scholarly journals Gabriel–Ulmer duality and Lawvere theories enriched over a general base

2009 ◽  
Vol 19 (3-4) ◽  
pp. 265-286 ◽  
Author(s):  
STEPHEN LACK ◽  
JOHN POWER
Keyword(s):  
Mathematical Theory ◽  
Locally Presentable Category ◽  
General Base ◽  
Functor Categories ◽  
The Relationship

AbstractMotivated by the search for a body of mathematical theory to support the semantics of computational effects, we first recall the relationship between Lawvere theories and monads onSet. We generalise that relationship fromSetto an arbitrary locally presentable category such asPosetand ωCpoor functor categories such as [Inj,Set] and [Inj, ωCpo]. That involves allowing the arities of Lawvere theories to be extended to being size-restricted objects of the locally presentable category. We develop a body of theory at this level of generality, in particular explaining how the relationship between generalised Lawvere theories and monads extends Gabriel–Ulmer duality.

PIOPLE. INFORMATION. DEGRADATION

2019 ◽  
pp. 44-53
Author(s):  
Andrey Varlamov ◽  
Vladimir Rimshin
Keyword(s):  
Information Theory ◽  
Mathematical Theory ◽  
Maximum Information ◽  
Building Models ◽  
Man And Nature ◽  
History Of ◽  
Nature And Society ◽  
Relationship Of ◽  
Link Information ◽  
The Relationship

Considered the issues of interaction between man and nature. Noted that this interaction is fundamental in the existence of modern civilization. The question of possible impact on nature and society with the aim of preserving the existence of human civilization. It is shown that the study of this issue goes towards the crea-tion of models of interaction between nature and man. Determining when building models is information about the interaction of man and nature. Considered information theory from the viewpoint of interaction between nature and man. Noted that currently information theory developed mainly as a mathematical theory. The issues of interaction of man and nature, the availability and existence of information in the material sys-tem is not studied. Indicates the link information with the energy terms control large flows of energy. For con-sideration of the interaction of man and nature proposed to use the theory of degradation. Graphs are pre-sented of the information in the history of human development. Reviewed charts of population growth. As a prediction it is proposed to use the simplest based on the theory of degradation. Consideration of the behav-ior of these dependencies led to the conclusion about the existence of communication energy and information as a feature of the degradation of energy. It justifies the existence of border life ( including humanity) at the point with maximum information. Shows the relationship of energy and time using potential energy.

The Changing Views of a Philosopher of Chemistry on the Question of Reduction

2016 ◽  
Author(s):  
Eric R. Scerri
Keyword(s):  
Quantum Mechanics ◽  
Mathematical Theory ◽  
Approximate Solutions ◽  
Electron Systems ◽  
Atomic Systems ◽  
Quantum Mechanical Description ◽  
The Subject ◽  
The Moment ◽  
The Relationship

The question of the reduction of chemistry to quantum mechanics has been inextricably linked with the development of the philosophy of chemistry since the field began to develop in the early 1990s. In the present chapter I would like to describe how my own views on the subject have developed over a period of roughly 30 years. A good place to begin might be the frequently cited reductionist dictum that was penned in 1929 by Paul Dirac, one of the founders of quantum mechanics. . . . The underlying laws necessary for the mathematical theory of a larger part of physics and the whole of chemistry are thus completely known, and the difficulty is only that exact applications of these laws lead to equations, which are too complicated to be soluble. (Dirac 1929) . . . These days most chemists would probably comment that Dirac had things backward. It is clear that nothing like “the whole of chemistry” has been mathematically understood. At the same time most would argue that the approximate solutions that are afforded by modern computers are so good as to overcome the fact that one cannot obtain exact or analytical solutions to the Schrödinger equation for many-electron systems. Be that as it may, Dirac’s famous quotation, coming from one of the creators of quantum mechanics, has convinced many people that chemistry has been more or less completely reduced to quantum mechanics. Another quotation of this sort (and one using more metaphorical language) comes from Walter Heitler who together with Fritz London was the first to give a quantum mechanical description of the chemical bond. . . . Let us assume for the moment that the two atomic systems ↑↑↑↑ . . . and ↓↓↓↓ . . . are always attracted in a homopolar manner. We can, then, eat Chemistry with a spoon. (Heitler 1927) . . . Philosophers of science eventually caught up with this climate of reductionism and chose to illustrate their views with the relationship with chemistry and quantum mechanics.

