chaatit, Vania Mascioni, Haskell P. Rosenthal
math/9312206
Cotype and summing properties in Banach spaces
It is well known in Banach space theory that for a finite dimensional space $E$ there exists a constant $c_E$, such that for all sequences $(x_k)_k \subset E$ one has \[ \summ_k \noo x_k \rrm \kl c_E \pl \sup_{\eps_k \pm 1} \noo \summ_k \eps_k x_k \rrm \pl .\] Moreover, if $E$ is of dimension $n$ the constant $c_E$ ran...
1993-12-22
2016-09-06
[ "math.FA" ]
Marius Junge
math/9312207
Hyperplane conjecture for quotient spaces of $L_p$
We give a positive solution for the hyperplane conjecture of quotient spaces F of $L_p$, where $1<p\kll\infty$. \[ vol(B_F)^{\frac{n-1}{n}} \kl c_0 \pl p' \pl \sup_{H \p hyperplane} vol(B_F\cap H) \pl.\] This result is extended to Banach lattices which does not contain $\ell_1^n$'s uniformly. Our main tools are tensor ...
1993-12-22
2008-02-03
[ "math.FA" ]
Marius Junge
math/9312205
Isometries of $L_p$-spaces of solutions of homogeneous partial differential equations
Let $ n\geq 2, A=(a_{ij})_{i,j=1}^{n}$ be a real symmetric matrix, $a=(a_i)_{i=1}^{n}\in \Bbb R^n.$ Consider the differential operator $D_A = \sum_{i,j=1}^n a_{ij}{\partial^2 \over \partial x_i \partial x_j}+ \sum_{i=1}^n a_i{\partial \over \partial x_i}.$ Let $E$ be a bounded domain in $\Bbb R^n,$ $p>0.$ Denote by $L_...
1993-12-15
2016-09-06
[ "math.FA" ]
Alexander Koldobsky
math/9311208
The Fourier transform of order statistics with applications to Lorentz spaces
We present a formula for the Fourier transforms of order statistics in $\Bbb R^n$ showing that all these Fourier transforms are equal up to a constant multiple outside the coordinate planes in $\Bbb R^n.$ For $a_1\geq ... \geq a_n\ge0$ and $q>0,$ denote by $\ell_{w,q}^n$ the $n$-dimensional Lorentz space with the nor...
1993-11-17
2016-09-06
[ "math.FA" ]
Stephen J. Dilworth, Alexander Koldobsky
math/9310217
On complemented subspaces of sums and products of Banach spaces
It is proved that there exist complemented subspaces of countable topological products (locally convex direct sums) of Banach spaces which cannot be represented as topological products (locally convex direct sums) of Banach spaces. (This is a revised version of the paper by the same name formerly contained in the file ...
1993-10-26
2010-09-07
[ "math.FA" ]
Mikhail I. Ostrovskii
math/9310218
Structure of total subspaces of dual Banach spaces
Let $X$ be a separable nonquasireflexive Banach space. Let $Y$ be a Banach space isomorphic to a subspace of $X^*$. The paper is devoted to the following questions: 1. Under what conditions does there exist an isomorphic embedding $T:Y\to X^*$ such that subspace $T(Y)\subset X^*$ is total? 2. If such embeddings exist, ...
1993-10-26
2010-09-07
[ "math.FA" ]
Mikhail I. Ostrovskii
math/9310216
Property $(M)$, $M$-ideals, and almost isometric structure of Banach spaces
We study $M$-ideals of compact operators by means of the property~$(M)$ introduced in \cite{Kal-M}. Our main result states for a separable Banach space $X$ that the space of compact operators on $X$ is an $M$-ideal in the space of bounded operators if (and only if) $X$ does not contain a copy of $\ell_{1}$, has the met...
1993-10-11
2016-09-06
[ "math.FA" ]
Nigel J. Kalton, Dirk Werner
math/9310215
Contractive projections in nonatomic function spaces
We prove that there is no 1-complemented subspace of finite codimension in separable rearrangament-invariant function spaces.
1993-10-11
2009-09-25
[ "math.FA" ]
Beata Randrianantoanina
math/9310214
Comparison of Sums of independent Identically Distributed Random Variables
Let S_k be the k-th partial sum of Banach space valued independent identically distributed random variables. In this paper, we compare the tail distribution of ||S_k|| with that of ||S_j||, and deduce some tail distribution maximal inequalities. Theorem: There is universal constant c such that for j < k Pr(||S_j|| ...
1993-10-07
2008-02-03
[ "math.FA" ]
Stephen J. Montgomery-Smith