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hep-th/9109015
On the solutions to the string equation
The set of solutions to the string equation $[P,Q]=1$ where $P$ and $Q$ are differential operators is described.It is shown that there exists one-to-one correspondence between this set and the set of pairs of commuting differential operators.This fact permits us to describe the set of solutions to the string equation i...
1991-09-10
2009-10-22
[ "hep-th" ]
A.Schwarz
hep-th/9109014
Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures
In this paper we examine the bi-Hamiltonian structure of the generalized KdV-hierarchies. We verify that both Hamiltonian structures take the form of Kirillov brackets on the Kac-Moody algebra, and that they define a coordinated system. Classical extended conformal algebras are obtained from the second Poisson bracket....
1991-09-10
2015-06-26
[ "hep-th" ]
Nigel J. Burroughs, Mark F. deGroot, Timothy J. Hollowood and J. Luis Miramontes
hep-th/9109010
W3 Constructions on Affine Lie Algebras
We use an argument of Romans showing that every Virasoro construction leads to realizations of $W_3$, to construct $W_3$ realizations on arbitrary affine Lie algebras. Solutions are presented for generic values of the level as well as for specific values of the level but with arbitrary parameters. We give a detailed di...
1991-09-09
2009-10-22
[ "hep-th" ]
A. Deckmyn and S. Schrans
hep-th/9109009
Bi-Hamiltonian Sturcture of Super KP Hierarchy
We obtain the bi-Hamiltonian structure of the super KP hierarchy based on the even super KP operator $\Lambda = \theta^{2} + \sum^{\infty}_{i=-2}U_{i} \theta^{-i-1}$, as a supersymmetric extension of the ordinary KP bi-Hamiltonian structure. It is expected to give rise to a universal super $W$-algebra incorporating all...
1991-09-06
2007-05-23
[ "hep-th" ]
Feng Yu
hep-th/9109008
Effective Superstrings
We generalize the method of quantizing effective strings proposed by Polchinski and Strominger to superstrings. The Ramond-Neveu-Schwarz string is different from the Green-Schwarz string in non-critical dimensions. Both are anomaly-free and Poincare invariant. Some implications of the results are discussed. The formal ...
1991-09-05
2009-10-22
[ "hep-th" ]
Zhu Yang
hep-th/9109007
High Temperature Limit of the Confining Phase
The deconfining transition in non-Abelian gauge theory is known to occur by a condensation of Wilson lines. By expanding around an appropriate Wilson line background, it is possible at large $N$ to analytically continue the confining phase to arbitrarily high temperatures, reaching a weak coupling confinement regime. T...
1991-09-05
2009-10-09
[ "hep-th" ]
Joseph Polchinski
hep-th/9109006
(2+1)-Dimensional Chern-Simons Gravity as a Dirac Square Root
For (2+1)-dimensional spacetimes with the spatial topology of a torus, the transformation between the Chern-Simons and ADM versions of quantum gravity is constructed explicitly, and the wave functions are compared. It is shown that Chern-Simons wave functions correspond to modular forms of weight 1/2, that is, spinors ...
1991-09-04
2014-11-18
[ "hep-th" ]
Steven Carlip
hep-th/9109004
Bosonisation of the Complex-boson realisation of $W_\infty$
We bosonise the complex-boson realisations of the $W_\infty$ and $W_{1+\infty}$ algebras. We obtain nonlinear realisations of $W_\infty$ and $W_{1+\infty}$ in terms of a pair of fermions and a real scalar. By further bosonising the fermions, we then obtain realisations of $W_\infty$ in terms of two scalars. Keeping the...
1991-09-04
2009-10-22
[ "hep-th" ]
X. Shen and X.J. Wang
hep-th/9109005
World Sheet and Space Time Physics in Two Dimensional (Super) String Theory
We show that tree level ``resonant'' $N$ tachyon scattering amplitudes, which define a sensible ``bulk'' S -- matrix in critical (super) string theory in any dimension, have a simple structure in two dimensional space time, due to partial decoupling of a certain infinite set of discrete states. We also argue that the g...
1991-09-04
2009-10-22
[ "hep-th" ]
P. Di Francesco and D. Kutasov
hep-th/9109002
Ashtekar's Approach to Quantum Gravity
A review is given of work by Abhay Ashtekar and his colleagues Carlo Rovelli, Lee Smolin, and others, which is directed at constructing a nonperturbative quantum theory of general relativity.
1991-09-03
2007-05-23
[ "hep-th" ]
Gary T. Horowitz
hep-th/9109003
The renormalization group flow in 2D N=2 SUSY Landau-Ginsburg models
We investigate the renormalization of N=2 SUSY L-G models with central charge $c=3p/(2+p)$ perturbed by an almost marginal chiral operator. We calculate the renormalization of the chiral fields up to $gg{^*}$ order and of nonchiral fields up to $g(g^{*})$ order. We propose a formulation of the nonrenormalization theore...
1991-09-03
2008-11-26
[ "hep-th" ]
Jadwiga Bienkowska
hep-th/9109001
Fractional Superstrings with Space-Time Critical Dimensions Four and Six
We propose possible new string theories based on local world-sheet symmetries corresponding to extensions of the Virasoro algebra by fractional spin currents. They have critical central charges $c=6(K+8)/(K+2)$ and Minkowski space-time dimensions $D=2+16/K$ for $K\geq2$ an integer. We present evidence for their existen...
