Search results for "Measure theory"
showing 10 items of 176 documents
Hyperbranched PEG by Random Copolymerization of Ethylene Oxide and Glycidol
2010
The synthesis of hyperbranched poly(ethylene glycol) (hbPEG) in one step was realized by random copolymerization of ethylene oxide and glycidol, leading to a biocompatible, amorphous material with multiple hydroxyl functionalities. A series of copolymers with moderate polydispersity ($\overline {M} _{{\rm w}} /\overline {M} _{{\rm n}} $ < 1.8) was obtained with varying glycidol content (3-40 mol-%) and molecular weights up to 49 800 g mol(-1) . The randomly branched structure of the copolymers was confirmed by (1) H and (13) C NMR spectroscopy and thermal analysis (differential scanning calorimetry). MTS assay demonstrated low cell toxicity of the hyperbranched PEG, comparable to the highly…
Quantification of low levels of amorphous content in maltitol
2004
A method for the quantification of low levels of amorphous content of maltitol with hyper-DSC (high speed DSC) was developed. The method is based on the fact that the change of specific heat ( � Cp) at the glass transition is linearly proportional to the amorphous content. Twelve synthetic mixtures with various degrees of crystalline and amorphous maltitol were prepared. � Cp was determined at both fictive and
Semiconductor-metal transitions in liquidIn100−xSexalloys: A concentration-induced transition
2004
The electronic and structural properties of ${\mathrm{In}}_{100\ensuremath{-}x}{\mathrm{Se}}_{x}$ liquid alloys close to their melting points have been investigated by combining x-ray-absorption experiments with ab initio molecular-dynamics simulations. Extended x-ray-absorption fine-structure data have been acquired at both the In and Se K edges in a large concentration range $(x=20%$ to $x=50%$ of Se content). Ab initio molecular-dynamics simulations have been carried out at the two most extreme concentrations explored experimentally. Liquid InSe is found to retain a semiconducting behavior which results from a low-dimensional structure, reminiscent of that of the ambient solid phase, cha…
DETERMINATION OF THE ALUMINUM CONTENT OF NATURAL AND SYNTHETIC ALUMOGOETHITES USING MÖSSBAUER SPECTROSCOPY
1980
Equivalence Revisited: Polish Perspectives on the Topic
2019
Fuzzy expected utility
1984
Decision making under uncertainty requires not only measures of the uncertainty of situations that we try to recognize , but also an estimate of the imprecision from which they are determined. This imprecision can be the result either of a lack of exactness in the measure of the elements which are necessary to the determination of the states of nature or the purely subjective interpretation of these states. Through a subjective measure of the non-measurable imprecision, the purpose of the fuzzy expected utility, which is investigated, is to translate with a great accuracy the imprecise behaviour of the decision-maker in an uncertain world. Consequently we propose to introduce first the prob…
Semianalyticity of isoperimetric profiles
2009
It is shown that, in dimensions $<8$, isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic.
Sets versus trial sequences, Hausdorff versus von Mises: “Pure” mathematics prevails in the foundations of probability around 1920
2010
Abstract The paper discusses the tension which occurred between the notions of set (with measure) and (trial-) sequence (or—to a certain degree—between nondenumerable and denumerable sets) when used in the foundations of probability theory around 1920. The main mathematical point was the logical need for measures in order to describe general nondiscrete distributions, which had been tentatively introduced before (1919) based on von Mises’s notion of the “Kollektiv.” In the background there was a tension between the standpoints of pure mathematics and “real world probability” (in the words of J.L. Doob) at the time. The discussion and publication in English translation (in Appendix ) of two …
Multi-resolution analysis generated by a seed function
2009
In this paper we use the equivalence result originally proved by the author, which relates a multiresolution analysis (MRA) of ℒ2(R) and an orthonormal set of single electron wave functions in the lowest Landau level, to build up a procedure which produces, starting with a certain square-integrable function, a MRA of ℒ2(R). © 2003 American Institute of Physics.
Integration of multifunctions with closed convex values in arbitrary Banach spaces
2018
Integral properties of multifunctions with closed convex values are studied. In this more general framework not all the tools and the technique used for weakly compact convex valued multifunctions work. We pay particular attention to the "positive multifunctions". Among them an investigation of multifunctions determined by vector-valued functions is presented. Finally, decomposition results are obtained for scalarly and gauge-defined integrals of multifunctions and a full description of McShane integrability in terms of Henstock and Pettis integrability is given.