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hep-th/9401039
A Study of Fermions Coupled to Gauge and Gravitational Fields on a Cylinder
Fermions on a cylinder coupled to gravity and gauge fields are examined by studying the geometric action associated with the symmetries of such a system. The gauge coupling constant is shown to be constrained and the effect of gravity on the masses is discussed. Furthermore, we introduce a new gravitational theory whic...
1994-01-11
2009-10-28
[ "hep-th" ]
R.P. Lano and V.G.J. Rodgers
hep-th/9401042
Construction of Field Algebras with Quantum Symmetry from Local Observables
It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics and locality was established. This work addresses to the reconstruction of quantu...
1994-01-11
2009-10-28
[ "hep-th" ]
Volker Schomerus
hep-th/9401043
2(2S+1)-Component Model and its Connection with Other Field Theories
This talk presents the review of forgotten but attractive formalism proposed by Joos and Weinberg in the sixties for description of high-spin particles. Problems raised in the recent works [Ahluwalia {\it et al.}] are discussed. New results obtained by the author in his preceding papers ["Hadronic J.", 1993, v. 16, No....
1994-01-11
2008-02-03
[ "hep-th", "hep-ph" ]
Valeri V. Dvoeglazov
hep-th/9401040
Low Energy Skyrmion-Skyrmion Scattering
We study the scattering of two Skyrmions at low energy and large separation. We use the method proposed by Manton for truncating the degrees of freedom of the system from infinite to a manageable finite number. This corresponds to identifying the manifold consisting of the union of the low energy critical points of the...
1994-01-11
2009-10-28
[ "hep-th" ]
T. Gisiger and M. B. Paranjape
hep-th/9401041
Strings and Two-dimensional QCD for Finite N
Minor corrections made and several references changed.
1994-01-11
2010-11-01
[ "hep-th" ]
J. Baez and W. Taylor
hep-th/9401036
The Geodesic Motion in Taub-Nut Spinning Space
The geodesic motion of pseudo-classical spinning particles in the Euclidean Taub-NUT space is analysed. The generalized Killing equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. A simple exact solution, corresponding to trajectories lying...
1994-01-10
2010-04-06
[ "hep-th", "gr-qc" ]
Mihai Visinescu
hep-th/9401034
Aspects of $\sigma$ Models
Some aspects and applications of $ \sigma$-models in particle and condensed matter physics are briefly reviewed.
1994-01-10
2007-05-23
[ "hep-th" ]
S. Randjbar-Daemi and J. Strathdee
hep-th/9401038
An Exact Solution to O(26) Sigma Model coupled to 2-D Gravity
By a mapping to the bosonic string theory, we present an exact solution to the O(26) sigma model coupled to 2-D quantum gravity. In particular, we obtain the exact gravitational dressing to the various matter operators classified by the irreducible representations of O(26). We also derive the exact form of the gravitat...
1994-01-10
2009-10-28
[ "hep-th" ]
Weidong Zhao
hep-th/9401035
Zero Modes of First Class Secondary Constraints in Gauge Theories
Zero modes of first class secondary constraints in the two-dimensional electrodynamics and the four-dimensional SU(2) Yang-Mills theory are considered by the method of reduced phase space quantization in the context of the problem of a stable vacuum. We compare the description of these modes in the Dirac extended metho...
1994-01-10
2007-05-23
[ "hep-th" ]
A. Khvedelidze, V. Pervushin
hep-th/9401033
Fermion Back-Reaction and the Sphaleron
Using a simple model, a new sphaleron solution which incorporates finite fermionic density effects is obtained. The main result is that the height of the potential barrier (sphaleron energy) decreases as the fermion density increases. This suggests that the rate of sphaleron-induced transitions increases when the fermi...
1994-01-10
2009-12-30
[ "hep-th" ]
Andre Roberge
hep-th/9401037
Hamiltonian Mechanics in 1+2 Dimensions
A complete list of all transitive symplectic manifolds of the Poincar\'e and Galilei group in 1+2 dimensions is given.
1994-01-10
2007-05-23
[ "hep-th" ]
D. R. Grigore
hep-th/9401031
Area-preserving structure of 2d-gravity
The effective action for 2d-gravity with manifest area-preserving invariance is obtained in the flat and in the general gravitational background. The cocyclic properties of the last action are proved, and generalizations on higher dimensions are discussed.
1994-01-10
2009-10-28
[ "hep-th" ]
D.R. Karakhanyan, R.P. Manvelyan, R.L. Mkrtchyan (Yerevan Physics Institute)
hep-th/9401032
Geometrical action for $w_\infty$ algebra as a reduced symplectic Chern-Simons theory
The geometric action on a certain orbit of the group of the area-preserving diffeomorphisms is considered, and it is shown, that it coincides with a special reduction of the three-dimensional Chern-Simons theory, under which group and space coordinates are identified.
1994-01-10
2009-10-28
[ "hep-th" ]
R.P. Manvelyan and R.L. Mkrtchyan (Yerevan Physics Institute)
hep-th/9401030
Topological Landau-Ginzburg Formulation and Integrable Structure of 2d String Theory
We construct a topological Landau-Ginzburg formulation of the two-dimensional string at the self-dual radius. The model is an analytic continuation of the $A_{k+1}$ minimal model to $k=-3$. We compute the superpotential and calculate tachyon correlators in the Landau-Ginzburg framework. The results are in complete agre...
