Weighted Bloch Spaces, Hp, and BMOA

It is determined which Bloch-type conditions on a function f _0<p<H^p ensure that f BMOA.     

Fuzzy Markov Chains and Decision-Making

Decision-making in an environment of uncertainty and imprecision for real-world problems is a complex task. In this paper it is introduced general finite state fuzzy Markov chains that have a finite convergence to a stationary (may be periodic) solution. The Cesaro average and the -potential for fuzzy Markov chains are defined, then it is shown that the relationship between them corresponds to the Blackwell formula in the classical theory of Markov decision processes. Furthermore, it is pointed out that recurrency does not necessarily imply ergodicity. However, if a fuzzy Markov chain is ergodic, then the rows of its ergodic projection equal the greatest eigen fuzzy set of the transition matrix. Then, the fuzzy Markov chain is shown to be a robust system with respect to small perturbations of the transition matrix, which is not the case for the classical probabilistic Markov chains. Fuzzy Markov decision processes are finally introduced and discussed.     

On Effective Conductivity on ℤ d Lattice

We study the effective conductivity _e for a random wire problem on the d-dimensional cubic lattice ^d , d2 in the case when random conductivities on bonds are independent identically distributed random variables. We give exact expressions for the expansion of the effective conductivity in terms of the moments of the disorder parameter up to the 5th order. In the 2D case using the duality symmetry we also derive the 6th order expansion. We compare our results with the Bruggeman approximation and show that in the 2D case it coincides with the exact solution up to the terms of 4th order but deviates from it for the higher order terms.     

Mixed-anion complexes with a bipyrazolyl ligand. A new entry to a realm of three-dimensional five-connected coordination topologies

Cross-linking of corrugated square grid coordination layers by anionic bridging groups generates five-connected coordination networks; the 3D topologies of mixed-anion cobalt(II) and nickel(II) complexes with a tetramethyl-substituted 4,4'-bipyrazolyl ligand are supported by mu-SO4(2-) functions and exist as neutral or cationic five-connected arrays involving additional terminal (NCS-) or non-coordinated (NO3-, ClO4-) groups.     

Bending of DNA by asymmetric charge neutralization: all-atom energy simulations

DNA dodecamers of the alternating d(CG).d(CG) sequence with six phosphate groups either charge-neutralized or substituted by neutral methylphosphonates across the major or minor groove have been subjected to energy minimization to determine the conformational effect of the asymmetric elimination of phosphate charge. We report bending angles, directions of bending, and detailed structural characteristics such as groove widths and local base-pair parameters. Our principal results are that charge neutralization on one face of the DNA induces significant bending toward the neutralized face, in agreement with theoretical predictions on a simplified model and experimental data on a similar base-pair sequence, and that the DNA conformation averaged over all stereospecific methylphosphonate substitutions is nearly the same as the conformation produced by charge neutralization of the phosphates. Individual isomers, however, cover a wide range of structures, with the magnitude and direction of overall bending sensitive to the precise stereochemical pattern of neutralization. Our simulation does not explicitly contain counterions, and the results therefore suggest that counterions can influence DNA structure by neutralizing the phosphate charge. These data provide new hints into the molecular mechanisms which underlie the deformations of DNA structure induced by the binding of positively charged proteins and other tightly associated cationic species.     

Hybrid density-functional theory and the insulating gap of UO2

We report the first calculations carried out with a periodic boundary condition code capable of examining hybrid density-functional theory (DFT) for f-element solids. We apply it to the electronic structure of the traditional Mott insulator UO2, and find that it correctly yields an antiferromagnetic insulator as opposed to the ferromagnetic metal predicted by the local spin density and generalized gradient approximations. The gap, density of states, and optimum lattice constant are all in good agreement with experiment. We stress that this results from the functional and the variational principle alone. We compare our results with the more traditional approximations.     

An Approach to Permittivity Determination at Microwave Frequencies Through the Eigenvalue Problem

A simple method of solving the inverse medium problem in order to determine the complex dielectric constant of a lossy dielectric material at microwave frequencies is presented. The arbitrarily shaped dielectric sample placed in a rectangular waveguide is considered. Electromagnetic fields in the waveguide are expanded in series of harmonic functions. A set of linear equations is obtained using the finite–difference technique. An additional empirical condition, which is related to the measured reflection and/or transmission coefficients and results in an overdetermined system, is added and then the system is defined by the addition of a trivial extra parameter. The sample's dielectric properties are obtained by solving the resulting eigenvalue problem. An algorithm to extract proper results from the set of eigenvalues is defined by considering the properties of numerical solution. The system is tested by using an alternative method.     

Optimal Recovery of the Derivative of Periodic Analytic Functions from Hardy Classes

LetS_β{z : |Im z|<β}. For 2π-periodic functions which are analytic inS_βwithp-integrable boundary values, we construct an optimal method of recovery off′(ξ), ξS_β, using information about the valuesf(x₁), mldr;, f(x_n), x_j[0, 2π).     

Observation of ω → π0μ+μ− decay

The results of studying the mass spectrum of μ⁺μ^?γγ systems produced in π^?p collisions at 25 and 33 GeV/c presented. The wide-aperture magnetic spectrometer with a hodoscope γ-detector was used to identify muon pairs and photons. There is a clear peak in the mass spectrum which corresponds to the decay ω → π⁰μ⁺μ^? previously not observed. The branching ratio for the decay is estimated to be 9 × 10^?5 with a systematic error of 50%.