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Wikipedia:Verónica Martínez de la Vega#0
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Verónica Martínez de la Vega y Mansilla is a Mexican mathematician whose research involves topology and hypertopology. She is a researcher in the Institute of Mathematics at the National Autonomous University of Mexico (UNAM). == Education and career == Martínez de la Vega was born in Mexico City, on January 5, 1971. Her family worked as lawyers, and discouraged her from going into science, but nevertheless she ended up studying mathematics at UNAM, and wrote an undergraduate thesis in topology that she published as a journal paper in Topology and its Applications. Continuing to graduate study in topology at UNAM, she completed her PhD in 2002 with the dissertation Estudio sobre dendroides y compactaciones supervised by Polish topologist Janusz J. Charatonik, becoming his only female doctoral student. After postgraduate research at UAM Iztapalapa and California State University, Sacramento, she joined the Institute of Mathematics as a researcher in 2005. == Recognition == Martínez de la Vega is a member of the Mexican Academy of Sciences. In 2017 UNAM gave her their "Reconocimiento Sor Juana Inés de la Cruz" award. == References ==
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Wikipedia:Veselin Jungić#0
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Veselin Jungić (born June 12, 1955) is a Canadian mathematician who is a teaching professor of mathematics at the Simon Fraser University, in its Department of Mathematics. His research interests are in Ramsey theory and mathematical education. == Early life and education == Veselin Jungić was born in the city of Banja Luka in former Yugoslavia and completed his undergraduate degree in mathematics at the University of Sarajevo, Bosnia and Herzegovina, earning a Bachelor of Science in 1977. He then pursued a master's degree in mathematics at the Faculty of Science, University of Zagreb in Croatia. In 1992, Jungić and his family moved to Vancouver, British Columbia, to escape the Bosnian War. He continued his academic journey in mathematics, earning his Ph.D. in 1999 from Simon Fraser University under the supervision of Tom Brown. His Ph.D. thesis was titled Elementary, Topological, and Experimental Approaches to the Family of Large Sets. == Career and research == After completing his Ph.D., Jungić began his academic career in Canada as a Postdoctoral Fellow in the Department of Mathematics at the University of British Columbia under the supervision of David William Boyd. From 2001 to 2006, he served as a lecturer at Simon Fraser University's Department of Mathematics. In 2007, he was promoted to Senior Lecturer in the same department. In 2015, Jungić was appointed as a Teaching Professor at Simon Fraser University, a position he continues to hold. Jungić's academic research primarily focuses on Ramsey Theory. In one of his early papers, Rainbow Arithmetic Progressions and Anti-Ramsey Results, Jungić and a group of researchers explored rainbow Ramsey Theory, investigating the existence of rainbow arithmetic progressions, where each element is a distinct color. The paper demonstrates that any 3-coloring of the natural numbers, with each color appearing at least 1/6 of the time, must contain a 3-term rainbow arithmetic progression. The study extends these findings to similar colorings of the integers and discusses the broader implications for anti-Ramsey theory. Jungić has also written numerous papers and articles aimed at promoting Ramsey Theory to a broader audience within the mathematical community. In addition, Jungić has contributed extensively to Crux Mathematicorum, authoring articles that present problems, examples, and notes on topics such as the Hales-Jewett Theorem, Ramsey Theorem, the chromatic number of the plane problem, and van der Waerden's Theorem. Jungić's research also encompasses a broad range of educational initiatives, with a focus on innovative teaching strategies and experimental mathematics. His work in large-class pedagogy addresses the challenges faced by both students and instructors, emphasizing the importance of building dialogue and mutual trust in such environments. He has also explored experimental mathematics, using dynamic visual models to bridge ancient ideas with modern technologies, offering fresh insights into mathematical education. == Math Catcher Outreach program == Since its inception in 2011, the Math Catcher Outreach program, developed by Jungić, has aimed to promote mathematics among elementary and high school students by demonstrating its relevance in everyday life and decision-making. The program places a strong emphasis on Indigenous education, creating learning resources in various First Nations languages. It includes original stories, problem-solving activities, and hands-on tasks, ensuring that math education is enjoyable, inclusive, and culturally relevant for young learners. Map of the places visited by the Math Catcher Outreach Program == Awards and honours == Veselin Jungić was inducted into the Canadian Mathematical Society's 2021 Class of Fellows, recognizing his significant contributions to mathematics education, research, and service within the Canadian mathematical community. This Fellowship honors members who have demonstrated excellence in their field and provided distinguished service to Canada's mathematical community, highlighting Jungić's ongoing commitment to advancing mathematics education. In 2020, Veselin Jungić received the Adrien Pouliot Award for his outstanding contributions to mathematics education, particularly through his leadership in the Math Catcher Outreach Program and initiatives that enhance learning experiences for Canadian post-secondary students. He co-organizes the Teaching Matters Seminar Series at Simon Fraser University and collaborates on educational initiatives like the "First Year Math and Stats in Canada" program. In 2015, Veselin Jungić was awarded the 3M National Teaching Fellowship, a highly respected recognition for excellence in educational leadership and teaching at the university and college level. Conferred by the Society for the Scholarship of Teaching and Learning in Higher Education (STLHE), this Fellowship acknowledges Dr. Jungić's exceptional contributions to teaching and learning in Canadian post-secondary education. As a recipient, Jungić became a member of the STLHE Council of Fellows, joining a distinguished group of educators committed to advancing the quality of education in Canada. Veselin Jungić was awarded the 2012 CMS Excellence in Teaching Award for his