1994-01-10
2009-09-29
[ "hep-th" ]
A. Hanany, Y. Oz, and M.R. Plesser
hep-th/9401026
Infinite dimensional geometry and quantum field theory of strings. III. Infinite dimensional W-geometry of a second quantized free string
The present paper is devoted to various objects of the infinite dimensional W-geometry of a second quantized free string. Our purpose is to include the W-symmetries into the general infinite dimensional geometrical picture related to the quantum field theory of strings, which was described in the first part of the pape...
1994-01-07
2009-10-28
[ "hep-th", "alg-geom", "funct-an", "math.AG", "math.FA" ]
D.Juriev
hep-th/9401028
Hydden Symmetry approach to the Extended Symmetries in Nonabelian Free Fermionic and WZNW Models
Higher spin extensions of nonabelian gauge symmetries for both free fermionic model and WZNW model are considered on a classical level. It is characteristic property of the WZNW model that the higher spin currents which correspond to linear realized higher spin extended affine algebra do not form an invariant space. An...
1994-01-07
2008-02-03
[ "hep-th" ]
Raiko P. Zaikov
hep-th/9401029
Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus
We compute the elliptic genus for arbitrary two dimensional $N=2$ Landau-Ginzburg orbifolds. This is used to search for possible mirror pairs of such models. We show that if two Landau-Ginzburg models are conjugate to each other in a certain sense, then to every orbifold of the first theory corresponds an orbifold of t...
1994-01-07
2009-10-28
[ "hep-th" ]
P. Berglund and M. Henningson
hep-th/9401027
Higher-Dimensional Loop Algebras, Non-Abelian Extensions and p-Branes
We postulate a new type of operator algebra with a non-abelian extension. This algebra generalizes the Kac--Moody algebra in string theory and the Mickelsson--Faddeev algebra in three dimensions to higher-dimensional extended objects ($p$-branes). We then construct new BRST operators, covariant derivatives and curvatur...
1994-01-07
2009-10-28
[ "hep-th" ]
M. Cederwall, G. Ferretti, B.E.W. Nilsson and A. Westerberg
hep-th/9401025
Exact Duality in String Effective Action
We formulate sigma-model duality transformations in terms of spin connection. This allows to investigate the symmetry of the string action including higher order $\alpha'$ corrections. An important feature of the new duality transformations is a simple homogeneous transformation rule of the spin connection (with torsio...
1994-01-07
2008-11-26
[ "hep-th" ]
Eric Bergshoeff, Ingeborg Entrop and Renata Kallosh
hep-th/9401012
Flavor-Dependence and Higher Orders of Gauge-Independent Solutions in Strong Coupling Gauge Theory
The fermion flavor $N_f$ dependence of non-perturbative solutions in the strong coupling phase of the gauge theory is reexamined based on the interrelation between the inversion method and the Schwinger-Dyson equation approach. Especially we point out that the apparent discrepancy on the value of the critical coupling ...
1994-01-06
2009-10-28
[ "hep-th" ]
Kei-Ichi Kondo, Takuya Iizuka, Eiji Tanaka and Toru Ebihara
hep-th/9401014
Classical Open String Models in 4-Dim Minkowski Spacetime
Classical bosonic open string models in fourdimensional Minkowski spacetime are discussed. A special attention is paid to the choice of edge conditions, which can follow consistently from the action principle. We consider lagrangians that can depend on second order derivatives of worldsheet coordinates. A revised inter...
1994-01-06
2010-11-01
[ "hep-th" ]
P.Wegrzyn
hep-th/9401021
Elliptic Calogero-Moser system from two dimensional current algebra
We show that elliptic Calogero-Moser system and its Lax operator found by Krichever can be obtained by Hamiltonian reduction from the integrable Hamiltonian system on the cotangent bundle to the central extension of the algebra of SL(N,C) currents.Elliptic deformation of Yang-Mills theory is presented.
1994-01-06
2007-05-23
[ "hep-th" ]
Alexander Gorsky and Nikita Nekrasov
hep-th/9401018
Quantum Spaces: Notes and Comments on a Lecture by S. L. Woronowicz
These notes are based on a lecture given by S. L. Woronowicz at the Institute of Mathematics, Polish Academy of Sciences.
1994-01-06
2007-05-23
[ "hep-th" ]
R. J. Budzynski and W. Kondracki
hep-th/9401022
Solutions of matrix models in the DIII generator ensemble
In this paper we solve two matrix models, using standard and new techniques. The two models are represented by special form of antisymmetric matrices and are classified in the DIII generator ensemble. It is shown that, in the double scaling limit, their free energy has the same behavior as previous models describing or...
1994-01-06
2015-06-26
[ "hep-th" ]
Harold Roussel
hep-th/9401017
Relativistic Calogero-Moser model as gauged WZW theory
We study quantum intergrable systems of interacting particles from the point of view, proposed in our previous paper. We obtain Calogero-Moser and Sutherland systems as well their Ruijsenaars relativistic generalization by a Hamiltonian reduction of integrable systems on the cotangent bundles over semi-simple Lie algeb...
1994-01-06
2009-10-28
[ "hep-th" ]
Alexander Gorsky and Nikita Nekrasov
hep-th/9401024
On the Hamiltonian Approach and Path Integration for a Point Particle Minimally Coupled to Electromagnetism
We {\em derive} the exact configuration space path integral, together with the way how to evaluate it, from the Hamiltonian approach for any quantum mechanical system in flat spacetime whose Hamiltonian has at most two momentum operators. Starting from a given, covariant or non-covariant, Hamiltonian, we go from the ti...
