Living Systems (Complexity) From the Point of Chaos and Self-Organization Theory

2015 ◽  
Vol 22 (3) ◽  
pp. 25-32 ◽  
Author(s):  
Филатова ◽  
O. Filatova ◽  
Еськов ◽  
Valeriy Eskov ◽  
Хадарцев ◽  
...  
Keyword(s):  
Organization Theory ◽  
Modern Science ◽  
Continuous Change ◽  
Random Samples ◽  
Capacity Modeling ◽  
Computing Method ◽  
Mixing Property ◽  
Complex Biosystems ◽  
Modern Mathematics ◽  
Mathematics And Physics

Attempts to describe complex biological systems (complexity) in terms of modern mathematics and physics continue. However, it is now evident that complexity cannot be the object of modern science because of their continuous change in the parameters and the absence of arbitrary repetition of initial parameters x (to) of any complexity. This article presents the the arguments of lack of capacity modeling of complex biophysical systems under deterministic and stochastic approaches due to the constant chaotic change of the state vector parameters x = x(t) = (x1,x2....,xm)Tof any complex biosystem (complexity). At any point of time h, the chaotic dynamics of homeostasis in signals, such as tapping tremors, electromyograms, neurograms, cardiograms, electroencephalograms, and other biochemical recordings, can be observed. During constant and chaotic changes of x(t) (i.e., dx/dteQ), the amplitude-frequency characteristics (AFC) and the autocorrelation functions A(t) constantly change. Therefore, the mixing property fails and the Lyapunov exponents can chaotically and randomly change signs. Chaos of complex biosystems differs from chaos of physical systems primarily due to the irreproducible initial value x(to). There are two methods for studying such systems: a stochastic method for processing random samples based on a matrix of pairwise comparisons and a computing method that utilizes quasi-attractor parameters, Vg for x(t), in the phase space of states. Here, such calculations are presented for biomechanics and electrophysiology.

Bernhard Riemann’s legacy of 1859

2009 ◽  
Vol 93 (528) ◽  
pp. 468-475
Author(s):  
Graham Hoare
Keyword(s):  
Number Theory ◽  
Mathematical Physics ◽  
Point Of View ◽  
German Version ◽  
Profound Impact ◽  
Almost All ◽  
University Of Göttingen ◽  
The University ◽  
Modern Mathematics ◽  
Mathematics And Physics

The German version of Riemann’s Collected Works is confined to a single volume of 690 pages. Even so, this volume has had an abiding and profound impact on modern mathematics and physics, as we shall see. In fifteen years of activity, from 1851, when he gained his doctorate at the University of Göttingen, to his death in 1866, two months short of his fortieth birthday, Riemann contributed to almost all areas of mathematics. He perceived mathematics from the analytic point of view and used analysis to illuminate subjects as diverse as number theory and geometry. Although regarded principally as a mathematician Riemann had an abiding interest in physics and researched significantly in the methods of mathematical physics, particularly in the area of partial differential equations.

Modern Mathematics in Germany

1936 ◽  
Vol 29 (8) ◽  
pp. 390-393
Author(s):  
W. Threlfall
Keyword(s):  
Scientific Knowledge ◽  
Golden Age ◽  
Possible Worlds ◽  
The Other ◽  
Space And Time ◽  
The World ◽  
Modern Mathematics ◽  
Mathematics And Physics

Since I am speaking to you about modern German mathematics, I wish to call your attention to a most important subject, namely to the world which surrounds us, and to our scientific knowledge of its extent in space and time. There can be no doubt about the fact that this world we are living in is not the best of all possible worlds. Financial, industrial, and political dieases, you know them just as well on the other side of the great pond as we do on this side. Nevertheless in one respect we are living just now in a golden age. The world of science is in an excellent state and few eras have seen as important successes of mathematics and physics as ours.

New Light on Medieval Philosophy: The Sophismata of Richard Kilvington

Dialogue ◽  
1992 ◽  
Vol 31 (3) ◽  
pp. 517-522 ◽  
Author(s):  
E. J. Ashworth
Keyword(s):  
Philosophy Of Language ◽  
Modern Science ◽  
Philosophical Logic ◽  
Medieval Philosophy ◽  
Medieval Logic ◽  
Before And After ◽  
The One ◽  
Domain I ◽  
Mathematics And Physics ◽  
Analysis Of Motion

