共查询到20条相似文献,搜索用时 15 毫秒
1.
Mathematical Notes - It is shown that the spaces of probability measures and of idempotent probability measures on the same metrizable compact space are homeomorphic. An example is given which... 相似文献
2.
Ukrainian Mathematical Journal - We prove that the idempotent barycenter map restricted to the points with nontrivial fibers is a trivial fibration with Hilbert cube fibers whenever it is open. 相似文献
3.
P. V. Chernikov 《Mathematical Notes》2006,79(1-2):283-284
It is proved that a compact space is homotopy equivalent to a CW-complex if and only if it is an absolute neighborhood h-retract. 相似文献
4.
Giulia Cavagnari Antonio Marigonda Khai T. Nguyen Fabio S. Priuli 《Set-Valued and Variational Analysis》2018,26(3):663-691
In this paper we formulate a time-optimal control problem in the space of probability measures. The main motivation is to face situations in finite-dimensional control systems evolving deterministically where the initial position of the controlled particle is not exactly known, but can be expressed by a probability measure on \(\mathbb {R}^{d}\). We propose for this problem a generalized version of some concepts from classical control theory in finite dimensional systems (namely, target set, dynamic, minimum time function...) and formulate an Hamilton-Jacobi-Bellman equation in the space of probability measures solved by the generalized minimum time function, by extending a concept of approximate viscosity sub/superdifferential in the space of probability measures, originally introduced by Cardaliaguet-Quincampoix in Cardaliaguet and Quincampoix (Int. Game Theor. Rev. 10, 1–16, 2008). We prove also some representation results linking the classical concept to the corresponding generalized ones. The main tool used is a superposition principle, proved by Ambrosio, Gigli and Savaré in Ambrosio et al. [3], which provides a probabilistic representation of the solution of the continuity equation as a weighted superposition of absolutely continuous solutions of the characteristic system. 相似文献
5.
刘秀贵 《数学年刊A辑(中文版)》2007,(3)
令G是一Abel群,m≥2是一整数.一个型为(G,m)的Moore空间是一单连通的CW-复形X,使得■_i(X)=G(i=m),0(i≠m).这里J_i为X的第i个整系数的约化同调群.众所周知,Moore空间存在,且任何两个型为(G,n)的Moore空间有相同伦型.取G=Z_k(模k的剩余类加群).p~n(k)=S~(n-1)∪_(kl_(n-1))e~n为型为(Z_k,n-1)的Moore空间.特别地,考虑k=8,决定了Moore空间p~n(8)的一些同伦群.主要证明工具是Toda引进的复合工具-Toda积,Gray的关于从p~n(8)到n维球面S~n的pinchin映射的同伦纤维的胞腔结构,以及关于亚稳定相对同伦群π_k(X,A)的同伦切割定理,其中A为维数小于n-1的有限CW-复形,X=A∪e~n. 相似文献
6.
令G是一Abel群,m≥2是一整数.一个型为(G,m)的Moore空间是一单连通的CW-复形X,使得Hi(X)=G(i=m),0(i≠m).这里Hi为X的第i个整系数的约化同调群.众所周知, Moore空间存在,且任何两个型为(G,n)的Moore空间有相同伦型.取G=Zk(模k的剩余类加群).Pn(k)=Sn-1∪kln-1en为型为(Zk,n-1)的Moore空间.特别地,考虑k=8,决定了Moore空间Pn(8)的一些同伦群.主要证明工具是Toda引进的复合工具-Toda积,Gray的关于从Pn(8)到n维球面Sn的pinchin映射的同伦纤维的胞腔结构,以及关于亚稳定相对同伦群π(X,A)的同伦切割定理,其中A为维数小于n-1的有限CW-复形,X=A∪en. 相似文献
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The minimisation problem for a functional
is considered, where
is an ℝ
n
-valued stochastic process, defined on some filtered probability space
, and P is an admissible probability measure in the sense that it obeys (1) some uniform equivalence condition with respect to the given measure ℙ
on Γ, and (2) a finite number (possibly zero) of arbitrarily given other conditions that require the expectation (with respect
to P) of some continuous bounded function φ of
, for t
1,…,t
k
∈[0,1], to lie within some closed set. We assume that u can be formulated through finite compositions of conditional expectations and bounded continuous functions.
Under the assumption of |φ| being uniformly bounded from below and some condition on the dimension of
, the existence of a solution on hyperfinite adapted probability spaces, as well as its minimality among admissible measures
on any other adapted probability space, is proven. Also, a coarseness result for the Loeb operation is established.
