Density effect and plasmon bremsstrahlung in the theory of plasmon excitation by large-angle scattered electrons

Experiments on plasmon excitation by electrons which scatter at large angles constitute one of the basic sources of information on plasmon in solids. These experiments provide spectra especially rich in detail, of electrons backscattered from targets having a comparatively perfect structure. Besides, these are the only experiments that are possible at low energies of incident electrons when no shooting of thin films can take place. In such experiments the lattice must absolutely be involved in the process of electron backscattering, since the plasmon cannot appreciably affect the direction of motion of electrons. However, the lattice not only causes the appearance of backscattered electrons, but can also affect the very process of plasmon excitation. In the present paper a theoretical treatment is given of the influence which the lattice exerts on the process of plasmon generation. This influence is displayed through two effects: the bremsstrahlung of plasmons and the density effect. These effects are due to the processes of either the plasmon emission beginning before the termination of the electron-lattice collision or the electron-lattice collision beginning before the termination of electron-plasmon collision event and to the interference of these processes. The most important result of the theory developed in the paper is that these effects lead to the broadening of the plasmon resonance line, which is of the same, or even greater, order of magnitude than that due to the traditional mechanisms.     

On a general spectrochemical method for the direct arcing of liquid-liquid extraction residues in a D.C. arc

A considerable reduction in volume of the enriched sample is combined with the high absolute sensitivity of a mixed cathode layer—cathode excitation, which is applied directly to organic extraction residues in a 1: 1 mixture with an aluminagraphite base. An oxygen protective atmosphere is used to increase the arc temperature, stabilize the column, and reduce cyanogen band interference. The method eliminates the need for subsequent mineralization or burning. Its application is discussed with reference to liquid-liquid extraction systems.     

Beitrag zur Trennung von Wolfram und Vanadium

Ohne ZusammenfassungJetzt: Hüttenlaboratorium der Akademie für Wissenschaften, Prag (Tschechoslowakei).     

Vanishing of the Kontsevich Integrals of the Wheels

We prove that the Kontsevich integrals (in the sense of the formality theorem) of all even wheels are equal to zero. These integrals appear in the approach to the Duflo formula via the formality theorem. The result means that for any finite-dimensional Lie algebra g, and for invariant polynomials f, g [S ^·(g)]^g one has f · g = f * g, where * is the Kontsevich star product, corresponding to the Kirillov–Poisson structure on g^*. We deduce this theorem form the result contained in math.QA/0010321 on the deformation quantization with traces.     

Analysis of nonlinear dynamics on arbitrary geometries with the Virtual Cell

The Virtual Cell is a modeling tool that allows biologists and theorists alike to specify and simulate cell-biophysical models on arbitrarily complex geometries. The framework combines an intuitive, front-end graphical user interface that runs in a web browser, sophisticated server-side numerical algorithms, a database for storage of models and simulation results, and flexible visualization capabilities. In this paper, we present an overview of the capabilities of the Virtual Cell, and, for the first time, the detailed mathematical formulation used as the basis for spatial computations. We also present summaries of two rather typical modeling projects, in order to illustrate the principal capabilities of the Virtual Cell. (c) 2001 American Institute of Physics.     

Linear discrete operators on the disk algebra

Let be the disk algebra. In this paper we address the following question: Under what conditions on the points do there exist operators such that

and , , for every ? Here the convergence is understood in the sense of norm in . Our first result shows that if satisfy Carleson condition, then there exists a function such that , . This is a non-trivial generalization of results of Somorjai (1980) and Partington (1997). It also provides a partial converse to a result of Totik (1984). The second result of this paper shows that if are required to be projections, then for any choice of the operators do not converge to the identity operator. This theorem generalizes the famous theorem of Faber and implies that the disk algebra does not have an interpolating basis.

     

An angle in Minkowski space

A new angular measure in Minkowski space is introduced. It is defined for a cone of any dimension, is additive and invariant under invertible linear transformations. For the dimension 2, it has a clear interpretation as an amount of rotation in the Minkowski space from a direction to another one.     

On rational isotropic congruences of lines

The aim of this paper is to show a way to find an explicit parametrization of rational isotropic congruences of lines in Euclidean three-space It will be shown that also the focal surfaces of these congruences admit a rational parametrization. Furthermore, the close relation of isotropic congruences of lines to minimal surfaces will be used to find the related polynomial minimal surfaces.