Classical Mathematics

1971 ◽  
Vol 55 (393) ◽  
pp. 341
Author(s):  
R. L. Goodstein ◽  
H. B. Griffiths ◽  
P. J. Hilton
Keyword(s):  
Classical Mathematics

scholarly journals Hybrid structures applied to ideals in near-rings

2021 ◽  
Author(s):  
B. Elavarasan ◽  
G. Muhiuddin ◽  
K. Porselvi ◽  
Y. B. Jun
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Real World ◽  
Rough Set Theory ◽  
Wide Spectrum ◽  
Hybrid Structure ◽  
Soft Set ◽  
Hybrid Structures ◽  
Classical Mathematics ◽  
Classical Means

AbstractHuman endeavours span a wide spectrum of activities which includes solving fascinating problems in the realms of engineering, arts, sciences, medical sciences, social sciences, economics and environment. To solve these problems, classical mathematics methods are insufficient. The real-world problems involve many uncertainties making them difficult to solve by classical means. The researchers world over have established new mathematical theories such as fuzzy set theory and rough set theory in order to model the uncertainties that appear in various fields mentioned above. In the recent days, soft set theory has been developed which offers a novel way of solving real world issues as the issue of setting the membership function does not arise. This comes handy in solving numerous problems and many advancements are being made now-a-days. Jun introduced hybrid structure utilizing the ideas of a fuzzy set and a soft set. It is to be noted that hybrid structures are a speculation of soft set and fuzzy set. In the present work, the notion of hybrid ideals of a near-ring is introduced. Significant work has been carried out to investigate a portion of their significant properties. These notions are characterized and their relations are established furthermore. For a hybrid left (resp., right) ideal, different left (resp., right) ideal structures of near-rings are constructed. Efforts have been undertaken to display the relations between the hybrid product and hybrid intersection. Finally, results based on homomorphic hybrid preimage of a hybrid left (resp., right) ideals are proved.

On the approximate inverse Laplace transform of the transfer function with a single fractional order

2020 ◽  
pp. 014233122097766
Author(s):  
Ali Yüce ◽  
Nusret Tan
Keyword(s):  
Transfer Function ◽  
Laplace Transform ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Transfer Functions ◽  
Inverse Laplace Transform ◽  
Fractional Order Systems ◽  
Approximate Inverse ◽  
Classical Mathematics ◽  
Curve Fitting Method

The history of fractional calculus dates back to 1600s and it is almost as old as classical mathematics. Although many studies have been published on fractional-order control systems in recent years, there is still a lack of analytical solutions. The focus of this study is to obtain analytical solutions for fractional order transfer functions with a single fractional element and unity coefficient. Approximate inverse Laplace transformation, that is, time response of the basic transfer function, is obtained analytically for the fractional order transfer functions with single-fractional-element by curve fitting method. Obtained analytical equations are tabulated for some fractional orders of [Formula: see text]. Moreover, a single function depending on fractional order alpha has been introduced for the first time using a table for [Formula: see text]. By using this table, approximate inverse Laplace transform function is obtained in terms of any fractional order of [Formula: see text] for [Formula: see text]. Obtained analytic equations offer accurate results in computing inverse Laplace transforms. The accuracy of the method is supported by numerical examples in this study. Also, the study sets the basis for the higher fractional-order systems that can be decomposed into a single (simpler) fractional order systems.

Brouwer, L.E.J. (1881–1966)

2018 ◽  
Author(s):  
Mark van Atten
Keyword(s):  
Philosophy Of Mind ◽  
Transcendental Phenomenology ◽  
Full Professor ◽  
Foundations Of Mathematics ◽  
Constructive Mathematics ◽  
Language Reform ◽  
Classical Mathematics ◽  
Mathematical Ontology ◽  
The University ◽  
Scale Alternative

L.E.J. Brouwer was a mathematician and philosopher. He graduated from the University of Amsterdam in 1907 and remained there, from 1913 to 1951, as full professor. Brouwer was a founding father of modern topology. In the foundations of mathematics he launched ‘intuitionism’: a mathematical ontology and epistemology, based on a philosophy of mind, that yields a form of constructive mathematics. Although intuitionism was designed as a Kantian approach, Brouwer’s conception of the intuition of time supports a much richer mathematics than Kant’s. Arguably, a closer affinity with Husserl’s transcendental phenomenology transpired as the latter was being developed. A by-product of intuitionism, intuitionistic logic, found application independently of the foundational programme. Intuitionism presented the first full-scale alternative to classical mathematics and logic. Brouwer was also interested in mysticism, and in language reform in the service of spiritual and political progress.