Relationship between Mean Value and Fourier Coefficients of a Time-Varying Function with Half-Period Rests: Theory and Application

1994 ◽  
Vol 116 (1) ◽  
pp. 26-30
Author(s):  
Jun-Yao Yu
Keyword(s):  
Fourier Coefficient ◽  
Mathematical Theory ◽  
Fourier Coefficients ◽  
Mean Value ◽  
Time Function ◽  
Half Period ◽  
Time Varying ◽  
Ic Engine ◽  
The Mean ◽  
The Relationship

The Fourier coefficients are investigated for such a periodic time function whose magnitude keeps constant during the time of every half-period. In this case the relationship between the mean value and the Fourier coefficients is achieved using appropriate mathematical theory. It was applied successfully to the study of torsional harmonic excitations due to gas pressure in a four-cycle IC engine. A formula relating the truncated Fourier coefficient series to MIP has been established with very little error. The series simulation of Fourier coefficients is utilized in the determination and analysis of excitations.

scholarly journals The Elementary Proof of the Riemann's Hypothesis

2020 ◽  
Author(s):  
Jan Feliksiak
Keyword(s):  
Mathematical Theory ◽  
Elementary Proof ◽  
Counting Function ◽  
Binomial Coefficients ◽  
Complex Issue ◽  
Logarithmic Integral ◽  
Prime Counting Function ◽  
Prime Gaps ◽  
The Relationship ◽  
Very High

This research paper aims to explicate the complex issue of the Riemann's Hypothesis and ultimately presents its elementary proof. The method implements one of the binomial coefficients, to demonstrate the maximal prime gaps bound. Maximal prime gaps bound constitutes a comprehensive improvement over the Bertrand's result, and becomes one of the key elements of the theory. Subsequently, implementing the theory of the primorial function and its error bounds, an improved version of the Gauss' offset logarithmic integral is developed. This integral serves as a Supremum bound of the prime counting function Pi(n). Due to its very high precision, it permits to verify the relationship between the prime counting function Pi(n) and the offset logarithmic integral of Carl Gauss. The collective mathematical theory, via the Niels F. Helge von Koch equation, enables to prove the RIemann's Hypothesis conclusively.

scholarly journals The Elementary Proof of the Riemann's Hypothesis

2021 ◽  
Author(s):  
Jan Feliksiak
Keyword(s):  
Mathematical Theory ◽  
Elementary Proof ◽  
Counting Function ◽  
Binomial Coefficients ◽  
Complex Issue ◽  
Logarithmic Integral ◽  
Prime Counting Function ◽  
Prime Gaps ◽  
The Relationship ◽  
Very High

This research paper aims to explicate the complex issue of the Riemann's Hypothesis and ultimately presents its elementary proof. The method implements one of the binomial coefficients, to demonstrate the maximal prime gaps bound. Maximal prime gaps bound constitutes a comprehensive improvement over the Bertrand's result, and becomes one of the key elements of the theory. Subsequently, implementing the theory of the primorial function and its error bounds, an improved version of the Gauss' offset logarithmic integral is developed. This integral serves as a Supremum bound of the prime counting function Pi(n). Due to its very high precision, it permits to verify the relationship between the prime counting function Pi(n) and the offset logarithmic integral of Carl Gauss. The collective mathematical theory, via the Niels F. Helge von Koch equation, enables to prove the RIemann's Hypothesis conclusively.

