481 research outputs found

    Analysis of Human Spleen Contamination

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    Besides carbon, oxygen and nitrogen, numerous other elements and their compounds are significant in the body of humans and other animals. Accumulation of some elements and their compounds is recognized by clinical and biochemical evaluation. The physical-chemical properties and topical characteristics of elements in tissues may play a crucial role in evaluation their effect on human body. The ^57^Fe Mössbauer measurement was used for evaluation of iron–oxide biomagnetic nanoparticles composition and properties. Absorption spectra of the powdered spleen recorded at 77K and 300K were measured and subsequently analyzed. From fitted data it is possible to obtain material composition as well as discuss the mean particle size (received from decrease hyperfine field in comparison with bulk value)

    Stochastic maximal LpL^p-regularity

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    In this article we prove a maximal LpL^p-regularity result for stochastic convolutions, which extends Krylov's basic mixed Lp(Lq)L^p(L^q)-inequality for the Laplace operator on Rd{\mathbb{R}}^d to large classes of elliptic operators, both on Rd{\mathbb{R}}^d and on bounded domains in Rd{\mathbb{R}}^d with various boundary conditions. Our method of proof is based on McIntosh's H∞H^{\infty}-functional calculus, RR-boundedness techniques and sharp Lp(Lq)L^p(L^q)-square function estimates for stochastic integrals in LqL^q-spaces. Under an additional invertibility assumption on AA, a maximal space--time LpL^p-regularity result is obtained as well.Comment: Published in at http://dx.doi.org/10.1214/10-AOP626 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

    On the R-boundedness of stochastic convolution operators

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    The RR-boundedness of certain families of vector-valued stochastic convolution operators with scalar-valued square integrable kernels is the key ingredient in the recent proof of stochastic maximal LpL^p-regularity, 2<p<∞2<p<\infty, for certain classes of sectorial operators acting on spaces X=Lq(ΞΌ)X=L^q(\mu), 2≀q<∞2\le q<\infty. This paper presents a systematic study of RR-boundedness of such families. Our main result generalises the afore-mentioned RR-boundedness result to a larger class of Banach lattices XX and relates it to the β„“1\ell^{1}-boundedness of an associated class of deterministic convolution operators. We also establish an intimate relationship between the β„“1\ell^{1}-boundedness of these operators and the boundedness of the XX-valued maximal function. This analysis leads, quite surprisingly, to an example showing that RR-boundedness of stochastic convolution operators fails in certain UMD Banach lattices with type 22.Comment: to appear in Positivit

    Embedding vector-valued Besov spaces into spaces of Ξ³\gamma-radonifying operators

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    It is shown that a Banach space EE has type pp if and only for some (all) dβ‰₯1d\ge 1 the Besov space Bp,p(1pβˆ’12)d(Rd;E)B_{p,p}^{(\frac1p-\frac12)d}(\R^d;E) embeds into the space \g(L^2(\R^d),E) of \g-radonifying operators L2(Rd)β†’EL^2(\R^d)\to E. A similar result characterizing cotype qq is obtained. These results may be viewed as EE-valued extensions of the classical Sobolev embedding theorems.Comment: To appear in Mathematische Nachrichte

    Stochastic integration in Banach spaces - a survey

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    This paper presents a brief survey of the theory of stochastic integration in Banach spaces. Expositions of the stochastic integrals in martingale type 2 spaces and UMD spaces are presented, as well as some applications of the latter to vector-valued Malliavin calculus and the stochastic maximal regularity problem. A new proof of the stochastic maximal regularity theorem is included.Comment: minor corrections. To appear in the proceedings of the 2012 EPFL Semester on Stochastic Analysis and Application
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