Robust Stabilization and H

This paper is concerned with the problem of robust stabilization and H∞ control for a class of uncertain neural networks. For the robust stabilization problem, sufficient conditions are derived based on the quadratic convex combination property together with Lyapunov stability theory. The feedback controller we design ensures the robust stability of uncertain neural networks with mixed time delays. We further design a robust H∞ controller which guarantees the robust stability of the uncertain neural networks with a given H∞ performance level. The delay-dependent criteria are derived in terms of LMI (linear matrix inequality). Finally, numerical examples are provided to show the effectiveness of the obtained results

γγ→tcˉ+ctˉ\gamma\gamma \to t\bar{c}+c\bar{t} in a supersymmetric theory with an explicit R-parity violation

We studied the process $\gamma\gamma \to t\bar{c}+c\bar{t}$ in a $R_{p}$ violating supersymmetric Model with the effects from both B- and L-violating interactions. The calculation shows that it is possible to detect a $R_{p}$ violating signal at the Next Linear Collider. Information about the B-violating interaction in this model could be obtained under very clean background, if we take the present upper bounds for the parameters in the supersymmetric $\rlap/ R_{p}$ interactions. Even if we can not detect a signal of $\rlap/R_{p}$ in the experiment, we may get more stringent constraints on the heavy-flavor $\rlap/R_{p}$ couplings.Comment: 16 pages, 6 figure

The Slater approximation for Coulomb exchange effects in nuclear covariant density functional theory

The relativistic local density approximation (LDA) for the Coulomb exchange functional in nuclear systems is presented. This approximation is composed of the well-known Slater approximation in the non-relativistic scheme and the corrections due to the relativistic effects. Its validity in finite nuclei is examined by comparing with the exact treatment of the Coulomb exchange term in the relativistic Hartree-Fock-Bogoliubov theory. The relativistic effects are found to be important and the exact Coulomb exchange energies can be reproduced by the relativistic LDA within 5% demonstrated by the semi-magic Ca, Ni, Zr, Sn, and Pb isotopes from proton drip line to neutron drip line.Comment: 6 pages and 4 figure

Tetrakis[μ-3-(3-pyridyl)acrylato-κ2 O:O′]bis{(1,10-phenanthroline-κ2 N,N′)[3-(3-pyridyl)acrylato-κ2 O,O′]europium(III)} pentahydrate

The europiumIII ion in the title compound, [Eu2(C8H6NO2)6(C12H8N2)2]·5H2O, is coordinated by seven carboxyl­ate O atoms and two N atoms from one phenanthroline mol­ecule. The carboxyl­ate groups of 3-(3-pyrid­yl)acrylate link pairs of europium(III) ions, forming centrosymmetric dinuclear units, which further assemble into a sheet parallel to the (001) plane through hydrogen-bonding inter­actions involving the uncoordinated water mol­ecules. One water molecule is disordered

2-tert-Butyl-6-[(4-chloro-2-nitro­phen­yl)diazen­yl]-4-methylphenol

In the title compound, C17H18ClN3O3, the dihedral angle between the planes of the two benzene rings is 1.03 (7)°. The overall conformation of the mol­ecule is influenced, in part, by electron delocalization and by an intra­molecular bifurcated O—H⋯(O,N) hydrogen bonds. The O atoms of the nitro group, one of which serves as an H bond acceptor, are disordered over two sets of sites with refined occupancies of 0.56 (3) and 0.44 (3)

Box-counting measure of metric spaces

In this paper, we introduce a new notion called the \emph{box-counting measure} of a metric space. We show that for a doubling metric space, an Ahlfors regular measure is always a box-counting measure; consequently, if $E$ is a self-similar set satisfying the open set condition, then the Hausdorff measure restricted to $E$ is a box-counting measure. We show two classes of self-affine sets, the generalized Lalley-Gatzouras type self-affine sponges and Bara\'nski carpets, always admit box-counting measures; this also provides a very simple method to calculate the box-dimension of these fractals. Moreover, among others, we show that if two doubling metric spaces admit box-counting measures, then the multi-fractal spectra of the box-counting measures coincide provided the two spaces are Lipschitz equivalent