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61.
Wei-yi SU~ 《中国科学A辑(英文版)》2007,50(7):1005-1014
The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R~n and the local field K are compared,so that one may interpret the essential differences between the analyses on R~n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m<(ln 2/ln 3). 相似文献
62.
Let Top
0
be the category of topological T
0-spaces, QU
0
the category of quasi-uniform T
0-spaces, T : QU
0
→ Top
0
the usual forgetful functor and K : QU
0
→ QU
0
the bicompletion reflector with unit k : 1 → K. Any T-section F : Top
0
→ QU
0
is called K-true if KF = FTKF, and upper (lower)
K-true if KF is finer (coarser) than FTKF. The literature considers important T-sections F that enjoy all three, or just one, or none of these properties. It is known that T(K,k)F is well-pointed if and only if F is upper K-true. We prove the surprising fact that T(K,k)F is the reflection to Fix(TkF) whenever it is idempotent. We also prove a new characterization of upper K-trueness. We construct examples to set apart some natural cases. In particular we present an upper K-true F for which T(K,k)F is not idempotent, and a K-true F for which the coarsest associated T-preserving coreflector in QU
0
is not stable under K.
We dedicate this paper to the memory of Sérgio de Ornelas Salbany (1941–2005). 相似文献
63.
Alexander J. Zaslavski 《Journal of Mathematical Analysis and Applications》2007,335(2):962-973
The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions. In this paper we consider a large class of optimal control problems which is identified with a complete metric space of integrands without convexity assumptions and show that for a generic integrand the corresponding optimal control problem possesses a unique solution and this solution is Lipschitzian. 相似文献
64.
Radu Miron 《Reports on Mathematical Physics》2004,54(2):131-147
The Randers spaces RFn were introduced by R. S. Ingarden. They are considered as Finsler spaces Fn = (M, α + β) equipped with the Cartan nonlinear connection. In the present paper we define and study what we call the Ingarden spaces, I Fn, as Finsler spaces I Fn = (M, α + β) equipped with the Lorentz nonlinear connection. The spaces R Fn and I Fn are completely different. For I Fn we discuss: the variational problem, Lorentz nonlinear connection, canonical N-metrical connection and its structure equations, the Cartan 1-form ω, the electromagnetic 2-form tF and the almost symplectic 2-form 0. The formula dω = F+θ is established. It has as a consequence the generalized Maxwell equations. Finally, the almost Hermitian model of I Fn is constructed. 相似文献
65.
V. S. Klimov 《Mathematical Notes》2007,81(1-2):61-71
We study homology characteristics of critical values and extremals of Lipschitz functionals defined on bounded closed convex subsets of a reflexive space that are invariant under deformations. Sufficient conditions for the existence of a bifurcation point of a multivalued potential operator (the switch principle for the typical number of an extremal) are established. 相似文献
66.
In the present paper, we consider the problem of the optimal reconstruction of the solution of the wave equation from the approximate values of the Fourier coefficients of the function specifying the initial form of the string. For an operator defined on the weight space of vectors from l 2, we present the solution of the more general problem of reconstruction from the approximate values of the coordinates of these vectors. 相似文献
67.
68.
J. -R. Chazottes P. Collet C. Külske F. Redig 《Probability Theory and Related Fields》2007,137(1-2):201-225
We present a new and simple approach to concentration inequalities in the context of dependent random processes and random
fields. Our method is based on coupling and does not use information inequalities. In case one has a uniform control on the
coupling, one obtains exponential concentration inequalities. If such a uniform control is no more possible, then one obtains
polynomial or stretched-exponential concentration inequalities. Our abstract results apply to Gibbs random fields, both at
high and low temperatures and in particular to the low-temperature Ising model which is a concrete example of non-uniformity
of the coupling.
相似文献
69.
Wei Gang SU Huai Jie ZHONG 《数学学报(英文版)》2006,22(2):515-522
This paper introduces the concept of the generalized Riesz operators and the concept of the generalized West decomposition of a general operator which generalizes the definition of the West decomposition of Riesz operators, and proves that the following three statements are equivalent on a general Banach space:
(a) Every generalized Riesz operator has the generalized West decomposition;
(b) Every operator makes strong Stampfli theorem true; Every operator has Apostol's compact correction. 相似文献
70.
Alexander Ya. Kruger 《Set-Valued Analysis》2006,14(2):187-206
The paper continues investigations of stationarity and regularity properties of collections of sets in normed spaces. It contains
a summary of different characterizations (both primal and dual) of regularity and a list of sufficient conditions for a collection
of sets to be regular. 相似文献