1991-09-02
2009-10-22
[ "hep-th" ]
Philip C. Argyres and S.-H. Henry Tye
hep-th/9108027
Factorization and Topological States in $c=1$ Matter Coupled to 2-D Gravity
Factorization of the $N$-point amplitudes in two-dimensional $c=1$ quantum gravity is understood in terms of short-distance singularities arising from the operator product expansion of vertex operators after the Liouville zero mode integration. Apart from the tachyon states, there are infinitely many topological states...
1991-08-30
2009-10-22
[ "hep-th" ]
Norisuke Sakai, Yoshiaki Tanii
hep-th/9108026
Superstring in Two Dimensional Black Hole
We construct superstring theory in two dimensional black hole background based on supersymmetric $SU(1,1)/U(1)$ gauged Wess-Zumino-Witten model.
1991-08-29
2011-04-20
[ "hep-th" ]
Shin'ichi Nojiri
hep-th/9108024
On the S-matrix of the Sub-leading Magnetic Deformation of the Tricritical Ising Model in Two Dimensions
We compute the $S$-matrix of the Tricritical Ising Model perturbed by the subleading magnetic operator using Smirnov's RSOS reduction of the Izergin-Korepin model. The massive model contains kink excitations which interpolate between two degenerate asymmetric vacua. As a consequence of the different structure of the tw...
1991-08-27
2015-06-26
[ "hep-th" ]
F. Colomo, A. Koubek, G. Mussardo
hep-th/9108023
Fock space resolutions of the Virasoro highest weight modules with c<=1
We extend Felder's construction of Fock space resolutions for the Virasoro minimal models to all irreducible modules with $c\leq 1$. In particular, we provide resolutions for the representations corresponding to the boundary and exterior of the Kac table.
1991-08-27
2009-09-11
[ "hep-th" ]
Peter Bouwknegt, Jim McCarthy and Krzysztof Pilch
hep-th/9108019
String Theory in Two Dimensions
I review some of the recent progress in two-dimensional string theory, which is formulated as a sum over surfaces embedded in one dimension.
1991-08-26
2008-02-03
[ "hep-th" ]
Igor R. Klebanov
hep-th/9108021
The big picture
We discuss the conformal field theory and string field theory of the NSR superstring using a BRST operator with a nonminimal term, which allows all bosonic ghost modes to be paired into creation and annihilation operators. Vertex operators for the Neveu-Schwarz and Ramond sectors have the same ghost number, as do strin...
1991-08-26
2009-10-22
[ "hep-th" ]
N. Berkovits, M.T. Hatsuda, and W. Siegel
hep-th/9108020
String Theory and the Donaldson Polynomial
It is shown that the scattering of spacetime axions with fivebrane solitons of heterotic string theory at zero momentum is proportional to the Donaldson polynomial.
1991-08-26
2009-09-17
[ "hep-th" ]
J.A.Harvey and A.Strominger
hep-th/9108022
Superstring Compactification and Target Space Duality
This review talk focusses on some of the interesting developments in the area of superstring compactification that have occurred in the last couple of years. These include the discovery that ``mirror symmetric" pairs of Calabi--Yau spaces, with completely distinct geometries and topologies, correspond to a single (2,2)...
1991-08-26
2007-05-23
[ "hep-th" ]
John H. Schwarz
hep-th/9108025
Correlation functions in super Liouville theory
We calculate three- and four-point functions in super Liouville theory coupled to super Coulomb gas on world sheets with spherical topology. We first integrate over the zero mode and assume that a parameter takes an integer value. After calculating the amplitudes, we formally continue the parameter to an arbitrary real...
1991-08-24
2009-10-22
[ "hep-th" ]
E. Abdalla, M.C.B. Abdalla, D.Dalmazi, Koji Harada
hep-th/9108015
A $U(N)$ Gauge Theory in Three Dimensions as an Ensemble of Surfaces
A particular $U(N)$ gauge theory defined on the three dimensional dodecahedral lattice is shown to correspond to a model of oriented self-avoiding surfaces. Using large $N$ reduction it is argued that the model is partially soluble in the planar limit.
1991-08-23
2009-10-22
[ "hep-th" ]
F. David, H. Neuberger
hep-th/9108018
Real Forms of Complex Quantum Anti de Sitter Algebra $U_q (Sp(4,C))$ and their Contraction Schemes
We describe four types of inner involutions of the Cartan-Weyl basis providing (for $ |q|=1$ and $q$ real) three types of real quantum Lie algebras: $U_{q}(O(3,2))$ (quantum D=4 anti-de-Sitter), $U_{q}(O(4,1))$ (quantum D=4 de-Sitter) and $U_{q}(O(5))$. We give also two types of inner involutions of the Cartan-Chevalle...
1991-08-23
2009-10-22
[ "hep-th" ]
J. Lukierski, A. Novicki and H. Ruegg
hep-th/9108017
A New Solution to the Star--Triangle Equation Based on U$_q$(sl(2)) at Roots of Unit
We find new solutions to the Yang--Baxter equation in terms of the intertwiner matrix for semi-cyclic representations of the quantum group $U_q(s\ell(2))$ with $q= e^{2\pi i/N}$. These intertwiners serve to define the Boltzmann weights of a lattice model, which shares some similarities with the chiral Potts model. An a...
1991-08-23
2009-10-22
[ "hep-th" ]
Cesar Gomez and German Sierra
hep-th/9108016
Non-Perturbative 2D Quantum Gravity, Again
This is a talk given by S.D. at the the workshop on Random Surfaces and 2D Quantum Gravity, Barcelona 10-14 June 1991. It is an updated review of recent work done by the authors on a proposal for non-perturbatively stable 2D quantum gravity coupled to c<1 matter, based on the flows of the (generalised) KdV hierarchy.