1994-01-06
2007-05-23
[ "hep-th" ]
K. Skenderis and P. van Nieuwenhuizen
hep-th/9401020
Instantons for Vacuum Decay at Finite Temperature in the Thin Wall Limit
In $N+1$ dimensions, false vacuum decay at zero temperature is dominated by the $O(N+1)$ symmetric instanton, a sphere of radius $R_0$, whereas at temperatures $T>>R_0^{-1}$, the decay is dominated by a `cylindrical' (static) $O(N)$ symmetric instanton. We study the transition between these two regimes in the thin wall...
1994-01-06
2009-10-28
[ "hep-th", "hep-ph" ]
Jaume Garriga
hep-th/9401019
Quantum Principal Fiber Bundles: Topological Aspects
We introduce the notion of locally trivial quantum principal bundles. The base space and total space are compact quantum spaces (unital $C^{\star}$-algebras), the structure group is a compact matrix quantum group. We prove that a quantum bundle admits sections if and only if it is trivial. Using a quantum version of \v...
1994-01-06
2007-05-23
[ "hep-th" ]
R. J. Budzynski and W. Kondracki
hep-th/9401016
The universal Vassiliev-Kontsevich invariant for framed oriented links
We give a generalization of the Reshetikhin-Turaev functor for tangles to get a combinatorial formula for the universal Vassiliev-Kontsevich invariant of framed oriented links which is coincident with the Kontsevich integral. The universal Vassiliev-Kontsevich invariant is constructed using the Drinfeld associator. We ...
1994-01-06
2008-02-03
[ "hep-th", "math.QA" ]
Le Tu Quoc Thang and Jun Murakami
hep-th/9401023
Topological field theories, string backgrounds and homotopy algebras
String backgrounds are described as purely geometric objects related to moduli spaces of Riemann surfaces, in the spirit of Segal's definition of a conformal field theory. Relations with conformal field theory, topological field theory and topological gravity are studied. For each field theory, an algebraic counterpart...
1994-01-06
2008-02-03
[ "hep-th", "math.QA" ]
Alexander A. Voronov
hep-th/9401013
Zero Mode Divergence Problem in String Theory
For $2D$ string theory, the perturbative $S$-matrices are not well-defined due to a zero mode divergence. Although there exist formal procedures to make the integral convergent, their physical meanings are unclear. We describe a method to obtain finite $S$-matrices physically to justify the formal schemes. The scheme u...
1994-01-06
2015-06-26
[ "hep-th" ]
Makoto Natsuume
hep-th/9401015
Conformal Foliations and Constraint Quantization
We show that the Classical Constraint Algebra of a Parametrized Relativistic Gauge System induces a natural structure of Conformal Foliation on a Transversal Gauge. Using the theory of Conformal Foliations, we provide a natural Factor Ordering for the Quantum Operators associated to the Canonical Quantization of such G...
1994-01-06
2015-06-26
[ "hep-th" ]
J.N. Tavares
hep-th/9401011
A new constraints separation for the original D=10 massless superparticle
We study the problem of covariant separation between first and second class constraints for the $D=10$ Brink-Schwarz superparticle. Opposite to the supersymmetric light-cone frame separation, we show here that there is a Lorentz covariant way to identify the second class constraints such that, however, supersymmetry is...
1994-01-05
2016-09-06
[ "hep-th" ]
D. Dalmazi
hep-th/9401009
Translations between Quaternion and Complex Quantum Mechanics
While in general there is no one-to-one correspondence between complex and quaternion quantum mechanics (QQM), there exists at least one version of QQM in which a {\em partial} set of {\em translations} may be made. We define these translations and use the rules to obtain rapid quaternion counterparts (some of which ar...
1994-01-05
2017-03-08
[ "hep-th" ]
S. De Leo and P. Rotelli
hep-th/9401008
Boundary S-matrix of the $O(N)$-symmetric Non-linear Sigma Model
We conjecture that the $O(N)$-symmetric non-linear sigma model in the semi-infinite $(1+1)$-dimensional space is ``integrable'' with respect to the ``free'' and the ``fixed'' boundary conditions. We then derive, for both cases, the boundary S-matrix for the reflection of massive particles of this model off the boundary...
1994-01-05
2009-10-28
[ "hep-th" ]
Subir Ghoshal
hep-th/9401010
Quantization of string theory for $c \leq 1$
We consider the canonical quantization scheme for $c \leq 1$ ($(p,q)$ -) string theories and compare it with what is known from matrix model approach. We derive explicitly a trivial ($\equiv $ topological) solution. We discuss a ``dressing" operator which in principle allows one to obtain a non-trivial solution, but an...
1994-01-05
2007-05-23
[ "hep-th" ]
S. Kharchev, A.Marshakov
hep-th/9401006
Currents, Charges, and Canonical Structure of Pseudodual Chiral Models
We discuss the pseudodual chiral model to illustrate a class of two-dimensional theories which have an infinite number of conservation laws but allow particle production, at variance with naive expectations. We describe the symmetries of the pseudodual model, both local and nonlocal, as transmutations of the symmetries...
1994-01-04
2009-10-02
[ "hep-th" ]
T. Curtright and C. Zachos
hep-th/9401007
The Multivalued Free-Field Maps of Liouville and Toda Gravities
Liouville and Toda gravity theories with non-vanishing interaction potentials have spectra obtained by dividing the free-field spectra for these cases by the Weyl group of the corresponding $A_1$ or $A_2$ Lie algebra. We study the canonical transformations between interacting and free fields using the technique of inte...
