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math/9411222
The complexity of broadcasting in bounded-degree networks
Broadcasting concerns the dissemination of a message originating at one node of a network to all other nodes. This task is accomplished by placing a series of calls over the communication lines of the network between neighboring nodes, where each call requires a unit of time and a call can involve only two nodes. We sh...
1994-11-18
2016-09-06
[ "math.CO", "cs.CC" ]
Michael J. Dinneen
math/9411221
Notes on the connectivity of Cayley coset digraphs
Hamidoune's connectivity results for hierarchical Cayley digraphs are extended to Cayley coset digraphs and thus to arbitrary vertex transitive digraphs. It is shown that if a Cayley coset digraph can be hierarchically decomposed in a certain way, then it is optimally vertex connected. The results are obtained by exten...
1994-11-10
2016-09-06
[ "math.CO" ]
Emanuel Knill
math/9411220
Generalized degrees and densities for families of sets
Let F be a family of subsets of {1,2,...,n}. The width-degree of an element x in at least one member of F is the width of the family {U in F | x in U}. If F has maximum width-degree at most k, then F is locally k-wide. Bounds on the size of locally k-wide families of sets are established. If F is locally k-wide and cen...
1994-11-08
2016-09-06
[ "math.CO" ]
Emanuel Knill
math/9411218
New large graphs with given degree and diameter
In this paper we give graphs with the largest known order for a given degree $\Delta$ and diameter $D$. The graphs are constructed from Moore bipartite graphs by replacement of some vertices by adequate structures. The paper also contains the latest version of the $(\Delta, D)$ table for graphs.
1994-11-03
2008-02-03
[ "math.CO" ]
Francesc Comellas, J. G\'omez
math/9411219
Lower bounds for identifying subset members with subset queries
An instance of a group testing problem is a set of objects $\cO$ and an unknown subset $P$ of $\cO$. The task is to determine $P$ by using queries of the type ``does $P$ intersect $Q$'', where $Q$ is a subset of $\cO$. This problem occurs in areas such as fault detection, multiaccess communications, optimal search, blo...
1994-11-03
2016-09-06
[ "math.CO", "cs.CC" ]
Emanuel Knill
math/9411240
Leaper graphs
An $\{r,s\}$-leaper is a generalized knight that can jump from $(x,y)$ to $(x\pm r,y\pm s)$ or $(x\pm s,y\pm r)$ on a rectangular grid. The graph of an $\{r,s\}$-leaper on an $m\times n$ board is the set of $mn$~vertices $(x,y)$ for $0\leq x<m$ and $0\leq y<n$, with an edge between vertices that are one $\{r,s\}$-leape...
1994-11-01
2008-02-03
[ "math.CO" ]
Donald E. Knuth
math/9411239
Self-complementary plane partitions by Proctor's minuscule method
A method of Proctor [European J. Combin. 5 (1984), no. 4, 331-350] realizes the set of arbitrary plane partitions in a box and the set of symmetric plane partitions as bases of linear representations of Lie groups. We extend this method by realizing transposition and complementation of plane partitions as natural linea...
1994-11-01
2008-02-03
[ "math.CO" ]
Greg Kuperberg (U Chicago)
math/9410211
A simple linear-time algorithm for finding path-decompositions of small width
We described a simple algorithm running in linear time for each fixed constant $k$, that either establishes that the pathwidth of a graph $G$ is greater than $k$, or finds a path-decomposition of $G$ of width at most $O(2^{k})$. This provides a simple proof of the result by Bodlaender that many families of graphs of bo...
1994-10-26
2009-09-25
[ "math.CO" ]
Kevin Cattell, Michael J. Dinneen, Michael R. Fellows
math/9410210
Optimal pooling designs with error detection
Consider a collection of objects, some of which may be `bad', and a test which determines whether or not a given sub-collection contains no bad objects. The non-adaptive pooling (or group testing) problem involves identifying the bad objects using the least number of tests applied in parallel. The `hypergeometric' case...
1994-10-18
2016-09-06
[ "math.CO" ]
David J. Balding, David C. Torney
math/9410209
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
This paper describes a general-purpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a consistent treatment for every single special case that can occur. The programs that use...
1994-10-12
2016-09-06
[ "math.CO", "cs.CC" ]
Herbert Edelsbrunner, Ernst M\"ucke
math/9410208
Three-dimensional alpha shapes
Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal notion of the family of $\alpha$-shapes of a finite point set in $\Real^3$. Eac...
1994-10-12
2016-09-06
[ "math.CO", "cs.CC", "math.MG" ]
Herbert Edelsbrunner, Ernst M\"ucke
math/9410224
Symmetries of plane partitions and the permanent-determinant method
In the paper [J. Combin. Theory Ser. A 43 (1986), 103--113], Stanley gives formulas for the number of plane partitions in each of ten symmetry classes. This paper together with results by Andrews [J. Combin. Theory Ser. A 66 (1994), 28-39] and Stembridge [Adv. Math 111 (1995), 227-243] completes the project of proving ...
1994-10-01
2016-09-06
[ "math.CO" ]
Greg Kuperberg (U Chicago)
math/9409224
An on-line algorithm for improving performance in navigation
Recent papers have shown optimally-competitive on-line strategies for a robot traveling from a point $s$ to a point $t$ in certain unknown geometric environments. We consider the question: Having gained some partial information about the scene on its first trip from $s$ to $t$, can the robot improve its performance on ...
