scholarly journals Contribution of Jonas Kubilius to the metric theory of Diophantine approximation of dependent variables

2021 ◽  
pp. 34-50
Author(s):  
Victor V. Beresnevich ◽  
Vasily I. Bernik ◽  
Friedrich Götze ◽  
Elena V. Zasimovich ◽  
Nikolai I. Kalosha
Keyword(s):  
Number Theory ◽  
Diophantine Approximation ◽  
Major Result ◽  
Dependent Variables ◽  
Academic School ◽  
Academy Of Sciences

The article is devoted to the latest results in metric theory of Diophantine approximation. One of the first major result in area of number theory was a theorem by academician Jonas Kubilius. This paper is dedicated to centenary of his birth. Over the last 70 years, the area of Diophantine approximation yielded a number of significant results by great mathematicians, including Fields prize winners Alan Baker and Grigori Margulis. In 1964 academician of the Academy of Sciences of BSSR Vladimir Sprindžuk, who was a pupil of academician J. Kubilius, solved the well-known Mahler’s conjecture on the measure of the set of S-numbers under Mahler’s classification, thus becoming the founder of the Belarusian academic school of number theory in 1962.

scholarly journals Projective metric number theory

2016 ◽  
Vol 2016 (712) ◽  
Author(s):  
Anish Ghosh ◽  
Alan Haynes
Keyword(s):  
Number Theory ◽  
Projective Space ◽  
Diophantine Approximation ◽  
Higher Dimension ◽  
Probabilistic Theory ◽  
Metric Number Theory ◽  
Projective Metric

AbstractIn this paper we consider the probabilistic theory of Diophantine approximation in projective space over a completion of ℚ. Using the projective metric studied in [Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 23 (1996), no. 2, 211–248] we prove the analogue of Khintchine's theorem in projective space. For finite places and in higher dimension, we are able to completely remove the condition of monotonicity and establish the analogue of the Duffin–Schaeffer conjecture.

scholarly journals Galina Yakovlevna Ilyina: On the occasion of her 90th Birthday

2020 ◽  
pp. 519-527
Author(s):  
Nadezhda N. Starikova
Keyword(s):  
Literary Critic ◽  
Foreign Countries ◽  
South Slavs ◽  
Russian Literary ◽  
Literary Process ◽  
Systematic Character ◽  
The Russian Federation ◽  
Academic School ◽  
Academy Of Sciences ◽  
Academic Personnel

Galina Yakovlevna Ilyina is an outstanding Russian literary critic specializing in Yugoslav literatures. A researcher of the history and typology of the literatures of the South Slavs, she devoted her whole life to their study and popularization. Thanks to her efforts, the development of the literary process of the Bulgarian, Bosnian, Macedonian, Serbian, Slovenian, Croatian and Montenegrin literature has acquired a complex and systematic character in our country. Galina Yakovlevna can rightfully be considered the founder of the academic school of literary Yugoslav studies in Russia, the academic personnel trained by her are currently successfully continuing to develop the themes and problems of the literatures of the Yugoslav and post-Yugoslavian space. Galina Yakovlevna became the first Yugoslav literary critic in the Russian Federation who was awarded the academic title of Professor of the Russian Academy of Sciences with the qualification Literature of the Peoples of Foreign Countries.

scholarly journals The Role of the Concept of Strategizing by V. L. Kvint in Economic Research of Strategies and its Features

2021 ◽  
pp. 45-57
Author(s):  
T. A. Alabina
Keyword(s):  
System Analysis ◽  
Modern Science ◽  
Integrated Approach ◽  
Point Of View ◽  
Economic Research ◽  
Scientific School ◽  
Academic School ◽  
The One ◽  
Academy Of Sciences

The two-part series of articles reveals the purpose of the research as determining the place of the concept of strategizing of a Foreign Member of the Russian Academy of Sciences — Academician, Doctor of Economics, Professor V. L. Kvint in the system of economic research of strategies abroad, in the USSR and modern Russia on the basis of the description of the content and systematization of the basic concepts of strategizing and a review of foreign and domestic regional economic research, as well as the author’s identification of the key characteristics of this scientific school of strategy.The object of the research is the theory of strategies abroad, in the USSR and modern Russia. The subject of the research is the concept of V L. Kvint’s strategizing in the system of economic research on strategy.The methodological tools include techniques and methods of system analysis, comparative analysis, logical analysis, principles of the dialectical-materialistic method of cognition and an integrated approach to the characterization of economic research, methods of generalization and concretization The description of the study uses a historical approach and a temporary generalization based on the key milestones in the development of economic research on the theory of strategy and the methodology and practice of strategizing.As the results of the second article in the series, the author’s characteristics are presented and the role of V. L. Kvint’s concept of strategizing in the system of economic research is determined. The article shows the practice of strategizing the academic school of science of V. L. Kvint as a matrix organizational structure, which indicates its complex hierarchical content and horizontal-vertical relationships between key elements. It is concluded that it is neoclassical and non-classical (atypical) in the sciences of strategy, since, on the one hand, the theory of strategy of V. L. Kvint is a new classical theory, where the classics become part of the modern science of strategy, at the same time, on the other hand, due to its characteristics such as novelty, relevance, universality, practice-oriented, simplicity, uniqueness and interdisciplinarity, it is not burdened with the cumbersome constructions of classical strategy studies, which are rejected, especially from the point of view of the practice of formal strategies and other documents.

