共查询到20条相似文献,搜索用时 15 毫秒
1.
Sophie Huczynska 《Journal of Combinatorial Theory, Series A》2009,116(4):831-843
Given a finite abelian group G (written additively), and a subset S of G, the size r(S) of the set may range between 0 and 2|S|, with the extremal values of r(S) corresponding to sum-free subsets and subgroups of G. In this paper, we consider the intermediate values which r(S) may take, particularly in the setting where G is Z/pZ under addition (p prime). We obtain various bounds and results. In the Z/pZ setting, this work may be viewed as a subset generalization of the Cauchy-Davenport Theorem. 相似文献
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Vern I. Paulsen 《Journal of Functional Analysis》2008,255(1):120-132
In these notes we develop a link between the Kadison-Singer problem and questions about certain dynamical systems. We conjecture that whether or not a given state has a unique extension is related to certain dynamical properties of the state. We prove that if any state corresponding to a minimal idempotent point extends uniquely to the von Neumann algebra of the group, then every state extends uniquely to the von Neumann algebra of the group. We prove that if any state arising in the Kadison-Singer problem has a unique extension, then the injective envelope of a C*-crossed product algebra associated with the state necessarily contains the full von Neumann algebra of the group. We prove that this latter property holds for states arising from rare ultrafilters and δ-stable ultrafilters, independent, of the group action and also for states corresponding to non-recurrent points in the corona of the group. 相似文献
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We study a dynamical system generalizing continuous iterated function systems and stochastic differential equations disturbed by Poisson noise. The main results provide us with sufficient conditions for the existence and uniqueness of an invariant measure for the considered system. Since the dynamical system is defined on an arbitrary Banach space (possibly infinite dimensional), to prove the existence of an invariant measure and its stability we make use of the lower bound technique developed by Lasota and Yorke and extended recently to infinite-dimensional spaces by Szarek. Finally, it is shown that many systems appearing in models of cell division or gene expressions are exactly as those we study. Hence we obtain their stability as well. 相似文献
6.
It is well known that infinite minimal sets for continuous functions on the interval are Cantor sets; that is, compact zero
dimensional metrizable sets without isolated points. On the other hand, it was proved in Alcaraz and Sanchis (Bifurcat Chaos
13:1665–1671, 2003) that infinite minimal sets for continuous functions on connected linearly ordered spaces enjoy the same
properties as Cantor sets except that they can fail to be metrizable. However, no examples of such subsets have been known.
In this note we construct, in ZFC, non-metrizable infinite pairwise non-homeomorphic minimal sets on compact connected linearly ordered spaces.
相似文献
7.
Fuqing Gao 《随机分析与应用》2016,34(2):258-277
In this article, we consider asymptotic behaviors for functionals of dynamical systems with small random perturbations. First, we present a deviation inequality for Gaussian approximation of dynamical systems with small random perturbations under Hölder norms and establish the moderate deviation principle and the central limit theorem for the dynamical systems by the deviation inequality. Then, applying these results to forward-backward stochastic differential equations and diffusions in small time intervals, combining the delta method in large deviations, we give a moderate deviation principle for solutions of forward-backward stochastic differential equations with small random perturbations, and obtain the central limit theorem, the moderate deviation principle and the iterated logarithm law for functionals of diffusions in small time intervals. 相似文献
8.
Arno Berger Leonid A. Bunimovich Theodore P. Hill 《Transactions of the American Mathematical Society》2005,357(1):197-219
Near a stable fixed point at 0 or , many real-valued dynamical systems follow Benford's law: under iteration of a map the proportion of values in with mantissa (base ) less than tends to for all in as , for all integer bases 1$">. In particular, the orbits under most power, exponential, and rational functions (or any successive combination thereof), follow Benford's law for almost all sufficiently large initial values. For linearly-dominated systems, convergence to Benford's distribution occurs for every , but for essentially nonlinear systems, exceptional sets may exist. Extensions to nonautonomous dynamical systems are given, and the results are applied to show that many differential equations such as , where is with F'(0)$">, also follow Benford's law. Besides generalizing many well-known results for sequences such as or the Fibonacci numbers, these findings supplement recent observations in physical experiments and numerical simulations of dynamical systems.
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The existence of solutions to a class of nonlinear problems depending on a parameter is proved using the Gaierkin method The principal difficulty is that when the parameter crosses a critical value the bound edness of the approximate solutions is no longer obvious. Applications are indicated. 相似文献
10.