1994-09-21
2016-09-06
[ "math.CO", "cs.CC" ]
Avrim Blum, Prasad Chalasani
math/9409225
The complexity of approximating PSPACE-Complete problems for hierarchical specifications
We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specified graphs, many of which are PSPACE-complete. Assuming P != PSPACE, the existence or nonexistence of such efficient approximation algorithms is characterized, for several standard graph theoretic and combina...
1994-09-21
2016-09-06
[ "math.CO", "cs.CC" ]
Madhav V. Marathe, Harry B. Hunt III, S. S. Ravi
math/9409223
On the minimum latency problem
We are given a set of points $p_1,\ldots , p_n$ and a symmetric distance matrix $(d_{ij})$ giving the distance between $p_i$ and $p_j$. We wish to construct a tour that minimizes $\sum_{i=1}^n \ell(i)$, where $\ell(i)$ is the {\em latency} of $p_i$, defined to be the distance traveled before first visiting $p_i$. This ...
1994-09-21
2009-09-25
[ "math.CO", "cs.CC" ]
Avrim Blum, Prasad Chalasani, Don Coppersmith, Bill Pulleyblank, Prabhakar Raghavan, Madhu Sudan
math/9409222
Spanning trees short or small
We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is the $k$MST problem in which we require a tree of minimum weight spanning at least...
1994-09-21
2009-09-25
[ "math.CO" ]
R. Ravi, R. Sundaram, Madhav V. Marathe, S. S. Ravi, Daniel J. Rosenkrantz
math/9409226
Geometry based heuristics for unit disk graphs
Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring and minimum dominat...
1994-09-21
2016-09-06
[ "math.CO", "cs.CC" ]
Madhav V. Marathe, H. Breu, Harry B. Hunt III, S. S. Ravi, Daniel J. Rosenkrantz
math/9409219
Proving probabilistic correctness statements: the case of Rabin's algorithm for mutual exclusion
The correctness of most randomized distributed algorithms is expressed by a statement of the form ``some predicate of the executions holds with high probability, regardless of the order in which actions are scheduled''. In this paper, we present a general methodology to prove correctness statements of such randomized a...
1994-09-19
2008-11-23
[ "math.CO", "cs.CC" ]
Isaac Saias
math/9409220
Number of faults a system can withstand without repairs
We consider the following scheduling problem. A system is composed of $n$ processors drawn from a pool of $N$. The processors can become faulty while in operation and faulty processors never recover. A report is issued whenever a fault occurs. This report states only the existence of a fault, but does not indicate its ...
1994-09-19
2009-09-25
[ "math.CO", "cs.CC" ]
Michel Goemans, Nancy Lynch, Isaac Saias
math/9409221
Proving time bounds for randomized distributed algorithms
A method of analyzing time bounds for randomized distributed algorithms is presented, in the context of a new and general framework for describing and reasoning about randomized algorithms. The method consists of proving auxiliary statements of the form U (t)->(p) U', which means that whenever the algorithm begins in a...
1994-09-19
2016-09-06
[ "math.CO", "cs.CC" ]
Nancy Lynch, Isaac Saias, Roberto Segala
math/9409218
The lattice of closure relations of a poset
In this paper we show that the set of closure relations on a finite poset P forms a supersolvable lattice, as suggested by Rota. Furthermore this lattice is dually isomorphic to the lattice of closed sets in a convex geometry (in the sense of Edelman and Jamison). We also characterize the modular elements of this latti...
1994-09-17
2016-09-06
[ "math.CO" ]
Michael Hawrylycz, Victor Reiner
math/9409212
Counting pairs of lattice paths by intersections
On an $r\times (n-r)$ lattice rectangle, we first consider walks that begin at the SW corner, proceed with unit steps in either of the directions E or N, and terminate at the NE corner of the rectangle. For each integer $k$ we ask for $N_k^{n,r}$, the number of {\em ordered\/} pairs of these walks that intersect in exa...
1994-09-16
2016-09-06
[ "math.CO" ]
Ira Gessel, Wayne Goddard, Walter Shur, Herbert S. Wilf, Lily Yen
math/9409217
Restricted routing and wide diameter of the cycle prefix network
The cycle prefix network is a Cayley coset digraph based on sequences over an alphabet which has been proposed as a vertex symmetric communication network. This network has been shown to have many remarkable communication properties such as a large number of vertices for a given degree and diameter, simple shortest pat...
1994-09-16
2016-09-06
[ "math.CO" ]
William Y. C. Chen, Vance Faber, Emanuel Knill
math/9409216
A geometric identity for Pappus' Theorem
An expression in the exterior algebra of a Peano space yielding Pappus' Theorem was originally given by Doubilet, Rota, and Stein. Motivated by an identity of Rota, we give an identity in a Grassmann-Cayley algebra of step 3, involving joins and meets alone, which expresses the Theorem of Pappus.
1994-09-16
2008-02-03
[ "math.CO" ]
Michael Hawrylycz
math/9409213
Inverting sets and the packing problem
Given a set $V$, a subset $S$, and a permutation $\pi$ of $V$, we say that $\pi$ permutes $S$ if $\pi (S) \cap S = \emptyset$. Given a collection $\cS = \{V; S_1,\ldots , S_m\}$, where $S_i \subseteq V ~~(i=1,\ldots ,m)$, we say that $\cS$ is invertible if there is a permutation $\pi$ of $V$ such that $\pi (S_i) \subse...
1994-09-16
2016-09-06
[ "math.CO" ]
Vance Faber, Mark Goldberg, Emanuel Knill, Thomas Spencer
math/9409214
Invertible families of sets of bounded degree
Let H = (H,V) be a hypergraph with edge set H and vertex set V. Then hypergraph H is invertible iff there exists a permutation pi of V such that for all E belongs to H(edges) intersection of(pi(E) and E)=0. H is invertibility critical if H is not invertible but every hypergraph obtained by removing an edge from H is in...
