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1.
Stadia are popular models of chaotic billiards introduced by Bunimovich in 1974. They are analogous to dispersing billiards
due to Sinai, but their fundamental technical characteristics are quite different. Recently many new results were obtained
for various chaotic billiards, including sharp bounds on correlations and probabilistic limit theorems, and these results
require new, more powerful technical apparatus. We present that apparatus here, in the context of stadia, and prove “regularity”
properties.
相似文献
2.
Sylvia Chiang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,151(1):940-959
We study the pressureless gas equations, with piecewise constant initial data. In the immediate solution, δ-shocks and contact
vacuum states arise and even meet (interact) eventually. A solution beyond the “interaction” is constructed. It shows that
the δ-shock will continue with the velocity it attained instantaneously before the time of interaction, and similarly, the
contact vacuum state will move past the δ-shock with a velocity value prior to the interaction. We call this the “no-effect-from-interaction”
solution.
We prove that this solution satisfies a family of convex entropies (in the Lax’s sense). Next, we construct an infinitely
large family of weak solutions to the “interaction”. Suppose further that any of these solutions satisfy a convex entropy,
it is necessary and suffcient that these solutions reduce to only the “no-effect-from-interaction” solution. In [1], Bouchut
constructed another entropy satisfying solution. As with other previous papers, it is obvious that it will not be sufficient
that a “correct” solution satisfies a convex entropy, in a non-strictly hyperbolic conservation laws system. 相似文献
3.
Sylvia Chiang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(6):940-959
We study the pressureless gas equations, with piecewise constant initial data. In the immediate solution, δ-shocks and contact
vacuum states arise and even meet (interact) eventually. A solution beyond the “interaction” is constructed. It shows that
the δ-shock will continue with the velocity it attained instantaneously before the time of interaction, and similarly, the
contact vacuum state will move past the δ-shock with a velocity value prior to the interaction. We call this the “no-effect-from-interaction”
solution.
We prove that this solution satisfies a family of convex entropies (in the Lax’s sense). Next, we construct an infinitely
large family of weak solutions to the “interaction”. Suppose further that any of these solutions satisfy a convex entropy,
it is necessary and suffcient that these solutions reduce to only the “no-effect-from-interaction” solution. In [1], Bouchut
constructed another entropy satisfying solution. As with other previous papers, it is obvious that it will not be sufficient
that a “correct” solution satisfies a convex entropy, in a non-strictly hyperbolic conservation laws system.
Research done in the University of Michigan-Ann Arbor, submission from Temasek Laboratories, National University of Singapore. 相似文献
4.
Aviad Heifetz 《International Journal of Game Theory》1999,28(3):435-442
Aumann (1989) argued that the natural partitions on the space of all maximally consistent sets of formulas in multi-player
S5 logic are necessarily “commonly known” by the players. We show, however, that there are many other sets of partitions on
this space that conform with the formulas that build the states – as many as there are subsets of the continuum! Thus, assuming
a set of partitions on this space is “common knowledge” is an informal but meaningful meta-assumption. 相似文献
5.
We prove exponential decay of correlations for a “reasonable” class of multi-dimensional dispersing billiards. The scatterers
are required to be C
3 smooth, the horizon is finite, there are no corner points. In addition, we assume subexponential complexity of the singularity
set.
Submitted: November 10, 2007. Accepted: May 23, 2008. 相似文献
6.
We construct an asymptotics of the solution the Laplace equation in a “long” rectangle with the directional derivative given
on its “long sides” and Dirichlet data on its “short sides.” By using the asymptotics, we calculate one of the integral characteristics,
namely, the magnetoresistance. We obtain new formulas for the low-magnetic field magnetoresistance.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 520–532, April, 1999. 相似文献
7.
A new quantitative definition of the “power index” is proposed for a voter in weighted voting systems (WV-schemes), where
the voters a priori do not have equal rights. The proposed “power index” is generated in a self-consistent manner from information
about the number of times that a voter enters any winning coalition in the WV-scheme. Explicit formulas are derived for computing
the “power index”. The discussion is illustrated with prototype examples.
__________
Translated from Prikladnaya Matematika i Informatika, No. 25, pp. 81–98, 2007. 相似文献
8.