innovative contributions to undergraduate mathematics education at Simon Fraser University. His pioneering use of online tools in large calculus classes, along with his dedication to student success and integration of Indigenous culture into mathematics education, underscores his effectiveness as an educator. In 2011, Veselin Jungić received the PIMS Education Prize from the Pacific Institute for the Mathematical Sciences for his role in enhancing public awareness and appreciation of mathematics. His contributions include leading educational programs like "Taste of Pi" for high school students, mentoring Indigenous students, and creating the animated film "Small Number Counts to 100," which integrates Indigenous storytelling into mathematics lessons. == Other publications == In 2023, Veselin Jungić published Basics of Ramsey Theory, an introductory textbook aimed at undergraduate students. The book is designed to introduce readers to Ramsey theory, a mathematical field at the intersection of number theory and combinatorics. In the same year, Jungic co-authored a textbook on differential calculus with Petra Menz and Randall Pyke, both from Simon Fraser University. The book offers over 900 problems covering key topics like limits, continuity, derivatives, and their applications, including optimization and curve sketching. Veselin Jungić is the creator and producer of the podcast No Strangers At This Party, which celebrates Ramsey theory and the mathematicians working in this vibrant field. The podcast features interviews with contemporary mathematicians who are actively engaged in Ramsey theory, discussing their early experiences with mathematics, their academic journeys, and their perspectives on Ramsey theory and mathematics as a whole. Jungić has contributed several writings addressing key issues in education, including the significance of mathematics, personal academic challenges, and the impact of academic dishonesty. Through a combination of personal reflection and professional insight, these works highlight the importance of integrity, perseverance, and the role of mathematics in developing critical thinking skills. His writings advocate for a deeper understanding of the educational process and the promotion of academic honesty. == References ==
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Wikipedia:Viacheslav V. Nikulin#0
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Viacheslav Valentinovich Nikulin (Slava) is a Russian mathematician working in the algebraic geometry of K3 surfaces and Calabi–Yau threefolds, mirror symmetry, the arithmetic of quadratic forms, and hyperbolic Kac–Moody algebras. He is a professor of mathematics at the University of Liverpool. A third chair of mathematics was established for Nikulin in 1999, the second chair having been established in 1964 for C. T. C. Wall and the first having been established in 1882. Nikulin has made contributions towards the solution of Hilbert's 16th problem. == Publications == Nikulin, V. V.; Shafarevich, I. R. (1994), Geometries and Groups, Springer, ISBN 3-540-15281-4; translated from the Russian by M. Reid; first published in English in 1987{{citation}}: CS1 maint: postscript (link) Alexeev, V.; Nikulin, V. V. (2006), Del Pezzo and K3 Surfaces, The Mathematical Society of Japan, ISBN 4-931469-34-5 == References ==
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Wikipedia:Vicsek fractal#0
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In mathematics the Vicsek fractal, also known as Vicsek snowflake or box fractal, is a fractal arising from a construction similar to that of the Sierpiński carpet, proposed by Tamás Vicsek. It has applications including as compact antennas, particularly in cellular phones. Box fractal also refers to various iterated fractals created by a square or rectangular grid with various boxes removed or absent and, at each iteration, those present and/or those absent have the previous image scaled down and drawn within them. The Sierpinski triangle may be approximated by a 2 × 2 box fractal with one corner removed. The Sierpinski carpet is a 3 × 3 box fractal with the middle square removed. == Construction == The basic square is decomposed into nine smaller squares in the 3-by-3 grid. The four squares at the corners and the middle square are left, the other squares being removed. The process is repeated recursively for each of the five remaining subsquares. The Vicsek fractal is the set obtained at the limit of this procedure. The Hausdorff dimension of this fractal is log ( 5 ) log ( 3 ) {\displaystyle \textstyle {\frac {\log(5)}{\log(3)}}} ≈ 1.46497. An alternative construction (shown below in the left image) is to remove the four corner squares and leave the middle square and the squares above, below, left and right of it. The two constructions produce identical limiting curves, but one is rotated by 45 degrees with respect to the other. == Properties == The Vicsek fractal has the surprising property that it has zero area yet an infinite perimeter, due to its non-integer dimension. At each iteration, four squares are removed for every five retained, meaning that at iteration n the area is ( 5 9 ) n {\displaystyle \textstyle {({\frac {5}{9}})^{n}}} (assuming an initial square of side length 1). When n approached infinity, the area approaches zero. The perimeter however is 4 ( 5 3 ) n {\displaystyle \textstyle {4({\frac {5}{3}})^{n}}} , because each side is divided into three parts and the center one is replaced with three sides, yielding an increase of three to five. The perimeter approaches infinity as n increases. The boundary of the Vicsek fractal is the Type 1 quadratic Koch curve. == Analogues in higher dimensions == There is a three-dimensional analogue of the Vicsek fractal. It is constructed by subdividing each cube into 27 smaller ones, and removing all but the "center cross", the central cube and the six cubes touching the center of each face. Its Hausdorff dimension is log ( 7 ) log ( 3 ) {\displaystyle \textstyle {\frac {\log(7)}{\log(3)}}} ≈ 1.7712. Similarly to the two-dimensional Vicsek fractal, this figure has zero volume. Each iteration retains 7 cubes for every 27, resulting in a volume of ( 7 27 ) n {\displaystyle \textstyle {({\frac {7}{27}})^{n}}} at iteration n, which approaches zero as n approaches infinity. There exist an infinite number of cross sections which yield the two-dimensional Vicsek fractal. == See also == Box-counting dimension Cross crosslet List of fractals by Hausdorff dimension Sierpinski carpet Sierpinski triangle n-flake == References == == External links == "Box Fractal". Wolfram Alpha Site. Retrieved 21 February 2019.
