The use of parallel and monochromatic beams for determining the composition of pseudobinary alloys by X-ray fluorescence

A simple X-ray fluorescence method using nearly parallel and monochromatic beams is analyzed and discussed in connection with the determination of the alloy fraction in pseudobinary A_1−x B _x C solid solutions. Applications to optoelectronic materials are considered. The reliability of the method has been analyzed and discussed for both bulk and thin film samples. Errors due to small angular divergence in the accepted beam are seen to be neglibile. Deviations from a symmetrical alignment of the sample can strongly influence the measured fluorescence intensity. The experimental analysis of this effect can be used for a perfect symmetrical orientation of thick samples. The measurement of the fluorescence intensity as a function of the glancing angle can give both thickness and composition in solid-solution thin-film samples. The contributions of the fluorescence radiation excited by the characteristic X-ray lines of atoms within the substrate is shown to be important in thin epitaxial layers. An approximate formula for calculating these contributions is given and discussed in the light of experimental results. Bulk crystals and thin-film samples, vapourphase grown Cd_1−x Zn _x S solid solutions, have been used for experiments in which the ZnK _α radiation excited by a MoK _α primary beam was measured.     

Generalized nuclearity conditions and the split property in quantum field theory

Generalized nuclearity conditions that are applicable in arbitrary superselection sectors of a quantum field theory and to theories with a maximal temperature are discussed. They are shown to imply the (distal) split property and to impose specific restrictions on the spectral properties of modular operators associated with local algebras and vectors of compact energy support.     

SDiff(2) Toda equation — Hierarchy,Tau function,and symmetries

A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda equation, is shown to have a Lax formalism and an infinite hierarchy of higher flows. The Lax formalism is very similar to the case of the self-dual vacuum Einstein equation and its hyper-Kähler version, however now based upon a symplectic structure on a cylinderS ¹×R. An analogue of the Toda lattice tau function is introduced. The existence of hidden SDiff(2) symmetries are derived from a Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function turn out to have commutator anomalies, hence give a representation of a central extension of the SDiff(2) algebra.     

Dirichlet norms,capacities and generalized isoperimetric inequalities for Markov operators

We define the notion of p-capacity for a reversible Markov operator on a general measure space and prove that uniform estimates for the ratio of capacity and measure are equivalent to certain imbedding theorems for the Orlicz and Dirichlet norms. As a corollary we get results on connections between embedding theorems and isoperimetric properties for general Markov operators and, particularly, a generalization of the Kesten theorem on the spectral radius of random walks on amenable groups for the case of arbitrary graphs with non-finitely supported transition probabilities.     

A non-linear version of Hunt-Lion's theorem from the point of view of T-accretivity

In the classical topological context, Dellacherie [10] has given a non-linear version of Hunt's theorem characterizing the proper kernels verifying the complete maximum principle as those closing a submarkovian resolvent. In this paper we study the relation between this non-linear version of Hunt's theorem and T-accretivity.     

Die Lasker-Bedingung für Nicht Endlich Erzeugte Moduln

Ohne Zusammenfassung

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REGULARITY OF WEAK SOLUTION TO P-LAPLACIAN WITH MEASURABLE COEFFICIENT

Holder continuity and C1-regularity for the weak solution in W1,p to P-Laplacianwith measurable coefficient were obtained.     

Iterated monoidal categories

We develop a notion of an n-fold monoidal category and show that it corresponds in a precise way to the notion of an n-fold loop space. Specifically, the group completion of the nerve of such a category is an n-fold loop space, and free n-fold monoidal categories give rise to a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an n-fold loop space. We also show directly that this operad has the same homotopy type as the n-th Smith filtration of the Barratt-Eccles operad and the n-th filtration of Berger's complete graph operad. Moreover, this operad contains an equivalent preoperad which gives rise to Milgram's small model for when n=2 and is very closely related to Milgram's model of for n>2.