1991-08-23
2009-10-22
[ "hep-th" ]
S.Dalley, C.Johnson and T.Morris
hep-th/9108014
Loop Equations and the Topological Phase of Multi-Cut Matrix Models
We study the double scaling limit of mKdV type, realized in the two-cut Hermitian matrix model. Building on the work of Periwal and Shevitz and of Nappi, we find an exact solution including all odd scaling operators, in terms of a hierarchy of flows of $2\times 2$ matrices. We derive from it loop equations which can be...
1991-08-22
2015-06-26
[ "hep-th" ]
C. Crnkovic, M. Douglas, G. Moore
hep-th/9108012
On the Perturbations of String-Theoretic Black Holes
The perturbations of string-theoretic black holes are analyzed by generalizing the method of Chandrasekhar. Attention is focussed on the case of the recently considered charged string-theoretic black hole solutions as a representative example. It is shown that string-intrinsic effects greatly alter the perturbed motion...
1991-08-22
2007-05-23
[ "hep-th" ]
Gerald Gilbert
hep-th/9108013
Differential Equations for Periods and Flat Coordinates in Two Dimensionsional Topological Matter Theories
We derive directly from the N=2 LG superpotential the differential equations that determine the flat coordinates of arbitrary topological CFT's.
1991-08-22
2009-10-22
[ "hep-th" ]
W.Lerche, D.Smit, and N. Warner
hep-th/9108010
String Winding in a Black Hole Geometry
$U(1)$ zero modes in the $SL(2,R)_k/U(1)$ and $SU(2)_k/U(1)$ conformal coset theories, are investigated in conjunction with the string black hole solution. The angular variable in the Euclidean version, is found to have a double set of winding. Region III is shown to be $SU(2)_k/U(1)$ where the doubling accounts for th...
1991-08-21
2007-05-23
[ "hep-th" ]
Mordechai Spiegelglas
hep-th/9108011
Twisted Black p-Brane Solutions in String Theory
It has been shown that given a classical background in string theory which is independent of $d$ of the space-time coordinates, we can generate other classical backgrounds by $O(d)\otimes O(d)$ transformation on the solution. We study the effect of this transformation on the known black $p$-brane solutions in string th...
1991-08-21
2009-09-15
[ "hep-th" ]
Ashoke Sen
hep-th/9108008
Novel Symmetries of Topological Conformal Field theories
We show that various actions of topological conformal theories that were suggested recentely are particular cases of a general action. We prove the invariance of these models under transformations generated by nilpotent fermionic generators of arbitrary conformal dimension, $\Q$ and $\G$. The later are shown to be the ...
1991-08-20
2007-05-23
[ "hep-th" ]
J. Sonnenschein and S. Yankielowicz
hep-th/9108009
Solving 3+1 QCD on the Transverse Lattice Using 1+1 Conformal Field Theory
A new transverse lattice model of $3+1$ Yang-Mills theory is constructed by introducing Wess-Zumino terms into the 2-D unitary non-linear sigma model action for link fields on a 2-D lattice. The Wess-Zumino terms permit one to solve the basic non-linear sigma model dynamics of each link, for discrete values of the bare...
1991-08-20
2009-10-22
[ "hep-th" ]
Paul A. Griffin
hep-th/9108006
Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity
It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat $SU(2)$ connections over a two-dimensional surface, which gives physical states in the $ISO(3)$ Chern-Simons gauge the...
1991-08-20
2009-09-17
[ "hep-th" ]
Hirosi Ooguri and Naoki Sasakura
hep-th/9108007
Infinite Quantum Group Symmetry of Fields in Massive 2D Quantum Field Theory
Starting from a given S-matrix of an integrable quantum field theory in $1+1$ dimensions, and knowledge of its on-shell quantum group symmetries, we describe how to extend the symmetry to the space of fields. This is accomplished by introducing an adjoint action of the symmetry generators on fields, and specifying the ...
1991-08-20
2015-06-26
[ "hep-th" ]
A. LeCLair and F. Smirnov
hep-th/9108005
Fusion Residues
We discuss when and how the Verlinde dimensions of a rational conformal field theory can be expressed as correlation functions in a topological LG theory. It is seen that a necessary condition is that the RCFT fusion rules must exhibit an extra symmetry. We consider two particular perturbations of the Grassmannian supe...
1991-08-19
2015-06-26
[ "hep-th" ]
Kenneth Intriligator
hep-th/9108004
Ground Ring Of Two Dimensional String Theory
String theories with two dimensional space-time target spaces are characterized by the existence of a ``ground ring'' of operators of spin $(0,0)$. By understanding this ring, one can understand the symmetries of the theory and illuminate the relation of the critical string theory to matrix models. The symmetry groups ...
1991-08-16
2010-04-07
[ "hep-th" ]
Edward Witten
hep-th/9108002
Hamiltonian construction of W-gravity actions
We show that all W-gravity actions can be easilly constructed and understood from the point of view of the Hamiltonian formalism for the constrained systems. This formalism also gives a method of constructing gauge invariant actions for arbitrary conformally extended algebras.
1991-08-15
2009-01-16
[ "hep-th" ]
A. Mikovic
hep-th/9108003
Supersymmetric Gelfand-Dickey Algebra
We study the classical version of supersymmetric $W$-algebras. Using the second Gelfand-Dickey Hamiltonian structure we work out in detail $W_2$ and $W_3$-algebras.