The effect of a change in the interest rate on life assurance premiums

1940 ◽  
Vol 70 (3) ◽  
pp. 380-390
Author(s):  
R. E. White ◽  
B. T. Holmes
Keyword(s):  
Interest Rate ◽  
Mathematical Theory ◽  
Related Subject ◽  
American Life ◽  
Life Assurance ◽  
The Interest Rate ◽  
Relationship Of ◽  
The Relationship

The recent paper by Dr Hagstroem (J.I.A. Vol. LXX, p. 119) directs attention to the very closely related subject of the effect on life assurance premiums of changes in the rate of interest. Some four years ago, in the course of an address before the American Life Convention, Mr V. R. Smith studied the relationship of the interest rate to life assurance premiums from a different angle. This note is an attempt to develop the mathematical theory underlying Mr Smith's method and to present some results on the basis of the A 1924–29 Table.

scholarly journals The Immanence of Truths and the Absolutely Infinite in Spinoza, Cantor, and Badiou

2020 ◽  
Vol 41 (2) ◽  
Author(s):  
Jana Ndiaye Berankova
Keyword(s):  
Mathematical Theory ◽  
Deductive Reasoning ◽  
Large Cardinals ◽  
Georg Cantor ◽  
Mathematical Concepts ◽  
Potential Infinity ◽  
Mathematical Ontology ◽  
The Absolute ◽  
And Mathematics ◽  
The Relationship

The following article compares the notion of the absolute in the work of Georg Cantor and in Alain Badiou’s third volume of Being and Event: The Immanence of Truths and proposes an interpretation of mathematical concepts used in the book. By describing the absolute as a universe or a place in line with the mathematical theory of large cardinals, Badiou avoided some of the paradoxes related to Cantor’s notion of the “absolutely infinite” or the set of all that is thinkable in mathematics W: namely the idea that W would be a potential infinity. The article provides an elucidation of the putative criticism of the statement “mathematics is ontology” which Badiou presented at the conference Thinking the Infinite in Prague. It emphasizes the role that philosophical decision plays in the construction of Badiou’s system of mathematical ontology and portrays the relationship between philosophy and mathematics on the basis of an inductive not deductive reasoning.

The Optimal Tolerance Assignment With Less Than Full Acceptance

1982 ◽  
Vol 104 (4) ◽  
pp. 855-860 ◽  
Author(s):  
W. Michael ◽  
J. N. Siddall
Keyword(s):  
Nonlinear Optimization ◽  
Manufacturing Process ◽  
Mathematical Theory ◽  
Production Cost ◽  
Engineering System ◽  
Important Distinction ◽  
Lower Limits ◽  
The Relationship ◽  
Tolerance Assignment ◽  
General Mathematical Theory

This paper proposes an approach that integrates the relationship between design and production engineers through the theory of nonlinear optimization. It attempts to cope with the problem of optimally allocating tolerances in a manufacturing process. The upper and lower limits of the random variables of an engineering system are allocated so as to minimize production cost, with allowance for the system scrap percentage. The approach is illustrated by an example, and the general mathematical theory is also provided. An important distinction between the design and the manufacturing scrap is introduced, and the cell technique is utilized to estimate efficiently the system scrap.

Interstellar gas in the central region of the Galaxy

1967 ◽  
Vol 31 ◽  
pp. 239-251 ◽  
Author(s):  
F. J. Kerr
Keyword(s):  
Central Region ◽  
Galactic Plane ◽  
Neutral Hydrogen ◽  
Continuum Emission ◽  
Galactic Centre ◽  
Interstellar Gas ◽  
Hydrogen Recombination ◽  
The Galaxy ◽  
Centre Region ◽  
The Relationship

A review is given of information on the galactic-centre region obtained from recent observations of the 21-cm line from neutral hydrogen, the 18-cm group of OH lines, a hydrogen recombination line at 6 cm wavelength, and the continuum emission from ionized hydrogen.Both inward and outward motions are important in this region, in addition to rotation. Several types of observation indicate the presence of material in features inclined to the galactic plane. The relationship between the H and OH concentrations is not yet clear, but a rough picture of the central region can be proposed.

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