1994-01-04
2009-10-07
[ "hep-th" ]
A. Anderson, B.E.W. Nilsson, C.N. Pope and K.S. Stelle
hep-th/9401005
Q-Exact Actions for BF Theories
The actions for all classical (and consequently quantum) $BF$ theories on $n$-manifolds is proven to be given by anti-commutators of hermitian, nilpotent, scalar fermionic charges with Grassmann-odd functionals. In order to show this, the space of fields in the theory must be enlarged to include ``mass terms'' for new,...
1994-01-04
2015-06-26
[ "hep-th" ]
R. Brooks and C. Lucchesi
hep-th/9401004
Vertex Operators are Not Closeable
We prove the uncloseability of the free vertex operators used in conformal field theory for the BRST--construction of primary fields. Our proof includes minimal models as well as WZNW--models.
1994-01-04
2015-06-26
[ "hep-th" ]
Wolfram Boenkost
hep-th/9401001
Remarks on the Collective Quantization of the SU(2) Skyrme Model
We point out the question of ordering momentum operator in the canonical \break quantization of the SU(2) Skyrme Model. Thus, we suggest a new definition for the momentum operator that may solve the infrared problem that appears when we try to minimize the Quantum Hamiltonian.
1994-01-03
2015-06-26
[ "hep-th" ]
Jorge Ananias Neto
hep-th/9401003
Local heterotic geometry in holomorphic coordinates
In the same spirit as done for N=2 and N=4 supersymmetric non-linear $\si$ models in 2 space-time dimensions by Zumino and Alvarez- Gaum\'e and Freedman, we analyse the (2,0) and (4,0) heterotic geometry in holomorphic coordinates. We study the properties of the torsion tensor and give the conditions under which (2,0) ...
1994-01-03
2010-04-06
[ "hep-th" ]
G. Bonneau, G. Valent
hep-th/9401002
Hard Thermal Loops, Static Response and the Composite Effective Action
First, we investigate the static non-Abelian Kubo equation. We prove that it does not possess finite energy solutions; thereby we establish that gauge theories do not support hard thermal solitons. A similar argument shows that "static" instantons are absent. In addition, we note that the static equations reproduce the...
1994-01-03
2009-10-28
[ "hep-th", "hep-ph" ]
R. Jackiw, Q. Liu and C. Lucchesi
hep-th/9312215
Knot invariants from rational conformal field theories
A framework for studying knot and link invariants from any rational conformal field theory is developed. In particular, minimal models, superconformal models and $W_N$ models are studied. The invariants are related to the invariants obtained from the Wess-Zumino models associated with the coset representations of these...
1994-01-02
2009-10-22
[ "hep-th" ]
P. Ramadevi, T.R. Govindarajan and R.K. Kaul
math/9401222
Conformal invariance in two-dimensional percolation
The immediate purpose of the paper was neither to review the basic definitions of percolation theory nor to rehearse the general physical notions of universality and renormalization (an important technique to be described in Part Two). It was rather to describe as concretely as possible, although in hypothetical form, ...
1994-01-01
2010-10-27
[ "math-ph", "math.MP" ]
Robert Langlands, Philippe Pouliot, Yvan Saint-Aubin
math/9412210
Links of prime ideals and their Rees algebras
In a previous paper we exhibited the somewhat surprising property that most direct links of prime ideals in Gorenstein rings are equimultiple ideals with reduction number $1$. This led to the construction of large families of Cohen--Macaulay Rees algebras. The first goal of this paper is to extend this result to arbitr...
1994-12-21
2008-02-03
[ "math.AC" ]
Alberto Corso and Claudia Polini
math/9411209
Analogs of Gr\"obner Bases in Polynomial Rings over a Ring
In this paper we will define analogs of Gr\"obner bases for $R$-subalgebras and their ideals in a polynomial ring $R[x_1,\ldots,x_n]$ where $R$ is a noetherian integral domain with multiplicative identity and in which we can determine ideal membership and compute syzygies. The main goal is to present and verify algorit...
1994-11-18
2009-09-25
[ "math.AC" ]
J. Lyn Miller
math/9409208
Laurent coefficients and Ext of finite graded modules
Let $R=\bigoplus_{n\ges0}R_n$ be a graded commutative ring generated over a field $K=R_0$ by homogeneous elements $x_1,\dots,x_e$ of positive degrees $d_1,\dots,d_e$. The Hilbert-Serre Theorem shows that for each finite graded $R$--module $M=\bigoplus_{n\in\BZ}M_n$ the {\it Hilbert series\/} $\sum_{n\in\BZ}(\rank_K M_n...
1994-09-23
2016-09-06
[ "math.AC" ]
Luchezar L. Avramov, Ragnar-Olaf Buchweitz, Judith D. Sally
math/9406208
On the Betti numbers of some Gorenstein ideals
Assume $R$ is a polynomial ring over a field and $I$ is a homogeneous Gorenstein ideal of codimension $g\ge3$ and initial degree $p\ge2$. We prove that the number of minimal generators $\nu(I_p)$ of $I$ that are in degree $p$ is bounded above by $\nu_0={p+g-1\choose g-1}-{p+g-3\choose g-1}$, which is the number of mini...
1994-06-20
2009-09-25
[ "math.AC" ]
Matthew Miller and Rafael H. Villarreal
math/9403204
Ideals associated to two sequences and a matrix
Let $\u_{1\times n}$, $\X_{n\times n}$, and $\v_{n\times 1}$ be matrices of indeterminates, $\Adj \X$ be the classical adjoint of $\X$, and $H(n)$ be the ideal $I_1(\u\X)+I_1(\X\v)+I_1(\v\u-\Adj \X)$. Vasconcelos has conjectured that $H(n)$ is a perfect Gorenstein ideal of grade $2n$. In this paper, we obtain the minim...