1994-09-16
2016-09-06
[ "math.CO" ]
Emanuel Knill
math/9409215
Graph generated union-closed families of sets
Let G be a graph with vertices V and edges E. Let F be the union-closed family of sets generated by E. Then F is the family of subsets of V without isolated points. Theorem: There is an edge e belongs to E such that |{U belongs to F | e belongs to U}| =< 1/2|F|. This is equivalent to the following assertion: If H is a ...
1994-09-16
2016-09-06
[ "math.CO" ]
Emanuel Knill
math/9407211
Proof of the Alternating Sign Matrix Conjecture
The number of $n \times n$ matrices whose entries are either -1, 0, or 1, whose row- and column- sums are all 1, and such that in every row and every column the non-zero entries alternate in sign, is proved to be $[1!4! >... (3n-2)!]/[n!(n+1)! ... (2n-1)!]$, as conjectured by Mills, Robbins, and Rumsey.
1994-07-02
2008-02-03
[ "math.CO" ]
Doron Zeilberger (Temple University)
math/9407212
A High-School Algebra and high-school (purely formal) calculus,. Wallet-Sized Proof, of the Bieberbach Conjecture [after L. Weinstein]
L. Weinstein's brilliant short proof of de Branges's Theorem is made even shorter by using computer algebra.
1994-07-02
2008-02-03
[ "math.CO" ]
Shalosh B. Ekhad (Temple University) and Doron Zeilberger (Temple University)
math/9406225
A matrix equation for association schemes
{Let ${\Cal X}$ be a self-dual P-polynomial association scheme. Then there are at most 12 diagonal matrices $T$ such that $(PT)^3=I$. Moreover, all of the solutions for the classical infinite families of such schemes (including the Hamming scheme) are classified.
1994-06-29
2016-09-06
[ "math.CO", "math.CA" ]
Laura M. Chihara, Dennis W. Stanton
math/9403215
Three Recitations on Holonomic Systems and Hypergeometric Series
A tutorial on what later became to be known as WZ theory, as well as a motivated account of the seminal Gosper algorithm.
1994-06-23
2008-02-03
[ "math.CO", "math.CA" ]
Doron Zeilberger (Temple University)
math/9406220
The Graphical Major Index
A generalization of the classical statistics ``maj'' and ``inv'' (the major index and number of inversions) on words is introduced, parameterized by arbitrary graphs on the underlying alphabet. The question of characterizing those graphs that lead to equi-distributed "inv" and "maj" is posed and answered.
1994-06-23
2008-02-03
[ "math.CO" ]
Dominique Foata (Univ. of Strasbourg) and Doron Zeilberger (Temple University)
math/9405212
How Joe Gillis Discovered Combinatorial Special Function Theory
How Enumerative Combinatorics met Special Functions, thanks to Joe Gillis
1994-05-20
2008-02-03
[ "math.CO" ]
Doron Zeilberger (Temple University)
math/9412202
On the reflection principle in C^n
We propose a reflection principle for holomorphic objects in ${\Bbb C}^n$. Our construction generalizes the classical principle of H.Lewy, S.Pinchuk and S.Webster.
1994-12-21
2009-09-25
[ "math.CV" ]
Alexander Sukhov
math/9412201
The Lu Qi-Keng Conjecture Fails Generically
The bounded domains of holomorphy in~$\mathbf{C}^n$ whose Bergman kernel functions are zero-free form a nowhere dense subset (with respect to a variant of the Hausdorff distance) of all bounded domains of holomorphy.
1994-12-21
2009-09-25
[ "math.CV" ]
Harold P. Boas
math/9411201
Propagation of Gevrey Regularity for a Class of Hypoelliptic Equations
We prove results on the propagation of Gevrey and analytic wave front sets for a class of $C^\infty$ hypoelliptic equations with double characteristics.
1994-11-30
2009-09-25
[ "math.CV" ]
Antonio Bove and David S. Tartakoff
math/9411202
Global (and Local) Analyticity for Second Order Operators Constructed from Rigid Vector Fields on Products of Tori
We prove global analytic hypoellipticity on a product of tori for partial differential operators which are constructed as rigid (variable coefficient) quadratic polynomials in real vector fields satisfying the H\"ormander condition and where $P$ satisfies a `maximal' estimate. We also prove an analyticity result that i...
1994-11-30
2016-09-06
[ "math.CV" ]
David S. Tartakoff
math/9407201
The Kobayashi metric for non-convex complex ellipsoids
In the paper we give some necessary conditions for a mapping to be a $\kappa$-geodesic in non-convex complex ellipsoids. Using these results we calculate explicitly the Kobayashi metric in the ellipsoids $\{|z_1|^2+|z_2|^{2m}<1\}\subset\bold C^2$, where $m<\frac12$.
1994-07-31
2009-09-25
[ "math.CV" ]
Peter Pflug and Wlodzimierz Zwonek
math/9406201
Continuity of the complex Monge-Ampere operator
The complex Monge-Amp\`ere operator $(dd^c)^n$ is an important tool in complex analysis. It would be interesting to find the right notion of convergence $u_j\to u$ such that $(dd^cu_j)^n\to (dd^cu)^n$ in the weak topology. In this paper, using the $C_{n-1}$-capacity, we give a sufficient condition of the weak convergen...
