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101.
We show that the existence of a non-metrizable compact subspace of a topological group G often implies that G contains an uncountable supersequence (a copy of the one-point compactification of an uncountable discrete space). The existence of uncountable supersequences in a topological group has a strong impact on bounded subsets of the group. For example, if a topological group G contains an uncountable supersequence and K is a closed bounded subset of G which does not contain uncountable supersequences, then any subset A of K is bounded in G?(K?A). We also show that every precompact Abelian topological group H can be embedded as a closed subgroup into a precompact Abelian topological group G such that H is bounded in G and all bounded subsets of the quotient group G/H are finite. This complements Ursul's result on closed embeddings of precompact groups to pseudocompact groups. 相似文献
102.
We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations. 相似文献
103.
We introduce triplet spaces for symmetric relations with defect index (1, 1) in a Pontryagin space. Representations of Pontryagin spaces by spaces of vector-valued analytic functions are investigated. These concepts are used to study 2×2-matrix valued analytic functions which satisfy a certain kernel condition. 相似文献
104.
Wojciech Bocian Jarosław Jaźwínski Lech Stefaniak Graham A. Webb 《Chemistry of Heterocyclic Compounds》1995,31(9):1103-1107
1H,13C,14N and15N NMR measurements are reported for four mesoionic 1-oxa-2, 3, 4-triazoles containing exocyclic nitrogenous groups. The NMR signal assignments are discussed and compared with those previously published for some corresponding oxatriazoles. The results obtained support the proposed cyclic mesoionic structures for the compounds studied. The questions of possible charge delocalization and valence tautomerism are addressed. Compound with N– H as a exocyclic group (Fig. 1) is found to be relatively unstable, this is attributed to proton migration in the corresponding non-cyclic form of this molecule.Published in Khimiya Geterotsikiicheskikh Soedinenii, No. 9, pp. 1260–1263, September, 1995. 相似文献
105.
Li-Chien Lin 《Optics Communications》2006,258(2):144-154
We examine perfect recovery in the optical encryption system based on joint transform correlator architecture, which requires the key mask to be space-limited and phase-only in the frequency domain. Accordingly, a discrete sinc function interpolation is used to generate a binary phase difference mask for image encryption and decryption. Furthermore, the optimal binary phase difference mask is derived from the interpolation process best approximating the ideal sinc function interpolation. The simulation results confirm better recovery of the decrypted image for applying the proposed key masks to the optical encryption system. Especially, the optimal binary phase difference mask significantly enhances the recovery performance. 相似文献
106.
Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints
Pham 《Applied Mathematics and Optimization》2002,46(1):55-78
Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility
and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as
a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value
function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a
stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear
equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation.
This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate
our results with several examples of stochastic volatility models popular in the financial literature. 相似文献
107.
Sergio Albeverio Volodymyr Koshmanenko Mykola Pratsiovytyi Grygoriy Torbin 《Positivity》2006,10(1):39-49
We introduce the conflict interaction with two positions between a couple of image probability measures and consider the associated
dynamical system. We prove the existence of invariant limiting measures and find the criteria for these measures to be a pure
point, absolutely continuous, or singular cotinuous as well as to have any topological type and arbitary Hausdorff dimension. 相似文献
108.
L. Sauguet B. Ameduri B. Boutevin 《Journal of polymer science. Part A, Polymer chemistry》2006,44(15):4566-4578
The radical terpolymerization of 8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene with vinylidene fluoride (VDF) and perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride is presented. Changing the feed compositions of these three fluorinated comonomers enabled us to obtain different random‐type poly[vinylidene fluoride‐ter‐perfluoro(4‐methyl‐3,6‐dioxaoct‐7‐ene) sulfonyl fluoride‐ter‐8‐bromo‐1H,1H,2H‐perfluorooct‐1‐ene] terpolymers containing various sulfonyl fluoride and brominated side groups. Yields higher than 70% were reached in all cases. The hydrolysis of the sulfonyl fluoride group into the ? SO3Li function in the presence of lithium carbonate was quantitatively achieved without the content of VDF being affected, and so dehydrofluorination of the VDF base unit was avoided. These original terpolymers were then crosslinked via dangling bromine atoms in the presence of a peroxide/triallyl isocyanurate system, which produced films insoluble in organic solvents such as acetone and dimethylformamide (which totally dissolved uncured terpolymers). The acidification of ? SO3Li into the ? SO3H function enabled protonic membranes to be obtained. The thermal stabilities of the crosslinked materials were higher than those of the uncured terpolymers, and their electrochemical performances were investigated. According to the contents of the sulfonic acid side functions, the ion‐exchange capacities ranged from 0.6 to 1.5 mequiv of H+/g, whereas the water uptake and conductivities ranged from 5–26% (±11%) and from 0.5 to 6.0 mS/cm, respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4566–4578, 2006 相似文献
109.
Armen Shirikyan 《Probability Theory and Related Fields》2006,134(2):215-247
We consider a class of dissipative PDE's perturbed by an external random force. Under the condition that the distribution
of perturbation is sufficiently non-degenerate, a strong law of large numbers (SLLN) and a central limit theorem (CLT) for
solutions are established and the corresponding rates of convergence are estimated. It is also shown that the estimates obtained
are close to being optimal. The proofs are based on the property of exponential mixing for the problem in question and some
abstract SLLN and CLT for mixing-type Markov processes. 相似文献
110.
We study the existence of positive solutions to the operator equation Lx = Nx, where L is a linear Fredholm mapping of index zero and N is a nonlinear operator. Using the properties of cones in Banach spaces and Leray-Schauder degree for completely continuous
operators, k-set contractions and condensing mappings, we obtain some refinements of the results established in [3] and [14].
Received: 9 July 2005; revised: 12 January 2006 相似文献