1991-08-15
2015-06-26
[ "hep-th" ]
Katri Huitu and Dennis Nemeschansky
hep-th/9108001
Exact Black String Solutions in Three Dimensions
A family of exact conformal field theories is constructed which describe charged black strings in three dimensions. Unlike previous charged black hole or extended black hole solutions in string theory, the low energy spacetime metric has a regular inner horizon (in addition to the event horizon) and a timelike singular...
1991-08-14
2009-10-22
[ "hep-th" ]
James H. Horne and Gary T. Horowitz
math/9201305
Alternating sign matrices and domino tilings
We introduce a family of planar regions, called Aztec diamonds, and study the ways in which these regions can be tiled by dominoes. Our main result is a generating function that not only gives the number of domino tilings of the Aztec diamond of order $n$ but also provides information about the orientation of the domin...
1991-06-01
2008-02-03
[ "math.CO" ]
Noam Elkies (Harvard), Greg Kuperberg (UC Berkeley), Michael Larsen (U Penn), James Propp (MIT)
math/9201299
Geometric finiteness and uniqueness for Kleinian groups with circle packing limit sets
In this paper, we assume that $G$ is a finitely generated torsion free non-elementary Kleinian group with $\Omega(G)$ nonempty. We show that the maximal number of elements of $G$ that can be pinched is precisely the maximal number of rank 1 parabolic subgroups that any group isomorphic to $G$ may contain. A group with ...
1991-12-11
2016-09-06
[ "math.DG", "math.GT" ]
Linda Keen, Bernard Maskit, Caroline Series
math/9201298
On removable sets for Sobolev spaces in the plane
Let $K$ be a compact subset of $\bar{\bold C} ={\bold R}^2$ and let $K^c$ denote its complement. We say $K\in HR$, $K$ is holomorphically removable, if whenever $F:\bar{\bold C} \to\bar{\bold C}$ is a homeomorphism and $F$ is holomorphic off $K$, then $F$ is a M\"obius transformation. By composing with a M\"obius trans...
1991-11-26
2016-09-06
[ "math.DS" ]
Peter Jones
math/9201297
Periodic orbits for Hamiltonian systems in cotangent bundles
We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a certain boundary condition given by a Riemannian metric on $M$. We discretize the varia...
1991-11-11
2008-02-03
[ "math.DS" ]
Christopher Gol\'e
math/9201296
On the realization of fixed point portraits (an addendum to Goldberg, Milnor: Fixed point portraits)
We establish that every formal critical portrait (as defined by Goldberg and Milnor), can be realized by a postcritically finite polynomial.
1991-10-27
2008-02-03
[ "math.DS" ]
Alfredo Poirier
math/9201294
On the quasisymmetrical classification of infinitely renormalizable maps: I. Maps with Feigenbaum's topology.
A semigroup (dynamical system) generated by $C^{1+\alpha}$-contracting mappings is considered. We call a such semigroup regular if the maximum $K$ of the conformal dilatations of generators, the maximum $l$ of the norms of the derivatives of generators and the smoothness $\alpha$ of the generators satisfy a compatibili...
1991-10-11
2016-09-06
[ "math.DS" ]
Yunping Jiang
math/9201295
On the quasisymmetrical classification of infinitely renormalizable maps: II. remarks on maps with a bounded type topology.
We use the upper and lower potential functions and Bowen's formula estimating the Hausdorff dimension of the limit set of a regular semigroup generated by finitely many $C^{1+\alpha}$-contracting mappings. This result is an application of the geometric distortion lemma in the first paper at this series.
1991-10-11
2016-09-06
[ "math.DS" ]
Yunping Jiang
math/9201293
Dynamics of certain non-conformal degree two maps on the plane
In this paper we consider maps on the plane which are similar to quadratic maps in that they are degree 2 branched covers of the plane. In fact, consider for $\alpha$ fixed, maps $f_c$ which have the following form (in polar coordinates): $$f_c(r\,e^{i\theta})\;=\;r^{2\alpha}\,e^{2i\theta}\,+\,c$$ When $\alpha=1$, ...
1991-09-26
2011-07-26
[ "math.DS" ]
Ben Bielefeld, Scott Sutherland, Folkert Tangerman, J. J. P. Veerman
math/9201292
Quasisymmetric conjugacies between unimodal maps
It is shown that some topological equivalency classes of S-unimodal maps are equal to quasisymmetric conjugacy classes. This includes some infinitely renormalizable polynomials of unbounded type.
1991-08-27
2009-09-25
[ "math.DS" ]
Michael Jakobson, Grzegorz Swiatek
math/9201291
The Fibonacci unimodal map
This paper will study topological, geometrical and measure-theoretical properties of the real Fibonacci map. Our goal was to figure out if this type of recurrence really gives any pathological examples and to compare it with the infinitely renormalizable patterns of recurrence studied by Sullivan. It turns out that the...
1991-08-12
2016-09-06
[ "math.DS" ]
Mikhail Lyubich, John W. Milnor
math/9201290
The "spectral" decomposition for one-dimensional maps
We construct the "spectral" decomposition of the sets $\bar{Per\,f}$, $\omega(f)=\cup\omega(x)$ and $\Omega(f)$ for a continuous map $f$ of the interval to itself. Several corollaries are obtained; the main ones describe the generic properties of $f$-invariant measures, the structure of the set $\Omega(f)\setminus \bar...