1994-03-23
2008-02-03
[ "math.AC" ]
Andrew R. Kustin
math/9411233
Stable vector bundles on algebraic surfaces
We prove an existence result for stable vector bundles with arbitrary rank on an algebraic surface, and determine the birational structure of certain moduli space of stable bundles on a rational ruled surface.
1994-11-15
2016-09-06
[ "math.AG" ]
Wei-ping Li, Zhenbo Qin
math/9410219
Configuration spaces and the space of rational curves on a toric variety
The space of holomorphic maps from $S^2$ to a complex algebraic variety $X$, i.e. the space of parametrized rational curves on $X$, arises in several areas of geometry. It is a well known problem to determine an integer $n(D)$ such that the inclusion of this space in the corresponding space of continuous maps induces i...
1994-10-01
2008-02-03
[ "math.AG" ]
Martin A. Guest
math/9401219
Genera of algebraic varieties and counting of lattice points
This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. --- and their associated characteristic classes, under morphisms of projective algebraic varieties. The formulas ...
1994-01-01
2009-09-25
[ "math.AG", "math.CV", "math.GT" ]
Sylvain E. Cappell, Julius L. Shaneson
math/9401220
The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory
The geometry of the Lubin-Tate space of deformations of a formal group is studied via an \'etale, rigid analytic map from the deformation space to projective space. This leads to a simple description of the equivariant canonical bundle of the deformation space which, in turn, yields a formula for the dualizing complex ...
1994-01-01
2023-12-04
[ "math.AT", "math.AG" ]
Michael J. Hopkins and Benedict H. Gross
math/9412226
Algebraische Darstellung transzendenter Funktionen
Ich m\"ochte in diesem Bericht algorithmische Methoden vorstellen, die im wesentlichen in diesem Jahrzehnt Einzug in die Computeralgebra gefunden haben. Die haupts\"achlichen Ideen gehen auf Stanley \cite{Sta} und Zeilberger \cite{Zei1}--\cite{Zei4} zur\"uck, vgl.\ die Beschreibung \cite{Strehl1}, und haben ihre Wurzel...
1994-12-17
2009-09-25
[ "math.CA" ]
Wolfram Koepf
math/9412228
REDUCE package for the indefinite and definite summation
This article describes the REDUCE package ZEILBERG implemented by Gregor St\"olting and the author. The REDUCE package ZEILBERG is a careful implementation of the Gosper and Zeilberger algorithms for indefinite, and definite summation of hypergeometric terms, respectively. An expression $a_k$ is called a {\sl hyperge...
1994-12-17
2009-09-25
[ "math.CA" ]
Wolfram Koepf
math/9412227
Algorithms for the indefinite and definite summation
The celebrated Zeilberger algorithm which finds holonomic recurrence equations for definite sums of hypergeometric terms $F(n,k)$ is extended to certain nonhypergeometric terms. An expression $F(n,k)$ is called a hypergeometric term if both $F(n+1,k)/F(n,k)$ and $F(n,k+1)/F(n,k)$ are rational functions. Typical example...
1994-12-17
2016-09-06
[ "math.CA" ]
Wolfram Koepf
math/9412224
Addition formula for 2-parameter family of Askey-Wilson polynomials
For a two parameter family of Askey-Wilson polynomials, that can be regarded as basic analogues of the Legendre polynomials, an addition formula is derived. The addition formula is a two-parameter extension of Koornwinder's addition formula for the little $q$-Legendre polynomials. A corresponding product formula is der...
1994-12-07
2016-09-06
[ "math.CA" ]
Erik Koelink
math/9411229
On a general q-Fourier transformation with nonsymmetric kernels
Wiener used the Poisson kernel for the Hermite polynomials to deal with the classical Fourier transform. Askey, Atakishiyev and Suslov used this approach to obtain a q-Fourier transform by using the continuous q-Hermite polynomials. Rahman and Suslov extended this result by taking the Askey--Wilson polynomials, conside...
1994-11-29
2016-09-06
[ "math.CA", "math.QA" ]
Richard A. Askey, Mizan Rahman, Serge\u{\i} K. Suslov
math/9411228
Extensions and results from a method for evaluating fractional integrals
We present a method derived from Laplace transform theory that enables the evaluation of fractional integrals. This method is adapted and extended in a variety of ways to demonstrate its utility in deriving alternative representations for other classes of integrals. We also use the method in conjunction with several di...
1994-11-28
2009-09-25
[ "math.CA" ]
M. Lawrence Glasser, Victor Kowalenko
math/9411226
Contiguous relations, basic hypergeometric functions, and orthogonal polynomials : III. associated continuous dual q-Hahn polynomials
Explicit solutions for the three-term recurrence satisfied by associated continuous dual $q$-Hahn polynomials are obtained. A minimal solution is identified and an explicit expression for the related continued fraction is derived. The absolutely continuous component of the spectral measure is obtained. Eleven limit cas...
1994-11-21
2008-02-03
[ "math.CA" ]
Dharma P. Gupta, Mourad E. H. Ismail, David R. Masson
math/9411227
Special functions associated with root systems: recent progress
In this paper I present a brief survey of the active area of Special Functions associated with Root Systems. The article is intended for a general mathematical audience. It will not suppose prerequisites on either special functions or root systems. It will also skip many technical details. Some early work in this area ...
