Recurrence of trajectories of systems of linear differential equations with conditionally periodic coefficients

Translated from Matematicheskie Zametki, Vol. 54, No. 1, pp. 52–56, July, 1993.     

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)     

Factorization of univalent analytic functions on compact Riemann surfaces with boundary

The paper is devoted to the theory of factorization of univalent analytic functions on a compact Riemann surface with boundary. The main component of the theory is a new method for the removal of the periods of certain functions (the natural analogues of the Schwarz integral and Blaschke products) along the boundary curves and bundle sections.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 285–313, 1989.     

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.     

Evaluation of atomic fluorescence, absorption and emission techniques for the determination of mercury

Summary Atomic fluorescence (AFS), absorption (AAS) and emission (AES) systems were evaluated for the determination of inorganic mercury. Identical vapour generation and amalgamation procedures were used to permit direct comparison of the performance of a commercial long-path AAS instrument to laboratory constructed non-dispersive AFS as well as He-MIP based AES instruments. Instrumental noise-limited detection limits (LOD) were 0.94, 2.4, 2.8 pg for AAS, AES and AFS techniques, respectively. Methodological LOD's were found to be blank controlled and similar for all three instruments, viz. 9, 25 and 16 pg for AAS, AFS and AES, respectively. All three systems produced accurate results at the low ng/l concentration, as verified by the analysis of a certified river water reference material (NRCC ORMS-1).