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2.
R. M. Dudley 《Probability Theory and Related Fields》1994,100(2):175-189
Summary In a separable metric space, if two Borel probability measures (laws) are nearby in a suitable metric, then there exist random variables with those laws which are nearby in probability. Specifically, by a well-known theorem of Strassen, the Prohorov distance between two laws is the infimum of Ky Fan distances of random variables with those laws. The present paper considers possible extensions of Strassen's theorem to two random elements one of which may be (compact) set-valued and/or non-measurable. There are positive results in finite-dimensional spaces, but with factors depending on the dimension. Examples show that such factors cannot entirely be avoided, so that the extension of Strassen's theorem to the present situation fails in infinite dimensions.This research was partially supported by a Guggenheim Fellowship, by National Science Foundation grant DMS 8505550 at MSRI-Berkeley, and other NSF grants 相似文献
3.
Ying‐Hung So Pamela Foster Jang‐Hi Im Philip Garrou Jack Hetzner Edmund Stark Kayla Baranek 《Journal of polymer science. Part A, Polymer chemistry》2006,44(5):1591-1599
Divinylsiloxane‐bisbenzocyclobutene (DVS‐bisBCB) polymer has very low dielectric constant and dissipation factor, good thermal stability, and high chemical resistance. The fracture toughness of the thermoset polymer is moderate due to its high crosslink density. A thermoplastic elastomer, polystyrene–polybutadiene–polystyrene triblock copolymer, was incorporated into the matrix to enhance its toughness. The cured thermoset matrix showed different morphology when the elastomer was added to the B‐staged prepolymer or when the elastomer was B‐staged with the DVS‐bisBCB monomer. Small and uniformly distributed elastomer domains were detected by transmission electron micrographs (TEM) in the former case, but TEM did not detect a separate domain in the latter case. A high percentage of the polystyrene–polybutadiene–polystyrene triblock copolymer could be incorporated into the DVS‐bisBCB thermoset matrix by B‐staging the triblock copolymer with the BCB monomer. The elastomer increased the fracture toughness of DVS‐bisBCB polymer as indicated by enhanced elongation at break and increased K1c values obtained by the modified edge‐lift‐off test. Elastomer modified DVS‐bisBCB maintained excellent electrical properties, high Tg and good thermal stability, but showed higher coefficient of linear thermal expansion values. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1591–1599, 2006 相似文献
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Dudley Paul Johnson 《Journal of Theoretical Probability》1989,2(4):433-436
We show that under suitable conditions $$\begin{gathered} E_x f\left\{ {a + \int_0^t \beta \left[ {b + \int_0^s {\alpha \left( {X_r } \right)dr, c + s, X_s } } \right]ds, b + \int_0^t {\alpha \left( {X_s } \right)ds, c + t, X_t } } \right\} \hfill \\ = e^{tG} f\left[ {a, b, c, x} \right] \hfill \\ \end{gathered} $$ whereX t is a Brownian motion andG is the generator of a (C 0) contraction semigroupe tG. 相似文献
6.
The synthesis of 2-methyl-5H-dibenz[b,f]azepine-5-carboxamide (2-methylcarbamazepine, 2-MCBZ, 8), a promising internal standard for chromatographic assays of the antiepileptic agent carbamazepine (CBZ, 1), is described. N-(p-Tolyl)anthranilic acid (2) was utilized as a starting material for the synthesis of a key compound, 2,9-dimethylacridine (4), which was converted in two steps to 2-methyl-9-hydroxymethylacridan (6). The acridan 6, in the presence of poly-phosphoric acid, was ring-expanded to form 2-methyl-5H-dibenz[b,f]azepine (7), this latter compound being converted by conventional reactions to its 5-carbamyl derivative, 2-MCBZ (8). 相似文献
7.
Dudley Williams and his colleagues discuss how ligands can gain binding energy to their receptors, and substrate transition states to their enzymes, by tightening the protein structures, with a decrease in their dynamic behaviour. 相似文献
8.
B.?Stark C.?Lach B.?Farago H.?Frey C.?Schlenk B.?StühnEmail author 《Colloid and polymer science》2003,281(7):593-600
A series of carbosilane dendrimers with perfluorinated end groups has been prepared. The structure of these molecules in dilute solution is studied using small angle neutron scattering. For generations g<3 we find a non-spherical shape of the particles and a tendency for aggregation. This result is supported by the analysis of the diffusion coefficient obtained from photon correlation spectroscopy. The overall shape of the molecules is that of a core-shell particle. The generation 4 molecule is obtained as a compact sphere. Neutron spin echo spectroscopy reveals a relaxation time which is attributed to the form fluctuations of this particle. 相似文献
9.
A series of enantiomerically pure 8-oxabicyclo[3.2.1]oct-6-en-3-ones functionalized in the unsaturated two-carbon bridge has been prepared by the title reaction. Carbocation reactivity has been fined-tuned at -95 degrees C and adjusted to diene nucleophilicity. Conventional electrophilic substitution of 3-silylated and 3-stannylated furan is suppressed in favor of the rapid 4 + 3 cycloaddition mode. In the case of cycloadduct 13A, stereoselectivity (17:1) is perfectly matched to regioselectivity (17:1). High stereoselection as well as unprecedented regioselection and chemoselection is attributed to the low-temperature cycloaddition protocol and the design of chiral auxiliary and tether. 相似文献
10.
A series of laboratory and modelling experiments on the oxidation of propene in the gas phase has been undertaken to determine conditions which give high yields of propene oxide. The conditions under which the experiments were conducted were 505–549 K and up to 4 bar pressure. It is proposed that propene oxide is formed from propene by reaction with several peroxy radicals including HO2 and CH3CO3. However, one of the more important radicals is hydroxypropylperoxy. Its reaction with propene, under these conditions is more important than concerted decomposition to formaldehyde and acetaldehyde. © 1995 John Wiley & Sons, Inc. 相似文献