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Wikipedia:Victor A. Vyssotsky#0
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Victor Alexander Vyssotsky (February 26, 1931 – December 24, 2012) was a mathematician and computer scientist. He was the technical head of the Multics project at Bell Labs and later executive director of Research in the Information Systems Division of AT&T Bell Labs. Multics, whilst not particularly commercially successful in itself, directly inspired Ken Thompson to develop Unix. Later, Vyssotsky was the founding director of Digital's Cambridge Research Lab. In 1960, Vyssotsky co-created the BLODI Block Diagram Compiler at Bell Labs. In 1961, together with Robert Morris Sr. and Doug McIlroy, he devised the computer game Darwin (later known as Core War) on an IBM 7090 at Bell Labs. == References == == External links == Core War at Virus Bulletin: Resources Victor A. Vyssotsky hosts a UNIX documentary UNIX: Making Computers Easier To Use -- AT&T Archives film from 1982, Bell Laboratories
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Wikipedia:Victor Aladjev#0
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Victor Zakharovich Aladjev (Belarusian: Віктар Захаравіч Алад'еў; born June 14, 1942 - dead April 9, 2025) was an Estonian mathematician and cybernetician, creator of the scientific school on the theory of homogeneous structures. == Early life and education == Victor Aladjev was born in 1942 in Grodno to parents Zakhar Ivanovich Aladjev and Maria Adolfovna Novogrotska. His father participated in the underground resistance organization during World War II while in German-occupied Grodno. Aladjev attended University of Grodno in 1959, later transferring to the University of Tartu, Estonia in 1962, where he earned his degree in mathematics in 1966. Subsequently, he entered the graduate school of the Estonian Academy of Sciences in 1969, achieving a doctorate in mathematics (DSc) in 1972, specializing in Theoretical Cybernetics and Technical Cybernetics. His doctoral work focused on the mathematical theory of homogeneous structures, resulting in the award of a DSc under the guidance of Professor Richard E. Bellman. == Scientific career == In 1970, Aladjev became the President of the Tallinn Research Group (TRG), contributing to the mathematical theory of homogeneous structures, particularly Cellular Automata (CA). Between 1972 and 1990, Aladjev held various senior positions in design, technological, and research organizations in Tallinn. His involvement in international mathematical publications includes serving as a referent and editorial board member for Zentralblatt für Mathematik since 1972 and being a member of International Association of Mathematical Modeling (IAMM) since 1980. In 1993, he was elected to the International Federation for Information Processing (IFIP) working group on the mathematical theory of homogeneous structures and its applications. In 1994, Aladjev was honored with election as an academician of the Russian Academy of Cosmonautics and the International Academy of Noosphere (IAN). The following year, in 1995, he achieved full membership in the Russian Academy of Natural Sciences (RANS). By 1998, he rose to the position of First Vice-president of the IAN. == Research == Aladjev is the author of more than 500 scientific works, including 90 monographs, textbooks, and articles. Particularly noteworthy is his 1972 monograph on the theory of homogeneous structures, acknowledged as one of the finest monographic publications by the Estonian Academy of Sciences. It received recognition in the Encyclopedia of Physical Science and Technology. This monograph not only unveiled numerous original findings, but also introduced fundamental terminology on cellular automata, now widely accepted in the field. Aladjev is a member of the editorial boards of a number of scientific journals. He created the Estonian School for the mathematical theory of homogeneous structures, whose fundamental results received international recognition and have made certain contributions in the basis of a new division of the modern mathematical cybernetics. He also created the UserLib6789 library of new software (more than 850 tools) for which he was won the Smart Award network award, and a large unified MathToolBox package (more than 1420 tools) for Maple and Mathematica systems. As part of the Visiting Professor program, Aladjev collaborated with various universities in the computer science, delivering lectures on Maple and Mathematica systems. In recognition of his contributions, he was awarded the Gold Medal European Quality in May 2015 by the European Scientific & Industrial Consortium (ESIC). == Personal life == Apart from his academic pursuits, Aladjev actively participated in the annual international sport events (Spartakiad) from 1976 to 1990, achieving success and winning several medals in athletics and volleyball. == Selected publications == Computability in homogeneous structures. V Aladyev, Izv. Akad. Nauk. Estonian SSR, Fiz.-Mat, 1972 Survey of research in the theory of homogeneous structures and their applications. V Aladyev, Mathematical Biosciences, 1974. Mathematical Theory of Homogeneous Structures and Their Applications. Victor Alajev. Valgus Press, Tallinn, 1980. Computer laboratory for engineering researches. VZ Aladjev, ML Shishakov, TA Trokhova, Intern. Conf. ACA-2000.–Saint-Petersburg, Russia, 2000. A workstation for solution of systems of differential equations. VZ Aladjev, ML Shishakov, TA Trokhova - 3rd Int., 2000. Educational computer laboratory of the engineer. VZ Aladjev, ML Shishakov, TA Trokhova - Proc. 8th Byelorussia Mathemat. Conf, 2000. Maple 6: Solution of the Mathematical, Statistical and Engineering–Physical Problems. V Aladjev, M Bogdevicius, Laboratory of Basic Knowledge's, Moscow, 2001. New software for mathematical package Maple of releases 6, 7 and 8. V Aladjev, M Bogdevičius, O Prentkovskis, Technika, 2002. Classical cellular automata. Homogeneous structures. Aladjev, V., Fultus Books, 2010. ISBN 9781596822221 Classical cellular automata: Mathematical theory and applications. Aladjev, V., Scholar's Press, 2014. ISBN 9783639713459 Toolbox for the Mathematica programmers. V. Aladjev, V. Vaganov., CreateSpace Independent Publishing Platform, 2016. ISBN 9781532748837 Software Etudes in the Mathematica: Tallinn Research Group. Aladjev, Victor; Shishakov, Michael, CreateSpace Independent Publishing Platform, 2017. ISBN 1979621888 Selected problems in the theory of classical cellular automata. Aladjev, Victor Zachar; Shishakov, Michael Leonid; Vaganov, Vjacheslav Alexei, Independently published, 2018. ISBN 173095037X Functional and procedural programming in Mathematica. Aladjev, V.; Shishakov, M.; Vaganov, V., TRG press, 2020. ISBN 9949018838 Cellular automata, mainframes, Maple, Mathematica and computer science in Tallinn Research Group. Aladjev, V., Kindle Press, 2022. ISBN 9798447660208 == References ==
