Related papers: Victor Borisovich Lidskii (1924-2008)
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
A categorized bibliography of combinators is given, providing what is believed to be a largely complete coverage of publications from the origination of combinators in 1920 to the present day.
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering. In decision theory, they can model…
This is an overview of mathematical heritage of Sergey Naboko in the area of functional models of non-self-adjoint operators. It covers the works by Sergey in model construction, the analysis of absolutely continuous and singular spectra…
We review the life and scientific work of F.V Atkinson, mathematician. The article consists of a brief overview of his academic and professional life followed by an extensive compilation of his life's work, some unpublished. He is best…
An algebraic construction more general and intimately connected with that of Faddeev$^1$, along with its application for generating different classes of quantum integrable models are summarised to complement the recent results of ref. 1 (…
We consider a rather general version of ladder operator $Z$ used by some authors in few recent papers, $[H_0,Z]=\lambda Z$ for some $\lambda\in\mathbb{R}$, $H_0=H_0^\dagger$, and we show that several interesting results can be deduced from…
A long standing problem of Gian-Carlo Rota for associative algebras is the classification of all linear operators that can be defined on them. In the 1970s, there were only a few known operators, for example, the derivative operator, the…
The short history of L.Kantorovich's transport problem and his metric in the framework of his activity in mathmatics and economics during a long and difficult period. We did not mention the recent impetuious developement of application of…
The regularization of propagators by means of a complex metric is considered. (The paper is an English translation of the first of two articles in Russian published by the author in 1987-88: V.D. Ivashchuk, Regularization by…
In this paper, we introduce the notion of curved $\mathcal{O}$-operator systems as a generalization of T. Brzezi\'{n}ski's (curved) Rota-Baxter systems, and then investigate their relations with $\mathcal{O}$-operator systems,…
Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras and von Neumann algebras, which is increasingly of interest in…
Mikhail Lomonosov (1711-1765) is the eminent Russian polymath and a towering figure of the European Enlightenment. This English translation of his seminal work Discourse on Greater Accuracy of Navigation concludes the series of English…
This article contains a summary of the author's contributions, one in collaboration with K. Bardakci, to dual models and string theory prior to the mid-seventies. Other workers' contributions, during and subsequent to this period, are…
Using the classical Lazard's elimination theorem, we obtain a decomposition theorem for Lie algebras defined by generators and relations of a certain type. This is a preprint version of the paper appearing in Communications in Algebra…
In this work we develop a theory of Vessels. This object arises in the study of overdetermined 2D systems invariant in one of the variables, which are usually called time invariant. To each overdetermined time invariant 2D systems there is…
This is an English translation of Nikolai Chebotaryov's paper "Die Probleme der modernen Galoisschen Theorie" from 1932. An excerpt from this paper was given as a lecture at the International Congress of Mathematicians in Z\"urich in 1932.…
We give an introduction to the realisation theory for infinite-dimensional systems. That is, we show that for any function $G$, analytic and bounded in the right half of the complex plane, there exists operators $A,B,C$ such that…
This survey presents in some detail the main advances that have been recently taking place in Computational Linguistics towards the unification of the two prominent semantic paradigms: the compositional formal semantics view and the…