1994-11-21
2016-09-06
[ "math.CA", "math.QA" ]
Tom H. Koornwinder
math/9411224
The quadratic formula made hard: A less radical approach to solving equations
It appears that, along with many of my friends and colleagues, I had been brainwashed by the great and tragic lives of Abel and Galois to believe that no general formulas are possible for roots of equations higher than quartic. This seemed to be confirmed by the brilliant and arduous solution of the general quintic by ...
1994-11-16
2016-09-06
[ "math.CA" ]
M. Lawrence Glasser
math/9409230
On Jacobi and continuous Hahn polynomials
Jacobi polynomials are mapped onto the continuous Hahn polynomials by the Fourier transform and the orthogonality relations for the continuous Hahn polynomials then follow from the orthogonality relations for the Jacobi polynomials and the Parseval formula. In a special case this relation dates back to work by Bateman ...
1994-09-21
2009-09-25
[ "math.CA" ]
Erik Koelink
math/9409231
Yet another basic analogue of Graf's addition formula
An identity involving basic Bessel functions and Al-Salam--Chihara polynomials is proved for which we recover Graf's addition formula for the Bessel function as the base $q$ tends to $1$. The corresponding product formula is derived. Some known identities for Jackson's $q$-Bessel functions are obtained as limiting case...
1994-09-21
2016-09-06
[ "math.CA" ]
Erik Koelink
math/9409229
The last of the hypergeometric continued fractions
A contiguous relation for complementry pairs of very well poised balanced ${}_{10}\phi_9$ basic hypergeometric functions is used to derive an explict expression for the associated continued fraction. This generalizes the continued fraction results associated with both Ramanujan's Entry 40 and Askey-Wilson polynomials w...
1994-09-12
2016-09-06
[ "math.CA" ]
David R. Masson
math/9409228
Painlev\'e equations for semi-classical recurrence coefficients
The title says it all.
1994-09-06
2008-02-03
[ "math.CA" ]
Alphonse P. Magnus
math/9409227
Numerical computation of real or complex elliptic integrals
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind). Numerical check values, consistency checks, and relations to Legendre's integrals a...
1994-09-06
2015-06-26
[ "math.CA" ]
Bille C. Carlson
math/9408210
Fractional integration for Laguerre expansions
The aim of this note is to provide a fractional integration theorem in the framework of Laguerre expansions. The method of proof consists of establishing an asymptotic estimate for the involved kernel and then applying a method of Hedberg \cite{pro}. We combine this result with sufficient $(p,p)$ multiplier criteria of...
1994-08-31
2008-02-03
[ "math.CA" ]
George Gasper Jr, Krzysztof Stempak, Walter Trebels
math/9408211
On a restriction problem of de Leeuw type for Laguerre multipliers
In 1965 K. de Leeuw \cite{deleeuw} proved among other things in the Fourier transform setting: {\it If a continuous function $m(\xi _1, \ldots ,\xi _n)$ on ${\bf R}^n$ generates a bounded transformation on $L^p({\bf R}^n),\; 1\le p \le \infty ,$ then its trace $\tilde{m}(\xi _1, \ldots ,\xi _m)=m(\xi _1, \ldots ,\xi _m...
1994-08-31
2016-09-06
[ "math.CA" ]
George Gasper Jr, Walter Trebels
math/9408209
The Askey-Wilson polynomials and q-Sturm-Lioville problems
We find the adjoint of the Askey-Wilson divided difference operator with respect to the inner procuct on L^2(-1,1,(1-x^2)^-1/2 dx) defined as a Cauchy principle value and show that the Askey-Wilson polynomials are solutions of a q-Sturm-Liouville problem. From these facts we deduce various properties of the polynomials...
1994-08-24
2016-09-06
[ "math.CA" ]
B. Malcolm Brown, William Desmond Evans, Mourad E. H. Ismail
math/9407213
Generalized orthogonality and continued fractions
The connection between continued fractions and orthogonality which is familiar for $J$-fractions and $T$-fractions is extended to what we call $R$-fractions of type I and II. These continued fractions are associated with recurrence relations that correspond to multipoint rational interpolants. A Favard type theorem is ...
1994-07-20
2008-02-03
[ "math.CA" ]
Mourad E. H. Ismail, David R. Masson
math/9406227
Ladder operators for Szeg\H{o} polynomials and related biorthogonal rational functions
We find the raising and lowering operators for orthogonal polynomials on the unit circle introduced by Szeg\H{o} and for their four parameter generalization to ${}_4\phi_3$ biorthogonal rational functions on the unit circle.
1994-06-30
2016-09-06
[ "math.CA" ]
Mourad E. H. Ismail, Mizan Rahman
math/9406226
Combinatorial orthogonal expansions
The linearization coefficients for a set of orthogonal polynomials are given explicitly as a weighted sum of combinatorial objects. Positivity theorems of Askey and Szwarc are corollaries of these expansions.
1994-06-29
2008-02-03
[ "math.CA", "math.CO" ]
Anne de M\'edicis, Dennis W. Stanton
math/9406222
A note on some peculiar nonlinear extremal phenomena of the Chebyshev polynomials
We consider the problem of maximizing the sum of squares of the leading coefficients of polynomials $P_{i_1}(x),\ldots ,P_{i_m}(x)$ (where $P_j(x)$ is a polynomial of degree $j$) under the restriction that the sup-norm of $\sum_{j=1}^m P_{i_j}^2(x)$ is bounded on the interval $[-b,b]$ ($b>0$). A complete solution of th...
