scholarly journals On scaling and regular variation

2015 ◽  
Vol 97 (111) ◽  
pp. 161-174 ◽  
Author(s):  
N.H. Bingham
Keyword(s):  
Mathematical Analysis ◽  
Regular Variation ◽  
Mathematical Physics ◽  
Self Similarity ◽  
Scaling Arguments

We survey scaling arguments, both asymptotic (involving regular variation) and exact (involving self-similarity), in various areas of mathematical analysis and mathematical physics.

Poisson's Memoirs on Electricity: Academic Politics and a New Style in Physics

1983 ◽  
Vol 16 (3) ◽  
pp. 239-259 ◽  
Author(s):  
R. W. Home
Keyword(s):  
Nineteenth Century ◽  
Mathematical Analysis ◽  
Mathematical Physics ◽  
Mathematical Creativity ◽  
Academic Politics ◽  
Major Figure

Siméon Denis Poisson (1781–1840) was a major figure in French science throughout the first forty years of the nineteenth century. Though his papers lack the brilliant mathematical creativity of some of those published by even more gifted contemporaries such as Joseph Fourier (1768–1830) and Augustin-Louis Cauchy (1789–1857), they nevertheless display a formidable talent for mathematical analysis, applied with great industry and success in a large number of investigations ranging over the whole domain of mathematical physics. Several were of such importance that even on their own they would have sufficed to win him lasting fame.

scholarly journals Blended Learning on Mathematical Analysis in Nomotex Digital Learning System

2020 ◽  
Vol 35 ◽  
pp. 03005
Author(s):  
Yury I. Dimitrienko ◽  
Michael P. Gordin ◽  
Elena A. Gubareva ◽  
Anna E. Pichugina
Keyword(s):  
Blended Learning ◽  
Conceptual Model ◽  
Mathematical Analysis ◽  
Mathematical Physics ◽  
Learning System ◽  
Digital Learning ◽  
State Technical ◽  
Mathematical Concepts ◽  
Computational Mathematics ◽  
Computer Visualization

The paper discusses the methodology and technology of teaching the discipline «Mathematical Analysis» using the new Digital Learning System Nomotex (the Nomotex DLS), developed at the Department of «Computational Mathematics and Mathematical Physics» Bauman Moscow State Technical University (BMSTU). A new conceptual model for conducting lectures and practical classes in blended learning is presented. Examples of interactive computer visualization of some mathematical concepts within the discipline «Mathematical analysis» are presented.

scholarly journals RENORMALIZATION GROUP SYMMETRY AND SOPHUS LIE GROUP ANALYSIS

1995 ◽  
Vol 06 (04) ◽  
pp. 503-512 ◽  
Author(s):  
DMITRIJ V. SHIRKOV
Keyword(s):  
Lie Group ◽  
Group Analysis ◽  
Mathematical Physics ◽  
The Self ◽  
Group Symmetry ◽  
Lie Group Analysis ◽  
Short Discussion ◽  
Self Similarity ◽  
Boundary Problems ◽  
Solution Property

We start with a short discussion of the content of a term Renormalisation Group in modern use. By treating the underlying solution property as a reparametrisation symmetry, we relate it with the self-similarity symmetry well-known in mathematical physics and explain the notion of Functional Self-similarity. Then we formulate a program of constructing a regular approach for discovering RG-type symmetries in different problems of mathematical physics. This approach based upon S. Lie group analysis allows one to analyse a wide class of boundary problems for different type of equations. Several examples are mentioned.

scholarly journals Mathematical Analysis. Basis: Nomotex E-course

2020 ◽  
Vol 35 ◽  
pp. 03004
Author(s):  
Yuriy I. Dimitrienko ◽  
Mikhail P. Gordin ◽  
Elena A. Gubareva ◽  
Anna E. Pichugina ◽  
Raisa K. Alesina ◽  
...  
Keyword(s):  
Mathematical Analysis ◽  
Teaching Methods ◽  
Mathematical Physics ◽  
Learning System ◽  
Digital Learning ◽  
State Technical ◽  
Innovative Teaching ◽  
Computational Mathematics ◽  
Technical University

The paper describes the peculiarities of the development of the digital course “Mathematical Analysis. 1st semester” in the digital learning system Nomotex (DLS “NOMOTEX”) [1], developed at the Department of Computational Mathematics and Mathematical Physics, Bauman Moscow State Technical University. The features of innovative teaching methods using this course are also presented.

scholarly journals Zeno and Nagarjuna on Motion from Mahamudra, Koan and Mathematical Physics

2017 ◽  
Author(s):  
Robert Paul
Keyword(s):  
Modern Philosophy ◽  
Mathematical Analysis ◽  
Analytic Philosophy ◽  
Mathematical Physics ◽  
Meditation Practice ◽  
Space And Time ◽  
History Of

Zeno’s Arrow and Nāgārjuna’s Fundamental Wisdom of the MiddleWay (Mūlamādhyamakakārikā, MMK) Chapter 2 (MMK/2) contain paradoxical, dialecticarguments thought to indicate that there is no valid explanation of motion, hence there is nophysical or generic motion. There are, however, diverse interpretations of the latter text, andI argue they apply to Zeno’s Arrow as well. I also find that many of the interpretations aredependent on a mathematical analysis of material motion through space and time. However,with modern philosophy and physics we find that the link from no explanation to nophenomena is invalid and that there is a valid explanation and understanding of physicalmotion. Hence, those arguments are both invalid and false, which banishes the MMK/2 andThe Arrow under this and derivative interpretations to merely the history of philosophy.However, a view that maintains their relevance is that each is used as a koan or sequence ofkoans designed to assist students in spiritual meditation practice. This view is partly justifiedby the realization that both Nāgārjuna and Zeno were likely meditation masters in addition tobeing logicians. The works are, therefore, not works that should be assessed as having validarguments and true conclusions by the standards of modern analytic philosophy—contrary tosome of the literature—but rather are therapeutic and perhaps more appropriatelyconsidered as part of an experientially focused philosophy such as existentialism,phenomenology or religion.

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