Recent zbMATH articles in MSC 01https://zbmath.org/atom/cc/012021-01-08T12:24:00+00:00Unknown authorWerkzeugIn memory of Ivan S. Volkov, rector of the Kuibyshev Polytechnical Institute.https://zbmath.org/1449.010182021-01-08T12:24:00+00:00"Barsova, A. A."https://zbmath.org/authors/?q=ai:barsova.a-a(no abstract)75th anniversary of Yuriĭ P. Samarin's birthday.https://zbmath.org/1449.010222021-01-08T12:24:00+00:00"Radchenko, V. P."https://zbmath.org/authors/?q=ai:radchenko.vladimir-pavlovich"Saushkin, M. N."https://zbmath.org/authors/?q=ai:saushkin.m-n(no abstract)Trigonometric functions in elementary mathematics.https://zbmath.org/1449.330012021-01-08T12:24:00+00:00"Smýkalová, Radka"https://zbmath.org/authors/?q=ai:smykalova.radkaThe book discusses various elementary aspects and applications of trigonometric functions. Most of the text is accessible to high-school students, but it will be useful to teachers as well. Despite being elementary, it contains a significant amount of advanced material, including olympiad-level problems. The contents are as follows:
Chapter 1 deals with the history of trigonometric functions, beginning with the roots or trigonometry in the ancient Greece, proceeding to the developments in the medieval India and Arabic lands, and concluding with Euler's analytical approach to trigonometric functions.
The next three chapters provide a modern and systematic treatment of high-school trigonometry and trigonometric functions. Chapter 2 begins with trigonometry in right triangles, and includes geometric derivations of the trigonometric addition formulas. It covers some slightly more advanced topics, such as the construction of a regular pentagon, or expressing the values of trigonometric functions for special angle values in terms of radicals. Chapters 3 proceeds to high-school trigonometry of general triangles, and extends the definitions of trigonometric functions to arguments from the interval \((90^\circ,180^\circ)\). It covers the well-known laws of sines and cosines, and the less familiar law of tangents and Mollweide's formula. Finally, Chapter 4 uses the unit circle to introduce trigonometric functions for an arbitrary real argument, discusses the validity of addition formulas in this more general setting, and devotes considerable space to the solution of trigonometric equations and inequalities.
Chapter 5 contains an overview of many advanced (but still elementary) identities and inequalities involving trigonometric functions. The final Chapter 6 describes some applications, such as the solution of algebraic equations using trigonometric substitutions, derivations of various identities and inequalities using the trigonometric form of complex numbers, and the appearance of trigonometric functions in cartography (with emphasis on the Mercator projection).
Reviewer: Antonín Slavík (Praha)In memory of Dyuis Danilovich Ivlev.https://zbmath.org/1449.010212021-01-08T12:24:00+00:00"Radaev, Yu. N."https://zbmath.org/authors/?q=ai:radaev.yu-n(no abstract)In memory of Vasiliĭ S. Vladimorov.https://zbmath.org/1449.010252021-01-08T12:24:00+00:00"Volovich, I. V."https://zbmath.org/authors/?q=ai:volovich.igor-v(no abstract)An in-depth study on Indian Kuttaka and comparison with the Chinese Dayan rule.https://zbmath.org/1449.010102021-01-08T12:24:00+00:00"Lv, Peng"https://zbmath.org/authors/?q=ai:lv.peng"Ji, Zhigang"https://zbmath.org/authors/?q=ai:ji.zhigangSummary: The word Kuttaka means the problem of first order indefinite analysis and also the operational algorithm of this kind of problem in the works of ancient Indian mathematics. After it first appeared in Aryabhata's Aryabhatiya (5th century A.D.), Kuttaka was an important topic for Indian mathematicians. Based on Sanskrit texts, we discuss aspects of the origin, improvement, main features and