1994-06-30
2008-02-03
[ "math.CV" ]
Yang Xing
math/9404201
CR manifolds with noncompact connected automorphism groups
The main result of this paper is that the identity component of the automorphism group of a compact, connected, strictly pseudoconvex CR manifold is compact unless the manifold is CR equivalent to the standard sphere. In dimensions greater than 3, it has been pointed out by D. Burns that this result follows from known ...
1994-05-02
2009-09-25
[ "math.CV" ]
John M. Lee
math/9402202
Entire periodic functions with plane zeros
We give a complete description of divisors of entire periodic functions in $\C^n$ with plane zeros.
1994-02-28
2009-09-25
[ "math.CV" ]
L. I. Ronkin and A. M. Russakovskii
math/9402201
Cartwright-type and Bernstein-type theorems for functions analytic in a cone
Cartwright-type and Bernstein-type theorems, previously known only for functions of exponential type in $\C^n$, are extended to the case of functions of arbitrary order in a cone.
1994-02-28
2009-09-25
[ "math.CV" ]
Vladimir Logvinenko and Alexander Russakovskii
math/9401223
Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces
We will announce two theorems. The first theorem will classify all topological types of degenerate fibers appearing in one-parameter families of Riemann surfaces, in terms of ``pseudoperiodic'' surface homeomorphisms. The second theorem will give a complete set of conjugacy invariants for the mapping classes of such ho...
1994-01-01
2016-09-06
[ "math.CV" ]
Yukio Matsumoto, Jos\'e Mari\'a Montesinos-Amilibia
math/9412221
On the Asymptotic Behavior of Counting Functions Associated to Degenerating Hyperbolic Riemann Surfaces
We develop an asymptotic expansion of the spectral measures on a degenerating family of hyperbolic Riemann surfaces of finite volume. As an application of our results, we study the asymptotic behavior of weighted counting functions, which, if $M$ is compact, is defined for $w \geq 0$ and $T > 0$ by $$N_{M,w}(T) = \sum\...
1994-12-14
2016-09-06
[ "math.DG" ]
Jonathan Huntley, Jay Jorgenson, Rolf Lundelius
math/9412232
Differential geometry of Cartan connections
For a more general notion of Cartan connection we define characteristic classes, we investigate their relation to usual characteristic classes.
1994-12-01
2009-09-25
[ "math.DG" ]
Dmitri V. Alekseevsky, Peter W. Michor
math/9407216
A theory of characteristic currents associated with a singular connection
This note announces a general construction of characteristic currents for singular connections on a vector bundle. It develops, in particular, a Chern-Weil-Simons theory for smooth bundle maps $\alpha : E \rightarrow F$ which, for smooth connections on $E$ and $F$, establishes formulas of the type $$ \phi \ = \ \text{\...
1994-07-01
2018-02-22
[ "math.DG" ]
Reese Harvey, H. Blaine Jr. Lawson
math/9412205
Rational Maps Whose Fatou Components Are Jordan Domains
We prove: If $f(z)$ is a critically finite rational map which has exactly two critical points and which is not conjugate to a polynomial, then the boundary of every Fatou component of $f$ is a Jordan curve. If $f(z)$ is a hyperbolic critically finite rational map all of whose postcritical points are periodic, then ther...
1994-12-19
2008-02-03
[ "math.DS" ]
Kevin M. Pilgrim
math/9412233
Laminations in holomorphic dynamics
We suggest a way to associate to a rational map of the Riemann sphere a three dimensional object called a hyperbolic orbifold 3-lamination. The relation of this object to the map is analogous to the relation of a hyperbolic 3-manifold to a Kleinian group. In order to construct the 3-lamination we analyze the natural ex...
1994-12-08
2016-09-06
[ "math.DS" ]
Mikhail Lyubich, Yair Minsky
math/9411238
Internal addresses in the Mandelbrot set and Galois groups of polynomials
We describe an interesting interplay between symbolic dynamics, the structure of the Mandelbrot set, permutations of periodic points achieved by analytic continuation, and Galois groups of certain polynomials. Internal addresses are a convenient and efficient way of describing the combinatorial structure of the Mande...
1994-11-21
2012-06-12
[ "math.DS" ]
Dierk Schleicher
math/9411237
Measures with infinite Lyapunov exponents for the periodic Lorentz gas
In \cite{Ch91a} it was shown that the billiard ball map for the periodic Lorentz gas has infinite topological entropy. In this article we study the set of points with infinite Lyapunov exponents. Using the cell structure developed in \cite{BSC90,Ku} we construct an ergodic invariant probability measure with infinite to...
1994-11-03
2016-09-06
[ "math.DS" ]
N. I. Chernov, Serge Troubetzkoy
math/9410223
Forcing of periodic orbits for interval maps and renormalization of piecewise affine maps
We prove that for continuous maps on the interval, the existence of an n-cycle, implies the existence of n-1 points which interwind the original ones and are permuted by the map. We then use this combinatorial result to show that piecewise affine maps (with no zero slope) cannot be infinitely renormalizable.
1994-10-17
2016-09-06
[ "math.DS" ]
Marco Martens, Charles Tresser
math/9410221
Frontiers in complex dynamics
Rational maps on the Riemann sphere occupy a distinguished niche in the general theory of smooth dynamical systems. First, rational maps are complex-analytic, so a broad spectrum of techniques can contribute to their study (quasiconformal mappings, potential theory, algebraic geometry, etc.). The rational maps of a giv...
1994-10-01
2016-09-06
[ "math.DS", "math.CV" ]
Curtis T. McMullen
math/9408217
Some remarks on periodic billiard orbits in rational polygons
A polygon is called rational if the angle between each pair of sides is a rational multiple of $\pi.$ The main theorem we will prove is Theorem 1: For rational polygons, periodic points of the billiard flow are dense in the phase space of the billiard flow. This is a strengthening of Masur's theorem, who has shown ...
