Search

Newly discovered, incomplete forms of special functions are increasing the interest of both pure and applied mathematicians. The main purpose of this work is to derive four theorems on partial derivatives with incomplete Aleph functions of two variables and generalize them up to r-variables. In addition to these theorems, we also established some novel formulae on the partial derivatives that play a key role in deriving the main results in terms of finite sum. Further, we generalize the result and obtain the finite sum for the incomplete Aleph functions with r-variables. Here, we also established some particular cases that are in most general character and including the results given earlier by Buschman and Deshpande and may prove significant in numerous interesting situations appearing in the literature on mathematical analysis, applied mathematics and mathematical physics. [ABSTRACT FROM AUTHOR]

Mustafa Salim [Tunakan] was a significant mathematician who flourished during the final years of the Ottoman Empire. He imparted knowledge of algebra, integration and machine theory at the universities of this period. In addition to his textbooks in these fields, he published one article in Osmanlı Mühendis ve Mimar Cemiyeti Mecmuası, one article in Mühendis Mektebi Mecmuası, two articles in Genç Mühendis and seven articles in Darülfünun Fünun Fakültesi Mecmuası. The aim of this study is to make a mathematical analysis of all of Mustafa Salim's articles published in the field of mathematics in the journals named Osmanlı Mühendis ve Mimar Cemiyeti Mecmuası, Mühendis Mektebi Mecmuası and Genç Mühendis. For this purpose, Mustafa Salim's four articles published in these journals were initially translated into Latin letters, after which mathematical analyses were conducted on the topics covered in the articles. In these articles; Mustafa Salim defined and solved problems at undergraduate levels in the subjects of integral, differential calculus, linear algebra, functions and geometric location. Mustafa Salim, who adopted a very simple and concise narrative style, did not make any mathematical mistakes in his articles, except for a few minor errors. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the scientific and pedagogical activities of Nikolay Dmitrievich Kopachevsky (1940–2020) — a well-known mathematician, head of the Department of Mathematical Analysis of the V. I. Vernadsky Crimean Federal University, organizer and head of the Crimean Autumn Mathematical School-Symposium (KROMSH). [ABSTRACT FROM AUTHOR]

The article "Modeling an Epidemic" presents a mathematical model to analyze the dynamics of an epidemic and how it is affected by quarantines and individual behavior. Different epidemiological models are discussed, including the basic SIR model that considers susceptible, infected, and recovered individuals as interacting population groups. The effect of different measures on the spread of the epidemic, such as lockdowns and public perception of risk, is analyzed. A mathematical model is also presented to study the impact of vaccination on the epidemic, showing that an effective vaccine can decrease the number of infected individuals. It is concluded that a good vaccination rate and responsible behavior from the population are key to controlling an epidemic. [Extracted from the article]

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this workshop 70 (43 at MFO, 27 online) leading mathematicians from Europe, United States, China, and Australia met at the MFO to discuss and present new developments in the mathematical and numerical analysis including discretizations of Hilbert complexes related to systems of partial differential equations, in particular the well known de Rham complex and the complexes of elasticity and the biharmonic equations. The report at hand offers the extended abstracts of their talks. [ABSTRACT FROM AUTHOR]

Lutsky in 2008 and 2009, where they investigated the invertibility of parabolic pseudo-differential operators with rapidly growing symbols and obtained estimates of exponential behaviour of solutions of pseudo-differential operators with growing and discontinuous symbols. During several years which followed the defense of the PhD thesis there appeared Vladimir's publications presenting interesting results for quasi-elliptic pseudodifferential operators and on solvability of Cauchy and Goursat problems for parabolic pseudodifferential equations (1971-1979 and later on), on solvability difference-differential equations (1978-1985 and later on), on Fredholmness of elliptic pseudodifferential operators and associated boundary value problems on noncompact manifolds (papers of 1971-1979). In 1993 he defended his doctoral thesis "The method of limit operators in solvability of pseudo-differential equations and convolution equations". [Extracted from the article]

This document is a preface to a special issue of the Serdica Mathematical Journal dedicated to the memory of Asen Lyubomirov Dontchev, a renowned mathematician who specialized in variational analysis, optimization, and optimal control. Dontchev passed away in 2021 at the age of 73. The preface provides a brief overview of Dontchev's career, including his education, research contributions, and publications. It also mentions his role as a mentor and his involvement in various mathematical journals. The special issue contains papers written by Dontchev's colleagues, friends, former students, and collaborators as a tribute to his work and influence. [Extracted from the article]