Diophantine approximation

2021 ◽  
Vol 34 (2) ◽  
pp. 205-229
Author(s):  
Noriko Hirata-Kohno
Keyword(s):  
Number Theory ◽  
Diophantine Approximation ◽  
Recent Progress ◽  
Padé Approximation ◽  
Pade Approximation ◽  
Fundamental Properties ◽  
Subspace Theorem ◽  
Diophantine Problems

This article gives an introductory survey of recent progress on Diophantine problems, especially consequences coming from Schmidt’s subspace theorem, Baker’s transcendence method and Padé approximation. We present fundamental properties around Diophantine approximation and how it yields results in number theory.

A NOTE ON MATRIX APPROXIMATION IN THE THEORY OF MULTIPLICATIVE DIOPHANTINE APPROXIMATION

2019 ◽  
Vol 100 (3) ◽  
pp. 372-377
Author(s):  
YUAN ZHANG
Keyword(s):  
Number Theory ◽  
Diophantine Approximation ◽  
Hausdorff Measure ◽  
Matrix Form ◽  
Matrix Approximation ◽  
The Matrix ◽  
Closing The Gap

We prove the Hausdorff measure version of the matrix form of Gallagher’s theorem in the inhomogeneous setting, thereby proving a conjecture posed by Hussain and Simmons [‘The Hausdorff measure version of Gallagher’s theorem—closing the gap and beyond’, J. Number Theory186 (2018), 211–225].

scholarly journals Kurt Mahler, 26 July 1903 - 26 February 1988

1994 ◽  
Vol 39 ◽  
pp. 263-279
Keyword(s):  
Number Theory ◽  
Diophantine Approximation ◽  
Transcendental Number ◽  
Mathematical Research ◽  
Geometry Of Numbers ◽  
Great Pleasure ◽  
The World

Kurt Mahler, F.R.S., F.A.A., was born on 26 July 1903 at Krefeld am Rhein in Germany; he died aged 85 on 26 February 1988 in Canberra, Australia. From 1933 onwards most of his life was spent outside of Germany; but his mathematical roots remained in the great school of mathematics which existed in Germany between the two world wars. Above all Mahler lived for mathematics; he took great pleasure in lecturing, researching and writing. It was no surprise that he remained active in research until the last days of his life. He was never a narrow specialist and had a remarkably broad and thorough knowledge of large parts of current and past mathematical research. At the same time he was oblivious to mathematical fashion, and very much followed his own path through the world of mathematics, uncovering new and simple ideas in many directions. In this way he made major contributions to transcendental number theory, diophantine approximation, p -adic analysis, and the geometry of numbers. Towards the end of his life, Kurt Mahler wrote a considerable amount about his own experiences; see ‘Fifty years as a mathematician’ , ‘How I became a mathematician’ , ‘Warum ich eine besondere Vorliebe für die Mathematik habe’, ‘Fifty years as a mathematician II’. There is also a recent excellent account of his life and work by Cassels (1991). In preparing this memoir we have freely used these sources. We have also drawn on our knowledge of, and conversations with, Mahler whom we first met when we were undergraduates in Australia in the early sixties.

scholarly journals DETERMINACY AND INDETERMINACY OF GAMES PLAYED ON COMPLETE METRIC SPACES

2014 ◽  
Vol 90 (2) ◽  
pp. 339-351
Author(s):  
LIOR FISHMAN ◽  
TUE LY ◽  
DAVID SIMMONS
Keyword(s):  
Number Theory ◽  
Approximation Theory ◽  
Diophantine Approximation ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Large Audience ◽  
Schmidt’S Game

AbstractSchmidt’s game is a powerful tool for studying properties of certain sets which arise in Diophantine approximation theory, number theory and dynamics. Recently, many new results have been proven using this game. In this paper we address determinacy and indeterminacy questions regarding Schmidt’s game and its variations, as well as more general games played on complete metric spaces (for example, fractals). We show that, except for certain exceptional cases, these games are undetermined on certain sets. Judging by the vast numbers of papers utilising these games, we believe that the results in this paper will be of interest to a large audience of number theorists as well as set theorists and logicians.

Multiplicative Number Theory I

2006 ◽  
Author(s):  
Hugh L. Montgomery ◽  
Robert C. Vaughan
Keyword(s):  
Number Theory
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