1994-08-26
2016-09-06
[ "math.DS" ]
Michael Boshernitzan, G. A. Galperin, Tyll Kr\"uger, Serge Troubetzkoy
math/9408216
Dual billiards, twist maps, and impact oscillators
In this paper techniques of twist map theory are applied to the annulus maps arising from dual billiards on a strictly convex closed curve G in the plane. It is shown that there do not exist invariant circles near G when there is a point on G where the radius of curvature vanishes or is discontinuous. In addition, when...
1994-08-08
2009-09-25
[ "math.DS" ]
Philip Boyland
math/9407223
Acceleration of bouncing balls in external fields
We introduce two models, the Fermi-Ulam model in an external field and a one dimensional system of bouncing balls in an external field above a periodically oscillating plate. For both models we investigate the possibility of unbounded motion. In a special case the two models are equivalent.
1994-07-22
2009-10-28
[ "math.DS" ]
Tyll Kr\"uger, L. D. Pustyl'nikov, Serge Troubetzkoy
math/9407218
Open sets of diffeomorphisms having two attractors, each with an everywhere dense basin
We announce the discovery of a diffeomorphism of a three-dimensional manifold with boundary which has two disjoint attractors. Each attractor attracts a set of positive $3$-dimensional Lebesgue measure whose points of Lebesgue density are dense in the whole manifold. This situation is stable under small perturbations.
1994-07-01
2016-09-06
[ "math.DS" ]
Ittai Kan
math/9406230
Coexistence of critical orbit types in sub-hyperbolic polynomial maps
We establish necessary and sufficient conditions for the realization of mapping schemata as post-critically finite polynomials, or more generally, as post-critically finite polynomial maps from a finite union of copies of the complex numbers {\bf C} to itself which have degree two or more in each copy. As a consequence...
1994-06-17
2008-02-03
[ "math.DS" ]
Alfredo Poirier
math/9405217
Ratio geometry, rigidity and the scenery process for hyperbolic Cantor sets
Given a $C^{1+\gamma}$ hyperbolic Cantor set $C$, we study the sequence $C_{n,x}$ of Cantor subsets which nest down toward a point $x$ in $C$. We show that $C_{n,x}$ is asymptotically equal to an ergodic Cantor set valued process. The values of this process, called limit sets, are indexed by a H\"older continuous set-v...
1994-05-31
2016-09-06
[ "math.DS" ]
Tim Bedford, Albert M. Fisher
math/9405216
The set of maps F_{a,b}: x -> x+a+{b/{2 pi}} sin(2 pi x) with any given rotation interval is contractible
Consider the two-parameter family of real analytic maps $F_{a,b}:x \mapsto x+ a+{b\over 2\pi} \sin(2\pi x)$ which are lifts of degree one endomorphisms of the circle. The purpose of this paper is to provide a proof that for any closed interval $I$, the set of maps $F_{a,b}$ whose rotation interval is $I$, form a contra...
1994-05-14
2016-09-06
[ "math.DS" ]
Adam Epstein, Linda Keen, Charles Tresser
math/9404238
A toral diffeomorphism with a non-polygonal rotation set
We construct a diffeomorphism of the two-dimensional torus which is isotopic to the identity and whose rotation set is not a polygon.
1994-04-26
2009-10-28
[ "math.DS" ]
Jaroslaw Kwapisz
math/9404237
Iterations of rational functions: which hyperbolic components contain polynomials?
Let $H^d$ be the set of all rational maps of degree $d\ge 2$ on the Riemann sphere which are expanding on Julia set. We prove that if $f\in H^d$ and all or all but one critical points (or values) are in the immediate basin of attraction to an attracting fixed point then there exists a polynomial in the component $H(f)$...
1994-04-09
2016-09-06
[ "math.DS" ]
Feliks Przytycki
math/9404235
Dynamical zeta functions for maps of the interval
A dynamical zeta function $\zeta$ and a transfer operator $\scr L$ are associated with a piecewise monotone map $f$ of the interval $[0,1]$ and a weight function $g$. The analytic properties of $\zeta$ and the spectral properties of $\scr L$ are related by a theorem of Baladi and Keller under an assumption of ``generat...
1994-04-01
2008-02-03
[ "math.DS" ]
David Ruelle
math/9403222
Hausdorff dimension and Kleinian groups
Let G be a non-elementary, finitely generated Kleinian group, Lambda(G) its limit set and Omega(G) = S \ Lambda(G) (S = the sphere) its set of discontinuity. Let delta(G) be the critical exponent for the Poincar\'e series and let Lambda_c be the conical limit set of G. Suppose Omega_0 is a simply connected component of...
1994-03-22
2016-09-06
[ "math.DS" ]
Christopher J. Bishop, Peter Jones
math/9403221
Inducing, slopes, and conjugacy classes
We show that the conjugacy class of an eventually expanding continuous piecewise affine interval map is contained in a smooth codimension 1 submanifold of parameter space. In particular conjugacy classes have empty interior. This is based on a study of the relation between induced Markov maps and ergodic theoretical be...
1994-03-05
2008-02-03
[ "math.DS" ]
Roza Galeeva, Marco Martens, Charles Tresser
math/9402215
Polynomial maps with a Julia set of positive measure
In this paper we shall show that there exists L_0 such that for each even integer L >= L_0 there exists $c_1 \in \rz$ for which the Julia set of $z --> z^L + c_1$ has positive Lebesgue measure. This solves an old problem. Editor's note: In 1997, it was shown by Xavier Buff that there was a serious flaw in the argumen...
