Numerical simulation of achromatic deflecting systems

A deflecting system formed by two parallel-plate capacitors on opposite sides of an optoelectronic element that alters the energy of a beam of charged particles, is calculated numerically. The conditions for correcting the chromatic beam spreading in the plane of the target are found. Good agreement with the results of an approximate analytical calculation is demonstrated. Zh. Tekh. Fiz. 67, 86–88 (December 1997)     

Euler decompositions for theta-series of even quadratic forms

For a generating Dirichlet vector series with coefficients equal to the number of representations of a quadratic form by another one we abtain a decomposition into the product of a finite number of Dirichlet L-functions and an infinite number of matrix polynomials. The coefficients of the polynomials are the Eichler-Brandt matrices of the basis double cosets of the local orthogonal Hecke rings. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 212, 1994, pp. 97–113. Translated by N. Yu. Netsvetaev.     

Decomposition methods: A new proof of convergence

We propose a new convergence proof of Adomian's technique based on properties of convergent series. Then we deduce some results about the speed of convergence of this method allowing us to solve nonlinear functional equations.     

Noncommutative differential geometry related to the Young-Baxter equation

An analogue of the differential calculus associated with a unitary solution of the quantum Young-Baxter equation is constructed. An example of a ring sheaf is considered in which local solutions of the Young-Baxter quantum equation are defined but there is no global section. Bibliography: 13 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 199, 1992, pp. 51–70. Translated by I. A. Izergina.     

Noncommutative four-dimensional subalgebras of conformal algebra integrable in the space R1,3

D'alambert's equation is used as an example to study the possibilities of a new method of exactly integrating systems of linear differential equations — the method of noncommutative integration (NI). The results confirm that use of the NI is equivalent to complete separation of the variables in the case of four-dimensional subalgebras of conformal algebra. However, the method does simplify determination of the exact solution in this instance.Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 120–124, February, 1995.     

Cellulose-polyamide 66 blends. Part II: Mechanical behavior

Blends of the natural polymer cellulose with a synthetic polymer, polyamide 66, are studied in order to determine if the expected strong interaction between them, due to hydrogen bonds, could improve their mechanical properties such as strength and elongation at break. In a previous work {Part I, J. Polym. Sci. Polym. Phys., 32 , 1437 (1994)}, the preparation technique and the characterization of cellulose-polyamide 66 (PA66) blends were described in detail. Several samples in the composition range between 0 to 70 wt % of PA66 were carefully dried and examined using dynamic mechanical and tensile tests. Based on previous work a new percolation model has been developed. It takes both linear and nonlinear mechanical behaviors into account and allows for the effect of adhesion between material domains. From comparison between experimental and predicted data, it is concluded that a partial miscibility between the amorphous phases of cellulose and PA66 exists and is responsible for a strong adhesion at their interface. Solid-state ¹³C nuclear magnetic resonance has also been used to study these samples and supports the existence of strong interactions between both homopolymers. © 1995 John Wiley & Sons, Inc.     

Axial Structure of the Field Intensity in Diffusion-Controlled Surface-Wave Produced Plasmas

Surface-wave gas discharges sustained under the conditions of a diffusion controlled regime are studied on the basis of the fluid plasma model. The self-consistent behaviour of the plasma density and of the field intensity along the discharge length is obtained. It is shown that the nonlinearity in the particle balance equation due to stepwise ionisation determines the plasma density in terms of the field intensity and ensures self-consistent behaviour of the wave ? discharge characteristics in a diffusion controlled regime.