1991-07-27
2016-01-25
[ "math.DS" ]
Alexander M. Blokh
math/9201289
Periods implying almost all periods, trees with snowflakes, and zero entropy maps
Let $X$ be a compact tree, $f$ be a continuous map from $X$ to itself, $End(X)$ be the number of endpoints and $Edg(X)$ be the number of edges of $X$. We show that if $n>1$ has no prime divisors less than $End(X)+1$ and $f$ has a cycle of period $n$, then $f$ has cycles of all periods greater than $2End(X)(n-1)$ and to...
1991-07-12
2016-01-25
[ "math.DS" ]
Alexander M. Blokh
math/9201287
Dynamics of certain smooth one-dimensional mappings III: Scaling function geometry
We study scaling function geometry. We show the existence of the scaling function of a geometrically finite one-dimensional mapping. This scaling function is discontinuous. We prove that the scaling function and the asymmetries at the critical points of a geometrically finite one-dimensional mapping form a complete set...
1991-06-27
2008-02-03
[ "math.DS" ]
Yunping Jiang
math/9201288
Dynamics of certain smooth one-dimensional mappings IV: Asymptotic geometry of Cantor sets
We study hyperbolic mappings depending on a parameter $\varepsilon $. Each of them has an invariant Cantor set. As $\varepsilon $ tends to zero, the mapping approaches the boundary of hyperbolicity. We analyze the asymptotics of the gap geometry and the scaling function geometry of the invariant Cantor set as $\varepsi...
1991-06-27
2016-09-06
[ "math.DS" ]
Yunping Jiang
math/9201286
Ergodic theory for smooth one-dimensional dynamical systems
In this paper we study measurable dynamics for the widest reasonable class of smooth one dimensional maps. Three principle decompositions are described in this class : decomposition of the global measure-theoretical attractor into primitive ones, ergodic decomposition and Hopf decomposition. For maps with negative Schw...
1991-06-12
2016-09-06
[ "math.DS" ]
Mikhail Lyubich
math/9201285
On the Lebesgue measure of the Julia set of a quadratic polynomial
The goal of this note is to prove the following theorem: Let $p_a(z) = z^2+a$ be a quadratic polynomial which has no irrational indifferent periodic points, and is not infinitely renormalizable. Then the Lebesgue measure of the Julia set $J(p_a)$ is equal to zero. As part of the proof we discuss a property of the cri...
1991-05-28
2016-09-06
[ "math.DS" ]
Mikhail Lyubich
math/9201284
The Teichm\"uller space of an Anosov diffeomorphism of $T^2$
In this paper we consider the space of smooth conjugacy classes of an Anosov diffeomorphism of the two-torus. The only 2-manifold that supports an Anosov diffeomorphism is the 2-torus, and Franks and Manning showed that every such diffeomorphism is topologically conjugate to a linear example, and furthermore, the eigen...
1991-05-12
2016-09-06
[ "math.DS" ]
Elise E. Cawley
math/9201283
Critical circle maps near bifurcation
We estimate harmonic scalings in the parameter space of a one-parameter family of critical circle maps. These estimates lead to the conclusion that the Hausdorff dimension of the complement of the frequency-locking set is less than $1$ but not less than $1/3$. Moreover, the rotation number is a H\"{o}lder continuous fu...
1991-04-27
2016-09-06
[ "math.DS" ]
Jacek Graczyk, Grzegorz Swiatek
math/9201282
The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets
It is shown that the boundary of the Mandelbrot set $M$ has Hausdorff dimension two and that for a generic $c \in \bM$, the Julia set of $z \mapsto z^2+c$ also has Hausdorff dimension two. The proof is based on the study of the bifurcation of parabolic periodic points.
1991-04-12
2016-09-06
[ "math.DS" ]
Mitsuhiro Shishikura
math/9201281
Expanding direction of the period doubling operator
We prove that the period doubling operator has an expanding direction at the fixed point. We use the induced operator, a ``Perron-Frobenius type operator'', to study the linearization of the period doubling operator at its fixed point. We then use a sequence of linear operators with finite ranks to study this induced o...
1991-03-28
2016-09-06
[ "math.DS" ]
Yunping Jiang, Takehiko Morita, Dennis Sullivan
math/9201280
Polynomial root-finding algorithms and branched covers
We construct a family of root-finding algorithms which exploit the branched covering structure of a polynomial of degree $d$ with a path-lifting algorithm for finding individual roots. In particular, the family includes an algorithm that computes an $ε$-factorization of the polynomial which has an arithmetic complexit...
1991-03-13
2025-10-20
[ "math.DS", "cs.NA", "math.NA" ]
Myong-Hi Kim, Scott Sutherland
math/9201279
A partial description of the parameter space of rational maps of degree two: Part 2
This continues the investigation of a combinatorial model for the variation of dynamics in the family of rational maps of degree two, by concentrating on those varieties in which one critical point is periodic. We prove some general results about nonrational critically finite degree two branched coverings, and finally ...
1991-02-25
2009-09-25
[ "math.DS" ]
Mary Rees
math/9201277
Dynamics of certain smooth one-dimensional mappings I: The $C^{1+\alpha}$-Denjoy-Koebe distortion lemma
We prove a technical lemma, the $C^{1+\alpha }$-Denjoy-Koebe distortion lemma, estimating the distortion of a long composition of a $C^{1+\alpha }$ one-dimensional mapping $f:M\mapsto M$ with finitely many, non-recurrent, power law critical points. The proof of this lemma combines the ideas of the distortion lemmas of ...
