Ivanov, V. E.
Published in
Technical Physics

It is demonstrated that singularities (with different topological indices) of the projection of a nonuniform magnetic field onto the plane of the magneto-optical indicator film are imaged as singularities of the magneto-optical image related to variations in the orientation of angular dependences of image intensity on the circles with the given rad...

Saati, H.
Published in
Journal of Mathematical Sciences

The Padmakar–Ivan (PI) index of a graph G is defined as PIG=∑e∈GneueG+neveG,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathrm{PI}(G)={\displaystyle \sum_{e\in G}...

Savin, A. Schrohe, E. Sternin, B.
Published in
Russian Journal of Mathematical Physics

We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely, differential operators with shifts induced by the action of a (not necessarily periodic) isometric diffeomorphism. The key to the solution is the method of uniformization. To the nonlocal problem we assign a pseudodifferential operator...

Nistor, V. Troitsky, E.
Published in
Russian Journal of Mathematical Physics

We continue our study of gauge equivariant K-theory. We thus study the analysis of complexes endowed with the action of a family of compact Lie groups and their index in gauge equivariant K-theory. We introduce various index functions, including an axiomatic one, and show that all index functions coincide. As an application, we prove a topological ...

Savin, A. Yu Sternin, B. Yu. Schrohe, E.
Published in
Journal of Mathematical Sciences

We give an elementary solution to the problem of the index of elliptic operators associated with shift operator along the trajectories of an isometric diffeomorphism of a smooth closed manifold. This solution is based on index-preserving reduction of the operator under consideration to some elliptic pseudo-differential operator on a higher-dimensio...

Virupaksha, Bastikar Alpana, Gupte Prashant, Khadke Uday, Deshpande Alessandro, Desideri
Published in
Journal of Cheminformatics

Makarenkov, O. Yu. Martynova, I. S.
Published in
Doklady Mathematics

Bachman, David
Published in
Mathematische Annalen

Let M1 and M2 be compact, orientable 3-manifolds with incompressible boundary, and M the manifold obtained by gluing with a homeomorphism \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} ...

Strizhakova, Yu. A. Ryzhov, A. N. Smolenskii, E. A. Lapidus, A. L.
Published in
Doklady Chemistry

Strizhakova, Yu. A. Ryzhov, A. N. Chuvaeva, I. V. Smolenskii, E. A. Lapidus, A. L.
Published in
Solid Fuel Chemistry

The yields of oil upon the semikoking of 21 oil shales from 21 different sources depending on their chemical composition and heats of combustions were considered. The simulation of these dependences made it possible to obtain calculation formulas with the very high statistical characteristics. These formulas allowed us to predict the yields of oil ...