Jing Hai Shao 《数学学报(英文版)》2011,27(6):1195-1204
In this paper, the dimensional-free Harnack inequalities are established on infinite-dimensional spaces. More precisely, we
establish Harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhlenbeck semigroup on the abstract
Wiener space. As an application, we establish the HWI inequality on the abstract Wiener space, which contains three important
quantities in one inequality, the relative entropy “H”, Wasserstein distance “W”, and Fisher information “I”. 相似文献
9.
Various statistics on wreath products are defined via canonical words, “colored” right to left minima and “colored” descents.
It is shown that refined counts with respect to these statistics have nice recurrence formulas of binomial-Stirling type.
These extended Stirling numbers determine (via matrix inversion) dual systems, which are also shown to have combinatorial
realizations within the wreath product. The above setting also gives rise to a MacMahon-type equi-distribution theorem over
subsets with prescribed statistics.
Partially supported by Minerva Grant No. 8441 and by EC's IHRP Programme, within the Research Training Network “Algebraic
Combinatorics in Europe”, grant HPRN-CT-2001-00272.
Partially supported by EC's IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe”, grant
HPRN-CT-2001-00272. 相似文献
10.
Dror Bar-Natan Stavros Garoufalidis Lev Rozansky Dylan P. Thurston 《Israel Journal of Mathematics》2000,119(1):217-237
We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured
independently by Deligne [De]) for the relation between the two natural products on the space of uni-trivalent diagrams. The
two formulas use the related notions of “Wheels” and “Wheeing”. We prove these formulas ‘on the level of Lie algebras’ using
standard techniques from the theory of Vassiliev invariants and the theory of Lie algebras. In a brief epilogue we report
on recent proofs of our full conjectures, by Kontsevich [Ko2] and by DBN, DPT, and T. Q. T. Le, [BLT].
This paper is available electronically 相似文献
11.
Adam B. Levy 《Journal of Optimization Theory and Applications》2012,153(3):633-649
We introduce and study decompositions of finite sets as well as coverings of their convex hulls, and use these objects to
develop various estimates of and formulas for the “hull-volume” of the sets (i.e., the volume of their convex hull). We apply
our results to the convergence analysis of the “iterate-sets” associated with each iteration of a reduce-or-retreat optimization
method (including pattern-search methods like Nelder–Mead as well as model-based methods). 相似文献
12.
In this paper, we give a new construction of the adapted complex structure on a neighborhood of the zero section in the tangent bundle of a compact, real-analytic Riemannian manifold. Motivated by
the “complexifier” approach of T. Thiemann as well as certain formulas of V. Guillemin and M. Stenzel, we obtain the polarization
associated to the adapted complex structure by applying the “imaginary-time geodesic flow” to the vertical polarization. Meanwhile,
at the level of functions, we show that every holomorphic function is obtained from a function that is constant along the
fibers by “composition with the imaginary-time geodesic flow.” We give several equivalent interpretations of this composition,
including a convergent power series in the vector field generating the geodesic flow. 相似文献
13.
G. E. Mints 《Journal of Mathematical Sciences》1997,87(1):3234-3252
The method of epsilon substitution was defined for arithmetic with interpretation of αxA(x) as the least x satisfying A(x).
It proceeds by a series of finite approximations “from below” to a solution of a fixed system of critical formulas. For the
predicate logic only approach “from above” similar to cut-elimination was available. We present a definition of epsilon substitution
for the predicate logic, prove the termination of the substitution process, and derive the corresponding Herbrand-type theorem.
Bibliography: 18 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 220, 1995, pp. 93–122.
Translated by G. E. Mints. 相似文献
14.
Jacob Feldman 《Israel Journal of Mathematics》1980,36(3-4):321-345
A new approach is given to the entropy of a probability-preserving group action (in the context ofZ and ofR
n
), by defining an approximate “r-entropy”, 0<r<1, and lettingr → 0. If the usual entropy may be described as the growth rate of the number of essential names, then ther-entropy is the growth rate of the number of essential “groups of names” of width≦r, in an appropriate sense. The approach is especially useful for actions of continuous groups. We apply these techniques to
state and prove a “second order” equipartition theorem forZ
m
×R
n
and to give a “natural” proof of Ornstein’s isomorphism theorem for Bernoulli actions ofZ
m
×R
n
, as well as a characterization of such actions which seems to be the appropriate generalization of “finitely determined”. 相似文献
15.
