Steady-state analytical solutions for the lattice boltzmann equation

A general class of analytical solutions of the lattice Boltzmann equation is derived for two-dimensional, steady-state unidirectional flows. A subset of the solutions that verifies the corresponding Navier-Stokes equations is given. It is pointed out that this class includes, e.g., the Couette and the Poiseuille flow but not, e.g., the basic Kolmogorov flow. For steady-state non-unidirectional flows, first and second order solutions of the lattice Boltzmann equation are derived. Practical consequences of the analysis are mentioned. Differences between the technique applied here and those used in some earlier works are emphasized.     

Investigating and ordering Quadrilaterals and their analogies in space—problem fields with various aspects

Problem fields with one or two generating problems and possibilities of varying existing problems give a good chance for self-activities of students and can be used for reaching different general aims. In this paper some topics concerning quadrilaterals will be presented. I hope they will animate teachers for more problem orientation in mathematics education. First we will reflect about different types of convex and non-convex quadrilaterals and possibilities of ordering them. Then we focus on middle-quadrilaterals and types of quadrilaterals with special middle-quadrilaterals as well as their logical ordering. Finally we investigate the analogies in space to the parallelogram and its sub-types and order them in the “house of parallelepipeds”.     

Smooth and Topological Equivalence of Functions on Surfaces

We obtain conditions under which the Morse functions defined on surfaces are smooth equivalent and functions with isolated critical (singular) points are topologically equivalent.     

Dynamical and Topological Methods in the Theory of Geodesically Equivalent Metrics

We suggest a new, more global, approach to the study of geodesically equivalent metrics which is based on application of the theory of integrable geodesic flows. Bibliography: 17 titles.     

Raman echo under medium excitation by extremely short pulses

A generalization of the Bloembergen-Shen model to Raman active molecules with an arbitrary number of normal modes was suggested. The generalized model was used to study Raman echo signal characteristics when a system of molecules was excited by pulses of widths up to one period of optical oscillations. It was shown that a large number of echo responses on Stokes and anti-Stokes components could arise even under a two-pulse action in a continuous monochromatic pumping field. The number of echo responses depended on the number of molecular normal modes and the geometry of measurements. At small exciting pulse “areas,” the echo responses whose Stokes and anti-Stokes components corresponded to normal vibrational modes of a molecule had the highest intensity, whereas the components formed by normal mode combinations were strongly suppressed.     

The Spirals of the Universe

Russian Physics Journal -     

Proteinases from Carica papaya Latex

Data on the proteinase complex from Carica papaya latex were reviewed. The properties and applications of the domestic preparation cucumazyme and known medicinal preparations based on papaya proteinases (caripazyme, lecozyme, lecopain) were compared.     

Cycloaddition of Thiourea to Tri(1-propenyl)amine

Russian Journal of General Chemistry -