1994-02-16
2009-09-25
[ "math.DS" ]
Tomasz Nowicki, Sebastian van Strien
math/9401225
Absorbing Cantor sets in dynamical systems: Fibonacci maps
In this paper we shall show that there exists a polynomial unimodal map f: [0,1] -> [0,1] which is 1) non-renormalizable(therefore for each x from a residual set, $\omega(x)$ is equal to an interval), 2) for which $\omega(c)$ is a Cantor set, and 3) for which $\omega(x)=\omega(c)$ for Lebesgue almost all x. So ...
1994-01-29
2008-02-03
[ "math.DS" ]
Henk Bruin, Gerhard Keller, Tomasz Nowicki, Sebastian van Strien
math/9401224
Henon mappings in the complex domain II: projective and inductive limits of polynomials
Let H: C^2 -> C^2 be the Henon mapping given by (x,y) --> (p(x) - ay,x). The key invariant subsets are K_+/-, the sets of points with bounded forward images, J_+/- = the boundary of K_+/-, J = the union of J_+ and J_-, and K = the union of K_+ and K_-. In this paper we identify the topological structure of these sets w...
1994-01-12
2016-09-06
[ "math.DS" ]
John Hubbard, Ralph W. Oberste-Vorth
math/9412219
The Mazur Intersection Property and Farthest Points
K.\ S.\ Lau had shown that a reflexive Banach space has the Mazur Intersection Property (MIP) if and only if every closed bounded convex set is the closed convex hull of its farthest points. In this work, we show that in general this latter property is equivalent to a property stronger than the MIP. As corollaries, w...
1994-12-22
2016-09-06
[ "math.FA" ]
Pradipta Bandyopadhyay
math/9412214
The Hardy Operator and Boyd Indices
We give necessary and sufficient conditions for the Hardy operator to be bounded on a rearrangement invariant quasi-Banach space in terms of its Boyd indices.
1994-12-19
2008-02-03
[ "math.FA" ]
Stephen J. Montgomery-Smith
math/9412216
Extremal properties of contraction semigroups on $c_o$
For any complex Banach space $X$, let $J$ denote the duality mapping of $X$. For any unit vector $x$ in $X$ and any ($C_0$) contraction semigroup $(T_t)_{t>0}$ on $X$, Baillon and Guerre-Delabriere proved that if $X$ is a smooth reflexive Banach space and if there is $x^* \in J(x)$ such that $|\langle T(t) \, x,J(x)\ra...
1994-12-19
2016-09-06
[ "math.FA" ]
P. K. Lin
math/9412217
Extension of Operators from Weak$^*$-closed Subspaces of $\ell_1$
It is proved that every operator from a weak$^*$-closed subspace of $\ell_1$ into a space $C(K)$ of continuous functions on a compact Hausdorff space $K$ can be extended to an operator from $\ell_1$ to $C(K)$.
1994-12-19
2009-09-25
[ "math.FA" ]
William B. Johnson, M. Zippin
math/9412218
Best constants for uncentered maximal functions
We precisely evaluate the operator norm of the uncentered Hardy-Littlewood maximal function on $L^p(\Bbb R^1)$. We also compute the operator norm of the uncentered Hardy-Littlewood maximal function over rectangles on $L^p(\Bbb R^n)$, and we show that the operator norm of the uncentered Hardy-Littlewood maximal function...
1994-12-19
2008-02-03
[ "math.FA" ]
L. Grafakos, Stephen J. Montgomery-Smith
math/9412215
Boyd Indices of Orlicz-Lorentz Space
Orlicz-Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. In this paper, we investigate their Boyd indices. Bounds on the Boyd indices in terms of the Matuszewska-Orlicz indices of the defining functions are given. Also, we give an example to show that the Boyd indices and Zippin indice...
1994-12-19
2008-02-03
[ "math.FA" ]
Stephen J. Montgomery-Smith
math/9412212
An elementary approach to the Daugavet equation
Let $T\dopu C(S)\to C(S)$ be a bounded linear operator. We present a necessary and sufficient condition for the so-called Daugavet equation $$ \|\Id+T\| = 1+\|T\| $$ to hold, and we apply it to weakly compact operators and to operators factoring through $c_{0}$. Thus we obtain very simple proofs of results by Foias, Si...
1994-12-12
2011-03-17
[ "math.FA" ]
Dirk Werner
math/9412213
Extreme contractions in ${\cal L}(\ell^p_2, \ell^q_2)$ and the mazur intersection property in $\ell^p_2 \otimes_{\p} \ell^q_2$
In this paper, we show that the projective tensor product of a two-dimen\-sional $\ell^p$ space with a two-dimensional $\ell^q$ space never has the Mazur Intersection Property for a large range of values of $p$ and $q$. For this purpose, we characterise the extreme contractions from $\ell^p_2$ to $\ell^q_2$ and obtain ...
1994-12-12
2016-09-06
[ "math.FA" ]
Pradipta Bandyopadhyay, A. K. Roy
math/9412211
On Convergence of Conditional Expectation Operators
Given an operator $T:U_X(\Sigma)\to Y$ or ${T:U(\Sigma)\to Y$, one may consider the net of conditional expectation operators $(T_\pi)$ directed by refinement of the partitions $\pi$. It has been shown previously that $(T_\pi)$ does not always converge to $T$. This paper gives several conditions under which this converg...