Denis S. Krotov 《Designs, Codes and Cryptography》2011,61(3):315-329
A vertex coloring of a graph is called “perfect” if for any two colors a and b, the number of the color-b neighbors of a color-a vertex x does not depend on the choice of x, that is, depends only on a and b (the corresponding partition of the vertex set is known as “equitable”). A set of vertices is called “completely regular”
if the coloring according to the distance from this set is perfect. By the “weight distribution” of some coloring with respect
to some set we mean the information about the number of vertices of every color at every distance from the set. We study the
weight distribution of a perfect coloring (equitable partition) of a graph with respect to a completely regular set (in particular,
with respect to a vertex if the graph is distance-regular). We show how to compute this distribution by the knowledge of the
color composition over the set. For some partial cases of completely regular sets, we derive explicit formulas of weight distributions.
Since any (other) completely regular set itself generates a perfect coloring, this gives universal formulas for calculating
the weight distribution of any completely regular set from its parameters. In the case of Hamming graphs, we prove a very
simple formula for the weight enumerator of an arbitrary perfect coloring. 相似文献
16.
Bruce R. Ebanks 《Central European Journal of Mathematics》2010,8(3):602-615
We present an axiomatic characterization of entropies with properties of branching, continuity, and weighted additivity. We
deliberately do not assume that the entropies are symmetric. The resulting entropies are generalizations of the entropies
of degree α, including the Shannon entropy as the case α = 1. Such “weighted” entropies have potential applications to the “utility of gambling” problem. 相似文献
17.
The combined quasineutral and relaxation time limit for a bipolar hydrodynamic model is considered. The resulting limit problem
is a nonlinear diffusion equation describing a neutral fluid. We make use of various entropy functions and the related entropy
productions in order to obtain strong enough uniform bounds. The necessary strong convergence of the densities is obtained
by using a generalized version of the “div-curl” Lemma and monotonicity methods. 相似文献
18.
E. A. Timofeev 《Journal of Mathematical Sciences》2011,176(2):255-269
We consider the problem of nonparametric entropy (entropy rate) estimation. We study the technique of nonparametric entropy
estimation based on the so-called “nearest neighbor distances” and obtain a closed-form expression of the bias for Markov
measures. This bias is a discontinuous function of transition probabilities. Bibliography: 20 titles. 相似文献
19.
Entropy structure 总被引:2,自引:0,他引:2
Tomasz Downarowicz 《Journal d'Analyse Mathématique》2005,96(1):57-116
Investigating the emergence of entropy on different scales, we propose an “entropy structure” as a kind of master invariant
for the entropy theory of topological dynamical systems. An entropy structure is a sequence of functionsh
k on the simplex of invariant measures which converges to the entropy functionh and which falls into a distinguished equivalence class defined by a natural equivalence relation capturing the “type of nonuniformity
in convergence”. An entropy structure recovers several existing invariants, including the symbolic extension entropy hsex and the Misiurewicz parameter h*. Entropy theories of Misiurewicz, Katok, Brin—Katok, Newhouse, Romagnoli, Ornstein—Weiss and others all yield candidate sequences
(h
k); we determine which of these exhibit the correct type of convergence and hence become entropy structures. One of the satisfactory
sequences arises from a new treatment of entropy theory strictly in terms of continuous functions (in place of partitions
or covers). The results allow the computation of symbolic extension entropy without reference to zero dimensional extensions.
New light is shed on the property of asymptotich-expansiveness.
Supported by the KBN grant 2 P03 A 04622. 相似文献
20.
V. P. Maslov 《Theoretical and Mathematical Physics》2000,125(2):1552-1567
We develop the theory of averaging the operators in a Fock space, introduced in our previous papers. We find the algebra of
mean operators. We introduce the quantum entropy and quantum free energy using the function f(z)=zlog(z) of the mean unit
operator (the “measure” of mean operators). Such a “quantum thermodynamics” determines the temperature dependence of the critical
speed (“the Landau criterion”) and the temperature distribution at which the speed of a superfluid system is nonzero even
at zero temperature. We generalize the consideration to the case where sparsely distributed bosons form clusters.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 2, pp. 297–314, November, 2000. 相似文献