1991-01-11
2016-09-06
[ "math.DS" ]
Yunping Jiang
math/9201278
Dynamics of certain smooth one-dimensional mappings II: geometrically finite one-dimensional mappings
We study geometrically finite one-dimensional mappings. These are a subspace of $C^{1+\alpha}$ one-dimensional mappings with finitely many, critically finite critical points. We study some geometric properties of a mapping in this subspace. We prove that this subspace is closed under quasisymmetrical conjugacy. We also...
1991-01-11
2008-02-03
[ "math.DS" ]
Yunping Jiang
math/9201236
On certain classes of Baire-1 functions with applications to Banach space theory
Certain subclasses of $B_1(K)$, the Baire-1 functions on a compact metric space $K$, are defined and characterized. Some applications to Banach spaces are given.
1991-12-31
2009-09-25
[ "math.FA" ]
Richard Haydon, Edward Odell, and Haskell P. Rosenthal
math/9201235
On the distribution of Sidon series
Let B denote an arbitrary Banach space, G a compact abelian group with Haar measure $\mu$ and dual group $\Gamma$. Let E be a Sidon subset of $\Gamma$ with Sidon constant S(E). Let r_n denote the n-th Rademacher function on [0, 1]. We show that there is a constant c, depending only on S(E), such that, for all $\alpha >...
1991-12-10
2008-02-03
[ "math.FA" ]
Nakhl\'e Asmar and Stephen J. Montgomery-Smith
math/9201234
Analytic Disks in Fibers over the Unit Ball of a Banach Space
We study biorthogonal sequences with special properties, such as weak or weak-star convergence to 0, and obtain an extension of the Josefson-Nissenzweig theorem. This result is applied to embed analytic disks in the fiber over 0 of the spectrum of H^infinity (B), the algebra of bounded analytic functions on the unit ba...
1991-10-11
2016-09-06
[ "math.FA" ]
B. J. Cole, T. W. Gamelin, William B. Johnson
math/9201233
On J. Borwein's concept of sequentially reflexive Banach spaces
A Banach space $X$ is reflexive if the Mackey topology $\tau(X^*,X)$ on $X^*$ agrees with the norm topology on $X^*$. Borwein [B] calls a Banach space $X$ {\it sequentially reflexive\/} provided that every $\tau(X^*,X)$ convergent {\it sequence\/} in $X^*$ is norm convergent. The main result in [B] is that $X$ is seque...
1991-10-09
2016-09-06
[ "math.FA" ]
Peter {\O}rno
math/9201232
The K_t-functional for the interpolation couple L_1(A_0),L_infinity(A_1)
Let (A_0,A_1) be a compatible couple of Banach spaces in the interpolation theory sense. We give a formula for the K_t-functional of the interpolation couples (l_1(A_0),c_0(A_1)) or (l_1(A_0),l_infinity(A_1)) and (L_1(A_0),L_infinity(A_1)).
1991-09-21
2008-02-03
[ "math.FA" ]
Gilles Pisier
math/9201230
Banach spaces with Property (w)
A Banach space E is said to have Property (w) if every (bounded linear) operator from E into E' is weakly compact. We give some interesting examples of James type Banach spaces with Property (w). We also consider the passing of Property (w) from E to C(K,E).
1991-07-24
2016-09-06
[ "math.FA" ]
Denny H. Leung
math/9201231
A Gordon-Chevet type Inequality
We prove a new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.
1991-07-24
2009-09-25
[ "math.FA" ]
B. Khaoulani
math/9201229
Interpolation between H^p spaces and non-commutative generalizations, I
We give an elementary proof that the $H^p$ spaces over the unit disc (or the upper half plane) are the interpolation spaces for the real method of interpolation between $H^1$ and $H^\infty$. This was originally proved by Peter Jones. The proof uses only the boundedness of the Hilbert transform and the classical factori...
1991-06-04
2008-02-03
[ "math.FA" ]
Gilles Pisier
math/9201228
A simple proof of a theorem of Jean Bourgain
We give a simple proof of Bourgain's disc algebra version of Grothendieck's theorem, i.e. that every operator on the disc algebra with values in $L_1$ or $L_2$ is 2-absolutely summing and hence extends to an operator defined on the whole of $C$. This implies Bourgain's result that $L_1/H^1$ is of cotype 2. We also prov...
1991-06-03
2009-09-25
[ "math.FA" ]
Gilles Pisier
math/9201226
Interpolation of operators when the extreme spaces are $L^\infty$
In this paper, equivalence between interpolation properties of linear operators and monotonicity conditions are studied, for a pair $(X_0,X_1)$ of rearrangement invariant quasi Banach spaces, when the extreme spaces of the interpolation are $L^\infty$ and a pair $(A_0,A_1)$ under some assumptions. Weak and restricted w...
1991-04-29
2008-02-03
[ "math.FA" ]
Jes\'us Bastero and Francisco J. Ruiz
math/9201225
An arbitrarily distortable Banach space
In this work we construct a ``Tsirelson like Banach space'' which is arbitrarily distortable.
1991-04-03
2007-06-13
[ "math.FA" ]
Thomas Schlumprecht
math/9201224
On Schreier unconditional sequences
Let $(x_n)$ be a normalized weakly null sequence in a Banach space and let $\varep>0$. We show that there exists a subsequence $(y_n)$ with the following property: $$\hbox{ if }\ (a_i)\subseteq \IR\ \hbox{ and }\ F\subseteq \nat$$ satisfies $\min F\le |F|$ then $$\big\|\sum_{i\in F} a_i y_i\big\| \le (2+\varep) \big\| ...