1994-06-07
2009-09-25
[ "math.CA" ]
Holger Dette
math/9406223
New bounds for Hahn and Krawichouk polynomials
For the Hahn and Krawtchouk polynomials orthogonal on the set $\{0, \ldots,N\}$ new identities for the sum of squares are derived which generalize the trigonometric identity for the Chebyshev polynomials of the first and second kind. These results are applied in order to obtain conditions (on the degree of the polynomi...
1994-06-07
2009-09-25
[ "math.CA" ]
Holger Dette
math/9406224
Some new asymptotic properties for the zeros of Jacobi, Laguerre and Hermite polynomials
For the generalized Jacobi, Laguerre and Hermite polynomials $P_n^{(\alpha_n, \beta_n)} (x), L_n^{(\alpha_n)} (x),$\break $H_n^{(\gamma_n)} (x)$ the limit distributions of the zeros are found, when the sequences $\alpha_n$ or $\beta_n$ tend to infinity with a larger order than $n$. The derivation uses special propertie...
1994-06-07
2016-09-06
[ "math.CA" ]
Holger Dette, William J. Studden
math/9406221
Characterizations of generalized Hermite and sieved ultraspherical polynomials
A new characterization of the generalized Hermite polynomials and of the orthogonal polynomials with respect to the maesure $|x|^\g (1-x^2)^{\a-1/2}dx$ is derived which is based on a "reversing property" of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of general...
1994-06-06
2008-02-03
[ "math.CA" ]
Holger Dette
math/9405213
Q-Hermite polynomials and classical orthogonal polynomials
We use generating functions to express orthogonality relations in the form of $q$-beta integrals. The integrand of such a $q$-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal
1994-05-24
2016-09-06
[ "math.CA" ]
Christian Berg, Mourad E. H. Ismail
math/9404224
Explicit representations of biorthogonal polynomials
Given a parametrised weight function $\omega(x,\mu)$ such that the quotients of its consecutive moments are M\"obius maps, it is possible to express the underlying biorthogonal polynomials in a closed form \cite{IN2}. In the present paper we address ourselves to two related issues. Firstly, we demonstrate that, subject...
1994-04-22
2015-06-26
[ "math.CA" ]
Arieh Iserles, Syvert Paul N{\o}rsett
math/9404223
Biorthogonal polynomials and zero-mapping transformations
The authors have presented in \cite{IN2} a technique to generate transformations $\cal T$ of the set ${\Bbb P}_n$ of $n$th degree polynomials to itself such that if $p\in{\Bbb P}_n$ has all its zeros in $(c,d)$ then ${\cal T}\{p\}$ has all its zeros in $(a,b)$, where $(a,b)$ and $(c,d)$ are given real intervals. The te...
1994-04-22
2016-09-06
[ "math.CA" ]
Arieh Iserles, Syvert Paul N{\o}rsett
math/9404219
A package on formal power series
Formal Laurent-Puiseux series are important in many branches of mathematics. This paper presents a {\it Mathematica} implementation of algorithms developed by the author for converting between certain classes of functions and their equivalent representing series. The package {\tt PowerSeries} handles functions of ratio...
1994-04-19
2025-10-20
[ "math.CA", "cs.NA", "math.NA" ]
Wolfram Koepf
math/9404221
Bounded nonvanishing functions and Bateman functions
We consider the family B-tilde of bounded nonvanishing analytic functions f(z) = a_0 + a_1 z + a_2 z^2 + ... in the unit disk. The coefficient problem had been extensively investigated, and it is known that |a_n| <= 2/e for n=1,2,3, and 4. That this inequality may hold for n in N, is know as the Kry\.z conjecture. ...
1994-04-19
2016-09-06
[ "math.CA", "math.CV" ]
Wolfram Koepf, Dieter Schmersau
math/9404218
Formal power series
In this article we will describe the \Maple\ implementation of an algorithm presented in~\cite{Koe92}--\cite{Koeortho} which computes an {\em exact\/} formal power series (FPS) of a given function. This procedure will enable the user to reproduce most of the results of the extensive bibliography on series~\cite{Han}. W...
1994-04-19
2009-09-25
[ "math.CA" ]
Dominik Gruntz, Wolfram Koepf
math/9404220
Algorithmic work with orthogonal polynomials and special functions
In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types of identities for those functions. Some of these identities like differential equ...
1994-04-19
2016-09-06
[ "math.CA" ]
Wolfram Koepf
math/9404222
Spaces of functions satisfying simple differential equations
In \cite{Koe92}--\cite{Koe93c} the first author published an algorithm for the conversion of analytic functions for which derivative rules are given into their representing power series $\sum\limits_{k=0}^{\infty}a_{k}z^{k}$ at the origin and vice versa, implementations of which exist in {\sc Mathematica} \cite{Wol}, (...
1994-04-19
2009-09-25
[ "math.CA" ]
Wolfram Koepf, Dieter Schmersau
math/9404217
A q-analogue of Graf's addition formula for the Hahn-Exton q-Bessel function
An addition and product formula for the Hahn-Exton $q$-Bessel function, previously obtained by use of a quantum group theoretic interpretation, are proved analytically. A (formal) limit transition to the Graf addition formula and corresponding product formula for the Bessel function is given.
1994-04-11
2008-02-03
[ "math.CA", "math.QA" ]
Erik Koelink, Ren\'e F. Swarttouw
math/9403216
q-Special functions, a tutorial
A tutorial introduction is given to q-special functions and to q-analogues of the classical orthogonal polynomials, up to the level of Askey-Wilson polynomials.