《Topology and its Applications》1986,22(2):139-144
Let X be a Tychonoff space and let all subsets of cardinality ⩽τ of X be closed (and C1-embedded). Then X can be embedded as a closed subspace in a pseudocompact Tychonoff space Y such that all subsets of cardinality ⩽τ of Y are closed (and C1-embedded). As an application of this result we construct a pseudocompact connected left-separated Tychonoff space having all its subsets of cardinality ⩽τ closed and C1-embedded. 相似文献
11.
Thomas Brihaye 《Mathematical Logic Quarterly》2006,52(2):165-170
In this paper we prove that the reachability problem is BSS‐undecidable for o‐minimal dynamical systems. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(3):649-655
An adaptive controller for stabilization of unknown unstable steady states (spirals, nodes and saddles) of nonlinear dynamical systems is considered and its robustness under the changes of the location of the fixed point in the phase space is demonstrated. An analog electronic controller, based on a low-pass filter technique, is described. It can be easily switched between a stable and an unstable mode of operation for stabilizing either spirals/nodes or saddles, respectively. Numerical and experimental results for two autonomous systems, the damped Duffing–Holmes oscillator and the chaotic Lorenz system, are presented. 相似文献
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This is a survey article dedicated to the study of
topological quantities in theory of normal metals discovered in
the works of the authors during the last years. Our results are
based on the theory of dynamical systems on Fermi surfaces. The
physical foundations of this theory (the so-called Geometric
Strong Magnetic Field Limit) were found by the school of I. M.
Lifshitz many years ago. Here the new aspects in the topology of
quasiperiodic functions are developed.Dedicated to IMPA on the occasion of its 50th anniversaryThe work of S. P. Novikov is partially supported by the
NSF Grant DMS 0072700. 相似文献
14.
The existence of pullback exponential attractors for nonautonomous dynamical system and applications to nonautonomous reaction diffusion equations
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First we establish some sufficient conditions for the existence of pullback exponential attractors by using $\omega-$limit compactness in the framework of process. Then we provide a new method to prove the existence of pullback exponential attractors. As a simple application, we prove the existence of pullback exponential attractors for nonautonomous reaction diffusion equations in $H_0^1$. 相似文献
15.
P. Diamond P. Kloeden V. Kozyakin A. Pokrovskii 《Proceedings of the American Mathematical Society》1998,126(7):2169-2174
We estimate the probability of replicating the asymptotic behaviour of a dynamical system generated by a monotonic mapping for randomly centered roundoff lattices.
16.
A topological space X whose topology is the order topology of some linear ordering on X, is called an interval space. A space in which every closed subspace is homeomorphic to a clopen subspace, is called a CO space. We regard linear orderings as topological spaces, by equipping them with their order topology. If L and K are linear orderings, then L
*, L+K, L·K denote respectively the reverse orderings of L, the ordered sum of L and K and the lexicographic order on L×K (so ·2=+ and 2·=). Ordinals are considered as linear orderings, and cardinals are initial ordinals. For cardinals , 0, let L(, )= + 1 +
* . Main theorem. Let X be a compact interval space. Then X is a CO space if and only if X is homeomorphic to a space of the form + 1 +
i
L(
i
,
i
), where is any ordinal, n, for every ii, i are regular cardinals and
i
i, and if n>0, then max({
i: i}) · . This first part is devoted to show the following result. Theorem: If X is a compact interval CO space, then X is a scattered space (that means that every subspace of X has an isolated point).Supported by the Université Claude-Bernard (Lyon-1), the Ben Gurion University of the Negev, and the C.N.R.S.: UPR 9016Supported by the City of Lyon 相似文献
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A topological spaceX whose topology is the order topology of some linear ordering onX, is called aninterval space. A space in which every closed subspace is homeomorphic to a clopen subspace, is called aCO space and a space isscattered if every non-empty subspace has an isolated point. We regard linear orderings as topological spaces, by equipping them with their order topology. IfL andK are linear orderings, thenL
*, L+K, L · K denote respectively the reverse ordering ofL, the ordered sum ofL andK and the lexicographic order onL x K (so · 2=+). Ordinals are considered as linear orderings, and cardinals are initial ordinals. For cardinals , l 0, letL(K,)=K+1+*.Theorem: Let X be a compact interval scattered space. Then X is a CO space if and only if X is homeomorphic to a space of the form +1+1
L(K
i
i), where is any ordinal, n , for every ii ,i are regular cardinals and Kii, and if n>0, then max({Ki:i相似文献
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Maria Letizia Bertotti 《Journal of Differential Equations》2010,249(11):2757-2770
In this paper we discuss and analyze a two-parameter family of systems of quadratic ordinary differential equations of interest in applied sciences, whose dynamics exhibits an emerging cluster structure. 相似文献