effectiveness of the Kuttaka algorithm. Then, comparing Kuttaka with the Chinese Dayan-Zongshu method, we confirm the similarity between Kuttaka and the Dayan Rule on the computation of the Euclidean Algorithm, as well as in their systematic design (i.e., iterative computation) and graphically (i.e., the creeper of remainders and the square of manipulating numbers). In fact, the Dayan-Qiuyi method is a special kind of Kuttaka; the power of the Kuttaka is equivalent to the Dayan Rule. However, the two are quite different in the whole structure of the algorithm and in historical development. Moreover, the Kuttaka method seems to be more general, simpler and easier because of a series of rules of reduction and continuity.Verification of the original English textbooks of \textit{Xingxue Beizhi}.https://zbmath.org/1449.010082021-01-08T12:24:00+00:00"Zhu, Jie"https://zbmath.org/authors/?q=ai:zhu.jieSummary: \textit{Xingxue Beizhi} is an important primary geometry textbook of the late Qing dynasty. It has generally been regarded in academic circles as a direct translation, which is not the case. By sorting out and comparing the various English originals, this paper argues that it is based on the revised version of Loomis' geometry textbook, with further reference to a number of other English textbooks, combined with some exercises created by Calvin Wilson Mateer himself. This paper also analyzes the compilation characteristics of \textit{Xingxue Beizhi}, and points out that it improved on the original English textbooks, and was more suitable for the national conditions of China at that time.In memory of Anatoliĭ A. Kilbas.https://zbmath.org/1449.010172021-01-08T12:24:00+00:00"Andreev, A. A."https://zbmath.org/authors/?q=ai:andreev.aleksandr-anatolevich"Dzhenaliev, M. T."https://zbmath.org/authors/?q=ai:jenaliyev.muvasharkhan-t"Zarubin, A. N."https://zbmath.org/authors/?q=ai:zarubin.aleksandr-nikolaevich"Kozhanov, A. I."https://zbmath.org/authors/?q=ai:kozhanov.aleksandr-ivanovich"Moiseev, E. I."https://zbmath.org/authors/?q=ai:moiseev.evgeny-ivanovich"Nakhushev, A. M."https://zbmath.org/authors/?q=ai:nakhushev.adam-maremovich"Nakhusheva, V. A."https://zbmath.org/authors/?q=ai:nakhusheva.v-a"Ogorodnikov, E. N."https://zbmath.org/authors/?q=ai:ogorodnikov.evgenii-nikolaevich"Pskhu, A. V."https://zbmath.org/authors/?q=ai:pskhu.arsen-vladimirovich"Pulkina, L. S."https://zbmath.org/authors/?q=ai:pulkina.lyadmila-stepanovna|pulkina.ludmila-s|pulkina.lyudmila-stepanovna"Radjabov, N. R."https://zbmath.org/authors/?q=ai:radjabov.n-r"Radchenko, V. P."https://zbmath.org/authors/?q=ai:radchenko.vladimir-pavlovich"Radkevich, E. V."https://zbmath.org/authors/?q=ai:radkevich.e-v"Repin, O. A."https://zbmath.org/authors/?q=ai:repin.oleg-aleksandrovna|repin.oleg-aleksandrovich"Sabitov, K. B."https://zbmath.org/authors/?q=ai:sabitov.kamil-basirovich"Soldatov, A. P."https://zbmath.org/authors/?q=ai:soldatov.aleksandr-pavlovich(no abstract)Research of dynamics of Aten asteroids in vicinity of resonance with inner planets.https://zbmath.org/1449.850122021-01-08T12:24:00+00:00"Zausaev, A. F."https://zbmath.org/authors/?q=ai:zausaev.anatolii-fedorovich"Altynbaev, F. Kh."https://zbmath.org/authors/?q=ai:altynbaev.f-khSummary: In the time interval from 1800 to 2200 we research the dynamics of Aten in vicinity of resonance with inner planets. It is shown that 238 among 320 Aten asteroids move in vicinity of resonance with one, two or three inner planets.Anatoly Naumovich Kochubei (to 70th birthday anniversary).https://zbmath.org/1449.010162021-01-08T12:24:00+00:00A. N. Kochubei (born in 1949) is a Ukrainian mathematician, Editor-in-Chief of MFAT. The paper describes his biography and main results in the fields of mathematics such as extensions of operators, fractional calculus, non-Archimedean analysis.