The fourteenth-century English philosopher and theologian Richard Kilvington (1302/5–61) presents a useful correction to popular views of medieval philosophy in two ways. On the one hand, he reminds us that to think of medieval philosophy in terms of Aquinas, Duns Scotus and Ockham, or to think of medieval logic in terms of Aristotelian syllogistic, is to overlook vast areas of intellectual endeavour. Kilvington, like many before and after him, was deeply concerned with problems that would now be assigned to philosophy of language; philosophical logic and philosophy of science. He discussed topics in epistemic logic, semantic paradoxes, problems of reference, particularly those connected with the interplay between quantifiers and modal or temporal operators, and problems arising from the use of infinite series in the analysis of motion and change. On the other hand, this very account of his work raises the important issue of conceptual domain. I have spoken as if Kilvington's work can be neatly classified in terms of contemporary interests; and the temptation to read medieval philosophy in modern terms is only strengthened when one recognizes Kilvington as the first member of the group of Oxford calculatores, men such as William Heytesbury and Richard Swineshead, whose discussions of mathematics and physics have caused them to be hailed as forerunners of modern science.

Crisis transformations of socio-economic systems

2021 ◽  
Vol 2021 (11) ◽  
pp. 7-20
Author(s):  
Tetiana IEFYMENKO ◽  
Keyword(s):  
Organization Theory ◽  
Modern Science ◽  
Industrial Sector ◽  
Global Scale ◽  
Theoretical Research ◽  
Economic Systems ◽  
Economic Science ◽  
Compensatory Mechanisms ◽  
Economic Competition ◽  
Economic Agents

Crisis phenomena threats are growing on national and global scale against the background of tightened geopolitical and geo-economic competition. Such trends as destruction and degradation, are becoming integral parts of change in the vital function of economic agents, institutional structures at different levels. Therefore, the search for an alternative paradigm for the study and assessment of the transformations of socio-economic systems (SES) is one of the topical directions in the development of economic science. In the objective conditions of constant renewal of world economic relations, proceeding from the multilevel nature of social changes, the article substantiates the need for innovative ways to search, develop and implement strategic guidelines that exclude the raw type of economic development. From the standpoint of the self-organization theory, it specifies that an open system is, as a rule, in a state of unstable equilibrium. The article proves that the purpose of theoretical research and practical actions should be the implementation of controlled effective evolutionary and revolutionary qualitative changes. At the turn of the third millennium, under the increasing impact of periodic civilizational shocks at the stages of economic and political cycles, the determinants of SES stability change over a long period. The transformation of natural factors requires scientific understanding - from motive levers into constraints on the potential for economic growth. The growing volumes of services and the virtual economy are hardly comparable with the products of the industrial sector, while the excessive polarization of incomes hinders economic dynamics. Arguments are given that the processes of changing existing SES can be accompanied by their deformation. The forces of the fall are opposed by compensatory mechanisms of reimbursement for the loss of material, human, information resources. The author focuses on the need to organize and manage the new approaches to the management of SES changes, having in mind time and space scale of the development of integral, interconnected bodies of social and economic agencies at state, corporative as well as individual levels. Crisis shocks of SES transformation are mainly linked with reasons stemming from financialization processes, weakening of sovereignty due to the expansion of global value chains, as well as from major emergencies and disasters, unexpected climate changes, etc. The article suggests improving the conceptual apparatus of transformational changes. The leading trend in modern science is interdisciplinarity. Integration of various scientific disciplines should affect both economics and institutional, social, spiritual, ethnic, moral spheres of life.

Cohen’s Logik der reinen Erkenntnis and Cassirer’s Substanzbegriff und Funktionsbegriff

Kant Yearbook ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 137-168
Author(s):  
Hernán Pringe
Keyword(s):  
Time And Space ◽  
Kantian Theory ◽  
And Function ◽  
Empirical Intuition ◽  
Modern Mathematics ◽  
Kantian Philosophy ◽  
Mathematics And Physics ◽  
Pure Knowledge

AbstractThis paper compares Cohen’s Logic of Pure Knowledge and Cassirer’s Substance and Function in order to evaluate how in these works Cohen and Cassirer go beyond the limits established by Kantian philosophy. In his Logic, Cohen seeks to ground in pure thought all the elements which Kant distinguishes in empirical intuition: its matter (sensation) as well as its form (time and space). In this way, Cohen tries to provide an account of knowledge without appealing to any receptivity. In accordance with Cohen’s project of reformulating the Kantian theory of sensibility, Cassirer undertakes in Substance and Function the task of developing an alternative doctrine of pure and empirical manifolds. But whereas Cohen analyzes the laws of pure thought, Cassirer aims to highlight the functional character of concepts in the development of modern mathematics and physics. I will discuss these two different approaches to the problems raised by Kantian philosophy and I will argue that Cassirer went further than Cohen in the project of critical idealism.

