Applications of Mathematics

Ali R. Soheili

Applications of Mathematics

2020

Abstract

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz 58 (2013) APPLICATIONS OF MATHEMATICS No. 4, 439-471

It gives me great pleasure to write this foreword for the "6th Mediterranean International Conference of Pure & Applied Mathematics and Related Areas (MICOPAM 2023), dedicated to my 60th birthday". In my academic life, I firstly participated in the III. Turkish National Mathematics Symposium, organized by Van Yüzüncü Yıl University in 1989. After this symposium, I have participated in many scientific events such as symposiums, conferences, workshops, seminars, etc. in almost every country in the world such as in Ukrainian Mathematics Symposium, in Jangjeon Mathematical Society Conferences, in Canadian Mathematics Symposium, in USA Mathematics Symposium, in European Mathematics Symposium and conferences, and the others. As I know that many important conferences may be named after countries, some may be dedicated to specific topics, some may be named after general mathematical names, or they may be named after mathematical societies. Some of them are dedicated to the age of researchers in mathematics (or in sciences). I must proudly state that I have been doing research on the following topics for more than 30 years: Complex Analysis, Modular Forms, Elliptic Functions Number Theory, p-adic Numbers and their applications Real and Complex Analysis Special numbers, Special Polynomials, Generating Functions, Special Functions, Generating Functions and Special Functions Associated with Superoscillations Functional Analysis, Integral Equations and Transforms q-Series and q-Analysis Analytic Number Theory (Modular form and Elliptic functions, Dedekind and Hardy Sums, theta functions), Zeta type functions, Dirichlet series and Lambert-type series p-adic analysis and p-adic Distribution Umbral Algebra and Umbral Analysis Combinatorial Analysis and their applications Probability Distribution functions and their Applications Computational Science and Engineering, Computational Algorithms Algebra of the Lyndon words Linear Algebra and their applications De Bruijn sequences and application to graph theory I am proud and honored to have the 6th Mediterranean International Conference of Pure & Applied Mathematics and Related Areas (MICOPAM 2023), which is dedicated to my 60th Anniversary, held at Université d'Evry in Paris, FRANCE on August 23-27, 2023, (https://micopam.com). Therefore, I would like to thank the main organizer, my friend (like as my brother) and colleague Professor Abdelmejid BAYAD. He gave his big energy and time in order to prepare this wonderful and high quality international conference at Université d'Evry in Paris, FRANCE. And also, I would like to thank Professor Vincent Bouhier (President of the University ofÉvry Paris-Saclay) and all staff of the University ofÉvry Paris-Saclay for their help in order to organize this wonderful conference. In addition, I would also like to thank other organizers: my friend and colleague Professor Mustafa ALKAN, my colleague and hardworking doctoral student, Associate Professorİrem KÜÇÜKOGLU, my colleague and hardworking doctoral student, Associate Professor Neslihan KILAR and my colleague and friend Associate Professor OrtaçÖNEŞ, who are very valuable members of the organizing committee of this conference. I would like to thank the other local organizers such as Assistant Professor Rahime DERE and Associate Professor Ayse Ceylan YILMAZ. I would also like to express my sincere gratitude to the following my friends and colleagues who are invaluable and distinguished invited speakers of this conference:

The book, having eight chapters, offers one semester course (with four credit hours per week) on diverse topics usually included in the mathematics syllabus of the first year Engineering class of most Universities. The first chapter deals with the introductory topics in 2-dimensional coordinate geometry: straight lines and conic sections. A brief discussion of theory of equations is given in the second chapter. Vectors (mostly in 3-dimensional space) are introduced in the third chapter. Vector algebra and products of vectors are included. The next chapter deals with the matrices and determinants. Matrix algebra including multiplication of matrices is given. Further concepts such as rank of a matrix etc. are avoided. A comprehensive course on convergence of infinite series forms the subject mater of Chapter 5. Presuming that the students already had a first course on calculus only main concepts and results of differentiation and integration of functions of single variable have been given in the chapter 6. Power series, Maclaurin’s and Taylor’s expansions are explained in detail in the same chapter. Two Eulerian integrals, usually called Beta and Gamma functions, are also introduced and some properties of Gamma functions are given. Applications of vectors to geometry dealing with the vector equations of straight lines and planes are given in the Chapter 7. The last chapter deals with the partial derivation of functions of more than one variable. Both vector and scalar functions are considered and the vector differential operator of the first order is introduced. The total derivative of functions and famous Euler’s theorem on homogeneous functions are explained. Besides several worked out exercises (called Examples), Chapters 5, 7 and 8 are also supplemented by Problem-sets of unsolved exercises with necessary hints to the challenging ones. Tutorial sheets and Test Papers containing model questions and a short bibliography of the topics are provided. The alphabetical index added at the end makes the access to the contents faster. Chapters are divided into Sections, which are numbered chapter-wise. The discussion within the Sections is presented in the form of Definitions, Theorems, Corollaries, Notes and (solved) Examples. These subtitles within the Sections are numbered in decimal pattern. For instance, the equation number (c.s.e) refers to the eth equation in the sth section of Chapter c. When the number c coincides with the chapter at hand it is dropped. Adequate references to the previously appeared results are made in the text and unnecessary repetitions are avoided.

Professor Janis S. Rimshans was a very pure soul. His main trait was boundless kindness to everything: to the people, to animals, to plants and to nature in general. This trait was so strong in Janis S. Rimshans that it was impossible to stay "unpurified" while talking with him even for 10-15 minutes, no matter what state of mind you had before. Janis S. Rimshans vainly dreamed for learning to say "no" and refuse people if they approached him with requests, fulfilling of which often caused an obvious material and/or moral damage both personally and indirectly to Janis S. Rimshans affairsscientific and organizational activities, which he had breathed and lived for. In a word, Janis S. Rimshans was rock-ribbed monolithic person by spiritual and moral qualities manifested in all-consuming kindness, unlike his multifaceted scientific talent, which will be discussed below. I met the Professor Janis S. Rimshans for the first time on April 8, 2006, in Liepaja during the second Conference of the Latvian mathematicians, organized by the Latvian Mathematical Society. On the same day, even in front of an acquaintance, I listened to the scientific report of professor Janis S. Rimshans devoted to quite complex initial-boundary problem for non-linear system modeling of the dynamics of incompressible viscous fluid in a vapor space when convective diffusion occurs at the impurity presence in liquid, which density is dependent on impurity concentration in a non-linear way. Listening to a report of Janis S. Rimshans, I was surprised by his scientific courage to "challenge" such a complicated problem, which is so far jointly studied by many research teams from worldwide known research institutes in Russia, Germany, France, etc. Looking ahead, I would like to note that in the following years, Professor Janis S. Rimshans surprised me with his scientific courage for many times: he often approached the most difficult problems in mathematical physics having global significance, inspiring with enthusiasm his numerous undergraduate, graduate and doctoral students. Getting back to the history of our acquaintance, I would like to emphasize the following: before Professor Janis S. Rimshans made his brilliant scientific report, which was mentioned above, three of his students (T.Bibinska-Doctor of Mathematical Sciences at present time; P.Morevsa doctoral student in the University of Latvia at the moment, scientific supervisor of the thesis was Professor Janis S. Rimshans; J.Kapuča) came up with three very meaningful scientific reports on the complex problems of mathematical physics; after the report of Professor Janis S. Rimshans there has been presented a sound scientific result of one more of his studentsdoctoral student D.Žaime. I remember very well that after all these brave, brilliant and successful from scientific perspective reports of Professor Janis S. Rimshans and his students, I asked two scientists, mathematicians from Riga who sat next to me, whom I knew well and collaborated with-Dr.Sc.Math., Professor of the University of Latvia, full member of

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