The idea of subset graph of a near-ring is presented in this section. This part comprises of three sections. The principal area manages the fundamental definitions required for the ensuing sections and the second area contains the primary outcomes. In the third area we talk about some initiated sub-graphs of the subset graph of a near-ring. All through this part N indicates a zero symmetric right abelian near-ring except if generally expressed. The study on graphs from algebraic structures is an interesting subject for mathematicians since the notion of Cayley graphs from groups. In recent years, many algebraist as well as graph theorists have focused on the zero-divisor graph of rings. [ABSTRACT FROM AUTHOR]

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The paper presents some interesting aspects related to the biography and works of Romanian mathematician Caius Iacob (1912--1992). He was famous for his works in the fields of mathematical analysis, fluid mechanics, classical hydrodynamics and compressible-flow theory. At the age of 19, he graduated from the Mathematics Faculty in Bucharest, and then he went to Paris to continue his studies at the Faculty of Sciences, where he worked on a PhD thesis under the advice of famous French mathematician Henri Villat. On 24 June 1935, Caius Iacob successfully presented to the Sorbonne committee his PhD thesis about "Determination of conjugated harmonic functions with some limit conditions, and their applications in hydrodynamics". Returning to Romania, Caius Iacob had a long and successful career teaching mathematics and mechanics at the universities of Timişoara, Cluj and Bucharest. His most important work is considered the "Mathematical introduction to the mechanics of fluids". This book, providing original ways to work with classical hydrodynamics and compressibleflow theory, was published in Romanian in 1952 and in French in 1959. In 1955, he was elected a Corresponding Member of the Romanian Academy, becoming a titular Member in 1963. He was also President of the Mathematics Section of the Romanian Academy from 1980 until the end of his life, in 1992. In 1991, he initiated the foundation of the "Romanian Academy Institute of Applied Mathematics". In 2001 the institute merged with the "Centre for Mathematical Statistics", which had been created in 1964 by mathematician Gheorghe Mihoc, thus creating the "Gheorghe Mihoc -- Caius Iacob Institute of Mathematical Statistics and Applied Mathematics" of the Romanian Academy. [ABSTRACT FROM AUTHOR]

Congruences involving sums of Harmonic numbers and binomial coefficients are considered in this paper. Recently, many great mathematicians have been interested to find congruences and relationships between these numbers such Sun & Tauraso, Koparal & Ömür, Mao & Sun and Meštrović & Andjić. In the present paper, some new combinatorial congruences are proved. These congruences are mainly determined modulo p² or p³ (in any prime) and they are motivated by a recent paper by Meštrović and Andjić. The first main result (Theorem 1) presents the congruence modulo p² (p > 3 is any prime) involving sum of products of two binomial coefficients and Harmonic numbers. Two interesting congruences modulo a prime p > 3 (Corollary 2) involving Harmonic numbers Hk, Catalan numbers ck and Fermat quotient q2 := (2p-1 - 1)/p are obtained as consequences of Theorem 1. The second main result (Theorem 2) presents the congruence modulo p³(p > 3 is any prime) involving sum of products of two binomial coefficients and Harmonic numbers. [ABSTRACT FROM AUTHOR]

The paper shows that, contrary to what has been held since the sixteenth-century mathematician Christoph Clavius, there is no application of consequentia mirabilis (CM) in Greek mathematical works. This is shown by means of a detailed discussion of the logical structure of the proofs where CM is allegedly employed. The point is further enlarged to a critical assessment of the unsound methodology applied by many interpreters in seeking for specific logical rules at work in ancient mathematical texts. [ABSTRACT FROM AUTHOR]

The notion of potential infinity dominated in mathematical thinking about infinity from Aristotle until Cantor. The coherence and philosophical importance of the notion are defended. Particular attention is paid to the question of whether potential infinity is compatible with classical logic or requires a weaker logic, perhaps intuitionistic. [ABSTRACT FROM AUTHOR]

The Bi-Lipschitz geometry is one of the main subjects in the modern approach of singularity theory. However, it rises from works of important mathematicians of the last century, especially Zariski. In this work we investigate the Bi-Lipschitz equisingularity of families of essentially isolated determinantal singularities inspired by the approach of Mostowski and Gaffney. [ABSTRACT FROM AUTHOR]