The main result of this paper, however, is a “standard result”: It does not include any reference to nonstandard analysis
and can be perfectly understood without any familiarity with nonstandard analysis.
相似文献
9.
《Journal of Mathematical Analysis and Applications》2002,266(2):420-431
Sensitive dependence on initial conditions is widely understood as being the central idea of chaos. We first give sufficient conditions (both topological and ergodic) on an endomorphism to ensure the sensitivity property. Then, a strong sensitivity concept is introduced. Sufficient conditions on a transformation implying strong sensitivity are given. We also provide bounds for the strong sensitivity constant. 相似文献
10.
A. N. Baushev 《Journal of Mathematical Sciences》2002,109(6):2037-2046
Necessary and sufficient conditions are obtained for weak convergence of Borel probability distributions in a separable strictly normed Banach space with a continuous modulus of convexity. These conditions are given in terms of simultaneous convergence of the distribution functions of the norm and of all linear continuous functionals with respect to the sequence of distributions under consideration. Bibliography: 9 titles. 相似文献
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12.
重点探索了三幂等矩阵的性质.主要从矩阵乘积、线性变换和矩阵的秩等角度出发,将幂等矩阵的性质向三幂等矩阵推广,对三幂等矩阵的性质进行探究,得到了15个相关结论,并给出部分性质的详细推导过程. 相似文献
13.
于林 《应用泛函分析学报》2003,5(4):362-368
证明了B值鞅空间,pH^Sr(X)和pH^σr(X)的共轭分别是qK^Sr′(X^*)与qK^σr′(X^*),此外还讨论了pK^Sr(X)和pKr(X),pK^σr(X)和pK^ r(X)的相互嵌入关系与Banach空间的P一致光滑性和q一致凸性之间的密切联系. 相似文献
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16.
S. S. Gabriyelyan 《Journal of Theoretical Probability》2011,24(3):595-614
Let μ and ν be fixed probability measures on a filtered space \((\varOmega, \mathcal{F}, \allowbreak(\mathcal{F}_{t} )_{t\in \mathbf{R}^{+} } )\). Denote by μ T and ν T (respectively, μ T? and ν T?) the restrictions of the measures μ and ν on \(\mathcal{F}_{T} \) (respectively, on \(\mathcal{F}_{T-} \)) for a stopping time T. We find the Hahn decomposition of μ T and ν T using the Hahn decomposition of the measures μ, ν and the Hellinger process h t in the strict sense of order \(\frac{1}{2}\). The norm of the absolutely continuous component of μ T? with respect to ν T? is computed in terms of density processes and Hellinger integrals. 相似文献
17.
The idempotent graph of a ring R, denoted by I(R), is a graph whose vertices are all nontrivial idempotents of R and two distinct vertices x and y are adjacent if and only if xy = yx = 0. In this paper, we show that diam\({(I(M_n(D))) = 4}\), for all natural number \({n \geq 4}\) and diam\({(I(M_3(D))) = 5}\), where D is a division ring. We also provide some classes of rings whose idempotent graphs are connected. Moreover, the regularity, clique number and chromatic number of idempotent graphs are studied. 相似文献
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19.
If X is a Hausdorff space we construct a 2-groupoid G
2
X with the following properties. The underlying category of G
2
X is the `path groupoid" of X whose objects are the points of X and whose morphisms are equivalence classes f, g of paths f, g in X under a relation of thin relative homotopy. The groupoid of 2-morphisms of G
2
X is a quotient groupoid X / N X, where X is the groupoid whose objects are paths and whose morphisms are relative homotopy classes of homotopies between paths. N X is a normal subgroupoid of X determined by the thin relative homotopies. There is an isomorphism G
2
X(f,f) 2(X, f(0)) between the 2-endomorphism group of f and the second homotopy group of X based at the initial point of the path f. The 2-groupoids of function spaces yield a 2-groupoid enrichment of a (convenient) category of pointed spaces.We show how the 2-morphisms may be regarded as 2-tracks. We make precise how cubical diagrams inhabited by 2-tracks can be pasted. 相似文献
20.
E. Yu. Mychka 《Differential Equations》2010,46(4):502-508
In the present paper, we establish a relationship between continuous local dynamical systems and spaces of the class A
ceu(X) of the Filippov theory. We suggest a construction method for a space of the class A
ceu(X) on the basis of a locally given dynamical system and conversely, a dynamical system is constructed locally in a specific
way on the basis of a given space of the class A
ceu(X). The suggested construction method provides a homeomorphism between the space of all local dynamical systems on a locally
compact metric space X and the space A
ceu(X). The obtained results generalize the Filippov theory to locally dynamical systems. 相似文献