Normality-Type Properties and Covariant Functors

Topological properties similar to normality are considered in subspaces of products and powers of topological spaces, of spaces of closed subsets, and of spaces having the form IE1.gif" alt=" $$\mathcal{F}$$ " align="middle" border="0"> (X), where IE2.gif" alt=" $$\mathcal{F}$$ " align="middle" border="0"> is a normal functor. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 2, pp. 57–98, 2003.     

Point Interactions: $$\mathcal{P}\mathcal{T}$$ -Hermiticity and Reality of the Spectrum

General point interactions for the second derivative operator in one dimension are studied. In particular, IE2.gif" alt=" $$\mathcal{P}\mathcal{T}$$ " align="middle" border="0"> -self-adjoint point interactions with the support at the origin and at points ±l are considered. The spectrum of such non-Hermitian operators is investigated and conditions when the spectrum is pure real are presented. The results are compared with those for standard self-adjoint point interactions.     

Stability of Hypersurfaces with Constant r-Mean Curvature

We deal with compact hypersurfaces immersed in space forms with constant IE2.gif" alt=" $$r$$ " align="middle" border="0"> -mean curvature. They are critical points for a variational problem. We show they are stable if and only if they are geodesic spheres, generalizing results on constant curvature hypersurfaces.     

The comprehension, some problems and suggestions to symbolic vector method and some defenses for Gibbs' symbol

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Numerical Simulation of Antennas with Improved Integral Equation Method

Simulating antennas around a conducting object is a challenge task in computational electromagnetism, which is concerned with the behaviour of electromagnetic fields. To analyze this model efficiently, an improved integral equation-fast Fourier transform (IE-FFT) algorithm is presented in this paper. The proposed scheme employs two Cartesian grids with different size and location to enclose the antenna and the other object, respectively. On the one hand, IE-FFT technique is used to store matrix in a sparse form and accelerate the matrix-vector multiplication for each sub-domain independently. On the other hand, the mutual interaction between sub-domains is taken as the additional exciting voltage in each matrix equation. By updating integral equations several times, the whole electromagnetic system can achieve a stable status. Finally, the validity of the presented method is verified through the analysis of typical antennas in the presence of a conducting object.     

Lp Contraction Semigroups for Vector Valued Functions

Let IE2.gif" alt=" $$\tilde T_t$$ " align="middle" border="0"> be a contraction semigroup on the space of vector valued functions IE3.gif" alt=" $$L^2 (X,m,K)$$ " align="middle" border="0"> ( IE4.gif" alt=" $$K$$ " align="middle" border="0"> is a Hilbert space). In order to study the extension of IE5.gif" alt=" $$\tilde T_t$$ " align="middle" border="0"> to a contaction semigroup on IE6.gif" alt=" $$L^p (X,m,K)$$ " align="middle" border="0"> , IE7.gif" alt=" $$1 \leqslant p{\text{ < }}\infty$$ " align="middle" border="0"> Shigekawa [Sh] studied recently the domination property IE8.gif" alt=" $$|\tilde T_t u|_K \leqslant T_t |u|_K$$ " align="middle" border="0"> where IE9.gif" alt=" $$T_t$$ " align="middle" border="0"> is a symmetric sub-Markovian semigroup on IE10.gif" alt=" $$L^2 (X,m,\mathbb{R})$$ " align="middle" border="0"> . He gives in the setting of square field operators sufficient conditions for the above inequality. The aim of the present paper is to show that the methods of [12] and [13] can be applied in the present setting and provide two ways for the extension of IE11.gif" alt=" $${\tilde T}$$ " align="middle" border="0"> to IE12.gif" alt=" $$L^p$$ " align="middle" border="0"> We give necessary and sufficient conditions in terms of sesquilinear forms for the IE13.gif" alt=" $$L^\infty -$$ " align="middle" border="0"> contractivity property IE14.gif" alt=" $$||\tilde T_t u||_{L^\infty } (X,m,K) \leqslant ||u||_{L^\infty } (X,m,K),$$ " align="middle" border="0"> as well as for the above domination property in a more general situation.     

The Abelian category of quotients of $$\mathcal{L}\mathfrak{F}$$ -spaces

We construct the category of quotients of IE2.gif" alt=" $$\mathcal{L}\mathfrak{F}$$ " align="middle" border="0"> -spaces and we show that it is Abelian. This answers a question of L. Waelbroeck from 1990.     

Anomalous dimensions of Wilson operators in the N = 4\mathcal{N} = 4 supersymmetric Yang-Mills theory

We present results for the universal anomalous dimension γ_un(j) of Wilson twist-2 operators in the IE2.gif" alt=" $$\mathcal{N} = 4$$ " align="middle" border="0"> supersymmetric Yang-Mills theory in the first three orders of the perturbation theory. We obtain these expressions by extracting the most complicated terms from the corresponding anomalous dimensions in QCD. The result obtained agrees with the hypothesis of the integrability of the IE3.gif" alt=" $$\mathcal{N} = 4$$ " align="middle" border="0"> supersymmetric Yang-Mills theory in the context of the AdS/CFT correspondence. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 249–262, February, 2007.     

Strong laws of large numbers for weighted sums of $$\tilde \rho $$ -mixing random variables

Strong laws are established for linear statistics that are weighted sums of a IE2.gif" alt=" $$\tilde \rho $$ " align="middle" border="0"> -mixing random sample. The results obtained generalize the results of Baxter et al. [SLLN for weighted independent indentically distributed random variables, J. Theoret. Probab. 17 (2004), 165–181] to IE3.gif" alt=" $$\tilde \rho $$ " align="middle" border="0"> -mixing random variables. This paper is supported by Key discipline of Zhejiang Province (Key discipline of Statistics of Zhejiang Gongshang University) and National Natural Science Foundation of China.     

Novel approaches for selenium speciation in foodstuffs and biological specimens: A review

Selenium is an essential element for human health. It has been recognized as an antioxidant and chemopreventive agent in cancer. Selenium is known to develop its biological activity via selenocysteine residue in the catalytically active centre of selenoproteins. The main source of selenium in human beings is the diet. However, in several regions of the world the content of selenium in diet has been estimated insufficient for a correct expression of the proteins. The beneficial effects of selenium on human health are strongly dependent on its chemical form and concentration. This review critically evaluated the state-of-the art of selenium speciation in biological matrices mainly focused in nutritional and food products. Besides the number of publications related to selenium speciation, isolation and accurate characterization and quantification of selenium species is still a challenge. Hyphenated techniques based on coupling chromatography separation with inductively coupled plasma spectrometry (ICP-MS) and its combination with molecular mass spectrometry (ESI-MS, ESI-MS-MS and MALDI-TOF) and isotopic dilution allow identification, quantification and structural characterization of selenium species. Particular attention is paid in the development of Se-enriched food and nutritional products and how the application of the techniques mentioned above is mandatory to get reliable results on selenium metabolisms in these particular matrices.