Reviewer: Mikhail P. Moklyachuk (Kyïv)Supplementary proofs and interpretations of Liu Yueyun's \textit{Ceyuan Haijing Tongshi}.https://zbmath.org/1449.010052021-01-08T12:24:00+00:00"Li, Zhaohua"https://zbmath.org/authors/?q=ai:li.zhaohuaSummary: Gougu Ceyuanshu (Method for finding the diameter of a circle in contact with nine right triangles) recorded in \textit{Ceyuan Haijing} (Sea Mirror of Circle Measurements, 1248) is one of the most important accomplishments of mathematics in pre-modern China. Furthermore, the method was improved and systematized by mathematicians in the late Qing dynasty. Among them was Liu Yueyun (1849--1917), who gained a better understanding of \textit{Ceyuan Haijing} and completed his book \textit{Ceyuan Haijing Tongshi} (A Concise Explanation of Ceyuan Haijing, 1896). However, owing to the lack of explanations and some textual errors in the transmitted text, his book is difficult to understand. Based on textual collation and calculations, this paper analyzes some of the knotty problems, and explains both Liu's theory and methods. The paper considers that, devoted to development of the theory of Gougu Ceyuan Shu, Liu's book is an example of research of considerable significance during the late Qing dynasty.Vratislav Horálek passed away.https://zbmath.org/1449.010192021-01-08T12:24:00+00:00"Beneš, Viktor"https://zbmath.org/authors/?q=ai:benes.viktor(no abstract)Abel Prize. The highest award for mathematics.https://zbmath.org/1449.010012021-01-08T12:24:00+00:00"Křížek, Michal"https://zbmath.org/authors/?q=ai:krizek.michal"Somer, Lawrence"https://zbmath.org/authors/?q=ai:somer.lawrence-e"Markl, Martin"https://zbmath.org/authors/?q=ai:markl.martin"Kowalski, Oldřich"https://zbmath.org/authors/?q=ai:kowalski.oldrich"Pudlák, Pavel"https://zbmath.org/authors/?q=ai:pudlak.pavel"Vrkoč, Ivo"https://zbmath.org/authors/?q=ai:vrkoc.ivoThis book is an account of the first fifteen winners of the Abel Prize in mathematics, which has been awarded on a yearly basis from 2003 onwards. Each of the fifteen chapters of roughly 10--15 pages contains a short biography of the winner(s) and also a description of the winner's celebrated result, presented in a simplified and popular fashion, readable by anyone with BSc degree in mathematics. The book is hardcover, printed on high-quality paper, with color pictures. It is written in Czech, English summary is included. See also [\textit{M. Křížek} et al., Prvních deset Abelových cen za matematiku (Czech). Prague: The Union of Czech Mathematicians and Physicists (2013; Zbl 1274.01048)].
Reviewer: Jan Brandts (Amsterdam)Pitiscus' numerical solution for \(\sin 1 \degree\).https://zbmath.org/1449.010112021-01-08T12:24:00+00:00"Guo, Yuanyuan"https://zbmath.org/authors/?q=ai:guo.yuanyuan"Dong, Jie"https://zbmath.org/authors/?q=ai:dong.jieSummary: Since the Ptolemy (about 90--168) era, the exact value of \(\sin 1\degree\) had been related to the overall accuracy of the Sine table. It was the Persian mathematician Jamshid Mas'ud al-Kashi (1380--1429) who made the first breakthrough on this issue. For a long time, this problem also had puzzled many European mathematicians in the 16th century. It was the German mathematician Bartholomaeus Pitiscus (1561--1613) who made the first achievements in solution of the problem. This paper focused on the analysis of the \(\sin 1\degree\) numerical solution of Pitiscus and gave comparison of the operation process of the numerical solution of the \(\sin 1\degree\) between al-Kashi and Pitiscus.Cardano's rule of proportional position.https://zbmath.org/1449.010132021-01-08T12:24:00+00:00"Zhao, Jiwei"https://zbmath.org/authors/?q=ai:zhao.jiwei"Li, Gang"https://zbmath.org/authors/?q=ai:li.gang.9|li.gang.10|li.gang.11|li.gang.2|li.gang.1|li.gang.8|li.gang.6|li.gang.4Summary: Based on systematical summarization of the seven problems in Chapter 33 of \textit{Artis Magnae} and careful analysis of Problem 4.1, the modern mathematical representation of the rule of proportional position is given and Cardano's deduction of this rule is reconstructed by the elimination method for systems of linear equations with two variables in Chapter 9 of \textit{Artis Magnae}. This rule reflected Cardano's efforts to solve a type of special five-term quartic equation, through which he could transform the five-term quartic equation into a new biquadratic equation. Meanwhile, it is suggested that Cardano did not grasp the solution of general five-term quartic equation.Wilder's thoughts on mathematical evolution and