There are 3 crises in the development of mathematics from its internal, and particularly, the 3th crisis extensively made it to be consistency in logic, which finally led to its more and more abstract, but getting away the reality of things. It should be noted that the original intention of mathematics is servicing other sciences to hold on the reality of things but today's mathematics is no longer adequate for the needs of other sciences such as those of theoretical physics, complex system and network, cytology, biology and economy developments change rapidly as the time enters the 21st century. Whence, a new crisis appears in front of mathematicians, i.e., how to keep up mathematics with the developments of other sciences? I call it the 4th crisis of mathematics from the external, i.e., the original intention of mathematics because it is the main topic of human beings. [ABSTRACT FROM AUTHOR]

The paper is the English variant, with additional remarks, of two earlier papers published by the author in Romanian, many years ago. It is motivated by the fact that in the last years many mathematicians were interested on the subject and they can't found copies of acceptable graphic quality. In the paper we introduce the notions of convex sequence of p order (p being a positive integer) and respectively system of subconvex sequence of first order. One proves that any subconvex sequence of second order and any system of subconvex sequences of first order are convergent. [ABSTRACT FROM AUTHOR]

In this paper, we find the greatest values $\alpha_{1},\alpha_{2}$ and the smallest values $\beta_{1},\beta_{2}$ such that the double inequalities $L_{\alpha_{1}}(a,b)<\operatorname{AG}(a,b)0$ with $a\neq b$ , where $\operatorname{AG}(a,b)$ , $T(a,b)$ and $L_{p}(a,b)$ are the arithmetic-geometric, Toader and generalized logarithmic means of two positive numbers a and b, respectively. [ABSTRACT FROM AUTHOR]

The modern research area of numerical analysiswas created to study the mathematics of computation after the second World War. Mathematicians in general and even specialists may not be aware of overall trends in research and especially not in quantifiable form because of the diverse subject matter. Bibliometric data show that the largest and most rapidly growing portion of numerical analysis is statistical computing. The geographic distribution of researchers is also uneven reflecting differences in national research policies. [ABSTRACT FROM AUTHOR]

In this note I am re ecting on interrelations between three concepts of truth: (1) that employed by Hilbert arguing his formalist view on the nature of math- ematics, (2) Freges idea of truth supported by mathematical intuition, and (3) known as Aristotelian correspondence idea of truth concerning any propositions not merely mathematical. [ABSTRACT FROM AUTHOR]

Jacques-Louis Lions was a prominent French mathematician known for his work in partial differential equations and his contribution to the development of applied mathematics. He was born in 1928 in Grasse, France, and had a successful academic career at the University of Nancy and the University of Paris. He was recognized for his use of mathematics in industry and for his role in establishing new scientific and mathematical centers. His son, Pierre-Louis Lions, is also a prominent mathematician. On the other hand, Xavier Jansà, son of a renowned meteorologist and brother of another prominent meteorologist, is an artist-painter and biologist-ecologist whose works reflect his knowledge and appreciation for meteorology, as well as his interest in phenological and ecological topics. [Extracted from the article]

In recent years, nonhomogeneous wavelet frames have attracted some mathematicians' interest. This paper investigates such problems in a Sobolev space setting. A characterization of nonhomogeneous wavelet dual frames in Sobolev spaces pairs is obtained. .. [ABSTRACT FROM AUTHOR]

Mathematics in Poland had good names in medieval times and in the first two centuries of modem times, e.g. Vitello, Copernicus, Broscius, Kochański. Since mid-XVII c., however, there begun a decline of the Polish-Lithuanian state and its culture which led to the loss of sovereignty and to partitions 1795-1918. On the other hand, it was a time of Newton and Leibniz who invented calculus and of their followers, the time of its fast development in XVIII and XIX centuries and the emergence of its many new branches, the totality of which is called mathematical analysis. That development was followed in Poland with a large delay and for a long time it resembled a pursuit after a fast running train. In spite of a long run, the pursuit eventually proved successful. The article traces its history since the translation of Bezout's extensive manual by Jakubowski (1781), soon followed by other translations from French, accompanied by the emerging Polish terminology related to higher mathematics. In consequence, the level of authority of Polish mathematicians concerning the area of higher mathematics was gradually increasing. The first Polish manual of mathematical analysis appeared in 1822 (Buchowski), then there were other ones, and the number of research papers in the area, predominantly concerning differential equations, grew as well. Near the end of the XIXth century some of those papers gained a high status and became widely known, e.g. some by Sochocki (analytic functions), Zaremba (differential equations), Zorawski (Lie groups). The number of Polish mathematicians and books in Polish grew, and in the last decade of XIX c. there appeared Polish mathematical journals. In 1918 there was a wave of a common enthusiasm upon regaining independence. Polish mathematicians have used the opportunity and soon there appeared mathematical schools in Warsaw and in Lvov, centered upon "the theory of sets and its applications". However, the choice of such a main area of interest meant a conscious neglect of mathematical analysis. Nevertheless, an interest in the latter, although for the time being in the shadow of flourishing schools, has not been altogether abandoned. And when, after War World II, the center of gravity of common mathematics has moved away from the main subjects of the Polish school, it was precisely mathematical analysis which allowed Polish mathematicians to keep abreast. Nowadays Polish mathematics has many areas of interest, including domains of modern mathematical analysis, and in most of them its high level is confirmed by an international cooperation. [ABSTRACT FROM AUTHOR]

