Super-Brownian motion with reflecting historical paths. II. Convergence of approximations

We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([1]) converges in probability to the “super-Brownian motion with reflecting historical paths.” This solves an open problem posed in [1], where only tightness was proved for the sequence of approximations. Several results on path behavior were proved in [1] for all subsequential limits–they obviously hold for the unique limit found in the present paper.Mathematics Subject Classification (2000): Primary 60H15, Secondary 35R60Supported in part by NSF Grant DMS-0071486, Israel Science Foundation Grants 12/98 and 116/01 - 10.0, and the U.S.-Israel Binational Science Foundation (grant No. 2000065).     

Stability of multi-additive mappings in non-Archimedean normed spaces

A function f:Vn→W, where V is a commutative semigroup, W is a linear space and n?1 is an integer, is called multi-additive if it is additive in each variable. In this paper we prove the generalized Hyers-Ulam stability of multi-additive mappings in non-Archimedean normed spaces, using the so-called direct method.     

Fission fragment mass yields of Th to Rf even-even nuclei

Fission properties of the actinide nuclei are deduced from theoretical analysis. We investigate potential energy surfaces and fission barriers and predict the fission fragment mass yields of actinide isotopes. The results are compared with experimental data where available. The calculations were performed in the macroscopic-microscopic approximation with the Lublin-Strasbourg Drop (LSD) for the macroscopic part, and the microscopic energy corrections were evaluated in the Yukawa-folded potential. The Fourier nuclear shape parametrization is used to describe the nuclear shape, including the non-axial degree of freedom. The fission fragment mass yields of the nuclei considered are evaluated within a 3D collective model using the Born-Oppenheimer approximation.     

The Armstrong–Frederick cyclic hardening plasticity model with Cosserat effects

We propose an extension of the cyclic hardening plasticity model formulated by Armstrong and Frederick which includes micropolar effects. Our micropolar extension establishes coercivity of the model which is otherwise not present. We study then existence of solutions to the quasistatic, rate-independent Armstrong–Frederick model with Cosserat effects which is, however, still of non-monotone, non-associated type. In order to do this, we need to relax the pointwise definition of the flow rule into a suitable weak energy-type inequality. It is shown that the limit in the Yosida approximation process satisfies this new solution concept. The limit functions have a better regularity than previously known in the literature, where the original Armstrong–Frederick model has been studied.     

On the vanishing viscosity method for first order differential-functional IBVP

We consider the initial-boundary value problem for first order differential-functional equations. We present the ‘vanishing viscosity’ method in order to obtain viscosity solutions. Our formulation includes problems with a retarded and deviated argument and differential-integral equations. Supported by KBN grant 2 PO3A, 01811.     

Potential operators associated with Hankel and Hankel-Dunkl transforms

We study Riesz and Bessel potentials in the settings of Hankel transform, modified Hankel transform and Hankel-Dunkl transform. We prove sharp or qualitatively sharp pointwise estimates of the corresponding potential kernels. Then we characterize those 1 ≤ p, q≤∞, for which the potential operators satisfy L ^p -L ^q estimates. In case of the Riesz potentials, we also characterize those 1 ≤ p, q ≤ ∞, for which two-weight L ^p -L ^q estimates, with power weights involved, hold. As a special case of our results, we obtain a full characterization of two power-weight L ^p -L ^q bounds for the classical Riesz potentials in the radial case. This complements an old result of Rubin and its recent reinvestigations by De Nápoli, Drelichman and Durán, and Duoandikoetxea.     

Low-background,digital gamma-ray spectrometer with BEGe detector and active shield: commissioning,optimisation and software development

Journal of Radioanalytical and Nuclear Chemistry - This paper presents results of the development process of low-background, digital gamma-rays spectrometer equipped with Broad Energy Germanium...     

Silicate Xerogels with Dopant-Induced Chirality

A series of silicate xerogels with entrapped chiral amino acids have been obtained via sol-gel technology. The transparent, glassy samples obtained exhibit chirality in the bulk due to the presence of the entrapped asymmetric molecules. Measurements of the optical activity of the doped xerogel samples revealed that the entrapment did not significantly influence the optical activity observed for liquid solutions of the amino acids. Thus, the sol-gel method enables the preparation of amorphous optical materials exhibiting properties of strictly spatially defined molecular systems. Apart from the obvious optical applications, such porous materials with asymmetric centers might find interesting applications in chiral chemical syntheses and separations.     

Spectrochemical Properties of Noncubical Transition Metal Complexes in Solutions. IX. The Mixed Tetragonal Distorted Bis(Salicylato)Cobalt(II) Complex in Various Solvents

Mixed cobalt(II) complexes with the monodentate ligands: 2-hydroxybenzoic acid deprotonated (sal^–, the salicylate ion) and water, have been investigated. The combined results of the spectrophotometric and conductance measurements, as well as known the X-ray structure for solids, were used to determine the structure of the studied complexes in solution. The electronic absorption spectra in aqueous acid (0.01M HClO₄), ethylene glycol (glycol), formamide (FM), N,N-dimethylformamide (DMF), and dimethyl sulfoxide (DMSO) solutions have been recorded. The d-d electronic spectra have been treated by the crystal-field model (CFM) and angular overlap model (AOM). Low-symmetry splittings of the broad asymmetric bands in the experimental spectra (solutions at room temperature) were found by Gaussian analysis. The effect of the and bonding of the monodentate ligands (with oxygen-donor ligators) on the central metal ion was described in the ligand–field framework. A comparison of the stereochemistry of the complex species in various solutions was made.