1994-12-05
2016-09-06
[ "math.FA" ]
C. Bryan Dawson
math/9411210
Isometries of Hilbert space valued function spaces
Let $X$ be a (real or complex) rearrangement-in\-va\-riant function space on $\Om$ (where $\Om = [0,1]$ or $\Om \subseteq \bbN$) whose norm is not proportional to the $L_2$-norm. Let $H$ be a separable Hilbert space. We characterize surjective isometries of $X(H).$ We prove that if $T$ is such an isometry then there ex...
1994-11-16
2016-09-06
[ "math.FA" ]
Beata Randrianantoanina
math/9410205
Pelczynski's property (V) on spaces of vector valued functions
Let $E$ be a separable Banach space and $\Omega$ be a compact Hausdorff space. It is shown that the space $C(\Omega,E)$ has property (V) if and only if $E$ does. Similar result is also given for Bochner spaces $L^p(\mu,E)$ if $1<p<\infty$ and $\mu$ is a finite Borel measure on $\Omega$.
1994-10-31
2016-09-06
[ "math.FA" ]
Narcisse Randrianantoanina
math/9410203
Nowhere Weak Differentiability of the Pettis Integral
For an arbitrary infinite-dimensional Banach space $\X$, we construct examples of strongly-measurable $\X$-valued Pettis integrable functions whose indefinite Pettis integrals are nowhere weakly differentiable; thus, for these functions the Lebesgue Differentiation Theorem fails rather spectacularly. We also relate the...
1994-10-31
2008-02-03
[ "math.FA" ]
Stephen J. Dilworth, Maria Girardi
math/9410204
Complemented copies of $\ell^1$ and Pelczynski's property (V*) in Bochner function spaces
Let $X$ be a Banach space and $(f_n)_n$ be a bounded sequence in $L^1(X)$. We prove a complemented version of the celebrated Talagrand's dichotomy i.e we show that if $(e_n)_n$ denotes the unit vector basis of $c_0$, there exists a sequence $g_n \in \text{conv}(f_n,f_{n+1},\dots)$ such that for almost every $\omega$, e...
1994-10-31
2016-09-06
[ "math.FA" ]
Narcisse Randrianantoanina
math/9408208
Isomorphic classification of atomic weak L^p spaces
Let $\msp$ be a measure space and let $1 < p < \infty$. The {\em weak $L^p$}\/ space $\wlp$ consists of all measurable functions $f$ such that \[ \|f\| = \sup_{t>0}t^{\frac{1}{p}}f^*(t) < \infty,\] where $f^*$ is the decreasing rearrangement of $|f|$. It is a Banach space under a norm which is equivalent to the exp...
1994-08-24
2009-09-25
[ "math.FA" ]
Denny H. Leung
math/9408206
The existence of primitives for continuous functions in a quasi-Banach space
We show that if $X$ is a quasi-Banach space with trivial dual then every continuous function $f:[0,1]\to X$ has a primitive, answering a question of M.M. Popov.
1994-08-24
2008-02-03
[ "math.FA" ]
Nigel J. Kalton
math/9408207
Unconditional bases and unconditional finite-dimensional decompositions in Banach spaces
Let $X$ be a Banach space with an unconditional finite-dimensional Schauder decomposition $(E_n)$. We consider the general problem of characterizing conditions under which one can construct an unconditional basis for $X$ by forming an unconditional basis for each $E_n.$ For example, we show that if $\sup \dim E_n<\inft...
1994-08-24
2009-09-25
[ "math.FA" ]
Peter G. Casazza, Nigel J. Kalton
math/9408205
The basic sequence problem
We construct a quasi-Banach space $X$ which contains no basic sequence.
1994-08-16
2008-02-03
[ "math.FA" ]
Nigel J. Kalton
math/9407210
Examples of asymptotically \ell_^1 Banach spaces
Two examples of asymptotic $\ell_{1}$ Banach spaces are given. The first, $X_{u}$, has an unconditional basis and is arbitrarily distortable. The second, $X$, does not contain any unconditional basic sequence. Both are spaces of the type of Tsirelson. We thus answer a question raised by W.T.Gowers.
1994-07-22
2016-09-06
[ "math.FA" ]
Spiros A. Argyros, Irene Deliyanni
math/9407209
Banach spaces with small spaces of operators
For a certain class of algebras $\cal A$ we give a method for constructing Banach spaces $X$ such that every operator on $X$ is close to an operator in $\cal A$. This is used to produce spaces with a small amount of structure. We present several applications. Amongst them are constructions of a new prime Banach space, ...
1994-07-20
2008-09-01
[ "math.FA" ]
W. T. Gowers, B. Maurey
math/9407215
Closed ideals of the algebra of absolutely convergent Taylor series
Let $\Gamma$ be the unit circle, $A(\Gamma)$ the Wiener algebra of continuous functions whose series of Fourier coefficients are absolutely convergent, and $A^+$ the subalgebra of $A(\Gamma)$ of functions whose negative coefficients are zero. If $I$ is a closed ideal of $A^+$, we denote by $S_I$ the greatest common div...
1994-07-01
2016-09-06
[ "math.FA", "math.CA" ]
Jean Esterle, Elizabeth Strouse, Fouad Zouakia
math/9406218
A Note on UMD Spaces and Transference in Vector-valued Function Spaces
We introduce the notion of an ACF space, that is, a space for which a generalized version of M. Riesz's theorem for conjugate functions with values in the Banach space is bounded. We use transference to prove that spaces for which the Hilbert transform is bounded, i\.e\. $X\in\text{HT}$, are ACF spaces. We then show th...
