On quantum matrix algebras satisfying the Cayley-Hamilton-Newton identities

The Cayley-Hamilton-Newton identities which generalize both the characteristic identity and the Newton relations have been recently obtained for the algebras of the RTT-type. We extend this result to a wider class of algebras M(R,F) defined by a pair of compatible solutions of the Yang-Baxter equation. This class includes the RTT-algebras as well as the Reflection equation algebras

The first Russian female soil scientist

The year 2021 is marked by the 175-th anniversary of the birth of Anna Egorovna and Vasiliy Vasilievich Dokuchaevs. This is a wonderful occasion to recall an amazing and remarkably modest woman who played an important role in the life and work of the great Russian natural scientist, the founder of genetic soil science. If many works were written about her outstanding world-wide known husband, films were made, pictures were created, his photos are preserved, then the life of his wife is undeservingly poorly described, and the appearance of this very beautiful woman is depicted in the only one famous portrait. This article, dedicated to the memory of Anna Egorovna Dokuchaeva, is based on both the quotations from the already published memoirs of the follower and the friend of V.V. Dokuchaev – Franz Yulievich Levinson-Lessing, and the excerpts from Anna Egorovna’s letters to Varvara Ippolitovna – the wife of F.Yu. Levinson-Lessing. These letters were collected from the archives of the Academy of Sciences in St. Petersburg and copied by the employee of the V.V. Dokuchaev Soil Science Institute – Sergey Petrovich Lyalin – in the 1980s, and they are now kindly provided by the Central Soil Museum by V.V. Dokuchaev (the Branch of the Federal Research Centre “V.V. Dokuchaev Soil Science Institute” in St. Petersburg)

Ignition of wood subjected to the decreasing radiant energy flux

In this paper we analyze the ignition of wood samples subjected to the decreasing heat flow. The experimental setup was created on the base of the optical wave "Uran-1". The intensity of the heat flow was changed during the experiment by moving the test sample along the optical axis of the elliptic reflector in the setup. Pine wood was used as the test samples. We received the delay times for ignition of pine wood during heating by the decreasing heat flow. The received data were compared with the data for a static heat flow

Bulk-boundary correspondence in three dimensional topological insulators

We discuss the relation between bulk topological invariants and the spectrum of surface states in three dimensional non-interacting topological insulators. By studying particular models, and considering general boundary conditions for the electron wavefunction on the crystal surface, we demonstrate that using experimental techniques that probe surface states, only strong topological and trivial insulating phases can be distinguished; the latter state being equivalent to a weak topological insulator. In a strong topological insulator, only the {\it parity} of the number of surface states, but not the number itself, is robust against time-reversal invariant boundary perturbations. Our results suggest a \z definition of the bulk-boundary correspondence, compatible with the \z classification of topological insulators.Comment: TeXLive (Unix), revtex4-1, 7 pages, 3 figure

Regularising algorithm of parameter identification of electric charge equivalent circuit

A new algorithm of parameter identification of equivalent circuit for electrical charge replacement is suggested. The approach is based on the solution of integral equation of the I type with respect to the function of indicial admittance, by which then determination of replacement circuit parameters is carried out. Application of smoothing splines and original regulating algorithm including kernel setting error of integration equation permits to obtain a stable algorithm of parameter identification. The investigation of algorithm shows high calculating efficiency and sufficient accuracy of parameter identification

Aspects of a new class of braid matrices: roots of unity and hyperelliptic qq for triangularity, L-algebra,link-invariants, noncommutative spaces

Various properties of a class of braid matrices, presented before, are studied considering $N^2 \times N^2 (N=3,4,...)$ vector representations for two subclasses. For $q=1$ the matrices are nontrivial. Triangularity $(\hat R^2 =I)$ corresponds to polynomial equations for $q$, the solutions ranging from roots of unity to hyperelliptic functions. The algebras of $L-$ operators are studied. As a crucial feature one obtains $2N$ central, group-like, homogenous quadratic functions of $L_{ij}$ constrained to equality among themselves by the $RLL$ equations. They are studied in detail for $N =3$ and are proportional to $I$ for the fundamental $3\times3$ representation and hence for all iterated coproducts. The implications are analysed through a detailed study of the $9\times 9$ representation for N=3. The Turaev construction for link invariants is adapted to our class. A skein relation is obtained. Noncommutative spaces associated to our class of $\hat R$ are constructed. The transfer matrix map is implemented, with the N=3 case as example, for an iterated construction of noncommutative coordinates starting from an $(N-1)$ dimensional commutative base space. Further possibilities, such as multistate statistical models, are indicated.Comment: 34 pages, pape

Quantum matrix algebra for the SU(n) WZNW model

The zero modes of the chiral SU(n) WZNW model give rise to an intertwining quantum matrix algebra A generated by an n x n matrix a=(a^i_\alpha) (with noncommuting entries) and by rational functions of n commuting elements q^{p_i}. We study a generalization of the Fock space (F) representation of A for generic q (q not a root of unity) and demonstrate that it gives rise to a model of the quantum universal enveloping algebra U_q(sl_n), each irreducible representation entering F with multiplicity 1. For an integer level k the complex parameter q is an even root of unity, q^h=-1 (h=k+n) and the algebra A has an ideal I_h such that the factor algebra A_h = A/I_h is finite dimensional.Comment: 48 pages, LaTeX, uses amsfonts; final version to appear in J. Phys.