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).     

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.     

Theory of electromagnetic stirring by AC fields

Electromagnetic fields are often used industrially to controlthe flow of liquid metal, and in particular this review is concernedwth applications of alternating fields. An alternating fieldinduces eddy currents in liquid metal which interact with thefield to give a Lorentz body force which is generally rotationaland which must therefore drive fluid motion. We derive generalexpressions for the Lorentz force, showing that it consistsof both steady and oscillatory components. The flow in a circularcylinder due to a rotating field is discussed in detail, sincethis problem is simple to analyse and illustrates several importantgeneral principles. In the high-frequency limit, the field isconfined to a narrow layer on the surface of the conductor,and we derive approximate methods for calculating the surfacemagnetic pressure andthe induced flow. We also examine the otherextreme of slowly alternating fields. As each problem is studied,we discuss practical applications.