The Impact of Mathematics and Mathematicians

2019 ◽  
pp. 156-160
Author(s):  
Benjamin Fine
Keyword(s):  
Seventeenth Century ◽  
Modern Science ◽  
Modern World ◽  
Human Beings ◽  
Science And Engineering ◽  
Technological Revolution ◽  
Hard Science ◽  
The Impact ◽  
Modern Mathematics ◽  
The Way

The 1600's ushered in our modern world, but not in the way most people learn in school. There was a revolution; started by Kepler, continued by Galileo, Descartes and Fermat and culminating in Newton and Leibniz. This revolution allowed for the development of modern mathematics which in turn led to modern science and engineering to advance. Hence, the technological revolution occurred which has shaped our present-day existence much more than anything else. In this article we examine these developments during the amazing seventeenth century. We keep an eye on the fact that for whatever reason human beings for the most part seem not to do hard engineering until the hard science is developed and not to do the hard science until the correct mathematics has been discovered.

scholarly journals Extensions of Hölder’s Inequality via Pseudo-Integral

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Jing-Feng Tian ◽  
Ming-Hu Ha
Keyword(s):  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Modern Mathematics ◽  
Mathematics And Physics

Hölder’s inequality and its various extensions are playing very important roles in many branches of modern mathematics and physics. In this paper, we present some extensions of Hölder’s inequality via pseudo-integral. Moreover, some related Hölder type inequalities are also given.

Continuous Transformations of Regular Solids

1946 ◽  
Vol 39 (4) ◽  
pp. 147-154
Author(s):  
H. v. Baravalle
Keyword(s):  
Functional Form ◽  
Point Of View ◽  
Descriptive Geometry ◽  
Mathematical Education ◽  
Continuous Change ◽  
Rhombic Dodecahedron ◽  
Crystal Forms ◽  
New Concepts ◽  
Modern Mathematics

In the development of modern mathematics transformations of different kinds have gained increasing importance and many new concepts have been derived from their studies, for instance, the concept “Invariance of Functional Form.” From the point of view of mathematical education, transformations provide stimulating material for experimenting, investigating, and for exercises in visualization. In the following article, transformations of regular solids are carried out which have their bearing on crystallography as they keep the angles of the intersecting planes constant and vary their distances, the characteristics of the variations in crystal forms. Through these transformations, relationships between different kinds of solids will become manifest, for instance, between a tetrahedron and a cube, or between an octahedron and a rhombic dodecahedron. In some of the following transformations no less than five different regular and semi-regular solids evolve from one another in a continuous change. Constructions of descriptive geometry furnish the tools to draw the various solids.

Using a Surface Triangle to Explore Curfvature

1994 ◽  
Vol 87 (2) ◽  
pp. 69-77
Author(s):  
James Casey
Keyword(s):  
High School ◽  
School Level ◽  
High School Level ◽  
High School Geometry ◽  
Variable Curvature ◽  
School Geometry ◽  
Geometrical Concepts ◽  
Graduating Students ◽  
Modern Mathematics ◽  
Mathematics And Physics

Although substantial improvements have been made during recent years in the standard high school geometry curriculum, certain weaknesses still exist. Few graduating students are aware of modern geometrical concepts and their fundamental significance for physics and engineering. Thus, for example, the notion of surface curvature, which has had a profound influence on both modern mathematics and physics, is rarely discussed in high school geometry. Of course, one cannot approach this topic in an analytical manner at the high school level, but one can certainly introduce the concept of curvature in an intuitive and physical fashion. Indeed, we are surrounded in our daily life by a wide variety of objects that are curved in the most fascinating ways. For instance, bowls, bottles, and bananas all possess interesting and variable curvature, whereas the globe has curvature that is constant over its surface.

scholarly journals Historical aspects of fractal theory appearance

2021 ◽  
Vol 24 (2) ◽  
pp. 113-126
Author(s):  
Viktor A. Kuznetsov
Keyword(s):  
Retrospective Analysis ◽  
Fractal Theory ◽  
Modern Science ◽  
Practical Application ◽  
Historical Aspects ◽  
Practical Applications ◽  
The Moment ◽  
Definition Of ◽  
And Function ◽  
Mathematics And Physics

In paper short definition of a fractal is made, its basic properties are resulted, historical preconditions of origination fractal theories in a context of terms assemblage and function which development is observed from the moment of their origination before formation of their notional apparatus are in detail observed. Names, years of life and a photo of the scientists who have brought in the basic contribution to development of observed terms are resulted. As result of the retrospective analysis, it is shown that appearance of the fractal theory is the integral stage in evolution of mathematics and physics. Short listed the main routes of the fractal theory practical application in the field of radio engineering and electronics among which some scientists who have brought in a practical mite in development of a modern science and its practical applications are gated out. In particular, pioneers of fractal theory which application found wide practical application are resulted.

Sign in / Sign up

Export Citation Format

Share Document