1991-03-22
2008-02-03
[ "math.FA" ]
Edward Odell
math/9201222
Non dentable sets in Banach spaces with separable dual
A non RNP Banach space E is constructed such that $E^{*}$ is separable and RNP is equivalent to PCP on the subsets of E.
1991-02-05
2009-09-25
[ "math.FA" ]
Spiros A. Argyros, Irene Deliyanni
math/9201223
Level sets and the uniqueness of measures
A result of Nymann is extended to show that a positive $\sigma$-finite measure with range an interval is determined by its level sets. An example is given of two finite positive measures with range the same finite union of intervals but with the property that one is determined by its level sets and the other is not.
1991-02-05
2008-02-03
[ "math.FA" ]
Dale E. Alspach
math/9201221
Comparison of Orlicz-Lorentz spaces
Orlicz-Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. They have been studied by many authors, including Masty\l o, Maligranda, and Kami\'nska. In this paper, we consider the problem of comparing the Orlicz-Lorentz norms, and establish necessary and sufficient conditions for them to ...
1991-01-02
2008-02-03
[ "math.FA" ]
Stephen J. Montgomery-Smith
math/9201304
Efficient representation of perm groups
This note presents an elementary version of Sims's algorithm for computing strong generators of a given perm group, together with a proof of correctness and some notes about appropriate low-level data structures. Upper and lower bounds on the running time are also obtained. (Following a suggestion of Vaughan Pratt, we ...
1991-01-01
2008-02-03
[ "math.GR" ]
Donald E. Knuth
math/9201247
On a conjecture of Tarski on products of cardinals
We look at an old conjecture of A. Tarski on cardinal arithmetic and show that if a counterexample exists, then there exists one of length omega_1 + omega .
1991-01-15
2009-09-25
[ "math.LO" ]
Thomas Jech, Saharon Shelah
math/9201248
A partition theorem for pairs of finite sets
Every partition of [[omega_1]^{< omega}]^2 into finitely many pieces has a cofinal homogeneous set. Furthermore, it is consistent that every directed partially ordered set satisfies the partition property if and only if it has finite character.
1991-01-15
2008-02-03
[ "math.LO" ]
Thomas Jech, Saharon Shelah
math/9201246
The primal framework. II. Smoothness
This is the second in a series of articles developing abstract classification theory for classes that have a notion of prime models over independent pairs and over chains. It deals with the problem of smoothness and establishing the existence and uniqueness of a `monster model'. We work here with a predicate for a cano...
1991-01-15
2016-09-06
[ "math.LO" ]
John T. Baldwin, Saharon Shelah
math/9201243
The Hanf numbers of stationary logic. II. Comparison with other logics
We show that the ordering of the Hanf number of L_{omega, omega}(wo) (well ordering), L^c_{omega, omega} (quantification on countable sets), L_{omega, omega}(aa) (stationary logic) and second order logic, have no more restraints provable in ZFC than previously known (those independence proofs assume CON(ZFC) only). We ...
1991-01-15
2013-10-22
[ "math.LO" ]
Saharon Shelah
math/9201245
Viva la difference I: Nonisomorphism of ultrapowers of countable models
We show that it is not provable in ZFC that any two countable elementarily equivalent structures have isomorphic ultrapowers relative to some ultrafilter on omega .
1991-01-15
2008-02-03
[ "math.LO" ]
Saharon Shelah
math/9201244
Strong partition relations below the power set: consistency, was Sierpinski right, II?
We continue here [She88] but we do not rely on it. The motivation was a conjecture of Galvin stating that 2^{omega} >= omega_2 + omega_2-> [omega_1]^{n}_{h(n)} is consistent for a suitable h: omega-> omega. In section 5 we disprove this and give similar negative results. In section 3 we prove the consistency of the con...
1991-01-15
2024-01-30
[ "math.LO" ]
Saharon Shelah
math/9201227
Remarks on complemented subspaces of von-Neumann algebras
In this note we include two remarks about bounded ($\underline{not}$ necessarily contractive) linear projections on a von Neumann-algebra. We show that if $M$ is a von Neumann-subalgebra of $B(H)$ which is complemented in B(H) and isomorphic to $M \otimes M$ then $M$ is injective (or equivalently $M$ is contractively c...
1991-05-31
2009-09-25
[ "math.OA", "math.FA" ]
Gilles Pisier
math/9201302
The quantum G_2 link invariant
We derive an inductive, combinatorial definition of a polynomial-valued regular isotopy invariant of links and tangled graphs. We show that the invariant equals the Reshetikhin-Turaev invariant corresponding to the exceptional simple Lie algebra G_2. It is therefore related to G_2 in the same way that the HOMFLY polyno...
1991-10-07
2016-09-06
[ "math.QA", "math.GT" ]
Greg Kuperberg (U Chicago)
alg-geom/9212004
Automorphisms and the K\"ahler cone of certain Calabi-Yau manifolds
For the Calabi-Yau threefolds $X$ constructed by C. Schoen as fiber products of generic rational elliptic surfaces, we show that the action of the automorphism group of $X$ on the K\"ahler cone of $X$ has a rationally polyhedral fundamental domain. The second author has conjectured that this statement will hold in gene...
1992-12-22
2008-02-03
[ "alg-geom", "math.AG" ]
Antonella Grassi and David R. Morrison
alg-geom/9212003
The enumeration of simultaneous higher-order contacts between plane curves
Using the Semple bundle construction, we derive an intersection-theoretic formula for the number of simultaneous contacts of specified orders between members of a generic family of degree $d$ plane curves and finitely many fixed curves. The contacts counted by the formula occur at nonsingular points of both the members...