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Wikipedia:Victor Buchstaber#0
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Victor Matveevich Buchstaber (Russian: Виктор Матвеевич Бухштабер, born 1 April 1943, Tashkent, Soviet Union) is a Soviet and Russian mathematician known for his work on algebraic topology, homotopy theory, and mathematical physics. == Work == Buchstaber's first research work was in cobordism theory. He calculated the differential in the Atiyah-Hirzebruch spectral sequence in K-theory and complex cobordism theory, constructed Chern-Dold characters and the universal Todd genus in cobordism, and gave an alternative effective solution of the Milnor-Hirzebruch problem. He went on to develop a theory of double-valued formal groups that led to the calculation of cobordism rings of complex manifolds having symplectic coverings and to the explicit construction of what are now known as Buchstaber manifolds. He devised filtrations in Hopf algebras and the Buchstaber spectral sequence, which were successfully applied to the calculation of stable homotopy groups of spheres. He worked on the deformation theory for mappings to groups, which led to the solution of the Novikov problem on multiplicative subgroups in operator doubles, and to construction of the quantum group of complex cobordisms. He went on to treat problems related both with algebraic geometry and integrable systems. He is also well known for his work on sigma-functions on universal spaces of Jacobian varieties of algebraic curves that give effective solutions of important integrable systems. Buchstaber created an algebro-functional theory of symmetric products of spaces and described algebraic varieties of polysymmetric polynomials. == Academic career == Buchstaber gained his Ph.D. in 1970 under Sergei Novikov and Dr. Sci. in 1984 from Moscow State University. He is currently a professor at the Faculty of Mathematics and Mechanics, Moscow State University, and an emeritus professor at the School of Mathematics, University of Manchester. He has supervised more than 30 Ph.D. students, including Serge Ochanine, Iosif Polterovich, Taras Panov and Alexander Gaifullin. In 1974 Buchstaber was an Invited Speaker at the International Congress of Mathematicians in Vancouver (but he did not give a lecture there). In 2004 was elected a corresponding fellow of the Royal Society of Edinburgh. In 2006 he was elected a corresponding member of the Russian Academy of Sciences. == Works == V. M. Buchstaber; Sergeĭ Petrovich Novikov, eds. (1997). Solitons, Geometry, and Topology: On the Crossroad. American Mathematical Soc. ISBN 978-0-8218-0666-1. Victor Buchstaber and Taras Panov, Toric Topology, American Mathematical Society, Providence, RI, 2015. == References == == External links == Home page at Russian Academy of Sciences [1] Birthday tribute in Moscow Mathematical Journal [2] Victor Buchstaber at the Mathematics Genealogy Project
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Wikipedia:Victor Hugo Duarte de Lemos#0
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The University of Lisbon (UL; Portuguese: Universidade de Lisboa, pronounced [univɨɾsiˈðaðɨ ðɨ liʒˈβoɐ]; Latin: Universitas Olisiponensis) was a public university in Lisbon, Portugal. It was founded in 1911 after the fall of the Portuguese monarchy and was later integrated in the new University of Lisbon along with the former Technical University of Lisbon. == History == The first Portuguese university school was founded in 1290 by King Dinis in Lisbon, and was called Studium Generale (Estudo Geral). In the following 247 years, this first university school was moved several times between Lisbon and Coimbra. In 1537, during the reign of João III, the university moved definitively to Coimbra. The entire university institution, including the teaching staff and all the books from its library, were moved to Coimbra where the University of Coimbra was definitively installed. Lisbon became a university city again in 1911 when the current University of Lisbon was founded, through the union of newly created and older schools, like the 19th century Polytechnic School (Escola Politécnica), the Royal Medical School of Lisbon (Real Escola Médico-Cirúrgica de Lisboa) and the Letters Higher Studies (Curso Superior de Letras). == Faculties == === Faculty of Law === The Faculty of Law (Portuguese: Faculdade de Direito) was officially created by a Decree of 22 March 1911 as Faculdade de Ciências Económicas e Políticas, but was only installed in 1913, and was given its current designation later in 1918. It was originally located at the Valmor Building (Edifício Valmor) at the Campo dos Mártires da Pátria. It was transferred to its current campus at the University City (Cidade Universitária) in 1957-1958. A new building, housing the Faculty's library, was built in the late 1990s. The only graduation given is law, and the specialised post-graduate studies available include several branches of the same area. Among the many graduates from the faculty of law are the former Presidents of Portugal Jorge Sampaio and Mário Soares, Prime Minister Marcelo Caetano, the President of the European Commission José Manuel Durão Barroso, Portuguese statesman, deputy, and professor Adriano Moreira and businessman and former Prime Minister Francisco Pinto Balsemão. Current President Marcelo Rebelo de Sousa was a full professor there for many years, before his election in 2016. First Republic political leader and several times Prime Minister Afonso Costa was a teacher at the faculty and its founder and first dean. Television pundit and geopolitics expert Nuno Rogeiro and the writer and university professor Jaime Nogueira Pinto also studied there. Miguel Trovoada, former Prime Minister (1975–1979) and President of São Tomé and Príncipe was also one of its students, as well as Francisca Van Dunem, currently the Portuguese Minister for Justice. João Vale e Azevedo, a lawyer and former chairman of SL Benfica, was also a student and an assistant lecturer at this faculty. === Faculty of Sciences === The Faculty of Sciences (Portuguese: Faculdade de Ciências, usually abbreviated FCUL) was created on 19 April 1911 by the transformation of the former Lisbon Polytechnic School (Escola Politécnica de Lisboa). The Polytechnic School itself had been created in 1837, by the transformation and merger of the previous Royal Marine Academy (1779) and Royal College of the Nobles (1761). From 1911 until 1985 (when it moved to its current site at Campo Grande), the Faculty of Sciences was located at the former Polytechnic School building, which currently hosts the National Museum of Natural History and Science. Its current grounds, over a built area of 75662 square meters, comprise eight buildings (labeled C1 through C8, where C stands for Ciências — Sciences) hosting classrooms, offices, cafeterias, libraries, a stationery shop, leisure areas and gardens. The faculty population, as of the 2009/2010 school year, consisted of (in parentheses, the numbers as of the 2008/2009 school year): 3055 graduation students (2964); 418 Joint degree (B.Sc.