1994-06-30
2008-02-03
[ "math.FA" ]
N. Asmar, B. Kelly, Stephen J. Montgomery-Smith
math/9406217
Differences of bounded semi-continuous functions, I
Structural properties are given for $D(K)$, the Banach algebra of (complex) differences of bounded semi-continuous functons on a metric space $K$. For example, it is proved that if all finite derived sets of $K$ are non-empty, then a complex function $\varphi$ operates on $D(K)$ (i.e., $\varphi\circ f\in D(K)$ for all ...
1994-06-20
2016-09-06
[ "math.FA" ]
Haskell P. Rosenthal
math/9406211
Stability and Dichotomy of Positive Semigroups on $L_p$
A new proof of a result of Lutz Weis is given, that states that the stability of a positive strongly continuous semigroup $(e^{tA})_{t \ge 0}$ on $L_p$ may be determined by the quantity $s(A)$. We also give an example to show that the dichotomy of the semigroup may not always be determined by the spectrum $\sigma(A)$.
1994-06-07
2008-02-03
[ "math.FA" ]
Stephen J. Montgomery-Smith
math/9406215
The Uniform Classification of Banach Spaces
This is a survey of results on the classification of Banach spaces as metric spaces. It is based on a series of lectures I gave at the Functional Analysis Seminar in 1984-1985, and it appeared in the 1984-1985 issue of the Longhorn Notes. I keep receiving requests for copies, because some of the material here does not ...
1994-06-07
2016-09-06
[ "math.FA" ]
Yoav Benyamini
math/9406216
Constructions of Majorizing Measures, Bernoulli processes and cotype
We present three methods to construct majorizing measures in various settings. These methods are based on direct constructions of increasing sequences of partitions through a simple exhaustion procedure rather than on the construction of well separated ultrametric subspaces. The first scheme of construction provides a ...
1994-06-07
2009-09-25
[ "math.FA" ]
Michel Talagrand
math/9406213
Tangent Sequences in Orlicz and Rearrangement Invariant Spaces
Let (f_n) and (g_n) be two sequences of random variables adapted to an increasing sequence of $\sigma$-algebras $({\cal F}_n)$ such that the conditional distributions of f_n and g_n given ${\cal F}_{n-1}$ coincide, and such that the sequence (g_n) is conditionally independent. Then it is known that $\normo{\sum f_k}_p ...
1994-06-07
2008-02-03
[ "math.FA" ]
Pawel Hitczenko, Stephen J. Montgomery-Smith
math/9406210
A remark on contraction semigroups on Banach spaces
Let $X$ be a complex Banach space and let $J:X \to X^*$ be a duality section on $X$ (i.e. $\langle x,J(x)\rangle=\|J(x)\|\|x\|=\|J(x)\|^2=\|x\|^2$). For any unit vector $x$ and any ($C_0$) contraction semigroup $T=\{e^{tA}:t \geq 0\}$, Goldstein proved that if $X$ is a Hilbert space and if $|\langle T(t) x,J(x)\rangle|...
1994-06-06
2016-09-06
[ "math.FA" ]
P. K. Lin
math/9406209
Uniform Kadec-Klee Property in Banach lattices
We prove that a Banach lattice $X$ which does not contain the $l^n_{\infty}$-uniformly has an equivalent norm which is uniformly Kadec-Klee for a natural topology $\tau$ on $X$. In case the Banach lattice is purely atomic, the topology $\tau$ is the coordinatewise convergence topology.
1994-06-06
2009-09-25
[ "math.FA" ]
Fouad Chaatit, M. Khamsi
math/9405211
Some properties of space of compact operators
Let $X$ be a separable Banach space, $Y$ be a Banach space and $\Lambda$ be a subset of the dual group of a given compact metrizable abelian group. We prove that if $X^*$ and $Y$ have the type I-$\Lambda$-RNP (resp. type II-$\Lambda$-RNP) then $K(X,Y)$ has the type I-$\Lambda$-RNP (resp. type II-$\Lambda$-RNP) provided...
1994-05-24
2016-09-06
[ "math.FA" ]
Narcisse Randrianantoanina
math/9405210
Complex interpolation and complementably minimal spaces
We construct a class of super-reflexive complementably minimal spaces, and study uniformly convex distortions of the norm on Hilbert space by using methods of complex interpolation.
1994-05-17
2009-09-25
[ "math.FA" ]
Peter G. Casazza, Nigel J. Kalton, Denka Kutzarova, M. Mastylo
math/9405209
The subspace problem for weighted inductive limits of spaces of holomorphic functions
We construct a countable inductive limit of weighted Banach spaces of holomorphic functions, which is not a topological subspace of the corresponding weighted inductive limit of spaces of continuous functions. The main step of our construction, using a special sequence of outer holomorphic functions, shows that a certa...
1994-05-11
2016-09-06
[ "math.FA" ]
J. Bonet, Jari Taskinen
math/9404216
Unconditionally converging polynomials on Banach spaces
We prove that weakly unconditionally Cauchy (w.u.C.) series and unconditionally converging (u.c.) series are preserved under the action of polynomials or holomorphic functions on Banach spaces, with natural restrictions in the latter case. Thus it is natural to introduce the unconditionally converging polynomials, defi...
1994-04-25
2015-06-26
[ "math.FA" ]
Manuel Gonzalez, Joaquin M. Gutierrez
math/9404215
When every polynomial is unconditionally converging
Letting $E$, $F$ be Banach spaces, the main two results of this paper are the following: (1) If every (linear bounded) operator $E\rightarrow F$ is unconditionally converging, then every polynomial from $E$ to $F$ is unconditionally converging (definition as in the linear case). (2) If $E$ has the Dunford-Pettis proper...
1994-04-25
2016-09-06
[ "math.FA" ]
Manuel Gonzalez, Joaquin M. Gutierrez