id large_stringlengths 9 16 | title large_stringlengths 1 382 | abstract large_stringlengths 3 6.09k | publish_date date32 | update_date date32 | categories large listlengths 1 13 | authors large_stringlengths 3 62.8k |
|---|---|---|---|---|---|---|
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 |
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