+M.Sc.) students (327) 1008 M.Sc. students (1218); 412 Ph.D. students (552); 388 teachers, about 95.3% hold a Ph.D. (417, 96.6%); 22 hired research staff (23) 186 non-teaching workers (204). The computer science department has been granted several honours, namely a finalist position in the Descartes Prize and two IBM Scientific Awards. The faculty's campus also comprises the Instituto de Biofísica e Engenharia Biomédica (IBEB), the Instituto de Oceanografia and the Instituto de Ciência Aplicada e Tecnologia (ICAT). There are 18 graduations available, in the following areas: Applied Mathematics Fundamental Applications branch Statistics and Operations Research branch Applied Statistics Biology Environmental Biology branch (Marine and Terrestrial profiles) Cell biology and Biotechnology branch Evolutionary and Developmental biology branch Functional and Systems Biology branch Molecular biology and Genetics branch Biochemistry Chemistry Computer Engineering — the Engineer title requires an additional 2-year Master programme, on one of the following: Computer Architecture, Systems and Networks (Distributed Systems, Security, Embedded Systems, Fault tolerance) Information systems (Database systems, Human-Computer Interaction, Mobile computing) Interaction and Knowledge (Artificial Intelligence-driven: multi-agent system, machine learning, Natural language processing and interaction, neural networks) Software Engineering (Software design, Algorithms, Programming) Information and Communications Technology Energy and Environment (partnership with Instituto Nacional de Engenharia, Tecnologia e Inovação) Geographical Engineering Geology Applied geology and Environment branch Geology and Natural resources branch Health Sciences (partnership with Faculty of Medicine of the University of Lisbon, Faculty of Dentary Medicine of the University of Lisbon, Faculty of Pharmacy of the University of Lisbon and Faculty of Letters of the University of Lisbon) Maths Physics Physics branch Astronomy and Astrophysics branch Computational Physics branch Meteorology, Oceanography and Geophysics Microbiology (partnership with Faculty of Medicine and Faculty of Pharmacy) Physics Engineering (Engineering Physics) Biomedical Engineering & Biophysics (Biomedical engineering) Technological Chemistry António de Sommer Champalimaud, a notable Portuguese business tycoon, studied at this Faculty of Sciences but did not graduate. João Magueijo, a Portuguese cosmologist and professor, studied at the Faculty of Sciences of the University of Lisbon (FCUL). Jorge Palma, singer-songwriter, studied for a while at the Faculty of Sciences before embracing a successful career in music. Nuno Crato, a Portuguese university professor, researcher, mathematician, economist, and writer who has been appointed president of both the Portuguese Mathematical Society and Taguspark, studied for a while at the Faculdade de Ciências before changing his mind and graduate at the ISEG - Instituto Superior de Economia e Gestão/Technical University of Lisbon, embracing a notable academic career. Pedro Passos Coelho, Prime Minister of Portugal, studied mathematics at the Faculty of Sciences, but did not graduate there. Branca Edmée Marques studied chemistry before moving to Paris to study radiology with Marie Curie. She would return to Lisbon to eventually become the first female professor of chemistry. Lidia Salgueiro taught physics and conducted research for over 30 years, becoming the first woman to be elected as a Corresponding Member of the Lisbon Academy of Sciences, an organization founded in 1779. === Faculty of Medicine === The Faculty of Medicine is a leading medical school, having its origins in the 19th century when the Real Escola Médico-Cirúrgica de Lisboa was founded in the city. Santa Maria's Hospital (Hospital de Santa Maria), one of the biggest Portuguese hospitals, is the teaching hospital of the faculty, and share the same installations. António Damásio and Alexandre Carlos Caldas studied at this faculty, and Egas Moniz (a Nobel Prize winner) was a professor there. Other noted personalities who studied at the Faculty of Medicine of the University of Lisbon include: António Lobo Antunes, (born 1 September 1942), Portuguese novelist. Joaquim Alberto Chissano, (born 22 October 1939), second President of Mozambique. (dropped out) João Lobo Antunes, (born 4 June 1944), a prominent Portuguese Neurosurgeon. Jonas Savimbi, (1934–2002), a guerrilla, military leader and politician from Angola. (dropped out) José Tomás de Sousa Martins, 19th century physician, noted for the esoteric cult-status achieved after his death. Agostinho Neto, (1922–1979), served as the first President of Angola. António Rendas (born 1949), medical academic and researcher Maria Elisa, (born in 1950), journalist and television presenter. (dropped out) Carlos Caldas, (born 1960), Chair of Cancer Medicine at the University of Cambridge. === Faculty of Letters === The Faculty of Letters (Portuguese: Faculdade de Letras), FLUL, was created in 1911 by the transformation of the previous Superior Studies in Letters, from which all students and professors were transferred. The Superior Studies in Letters itself had been created in 1859 by King Pedro V, from which all students and professors were transferred. The Faculty of Letters remained installed on the facilities of the Superior Studies, an annex to the Academy of Science, until 1957, when it changed to the current building, in the University City (Cidade Universitária). In 1975, a new pavilion was built to accommodate the large influx of students who arrived after the democratization of higher education in Portugal, a consequence of the Carnation Revolution. The pavilion, theoretically provisional, still stands today. In 2001, two new buildings were finished: one to accommodate new classrooms and the Computer Room, and the Library Building, which is now the second biggest library in Portugal. Although the faculty's graduation with most studies is modern languages and literatures (Línguas e Literaturas Modernas) (which has a number of variants, including studies in Portuguese, Spanish, English, French, German and Italian), it also offers philosophy, history (and archeology), African studies, Asian studies, European studies, cultural studies and classical studies (the degree itself is named classic languages and literatures). It is also the former home of the degree in psychology. In the mid-1980s a new Faculty of Psychology [1] was created to accommodate it. Notable professors at the faculty include the second President of the Portuguese Republic, Teófilo Braga, and writers Vitorino Nemésio and Urbano Tavares Rodrigues. The poet Fernando Pessoa was a former student, though only attended for less than a year. Fialho Gouveia, a noted Portuguese television presenter, attended the Romance Philology course at the Faculdade de Letras but dropped out in order to follow a successful career in radio and television. The writer Luiz Pacheco was a student at FLUL before dropping out. The actress Alexandra Lencastre and Moonspell frontman Fernando Ribeiro also attended the philosophy course but did not graduate. Famous musician and composer Fernando Lopes-Graça also dropped out of FLUL. Football player and manager Artur Jorge graduated by FLUL after has been a student at the University of Coimbra's FLUC. == Research == The Instituto de Medicina Molecular of the University of Lisbon, a research institute in molecular medicine, is one of the most noted biosciences research institutions in Portugal. The Instituto Geofisico do Infante Dom Luiz exists since 1853 and is a research and operational unit that maintains the longest meteorological series of Portugal. Research is organized and funded through CGUL, the leading Portuguese geophysical research unit, and Associated Laboratory (with LATTEX) of the Portuguese Ministry of Science and Technology. Researchers of LaSIGE, a research laboratory for large-scale information systems (integrated into the Department of Computer Science), have received several honors, namely an IBM Scientific Award, an Order of Engineers distinction and a place among the eight finalists of the Descartes Prize. === Instituto de Ciências Sociais (Institute of Social Sciences) === The Instituto de Ciências Sociais (ICS), an associated state laboratory, is a university institution devoted to research and advanced training in the social sciences. The ICS focuses its research on five main subject areas: the formation of the contemporary world; the study of citizenship and democratic institutions; the problems of sustainability, linking the environment, risk and space; social changes and individual action in the context of the family, lifestyles and schooling; and issues concerning identity, migration and religion. The main subjects represented at the institute are social and cultural anthropology, political science, economics, human geography, history, social psychology and sociology. The independent Social Science Research Group (GIS) was founded by Adérito Sedas Nunes in 1962. It became an autonomous institute of the University of Lisbon in 1982 and acquired the status of associated state laboratory in 2002. The central activities of the ICS include: publishing research in book form and in articles in Portuguese and international journals of reference; advanced education to the level of master's degrees and doctorates; maintaining a dialogue with the international scientific community; and spreading knowledge in the wider community—an increasingly important activity to ensure the necessary interaction between science and citizenship. Análise Social (Social Analysis), Portugal's oldest and most prestigious peer-reviewed social science journal, together with the ICS's own publishing house, Imprensa de Ciências Sociais (Social Science Press) are the most visible manifestations of the institute's activities. The ICS is located at the University of Lisbon campus in a central area of the city next to the national library (Biblioteca Nacional). Its new offices, opened in 2003, were especially designed for the institute's research activities and postgraduate courses. The Library, which has 40,000 books and subscribes to 313 periodicals, is also home to the fast-growing Social History Archive (AHS). Currently (2008), the institute has about 70 researchers and 100 postgraduate students and is engaged in about 200 research projects. Nearly 70 per cent of its activities are financed from its own funds, which are obtained competitively. == See also == List of universities in Portugal Higher education in Portugal == References == == External links == Official website (in Portuguese)
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Wikipedia:Victor Isakov#0
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Victor Isakov (November 4, 1947 – May 14, 2021) was a mathematician working in the field of inverse problems for partial differential equations and related topics (potential theory, uniqueness of continuation and Carleman estimates, nonlinear functional analysis and calculus of variation). He was a distinguished professor in the Department of Mathematics and Statistics at Wichita State University. His areas of professional interest included: Inverse problems of gravimetry (general uniqueness conditions and local solvability theorems) and related problems of imaging including prospecting active part of the brain and the source of noise of the aircraft from exterior measurements of electromagnetic and acoustical fields. Inverse problems of conductivity (uniqueness of discontinuous conductivity and numerical methods) and their applications to medical imaging and nondestructive testing of materials for cracks and inclusions. Inverse scattering problems (uniqueness and stability of penetrable and soft scatterers). Finding constitutional laws from experimental data (reconstructing nonlinear partial differential equation from all or some boundary data). Uniqueness of the continuation for hyperbolic equations and systems of mathematical physics. The inverse option pricing problem. == Publications == Isakov has over 90 publications in print or in preparation as of late 2005, which include: Increased stability in the continuation of solutions to the Helmholtz equation (with Tomasz Hrycak), Inverse Problems, 20(2004), 697-712. Inverse Problems for Partial Differential Equations, Applied Mathematical Sciences (Springer-Verlag), Vol 127, 2nd ed., 2006. ISBN 0-387-25364-5 Presentations: During the last 15 years, he delivered approximately 90 invited talks at international and national conferences and universities in Austria, Canada, China, Finland, France, Germany, Italy, Japan, Poland, Russia, Sweden, Switzerland, South Korea, Tunisia, and United Kingdom. He was a principal speaker at the summer AMS-SIAM research conferences in Boulder, CO (1999), South Hadley, MA (1998, 1995), Seattle, WA (1995), at programs on Inverse Problems at MSRI, Berkeley, CA(2001), IPAM, Los Angeles (2003, 2005, 2006), RICAM, Linz, Austria (2009), Universidad Autonoma de Madrid, Spain, Isaac Newton