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51.
Annalisa Baldi 《Journal of Mathematical Analysis and Applications》2008,340(1):197-208
In this note, a classical extension result for BV functions due to Yu.D. Burago and V.G. Maz'ja [Yu.D. Burago, V.G. Maz'ja, Potential Theory and Function Theory for Irregular Regions, Seminars in Math., vol. 3, V.A. Steklov Math. Inst., Leningrad, 1969 (translated from Russian)] is generalized to the abstract setting of doubling metric measure spaces endowed with a differentiation structure called D-structure. 相似文献
52.
Read-once functions have gained recent, renewed interest in the fields of theory and algorithms of Boolean functions, computational learning theory and logic design and verification. In an earlier paper [M.C. Golumbic, A. Mintz, U. Rotics, Factoring and recognition of read-once functions using cographs and normality, and the readability of functions associated with partial k-trees, Discrete Appl. Math. 154 (2006) 1465-1677], we presented the first polynomial-time algorithm for recognizing and factoring read-once functions, based on a classical characterization theorem of Gurvich which states that a positive Boolean function is read-once if and only if it is normal and its co-occurrence graph is P4-free.In this note, we improve the complexity bound by showing that the method can be modified slightly, with two crucial observations, to obtain an O(n|f|) implementation, where |f| denotes the length of the DNF expression of a positive Boolean function f, and n is the number of variables in f. The previously stated bound was O(n2k), where k is the number of prime implicants of the function. In both cases, f is assumed to be given as a DNF formula consisting entirely of the prime implicants of the function. 相似文献
53.
Randomized approximation of Sobolev embeddings, III 总被引:1,自引:1,他引:0
We continue the study of randomized approximation of embeddings between Sobolev spaces on the basis of function values. The source space is a Sobolev space with nonnegative smoothness order; the target space has negative smoothness order. The optimal order of approximation (in some cases only up to logarithmic factors) is determined. Extensions to Besov and Bessel potential spaces are given and a problem recently posed by Novak and Woźniakowski is partially solved. The results are applied to the complexity analysis of weak solution of elliptic PDE. 相似文献
54.
We study Hilbert spaces expanded with a unitary operator with a countable spectrum. We show that the theory of such a structure is ω ‐stable and admits quantifier elimination. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
55.
Let X,Y be Banach spaces and M a linear manifold in X×Y={{x,y}∣x∈X,y∈Y}. The central problem which motivates many of the concepts and results of this paper is the problem of characterization and construction of all extremal solutions of a linear inclusion y∈M(x). First of all, concept of metric operator parts and metric generalized inverses for linear manifolds are introduced and investigated, and then, characterizations of the set of all extremal or least extremal solutions in terms of metric operator parts and metric generalized inverses of linear manifolds are given by the methods of geometry of Banach spaces. The principal tool in this paper is the generalized orthogonal decomposition theorem in Banach spaces. 相似文献
56.
We obtain several extensions of Talagrand’s lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential behaviour of covering numbers. The corresponding results are also proved for non-Gaussian symmetric stable processes, both for the cases of critically small and critically large entropy. The results extensively use the classical chaining technique; at the same time they are meant to explore the limits of this method. 相似文献
57.
In the framework of the theory of normal coderivative for multifunctions, new implicit function theorems are obtained. The main tools of the proofs are the Ekeland variational principle, a nonsmooth version of Fermat's rule, a sum rule, and the differential estimate for marginal functions established by B.S. Mordukhovich and Y. Shao [B.S. Mordukhovich, Y. Shao, Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc. 348 (1996) 1235-1280]. 相似文献
58.
We compute Hölder Complexes, i.e. the complete bi-Lipschitz invariants, for germs of real weighed homogeneous algebraic or semialgebraic surfaces. 相似文献
59.
We described the design and synthesis of a colorimetric and ratiometric fluorescent probe based on a conjugated π-electron system that displayed differential fluorescence responses towards cyanide and sulfide and demonstrated its utility in intracellular ion imaging and logic gate. 相似文献
60.
Inorganic nanoparticles are widely used to improve space charge behavior, DC breakdown strength and other electrical properties of polymer insulating materials, but the uniform distribution of inorganic nanofillers in matrix is difficult due to their agglomeration and bad compatibility with the polymeric matrix. In this paper, polypropylene (PP)/polystyrene (PS) blends were prepared to suppress space charge accumulation and improve DC breakdown strength. Polypropylene-g-polystyrene (PP-g-PS) graft copolymer was used as compatibilizer to improve the compatibility of PP matrix and PS filler. The evolution of microstructure of PP/PS blends were investigated by scanning electron microscope (SEM), the space charge distributions were measured by a pulsed electro-acoustic (PEA) system, and DC breakdown strength was also tested. The morphologies show that the size of PS particles reduced to 310 nm when the content of PP-g-PS graft copolymer increased to 24 wt%, and the interaction between PP matrix and PS particles enhanced. The presence of PS particles in all PP/PS blends suppressed the space charge accumulation compared to neat PP, but the DC breakdown strength in uncompatibilized blend was lower than neat PP. The increasing of content of PP-g-PS improved the DC breakdown strength with the maximum value of 408.9 kV/mm was obtained. This may attribute to excellent interface structure formed between PP matrix and PS particles. 相似文献