others' comments.https://zbmath.org/1449.010262021-01-08T12:24:00+00:00"Liu, Pengfei"https://zbmath.org/authors/?q=ai:liu.pengfeiSummary: Wilder is a famous American mathematician who contributed a great deal in the field of topology research. Affected by his interest and study in anthropology, he tried to apply the method of cultural anthropology research to the history of mathematics when he started the philosophical thinking on mathematical basis problem. He looked mathematics as a sub-cultural system in the whole human cultural system and described the mathematical development from the beginning to modern times as a natural process of culture evolution. He revealed the driving forces and laws of mathematics evolution and his thoughts on mathematics evolution were reviewed by many famous mathematicians, philosophers, historians and anthropologists. It would be very inspiring to study the Wilder's theory for our research on the history of mathematics.Celestial element method and algebra in the late Qing dynasty -- a case of Chinese traditional mathematics' modernization process.https://zbmath.org/1449.010032021-01-08T12:24:00+00:00"Guo, Shirong"https://zbmath.org/authors/?q=ai:guo.shirong"Wei, Xuegang"https://zbmath.org/authors/?q=ai:wei.xuegangSummary: On the basis of analyzing the fundamental state of celestial element method in the late Qing dynasty, we compared Chinese mathematicians' concept of celestial element method and algebra and reviewed the process of competition and integration between the two traditions in this paper. By profoundly rethinking the modernization of Chinese traditional mathematics, we concluded that the introduction of western mathematical knowledge was the premise of modernization. We also realized that study of algebra and the comparison between celestial element method and algebra were the necessary steps to the modernization of celestial element method. Meanwhile, we got more clearly understanding that the art of celestial element method promoted the acceptance of algebra and the old tradition was the greatest obstruction of its modernization.The reasoning argumentation about the golden section in the early Qing dynasty.https://zbmath.org/1449.010022021-01-08T12:24:00+00:00"Dong, Jie"https://zbmath.org/authors/?q=ai:dong.jieSummary: Due to the cultural differences, the understanding and research on the golden section by the Chinese scholars in the 17th century are distinctively different from their counterpart in the West. In the late Ming dynasty, it was through Euclid's \textit{Elements} that the golden section was introduced into China. The novelty was seen by Chinese mathematicians in terms of the logic reasoning even though their understanding might be incomplete. Under the strong influence of Chinese tradition, Chinese scholars' first consideration was focused on how to use the golden section as they were mindful of the utility of knowledge. At the same time, in the process of making argumentation in understanding the golden section, experience and deduction also interacted with each other and the Western logical deduction system was accepted among the Chinese mathematicians gradually.Mei Wending and \textit{Ouluoba Xijinglu}.https://zbmath.org/1449.010042021-01-08T12:24:00+00:00"He, Lei"https://zbmath.org/authors/?q=ai:he.lei"Ji, Zhigang"https://zbmath.org/authors/?q=ai:ji.zhigangSummary: \textit{Ouluoba Xijinglu} (The Records of Europe's Western Mirror) is an important work for the introduction of western manual calculation in the late Ming or early Qing. Mei Wending, who got this book occasionally, did an intensive studies and made annotation for it. By analyzing Mei's notes and his understanding about the \textit{Ouluoba Xijinglu} and comparing with his books of \textit{Bi Suan} (Manual calculation) and \textit{Shaoguang Shiyi} (Supplement to Shaoguang), we found that Mei Wending absorbed from \textit{Ouluoba Xijinglu} a lot, which was reflected in his expansion of the power table and the initial quotient table and the application of the positioning method of western arithmetic in the multiplication and division methods by him. The study reviewed the process of Mei's absorption of Western mathematical knowledge and did an exploration for the sources of Mei's mathematical thought from a new perspective.The development of the problems of the excess and deficit in the early period of China: an investigation based on the Shu on the Qin bamboo strips preserved at Yuelu Academy.https://zbmath.org/1449.010092021-01-08T12:24:00+00:00"Zou, Dahai"https://zbmath.org/authors/?q=ai:zou.dahaiSummary: The new collations and new interpretations were given for the materials about the Yingbuzu (excess and deficit) in the book \textit{Shu} (On Numbers) on the Qin bamboo strips preserved at Yuelu Academy and some difficult and complicated problems were clarified in this paper. Together with the corresponding materials in the \textit{Jiuzhang Suanshu} (Nine Chapters on Mathematical Procedures) and the \textit{Suanshu Shu} (A Book on Numbers and Computation), we investigated the development of the Yingbuzu problems in early China. The textual analysis revealed that the problems of Yingbuzu could be traced back to the Qin dynasty and the pre-Qin period according the \textit{Shu}, the \textit{Shu} had no textual influence on the \textit{Jiuzhang Suanshu}, while the solution methods of Yingbuzu in the pre-Qin ancestors or its derivatives in the \textit{Jiuzhang Suanshu} was likely to have direct or indirect influence on the \textit{Shu}. After comparing and analyzing the 15th problem of the Yingbuzu in the \textit{Jiuzhang Suanshu} with corresponding problem in the \textit{Shu} and the \textit{Suanshu Shu}, we realized that the opinion of some scholars that ancients had carelessly put this problem into the Yingbuzu chapter was not appropriate and held that the composers of the \textit{Jiuzhang Suanshu} maintained high degree of consistency with the \textit{Shu} and the \textit{Suanshu Shu} in selection of problems for the chapter.Ming Antu's representation and treatment of alternative series.https://zbmath.org/1449.010062021-01-08T12:24:00+00:00"Wang, Xinyi"https://zbmath.org/authors/?q=ai:wang.xinyi"Guo, Shirong"https://zbmath.org/authors/?q=ai:guo.shirongSummary: \textit{Ge Yuan Mi Lu Jie Fa} (Quick methods for trigonometry and for determining the precise ratio of the circle) was the first book in the history of Chinese mathematics to expand the trigonometric string vector function into infinite series. Following the author's thinking and method, this paper analyzes the author's right and left writing form of positive and negative terms of alternative series and the proper treatment of alternative series in the \textit{Ge Yuan Mi Lu Jie Fa}. This paper holds that: firstly, the author's expression and treatment of alternative series had its origin from Western method and the classification method used by Mei Juecheng in \textit{Chi Shui Yi Zhen}. Secondly, the author treated alternative series as a formal series, and performed infinite series with polynomials. On the premise of convergence of series, the operation is feasible and the result is correct. This enhances the historical understanding of the methods dealing with alternative series in modern analytics.Research on several related issues from Daishu Xue to Daishu Shu.https://zbmath.org/1449.010072021-01-08T12:24:00+00:00"Zhang, Bisheng"https://zbmath.org/authors/?q=ai:zhang.bishengSummary: Daishu Xue that is translated from De Morgan's \textit{Elements of Algebra} and Daishu Shu that is translated from Wallace's \textit{Algebra} are two classic translations that introduced Western mathematics theory into China during the late Qing dynasty. The two books both present Western algebraic theory. They are mutually linked with continuous content. The latter has a larger theoretical research scope, deeper discussion and improved terminology. The Western algebra theory introduced in Daishu Xue mainly focuses on the issues of symbol algebra, series and simple equations, while Daishu Shu introduces more complex algebra theory, including Cardano's formula, special methods for higher order equations, continuous fractional operations, and indeterminate analysis. Moreover, economic calculations, complex series operation, trigonometric functions and their applications are introduced in terms of calculation in Daishu Shu. They have far-reaching influence on science and education in the late Qing Dynasty. In particular, their content on related issues provided new methods and ideas for later Chinese scholars to study Western algebra theory. They guided the research direction of algebra, and laid the theoretical foundation for the westernization of Chinese algebra and the introduction of abstract algebra.Clavius' unified solutions by the method of twofold double false positions.https://zbmath.org/1449.010122021-01-08T12:24:00+00:00"Liu, Di"https://zbmath.org/authors/?q=ai:liu.di"Zhao, Jiwei"https://zbmath.org/authors/?q=ai:zhao.jiweiSummary: In 1202, the Italian mathematician Fibonacci (ca.1170 -- ca.1250) published \textit{Liber Abaci}, in which the system of linear equations was solved by multi-fold double false positions for the first time in Europe. This method became the standard algorithm until the late 16th century when European mathematicians treated with such problems. In 1583, the German mathematician Clavius (1538--1612) dealt with the system of 3-variable linear equations by the method of twofold double false positions in his \textit{Epitome Arithmeticae Practicae}, he discovered the consistence of the solution formula of double false positions, which became the earliest simplification to Fibonacci's method. By comparing the similarities and differences between the two methods, this paper presents a quantitative analysis of how Clavius' simplified method works, and explains the mathematical principles of Clavius' consistence of the solution formula, and proposes that Clavius' discovery of the consistency of solution formula may be based on analysis and induction of the concrete mean results during his solution of 4 special systems of 3-variable linear equations.Study of the cosmic rays transport problems using second order parabolic type partial differential equation.https://zbmath.org/1449.850132021-01-08T12:24:00+00:00"Gil, Agnieszka"https://zbmath.org/authors/?q=ai:gil.agnieszka"Alania, Michael V."https://zbmath.org/authors/?q=ai:alania.michael-vSummary: It has been exactly 100 years since Hess's historical discovery: an extraterrestrial origin of cosmic rays [\textit{E. N. Parker}, ``Dynamics of the interplanetary gas and magnetic fields'', Astrophys. J. 128, 664--676 (1958; \url{doi:10.1086/146579})]. Galactic cosmic rays (GCR) being charged particles, penetrate the heliosphere and are modulated by the solar magnetic field. The propagation of cosmic rays is described by Parker's transport equation [\textit{V. F. Hess}, ``Über Beobachtungen der durchdringenden Strahlung bei sieben Freiballonfahrten'', Phys. Z. 13, 1084--1091 (1912)], which is a second order parabolic type partial differential equation. It is time dependent 4-variables (with \(r\), \(\theta\), \(\varphi\), \(R\), meaning: distance from the Sun, heliolatitudes, heliolongitudes and particles' rigidity, respectively) equation which is a well known tool for studying problems connected with solar modulation of cosmic rays. Transport equation contains all fundamental processes taking place in the heliosphere: convection, diffusion, energy changes of the GCR particles owing to the interaction with solar wind's inhomogeneities, drift due to the gradient and curvature of the regular interplanetary magnetic field and on the heliospheric current sheet.
In our paper we investigate a topic of the 27-day variation of the galactic cosmic rays intensity, which is connected with solar rotation. We numerically solve the Parker's transport equation involving in situ measurements of solar wind and magnetic field.In memoriam Roger Charles Alperin (1947--2019).https://zbmath.org/1449.010152021-01-08T12:24:00+00:00(no abstract)In memory of Oleg Vasil'evich Sosnin.https://zbmath.org/1449.010232021-01-08T12:24:00+00:00"Tsvelodub, I. Yu."https://zbmath.org/authors/?q=ai:tsvelodub.i-yu"Radchenko, V. P."https://zbmath.org/authors/?q=ai:radchenko.v-p.1|radchenko.vladimir-pavlovich(no abstract)In memory of Boris Leonidovich Shtrikov.https://zbmath.org/1449.010142021-01-08T12:24:00+00:00(no abstract)Beginnings of matrix theory in the Czech Republic and their results.https://zbmath.org/1449.150012021-01-08T12:24:00+00:00"Štěpánová, Martina"https://zbmath.org/authors/?q=ai:stepanova.martinaThe book traces the early history of matrix theory in the Czech lands approximately in the period 1850--1950. The main emphasis is on the outstanding results of Eduard Weyr (1852--1903) dealing with the so-called Weyr characteristic and Weyr canonical form. These concepts are closely related to the well-known Segre characteristic and Jordan canonical form of a square matrix. Despite Weyr's priority over Jordan, his results remained almost forgotten for about a century. The Weyr characteristic has become increasingly popular since the 1980s thanks to H. Schneider, D. Hershkowitz, and their followers, who were studying relations between matrices and their associated graphs. The Weyr canonical form has been rediscovered several times, and became more widely known due to \textit{H. Shapiro}'s paper [Am. Math. Mon. 106, No. 10, 919--929 (1999; Zbl 0981.15008)], who introduced it to nonspecialists and gave proper credit to Weyr.