1992-12-08
2008-02-03
[ "alg-geom", "math.AG" ]
Susan Jane Colley and Gary Kennedy
alg-geom/9212002
On the stable rationality of $X/G$
Let $G$ be a connected, reductive algeraic group whose Dynkin diagram contains no components of type $G_2,$ $F_4,$ $E_6,$ $E_7$ or $E_8.$ That is, all the components are of classical type. Suppose $X$ is an affine variety, and suppose $G$ acts freely on $X.$ Then $X$ and $X/G$ are stably birationally equivalent.
1992-12-04
2012-01-20
[ "alg-geom", "math.AG" ]
Amnon Neeman
alg-geom/9212001
Algebraic approximations of holomorphic maps from Stein domains to projective manifolds
It is shown that every holomorphic map $f$ from a Runge domain $\Omega$ of an affine algebraic variety $S$ into a projective algebraic manifold $X$ is a uniform limit of Nash algebraic maps $f_\nu$ defined over an exhausting sequence of relatively compact open sets $\Omega_\nu$ in $\Omega$. A relative version is also g...
1992-12-01
2008-02-03
[ "alg-geom", "math.AG" ]
Jean-Pierre Demailly, Laszlo Lempert and Bernard Shiffman
alg-geom/9211001
Stable pairs on curves and surfaces
We describe stability conditions for pairs consisting of a coherent sheaf and a homomorphism to a fixed coherent sheaf on a projective variety. The corresponding moduli spaces are constructed for pairs on curves and surfaces. We consider two examples. The fixed sheaf is the structure sheaf or is a vector bundle on a di...
1992-11-09
2008-02-03
[ "alg-geom", "math.AG" ]
Daniel Huybrechts and Manfred Lehn
alg-geom/9210009
Elliptic Three-folds I: Ogg-Shafarevich Theory
We calculate the Tate-Shafarevich group of an elliptic three-fold $f:X\rightarrow S$ when $X$ and $S$ are regular and $f$ is flat, relating it to the Brauer group of $X$ and $S$. We show that given certain hypotheses on $f$, the Tate-Shafarevich group has the interpretation of isomorphism classes of elliptic curves ove...
1992-10-30
2008-02-03
[ "alg-geom", "math.AG" ]
I. Dolgachev and M. Gross
alg-geom/9210008
Erratum to "The Homogeneous Coordinate Ring of a Toric Variety", along with the original paper
This submission consists of two papers: 1) an erratum that corrects an error in the proof of Proposition 4.3 in my paper "The Homogeneous Coordinate Ring of a Toric Variety", and 2) the original (unchanged) version of the paper, published in 1995. The original paper introduced the homogeneous coordinate ring of a toric...
1992-10-22
2014-03-07
[ "alg-geom", "math.AG" ]
David A. Cox (Amherst College)
alg-geom/9210007
Stable pairs, linear systems and the Verlinde formula
We study the moduli problem of pairs consisting of a rank 2 vector bundle and a nonzero section over a fixed smooth curve. The stability condition involves a parameter; as it varies, we show that the moduli space undergoes a sequence of flips in the sense of Mori. As applications, we prove several results about moduli ...
1992-10-19
2008-02-03
[ "alg-geom", "math.AG" ]
Michael Thaddeus
alg-geom/9210006
Reductive group actions on K\"ahler manifolds
We prove that the action of a reductive complex Lie group on a K\"ahler manifold can be linearized in the neighbourhood of a fixed point, provided that the restriction of the action to some compact real form of the group is Hamiltonian with respect to the K\"ahler form.
1992-10-14
2008-02-03
[ "alg-geom", "math.AG" ]
Eugene Lerman and Reyer Sjamaar
alg-geom/9210005
Degrees of Curves in Abelian Varieties
The degree of a curve $C$ in a polarized abelian variety $(X,\lambda)$ is the integer $d=C\cdot\lambda$. When $C$ generates $X$, we find a lower bound on $d$ which depends on $n$ and the degree of the polarization $\lambda$. The smallest possible degree is $d=n$ and is obtained only for a smooth curve in its Jacobian w...
1992-10-13
2008-02-03
[ "alg-geom", "math.AG" ]
Olivier Debarre
alg-geom/9210004
Points of Low Degree on Smooth Plane Curves
The purpose of this note is to provide some applications of Faltings' recent proof of S. Lang's conjecture to smooth plane curves. Let $C$ be a smooth plane curve defined by an equation of degree $d$ with integral coefficients. We show that for $d\ge 7$, the curve $C$ has only finitely many points whose field of defini...
1992-10-13
2008-02-03
[ "alg-geom", "math.AG" ]
Olivier Debarre and Matthew Klassen
alg-geom/9210003
The simple method of distinguishing the underlying differentiable structures of algebraic surfaces
The simplest version of the Spin-polynomial invariants of the underlying differentiable structures of algebraic surfaces were considered and the simplest arguments were used in order to distinguish the underlying smooth structures of certain algebraic surfaces.
1992-10-10
2008-02-03
[ "alg-geom", "math.AG" ]
Andrej Tyurin
alg-geom/9210002
Chow quotients of Grassmannian I
We introduce a certain compactification of the space of projective configurations i.e. orbits of the group $PGL(k)$ on the space of $n$ - tuples of points in $P^{k-1}$ in general position. This compactification differs considerably from Mumford's geometric invariant theory quotient. It is obtained by considering limit ...
1992-10-07
2008-02-03
[ "alg-geom", "math.AG" ]
M.Kapranov