Combinatorial invariant for Morse-Smale diffeomorphisms on surfaces with orientable heteroclinic.

In this paper, we consider a class of orientation-preserving Morse-Smale diffeomorphisms defined on an orientable surface. The papers by Bezdenezhnykh and Grines showed that such diffeomorphisms have a finite number of heteroclinic orbits. In addition, the classification problem for such diffeomorphisms is reduced to the problem of distinguishing orientable graphs with substitutions describing the geometry of a heteroclinic intersection. However, such graphs generally do not admit polynomial discriminating algorithms. This article proposes a new approach to the classification of these cascades. For this, each diffeomorphism under consideration is associated with a graph that allows the construction of an effective algorithm for determining whether graphs are isomorphic. We also identified a class of admissible graphs, each isomorphism class of which can be realized by a diffeomorphism of a surface with an orientable heteroclinic. The results obtained are directly related to the realization problem of homotopy classes of homeomorphisms on closed orientable surfaces. In particular, they give an approach to constructing a representative in each homotopy class of homeomorphisms of algebraically finite type according to the Nielsen classification, which is an open problem today.

[Study of fine structure changes in the human constant electrical field in a series of eye diseases]. / Issledovanie izmenenii tonkoi struktury postoiannogo élektricheskogo polia cheloveka pri riade zabolevanii organov zreniia.

Using external non-polarized electrodes Ag/AgCl the potential difference was measured between four measure points and a referent point, situated on the skin of humans with normal sight function and of ones suffering from cataracta, glaucoma and toxic neurite. Three points, situated on the face skin and a point at the corner of the nail couch of the forefingers of both hands were used as the measure points. The referent point was always situated on the neck in the place of the crossing of the cowl muscle and clavicle-nipple one. The investigation has shown that the potential difference between all the measured points and the referent point varies for all the diseases, mentioned above, and hence, the fine structure of the electric field changes in a different way at all these diseases. Thus, a regulator of life processes the constant electric field of the organism-searches all the pathologic changes and gives broad possibilities for the diagnostics of both the whole organism state and a particular organ one.

[Effect of polymer modification of insulin on its enzymatic hydrolysis and conformation properties]. / Vliianie polimernoi modifikatsii insulina na ego fermentativnyi gidroliz i konformatsionnye svoistva.

AI, B29 insulin polymeric derivatives in which the polymeric chains (N-polyvinylimidazole, N-polyvinylpyrrolydone and polyacrylic acid) are bonded to the insulin molecule at one point were synthesized. The hydrolysis of the modified insulin by trypsin is dependent to a great extent on the chemical nature of the modifying polymer and is virtually independent of its molecular weight up to 20 kD. The effect of the modifying polymer manifests itself mainly in a change of the Michaelis constant. Investigation of the conformational properties of the insulin derivatives by the method of optical rotatory dispersion revealed that insulin modification by polymers caused a decrease of the amino acid content in the alpha-helical sequence from 41 to 33-30%. The chemical nature of the modifying polymer and its molecular weight have a profound effect on the conformational stability of the residual spatial structure of the modified insulin in alkaline media.