The text represents an expanded version of the author's dissertation thesis. It is based on a careful study of a large number of primary sources spanning the period of about 150 years. Weyr's results are first described in a proper historical context, and then explained once again in the language of modern mathematics. A considerable portion of the book is devoted to the reception of Weyr's work since its publication until the present day. The book is very well written and will be of interest to all historians of mathematics. Readers who are not fluent in Czech can take advantage of a twenty-page-long English summary.
Reviewer: Antonín Slavík (Praha)Preface.https://zbmath.org/1449.010202021-01-08T12:24:00+00:00"Guo, Benqi (ed.)"https://zbmath.org/authors/?q=ai:guo.benqi"Ma, Heping (ed.)"https://zbmath.org/authors/?q=ai:ma.heping"Shen, Jie (ed.)"https://zbmath.org/authors/?q=ai:shen.jie"Shu, Chi-Wang (ed.)"https://zbmath.org/authors/?q=ai:shu.chi-wang"Wang, Li-Lian (ed.)"https://zbmath.org/authors/?q=ai:wang.lilianFrom the text: This is a focused issue dedicated to the memory of the late Professor Ben-yu Guo (1942--2016), a prominent numerical analyst at Shanghai University and Shanghai Normal University, and a prolific researcher with more than 300 peer-reviewed publications, many of which are in prestigious journals.A conversation with Oscar Bustos. (Comments from Jorge G. Adrover, Hector Allende O. and Alejandro C. Frery).https://zbmath.org/1449.010242021-01-08T12:24:00+00:00"Vallejos, Ronny O."https://zbmath.org/authors/?q=ai:vallejos.ronny-o"Ojeda, Silvia M."https://zbmath.org/authors/?q=ai:ojeda.silvia-mariaSummary: Oscar Bustos was born on March 20, 1947, in San Nicolás de los Arroyos, Argentina. He completed a B.A. degree in Mathematics in 1970 at the Universidad Nacional de Córdoba (UNC), Argentina. In the period 1970--1976 he worked as a part-time instructor in the same department. In 1976 he went to the Universidad Nacional de San Luis, Argentina, where he completed a Ph.D. degree in Mathematics in 1978 under the supervision of Dr. Ricardo Maronna. Because the situation in Argentina at that moment was difficult he decided to move to Brazil (Instituo Nacional de Matemática Pura e Aplicada, IMPA) where his academic career was highly enriched by the interaction with other colleagues and students. In 1992 he returned to Argentina and the same year he joined the UNC as a full professor in the department of Mathematics, Astronomy, and Physics. Dr. Bustos since then has been a very active investigator in robustness, time series, image processing, satellite acquisition systems, among other fields. He has been the chair of the Probability and Statistics group in the same university since 1992 supervising eleven Ph.D. students, more than thirty master students and leading a number of activities such as participating in the evaluation of programs, editorial service for many journals, the creation of master's and doctoral programs in statistics and establishing a constant interaction with the National Commission on Space Activities (CONAE in Spanish). For these and other reasons he is a distinguished professor in the department of Mathematics, Astronomy, and Physics (FAMAF) at UNC, Córdoba, Argentina. Since 1990 he has been in touch with chilean investigators interacting and developing statistical methods with applications in image processing and time series.
The following conversation took place at FAMAF, UNC, Córdoba, Argentina, May 4, 2014.The work of Fernando de Helguero on non-normality arising from selection.https://zbmath.org/1449.620012021-01-08T12:24:00+00:00"Azzalini, Adelchi"https://zbmath.org/authors/?q=ai:azzalini.adelchi"Regoli, Giuliana"https://zbmath.org/authors/?q=ai:regoli.giulianaSummary: The current literature on so-called `skew-symmetric distributions' is closely linked to the idea of a selection mechanism operated by some latent variable. We illustrate the pioneering work of Fernando de Helguero who in 1908 [Rom. 4. Math. Kongr. 8. 288--299 (1909; JFM 40.0294.03)] put forward a formulation for the genesis of non-normal distributions via a selection mechanism, which perturbs a normal distribution, hence employing a closely connected argument with the one now widely used in this context. Arguably, de Helguero can then be considered the precursor of the current idea of skew-symmetric distributions. Unfortunately, a tragic quirk of fate did not allow him to pursue his project beyond the initial formulation and his work went unnoticed for the rest of the 20th century.