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In this paper we reconsider the basic topological and metric structures on spaces of probability measures and random variables, such as e.g. the weak topology and the total variation metric, replacing them with more intrinsic and richer approach structures. We comprehensibly investigate the relationships among, and basic facts about these structures, and prove that fundamental results, such as e.g. the portmanteau theorem and Prokhorov?s theorem, can be recaptured in a considerably stronger form in the new setting. 相似文献
6.
Overtone spectrum of o, m and p-nitrobenzaldehydes and p-chlorobenzaldehyde has been studied in 2000–12000 cm−1 region. Vibrational frequencies and anharmonicity constants for aryl as well as alkyl CH stretch vibrations have been determined.
We have also determined the internuclear distances for the aryl CH bond in the different molecules. The small variation observed
in these distances is an indication of the substitution effect.
It is observed that in the case of p-disubstituted benzens, the shift in aryl CH bond is proportional to sum of the Hammet σ of the substituents. However in the
case of o-disubstituted benzenes it is only 80% of the para-substituted shift. 相似文献
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Stephen V. Lowen David MacInnes B. Lionel Funt 《Journal of polymer science. Part A, Polymer chemistry》1989,27(12):4087-4097
Solutions of 3-methoxythiophene (MeOT) in dimethylformamide (DMF) were electrolyzed at controlled electrode potentials. The polymerizations were studied under homogeneous conditions in solutions in which the polymer was soluble in the medium, and no coating of the electrodes occurred. The reaction proceeded at high coulombic efficiency and a first order dependence on monomer concentration was observed. The molecular weights of the polymers were determined by gel permeation chromatography. All samples showed a narrow distribution of molecular weights, with Mw/Mn ranging from 1.01 to 1.07. The molecular weight was low (about 3000 Daltons) and did not change in magnitude during the course of the reaction from 10 to 86% conversion, or with change in electrode potential from 1.55 to 1.65 V vs. SCE. The data are interpreted on a model based upon the competitive formation of chemically unreactive bipolarons. 相似文献
9.
Gregory T. Lowen Merrick R. Almond Janet L. Rideout 《Journal of heterocyclic chemistry》1992,29(6):1663-1665
A novel synthesis of 3-vinylpiperidine from commercially available ethyl 3-pyridylacetate is described. 相似文献
10.
In Lowen and Wuyts (Appl Categ Struct 8:235–245, 2000) the authors studied the simultaneously concretely reflective and concretely coreflective subconstructs of the category Ap of approach spaces. For the sake of shortness we call such subconstructs stable. Using a technique introduced in Herrlich and Lowen (1999) it was possible to explicitly describe such stable subconstructs by a condition on the objects which used certain subsets
of [0, ∞ ]. Thus each stable subconstruct Ap
m
described in [9] corresponds to the subset {0} ∪ [m, ∞ ] ⊂ [0, ∞ ] for m ∈ [0, ∞ ]. Although this characterization is correct, Theorem 4.7 in [9] stating that the subconstructs Ap
m
were the only stable subconstructs of Ap is not. The main results, which together prove that the only stable subconstructs are those where a restriction is put on
the range of the distances of the objects, are upheld, but it turns out that not only the sets {0} ∪ [m, ∞ ], but actually each closed subsemigroup of [0, ∞ ] determines a stable subconstruct (albeit again in exactly the same
way as characterized in [9]). In the first part of our paper, Sections 1 and 2, we develop the general technique, which is totally different to the
one from [3], and in Theorem 2.13 we prove the main result for the case of approach spaces. The technique which we develop is also applicable
to other cases. Thus, in Section 3, more precisely in Theorems 3.9 and 3.11, we give the complete solution to the corresponding
characterization problem for the constructs pq
Met
∞ of pseudo-quasi-metric spaces and p
Met
∞ of pseudometric spaces and in Section 4 we briefly sketch how the technique can be adapted and used to also completely solve
the problem in the case of more general types of approach spaces and metric spaces. At the same time, in all cases, we are
able to give necessary and sufficient conditions under which two stable subconstructs of one of these topological constructs
are concretely isomorphic. It turns out that in all cases there are 2à02^{\aleph_0} non-concretely isomorphic stable subconstructs. 相似文献