Institute for Mathematical Sciences, Cambridge, England,(2011), and at international conferences in Edinburgh, UK (2000), St. Petersburg, Russia, Gargnano, Italy, Hong Kong, China (2001), Cortona and Pisa, Italy (2002), Banff Center and the Fields Institute, Toronto, Canada, and Seville, Spain (2003), IMA, Minneapolis, Helsinki, Finland, Fethiye, Turkey (2004), Catania, Italy (2005), Banff, Canada, Sapporo, Japan (2006), Cracow, Poland, vancouver, Canada (2007), Ecole Normale, Paris, France, Orlando, Florida, Cortona, Italy, Shanghai, China (2008), Linz, Austria, Manchester, England (2009), Valparaiso, Chile, Wuhan, China, Dresden, Germany, Pisa, Bologna, Italy (2010), Trieste, Gargnano, Italy (2011). He has given colloquium talks at the Courant Institute of New York University, Northwestern University, City University of Hong Kong, Fudan University (China), Universities of Goettingen, Muenster (Germany), Florence, Milan, Rome, Trieste (Italy), Linz (Austria), Kyoto and Tokyo (Japan). He was on editorial boards of the international journals Applicable Analysis, Inverse Problems and Imaging, Evolution Equations and Control Theory, J. Inverse Ill-Posed Problems. Since 1990, his research has been supported by the NSF. The latest grant was: "Stability issues in some biomedical, financial, and geophysical inverse problems" NSF DMS-2008154 (2020-2023) $ 255,214 == External links == Obituary
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Wikipedia:Victor Ivrii#0
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Victor Ivrii (Russian: Виктор Яковлевич Иврий), (born 1 October 1949) is a Russian, Canadian mathematician who specializes in analysis, microlocal analysis, spectral theory and partial differential equations. He is a professor at the University of Toronto Department of Mathematics. He was an invited speaker at International Congress of Mathematicians, Helsinki—1978 and Berkeley—1986. == Education and Degrees == He graduated from Physical Mathematical School at Novosibirsk State University in 1965, received his University Diploma (equivalent to MSci) in 1970 and PhD in 1973 in Novosibirsk State University. He defended his Doktor nauk thesis in St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences in 1982. == Scientific contributions == === Weakly hyperbolic equations === His first main works were devoted to the well-posedness of the Cauchy problem for weakly hyperbolic equations. In particular he discovered a necessary (later proven to be sufficient) condition for Cauchy problem to be well-posed no matter what the lower terms in the equation are. === Propagation of singularities === In a series of papers he explored propagation of singularities of symmetric hyperbolic systems inside of the domain and near the boundary. He was invited to give a talk at ICM—1978, Helsinki but was not granted an exit visa by the Soviet authorities; however his talk was published in the Proceedings of the Congress. === Asymptotic distribution of eigenvalues === His work in propagation of singularities logically guided him to the theory of asymptotic distribution of eigenvalues (a subject he has been studying ever since). V. Ivrii's debut in this field was a proof of Weyl conjecture (1980). Then he developed a rescaling technique which allowed to consider domains and operators with singularities. He again was invited give a talk at ICM—1986, Berkeley but again was not granted an exit visa by the Soviet authorities. His talk was read by Lars Hörmander and published in the Proceedings of the Congress. V. Ivrii wrote three research monographs, and, all published by Springer-Verlag. === Multiparticle quantum theory === The methods developed by V. Ivrii were very useful for the rigorous justification of Thomas-Fermi theory. Together with Israel Michael Sigal he justified the Scott correction term for molecules. Later V. Ivrii justified the Dirac and Schwinger correction terms. == Institutions == 1973-1990 Magnitogorsk Mining and Metallurgical Institute 1990-1992 École Polytechnique 1992–present University of Toronto Department of Mathematics == Awards and honors == 1998 Elected as Fellow of Royal Society of Canada. 2002-2004 Killam Research Fellow. 2012 Fellow of the American Mathematical Society. == References == == External links == Victor Ivrii at the Mathematics Genealogy Project Victor Ivrii infopage at University of Toronto Department of Mathematics Items authored by or related to Ivriĭ, V. Ya.
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Wikipedia:Victor Kac#0
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Victor Gershevich (Grigorievich) Kac (Russian: Виктор Гершевич (Григорьевич) Кац; born 19 December 1943) is a Soviet and American mathematician at MIT, known for his work in representation theory. He co-discovered Kac–Moody algebras, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the finite-dimensional simple Lie superalgebras, and found the Kac determinant formula for the Virasoro algebra. He is also known for the Kac–Weisfeiler conjectures with Boris Weisfeiler. == Biography == Kac studied mathematics at Moscow State University, receiving his MS in 1965 and his PhD in 1968. From 1968 to 1976, he held a teaching position at the Moscow Institute of Electronic Machine Building (MIEM). He left the Soviet Union in 1977, becoming an associate professor of mathematics at MIT. In 1981, he was promoted to full professor. Kac received a Sloan Fellowship and the Medal of the Collège de France, both in 1981, and a Guggenheim Fellowship in 1986. He received the Wigner Medal (1996) "in recognition of work on affine Lie algebras that has had wide influence in theoretical physics". In 1978 he was an invited speaker (Highest weight representations of infinite dimensional Lie algebras) at the International Congress of Mathematicians (ICM) in Helsinki. Kac was a plenary speaker at the 1988 American Mathematical Society centennial conference. In 2002 he gave a plenary lecture, Classification of Supersymmetries, at the ICM in Beijing. Kac is a Fellow of the American Mathematical Society, an honorary member of the Moscow Mathematical Society, Fellow of the American Academy of Arts and Sciences and a Member of the National Academy of Sciences. The research of Victor Kac primarily concerns representation theory and mathematical physics. His work appears in mathematics and physics and in the development of quantum field theory, string theory and the theory of integrable systems. Kac has published 13 books and over 200 articles in mathematics and physics journals and is listed as an ISI highly cited researcher. Victor Kac was awarded the 2015 AMS Leroy P. Steele Prize for Lifetime Achievement. He was married with Michèle Vergne and they have a daughter, Marianne Kac-Vergne, who is a professor of American civilization at the university of Picardie. His brother Boris Katz is a principal research scientist at MIT. == Kac–Moody algebra == "Almost simultaneously in 1967, Victor Kac in the USSR and Robert Moody in Canada developed what was to become Kac–Moody algebra. Kac and Moody noticed that if Wilhelm Killing's conditions were relaxed, it was still possible to associate to the Cartan matrix a Lie algebra which, necessarily, would be infinite dimensional." – A.J. Coleman == Bibliography == Kac, Victor G. (1994) [1985]. Infinite-Dimensional Lie Algebras (3rd ed.). Cambridge University Press. ISBN 0-521-46693-8. Kac, V. (1985). Infinite Dimensional Groups with Applications. New York: Springer. ISBN 9781461211044. OCLC 840277997. Seligman, George B. (1987). "Review: Infinite-dimensional Lie algebras, by Victor G. Kac, 2nd edition" (PDF). Bull. Amer. Math. Soc. (N.S.). 