1994-03-21
2013-10-15
[ "math.CA" ]
Tom H. Koornwinder
math/9403214
Asymptotics for the simplest generalized Jacobi polynomials recurrence coefficients from Freud's equations: numerical explorations.
Generalized Jacobi polynomials are orthogonal polynomials related to a weight function which is smooth and positive on the whole interval of orthogonality up to a finite number of points, where algebraic singularities occur. The influence of these singular points on the asymptotic behaviour of the recurrence coefficien...
1994-03-18
2016-09-06
[ "math.CA" ]
Alphonse P. Magnus
math/9403213
Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product
We investigate the asymptotic properties of orthogonal polynomials for a class of inner products including the discrete Sobolev inner products $\langle h,g \rangle = \int hg\, d\mu + \sum_{j=1}^m \sum_{i=0}^{N_j} M_{j,i} h^{(i)}(c_j) g^{(i)}(c_j)$, where $\mu$ is a certain type of complex measure on the real line, and ...
1994-03-15
2016-09-06
[ "math.CA" ]
G. L\'opez, Francisco Marcell\'an, Walter Van Assche
math/9402212
A characterization of the Rogers q-Hermite polynomials
In this paper we characterize the Rogers q-Hermite polynomials as the only orthogonal polynomial set which is also ${\cal D}_q$-Appell where ${\cal D}_q $ is the Askey-Wilson finite difference operator.
1994-02-25
2016-09-06
[ "math.CA" ]
Waleed A. Al-Salam
math/9402216
Bracket notation for the `coefficient of' operator
When $G(z)$ is a power series in $z$, many authors now write `$[z^n] G(z)$' for the coefficient of $z^n$ in $G(z)$, using a notation introduced by Goulden and Jackson in [\GJ, p. 1]. More controversial, however, is the proposal of the same authors [\GJ, p. 160] to let `$[z^n/n!] G(z)$' denote the coefficient of $z^n/n!...
1994-02-23
2008-02-03
[ "math.CA" ]
Donald E. Knuth
math/9401208
Criterion for the resolvent set of nonsymmetric tridiagonal operators
We study nonsymmetric tridiagonal operators acting in the Hilbert space $\ell^2$ and describe the spectrum and the resolvent set of such operators in terms of a continued fraction related to the resolvent. In this way we establish a connection between Pad\'e approximants and spectral properties of nonsymmetric tridiago...
1994-01-21
2009-09-25
[ "math.CA" ]
A. I. Aptekarev, Valeri\u{\i} A. Kaliaguine, Walter Van Assche
math/9401209
Weak convergence of orthogonal polynomials
The weak convergence of orthogonal polynomials is given under conditions on the asymptotic behaviour of the coefficients in the three-term recurrence relation. The results generalize known results and are applied to several systems of orthogonal polynomials, including orthogonal polynomials on a finite set of points.
1994-01-21
2016-09-06
[ "math.CA" ]
Walter Van Assche
math/9412223
The degree-diameter problem for several varieties of Cayley graphs, I: the Abelian case
We address the degree-diameter problem for Cayley graphs of Abelian groups (Abelian graphs), both directed and undirected. The problem turns out to be closely related to the problem of finding efficient lattice coverings of Euclidean space by shapes such as octahedra and tetrahedra; we exploit this relationship in both...
1994-12-17
2021-02-09
[ "math.CO" ]
Randall Dougherty, Vance Faber
math/9412222
Efficient pooling designs for library screening
We describe efficient methods for screening clone libraries, based on pooling schemes which we call ``random $k$-sets designs''. In these designs, the pools in which any clone occurs are equally likely to be any possible selection of $k$ from the $v$ pools. The values of $k$ and $v$ can be chosen to optimize desirable ...
1994-12-04
2016-09-06
[ "math.CO", "q-bio" ]
William J. Bruno, Emanuel Knill, David J. Balding, D. C. Bruce, N. A. Doggett, W. W. Sawhill, R. L. Stallings, Craig C. Whittaker, David C. Torney
math/9411217
Eigenfunctions on the Finite Poincar\'e Plane
Let $F$ be a finite field of odd number of elements. Let $F(\sqrt{\delta})$ be its quadratic extension. $F(\sqrt{\delta})-F$ is the so-called finite Poincare plane. This paper relates the bases of eigenfunctions constructed by Evans and by Kuang. The finite Poincare plane can be viewed as a Ramanujan graph. This paper ...
1994-11-29
2008-02-03
[ "math.CO", "math.NT" ]
Jinghua Kuang
math/9411216
A note on tiling with integer-sided rectangles
We show how to determine if a given simple rectilinear polygon can be tiled with rectangles, each having an integer side.
1994-11-28
2009-09-25
[ "math.CO", "math.MG" ]
Richard Kenyon
math/9411215
Tiling a rectangle with the fewest squares
We show that a square-tiling of a $p\times q$ rectangle, where $p$ and $q$ are relatively prime integers, has at least $\log_2p$ squares. If $q>p$ we construct a square-tiling with less than $q/p+C\log p$ squares of integer size, for some universal constant $C$.
1994-11-28
2016-09-06
[ "math.CO", "math.MG" ]
Richard Kenyon
math/9411223
Algorithms for learning and teaching sets of vertices in graphs
The learning complexity of special sets of vertices in graphs is studied in the model(s) of exact learning by (extended) equivalence and membership queries. Polynomial-time learning algorithms are described for vertex covers, independent sets, and dominating sets. The complexity of learning vertex sets of fixed size is...
1994-11-22
2016-09-06
[ "math.CO" ]
Lane H. Clark, Patricia A. Evans, Michael R. Fellows, Walter D. Wallis