Effect of the anode-current magnetic field on the motion of electrons in a triode with a virtual cathode

The effect of the anode-current magnetic field on the electron motion in a triode with a virtual cathode is considered. It is shown that the anode-current magnetic field influences the oscillation period and trajectories of electrons. The condition of self-isolation of the electron beam is investigated as a function of the diode parameter. It is shown that the displacement of the beam electrons under the action of the anode-current magnetic field leads to a decrease in the electron phase modulation and an increase in the spread in the electron oscillation amplitude; as a result, the generation efficiency of microwave radiation decreases.     

Substituents influences on the rate of α-alkylacroleins dimerization

Kinetics of α-alkylacroleins dimerization was studied. It was established that both electronic and steric factors affect the process rate, with the prevalence of the latter factors.     

On the possibility of TEM mode excitation in a virtual-cathode triode

It is demonstrated theoretically and experimentally that generation of the TEM mode in a virtualcathode triode is a possibility. Conditions favoring TEM mode excitation in the domain where an electron beam interacts with an electromagnetic wave are determined.     

Characterizations of the Random Order Values by Harsanyi Payoff Vectors

A Harsanyi payoff vector (see Vasil’ev in Optimizacija Vyp 21:30–35, 1978) of a cooperative game with transferable utilities is obtained by some distribution of the Harsanyi dividends of all coalitions among its members. Examples of Harsanyi payoff vectors are the marginal contribution vectors. The random order values (see Weber in The Shapley value, essays in honor of L.S. Shapley, Cambridge University Press, Cambridge, 1988) being the convex combinations of the marginal contribution vectors, are therefore elements of the Harsanyi set, which refers to the set of all Harsanyi payoff vectors.The aim of this paper is to provide two characterizations of the set of all sharing systems of the dividends whose associated Harsanyi payoff vectors are random order values. The first characterization yields the extreme points of this set of sharing systems and is based on a combinatorial result recently published (Vasil’ev in Discretnyi Analiz i Issledovaniye Operatsyi 10:17–55, 2003) the second characterization says that a Harsanyi payoff vector is a random order value iff the sharing system is strong monotonic.This work was partly done whilst Valeri Vasil’ev was visiting the Department of Econometrics at the Free University, Amsterdam. Financial support from the Netherlands Organisation for Scientific Research (NWO) in the framework of the Russian-Dutch programme for scientific cooperation, is gratefully acknowledged. The third author would also like to acknowledge partial financial support from the Russian Fund of Basic Research (grants 98-01-00664 and 00-15-98884) and the Russian Humanitarian Scientific Fund (grant 02-02-00189a).     

Blockwise estimate of the fundamental matrix of linear singularly perturbed differential systems with small delay and its application to uniform asymptotic solution

A singularly perturbed system of linear differential equations with a small delay is considered. Estimates of blocks of the fundamental matrix solution to this system uniformly valid for all sufficiently small values of the parameter of singular perturbations are obtained in the cases of time-independent and time-dependent coefficients of the system. In the first case the system is considered on an infinite time-interval, while in the second case it is considered on a finite one. These estimates are applied to justify a uniform asymptotic solution of an initial-value problem for this system in both cases.     

Coherent Transmission and Reflection by a monolayer of discrete scatterers

Coherent transmission and reflection of a plane wave through a monolayer of discrete particles are considered on the basis of simple and physically transparent formulae for the single scattering approximation (SSA) corrected by introducing a multiple scattering permittivity factor. This factor allows for multiple scattering of Waves between monolayer particles, opposite to the SSA. The multiple scattering permittivity factor is considered on the basis of the quasi-crystalline approximation (QCA) via ? matrix formalism. The multiple scattering permittivity factor and parameters for obtaining coherent transmission and reflection coefficients (the effective extinction coefficient and the transmission and reflection coefficients due to rescattering) are calculated within the scope of QCA and plotted for comparison with SSA results. The expressions for these values are simplified for small Rayleigh particles to simple analytical formulae.