Solving the eigenvalue problem for sparse matrices

A modification of the Danilewski method is presented, permitting the solution of the eigenvalue problem for a constant sparse matrix of large order to be reduced to the solution of the same problem for a polynomial matrix of lower order. Certain solution algorithms are proposed for a partial eigenvalue problem for the polynomial matrix. Questions of the realization of the algorithms on a model PRORAB computer are examined.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 58, pp. 92–110, 1976.     

An investigation of the fractional composition of dioxane lignin of the cotton plant by the PMR method

Analysis of the PMR spectra of six fractions of the dioxane lignins of the cotton plant differing considerably in molecular weight has confirmed their chemical nonidentity. It has been established that the low-molecular-weight fractions are less condensed than the high-molecular-weight fractions. It has been found that aliphatic OH groups are approximately evenly distributed between the - and -C atoms of the lignin side chain.Institute of the Chemistry of Plant Substances, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 1, pp. 116–120, January–February, 1980.     

Evolution of phase transitions in SrTiO3-BiFeO3 solid solutions

The dielectric and acoustic properties of (1 ? x)SrTiO₃?xBiFeO₃ solid solutions (0 ≤ x ≤ 1) have been studied in the temperature range from 4.2 to 850 K. Evolution of the antiferrodistortive transition and its suppression in the concentration range 0.1 < x < 0.2 have been revealed. X-ray diffraction data obtained at room temperature, as well as the observed acoustic anomalies combined with dielectric measurements, have been used to estimate the concentration range of the existence of the relaxor state, as well as of the formation and coexistence of the antiferromagnetic and ferroelectric phases at high BiFeO₃ concentrations.     

Dissipative plasmon‐solitons in multilayer graphene

Nonlinear properties of a multi‐layer stack of graphene sheets are studied. It is predicted that such a structure may support dissipative plasmon‐solitons generated and supported by an external laser radiation. Novel nonlinear equations describing spatial dynamics of the nonlinear plasmons driven by a plane wave in the Otto configuration are derived and the existence of single and multi‐hump dissipative solitons in the graphene structure is predicted.