Fuzzy Set Theory Applied to Accounting Sciences

2020 ◽  
Vol 16 (01) ◽  
pp. 1-16
Author(s):  
Carmen Lozano ◽  
Enriqueta Mancilla-Rendón
Keyword(s):  
Social Sciences ◽  
Fuzzy Logic ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Hamming Distance ◽  
Great Acceptance ◽  
Classical Mathematics ◽  
Triangular Numbers ◽  
And Mathematics

Fuzzy set theory and fuzzy logic have been successfully developed in engineering and mathematics. However, these concepts have found great acceptance in social sciences in recent years since they provide an answer to those problems in the real world that cannot be modeled using classical mathematics. In this paper, we propose a new methodology for accounting science based on fuzzy triangular numbers. The methodology uses Hamming distance between fuzzy triangular numbers and arithmetic operations to evaluate corporate governance of multinational public stock corporations (PSCs) in the telecommunications sector.

Old and New Results on Knots

1950 ◽  
Vol 2 ◽  
pp. 1-15 ◽  
Author(s):  
Herbert Seifert ◽  
William Threlfall
Keyword(s):  
Infinite Number ◽  
Mathematical Foundation ◽  
Topological Methods ◽  
Double Points ◽  
Felix Klein ◽  
Short Summary ◽  
Classical Mathematics ◽  
Complete Survey ◽  
Plane Projection

The theory of knots undertakes the task of giving a complete survey of all existing knots. A solid mathematical foundation was not laid to this theory until our century. A mathematician of the rank of Felix Klein thought it to be nearly hopeless to treat knot problems with the same exactness as we are accustomed to from classical mathematics. We want to give here a short summary of the modern topological methods enabling us to approach the knot problem in a mathematical way.In order to exclude pathological knots, as for instance knots being entangled an infinite number of times, we will define a knot as a polygon lying in the space. In other words: a knot is a closed sequence of segments without double points. In Figure 1 some examples of knots are given in plane projection.

Report on some investigations concerning the consistency of the axiom of reducibility

1951 ◽  
Vol 16 (1) ◽  
pp. 35-42 ◽  
Author(s):  
John Myhill
Keyword(s):  
Point Of View ◽  
Quantification Theory ◽  
Classical Mathematics

The purpose of this paper is to construct a non-finitary system of logic S, based on the theory of types, in which classical quantification theory holds without restriction and the axiom of reducibility holds with such slight restriction as is perhaps unlikely to interfere with the construction of classical mathematics. The system will be shown to be consistent.For purposes of orientation, a rough description of the ontology of the system will first be given. The ‘individuals’ are expressions built up in the following way: ‘0’ is an individual, and if ϕ and ψ are individuals, so is ˹*ϕψ˺. The usual apparatus of truth functional connectives and quantifiers is employed, and one primitive four place predicate ‘S’. ˹Sϕψχω˺ says that ϕ is the result of writing ψ for all occurrences of χ in ω, where ϕ, ψ, χ and ω may be formulae, individuals, or members of a wider category called ‘expressions’ which includes individuals, formulae, and other things as well. (At first sight this looks like a confusion of use and mention, but the formation rules and rules of inference are so phrased that no ambi guity arises.)The individuals are divided into types concentrically, so that type 0 has them all as members and type n includes type m for m > n. There is no highest type, but we shall find it convenient from the point of view of exposition to construct an infinity of ‘auxiliary’ systems Q(k), restricted to types ≦ k, before presenting the system S.

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