The article discusses the rule of mathematician Paolo Ruffini which is an efficient method to divide a polynomial with the use of a linear factor. Topics discussed include the extension of the technique to polynomial divisors, the coefficient of the leading term required by the rule, and the publication of the rule online by American mathematics teacher Pat Bellew.

The article discusses mathematical problems and solutions which are intended to challenge students and teachers of college mathematicians. Among the problems and solutions discussed include one from Spiros P. Andriopoulos on sines and exponentials, one from Michel Bataille concerning a sum minus a product, and a solution from Elias Lampakis on convex n-gons.

With the arrival of the nineteenth century, a process of change guided the treatment of three basic elements in the development of mathematics: rigour, the arithmetization and the clarification of the concept of function, categorised as the most important tool in the development of the mathematical analysis. In this paper we will show how several prominent mathematicians contributed greatly to the development of these basic elements that allowed the solid underpinning of mathematics and the consideration of mathematics as an axiomatic way of thinking in which anyone can deduce valid conclusions from certain types of premises. This nineteenth century stage shares, possibly with the Heroic Age of Ancient Greece, the most revolutionary period in all history of mathematics. [ABSTRACT FROM AUTHOR]

In the present study, we have introduced the concept of Abel summability for sequences and series of fuzzy numbers. Also, some tauberian results in classical analysis have been generalized to fuzzy analysis. [ABSTRACT FROM AUTHOR]

Abstract. The remarkable class of measurable functions was introduced by classics of function theory. It has found different applications in various branches of mathematics. However this class turned out too restrictive for solving some natural mathematical problems because it is essentially connected with the property of countability. Therefore, along with it another remarkable class, essentially connected with the property of finiteness, was introduced. It is the class of uniform functions. Measurable functions are described both in the classical Lebesgue-Borel language of preimages and in the quite new language of covers. Uniform functions are described in the language of covers exclusively. Both the families of measurable functions and the families of uniform functions are determined by the rigid structure of their supports (descriptive spaces). For this reason, mathematicians weakened more that once the rigidity of the structure of descriptive spaces at the expense of using the additional property of negligence. The present paper is devoted to a contemporary formalization of the indicated ideas. Some applications of the introduced classes of functions to solving a number of known mathematical problems is traced in the paper. [ABSTRACT FROM AUTHOR]

The essay is in the form of a dialogue between the two authors. We take John Wheeler's idea of “It from Bit” as an essential clue and we rework the structure of the bit not to the qubit, but to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We emphasize that mathematics is a combination of calculation and concept. At the conceptual level, mathematics is structured to be independent of time and multiplicity. Mathematics in this way occurs before number and counting. From this timeless domain, mathematics and mathematicians can explore worlds of multiplicity and infinity beyond the apparent limitations of the physical world and see that among these possible worlds there are coincidences with what is observed. [ABSTRACT FROM AUTHOR]

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck . [ABSTRACT FROM AUTHOR]

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: 'It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.' This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, 'The laws of Nature are written in the language of mathematics $$\ldots $$ the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.' Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, ). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot 'solve' these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology. [ABSTRACT FROM AUTHOR]

In this paper we address the general problem of including inflationary models exhibiting Starobinsky-like potentials into (symmetric) [ABSTRACT FROM AUTHOR]

This article reports on an exploratory study designed to investigate the reasoning behind algebraists’ selection of examples. Variation theory provided a lens to analyze their collections of examples. Our findings include the classes of examples of groups and rings that algebraists believe to be most pedagogically useful. Chief among their selection criteria was that these examples illustrate not only the concept at hand but also lay the foundation for more abstract constructions. Additionally, we found that the algebraists, tending to think in terms of classes of examples, used a relatively small number in their own teaching and research. [ABSTRACT FROM AUTHOR]

The article presents changes and developments of the Fourier Method, after and before the time of the Russian mathematician Vladimir Andreevich Stekhov. It mentions the strategies of solving the Fourier method prior and after the birth of Stekhov. Moreover, it cites the contributions of Stekhov to the country.