Virtual parity Alexander polynomial

In this paper, we define the virtual Alexander polynomial following the works of Boden et al. (2016) [Alexander invariants for virtual knots, J. Knot Theory Ramications 24(3) (2015) 1550009] and Kaestner and Kauffman [Parity biquandles, in Knots in Poland. III. Part 1, Banach Center Publications, Vol. 100 (Polish Academy of Science Mathematical Institute, Warsaw, 2014), pp. 131–151]. The properties of this invariant are explored and some examples are computed. In particular, the invariant demonstrates that many virtual knots cannot be unknotted by crossing changes on only odd crossings.

Repeated measurements with unintended feedback

An econometric analysis of consumer research data which hit newspaper headlines in the Netherlands illustrates almost everything that can go wrong when standard statistical models are fit to the superficial characteristics of a data-set with no attention paid to the data generation mechanism. Author: Richard D. Gill, Mathematical Institute, Leiden University, The Netherlands; email address: [email protected].

Destinies and Seminars. On the Seminar «Problems of Reducing the Exhaustive Search» at LETI in a Historico-Scientific Context

Exhaustive Search» organized at the Leningrad Electrotechnical Institute (LETI) by R.I. Freidson (1942-2018) is considered. The seminar opened in 1982, one of its main aims being the development of scientific ideas of S. Yu. Maslov (1939-1982). The meetings continued regularly until the beginning of 1990es. The historico-scientific context is outlined, including the links with other contemporary seminars, such as the S.Yu. Maslov’s seminar and the seminar on mathematical logic at the Leningrad Branch of the Steklov Mathematical Institute (LOMI); the ideas developed at the seminar and main results represented by scientific publications are considered. The pedagogical role of the seminar (its formative influence on young researchers), the organizational talent of R.I. Freidson and the effect of his personality on seminar’s creative atmosphere are considered as well.

The Growth and Marcescence of the “System for Optimal Functioning of the Economy” (SOFE)

This article discusses the perhaps most systematic attempt to develop mathematical methods for use in planning and management of the Soviet economy: the system for optimal functioning of the economy (SOFE). The intellectual ferment of the post-Stalin “thaw,” and increasing difficulties in managing the growing economy, opened the way to new approaches to Soviet economics. Scholars, primarily at a new Academy of Sciences institute for applying mathematics to economic problems—the Central Economic-Mathematical Institute—developed a series of models and policy recommendations in dozens of monographs, articles, and conference reports from 1963 to the mid-1980s. Despite evident support at two CPSU Party Congresses (1966, 1971), SOFE never got traction in the official planning or administrative organs, although some specific mathematical methods and recommendations derived from SOFE were used experimentally, and indeed partially applied in plan implementations. The last act of SOFE came with the incorporation of many of its ideas in the final Soviet reform—Mikhail Gorbachev’s perestroika. I survey the evolution of the SOFE research program and its policy recommendations, arguing that it was inherently incapable of providing viable reform recommendations due not only to the difficulty of that task but also the political opposition to the recommendations derived from that program.

Ideology and Science (based on the discussion in CEMI RAS)

The debating society “Makarov’s tea party” chaired by the academician V.L. Makarov met on the 18th April 2019 in the Central Economic Mathematical Institute of the Russian Academy of Sciences in order to discuss the interrelationship between ideology and science. The society raised such issues as opposition and interpenetration of science and ideology; ideology and the genetic code of a nation; ideology and manipulation of conscience; numbers and facts as tools of ideological intervention. Here we present the most interesting points of the discussion. The authors of the reports: Makarov Valery, Doctor of Phys.-math., member of the Russian Academy of Sciences; Dementiev Victor, Doctor of Economics, Corr. RAS; Grebennikov Valery, Doctor of Economics; Ustyuzhanina Elena, Doctor of Economics.

The beginnings of mathematical institutions in Serbia

Institutional development of mathematics in Serbia rests on two national institutions: Belgrade Higher School established in 1863, from 1905 the University of Belgrade, and the Serbian Royal Academy founded in 1886, later the Serbian Academy of Sciences and today the Serbian Academy of Sciences and Arts. Dimitrije Nesic, professor of mathematics and rector of the Belgrade Higher School, founded the first mathematics library in Serbia in 1871. In time, as a result of the collaboration between the Academy and the University and overlapping activities, it had become the main place for mathematicians to gather and work and became known as the Mathematical Seminar of the University of Belgrade. The year 1896 is considered to be the year when the Seminar was officially founded and when it began its activities as an institution. Professors Mihailo Petrovic and Bogdan Gavrilovic, members of the Serbian Royal Academy, were the two people most responsible for its establishing. The period between the two world wars is the most significant period in the development and institutionalization of the activities of the Mathematical Seminar and Petrovic?s school of mathematics, which represent the root of the overall development of mathematics in Serbia. The Mathematical Institute was founded in 1946 under the authority of the Serbian Academy of Sciences. All Institute achievements and activities - publishing activities, organization of scientific seminars, introducing young and talented mathematicians to scientific work, improving the education process at the University of Belgrade - are pointed out. Today, after 70 years, the Mathematical Institute developed into the most significant Serbian institution of mathematics.

PULSARS: GIGANTIC NUCLEI

What is the real nature of pulsars? This is essentially a question of the fundamental strong interaction between quarks at low-energy scale and hence of the non-perturbative quantum chromo-dynamics, the solution of which would certainly be meaningful for us to understand one of the seven millennium prize problems (i.e., "Yang-Mills Theory") named by the Clay Mathematical Institute. After a historical note, it is argued here that a pulsar is very similar to an extremely big nucleus, but is a little bit different from the gigantic nucleus speculated 80 years ago by L. Landau. The paper demonstrates the similarity between pulsars and gigantic nuclei from both points of view: the different manifestations of compact stars and the general behavior of the strong interaction.