16: 144–149. doi:10.1090/S0273-0979-1987-15492-9. Kac, Victor G.; Raina, A. K. (1987). Bombay lectures on highest weight representations of infinite-dimensional Lie algebras. Singapore: World Scientific. ISBN 9971503956. OCLC 18475755. Kac, Victor (1997). Vertex Algebras for Beginners (University Lecture Series, No 10). American Mathematical Society. ISBN 0-8218-0643-2. Kac, Victor G.; Cheung, Pokman (2002). Quantum calculus. New York: Springer. ISBN 0387953418. OCLC 47243954. Kac, Victor G.; Raina, A. K. (2013). Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras. Advanced Series in Mathematical Physics. Vol. 29 (2nd ed.). World Scientific Publishing. doi:10.1142/8882. ISBN 978-981-4522-18-2. == References == == External links == Victor Kac's home page at MIT Victor Kac at the Mathematics Genealogy Project Victor Kac, A Biographical Interview, [2]
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Wikipedia:Victor Kolyvagin#0
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Victor Alexandrovich Kolyvagin (Russian: Виктор Александрович Колывагин, born 11 March, 1955) is a Russian mathematician who wrote a series of papers on Euler systems, leading to breakthroughs on the Birch and Swinnerton-Dyer conjecture, and Iwasawa's conjecture for cyclotomic fields. His work also influenced Andrew Wiles's work on Fermat's Last Theorem. == Career == Kolyvagin received his Ph.D. in Mathematics in 1981 from Moscow State University, where his advisor was Yuri I. Manin. He then worked at Steklov Institute of Mathematics in Moscow until 1994. Since 1994 he has been a professor of mathematics in the United States. He was a professor at Johns Hopkins University until 2002 when he became the first person to hold the Mina Rees Chair in mathematics at the Graduate Center of the City University of New York. == Awards == In 1990 he received the Chebyshev Prize of the USSR Academy of Sciences. == References == == Link == Victor Kolyvagin at the Mathematics Genealogy Project Kolyvagin's Biography
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Wikipedia:Victor Lidskii#0
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Victor Borisovich Lidskii (Russian: Виктор Борисович Лидский, 4 May 1924, Odessa – 29 July 2008, Moscow) was a Soviet and Russian mathematician who worked in spectral theory, operator theory, and shell theory. Lidskii discovered the Lidskii theorem in 1959. His adviser at Moscow State University was Israel Gelfand. == References == Levitin, M.; Vassiliev, D. (2010). "Victor Borisovich Lidskii (1924–2008)". Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924–2008). American Mathematical Society Translations – Series 2. Vol. 231. American Mathematical Society. pp. 1–5. arXiv:1008.2669. Bibcode:2010arXiv1008.2669L. == External links == Victor Lidskii at the Mathematics Genealogy Project
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Wikipedia:Victor Lomonosov#0
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Victor Lomonosov (7 February 1946 – 29 March 2018) was a Russian-American mathematician known for his work in functional analysis. In operator theory, he is best known for his work in 1973 on the invariant subspace problem, which was described by Walter Rudin in his classical book on Functional Analysis as "Lomonosov's spectacular invariant subspace theorem". Lomonosov gives a very short proof, using the Schauder fixed point theorem, that if a bounded linear operator T on a Banach space commutes with a non-zero compact operator then T has a non-trivial invariant subspace. Lomonosov has also published on the Bishop–Phelps theorem and Burnside's Theorem. Lomonosov received his master's degree from the Moscow State University in 1969 and his Ph.D. from National University of Kharkiv in 1974 (adviser Vladimir Matsaev). He was appointed at the rank of Associate Professor at Kent State University in the fall of 1991, becoming Professor at the same university in 1999. == References ==
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Wikipedia:Victor Mazurov#0
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Victor Danilovich Mazurov (Russian: Виктор Данилович Мазуров; born January 31, 1943) is a Russian mathematician. He is well known for his works in group theory and is the founder of the Novosibirsk school of finite groups. Mazurov is a Corresponding Member of the Russian Academy of Sciences. Mazurov's parents Daniil Petrovich and Evstolia Ivanovna were teachers. Victor went to elementary school in a village of Kuvashi and finished high school with highest honors in Zlatoust. He then moved to Sverdlovsk (now Yekaterinburg) to study mathematics in Ural State University. His advisers in Sverdlovsk were Victor Busarkin and Albert Starostin. In 1963 Mazurov married his university classmate Nadezhda Khomenko. After graduating in 1965, they moved to Novosibirsk where Mazurov joined the research staff of the Sobolev Institute of Mathematics (Russian: Институт математики СО РАН). Mazurov is an editor (with Evgenyj Khukhro) of the "Kourovka Notebook", a periodically updated collection of over 1,000 open problems in Group Theory. Mazurov obtained several results that contributed to the proof of the classification of finite simple groups, also known as the Enormous Theorem and considered one of the greatest achievements in mathematics of the 20th century. He is one of the initial group of fellows of the American Mathematical Society. == References == == External links == Victor D. Mazurov Personal webpage at the Sobolev Institute of Mathematics
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Wikipedia:Victor W. Marek#0
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Victor Witold Marek, formerly Wiktor Witold Marek known as Witek Marek (born 22 March 1943) is a Polish mathematician and computer scientist working in the fields of theoretical computer science and mathematical logic. == Biography == Victor Witold Marek studied mathematics at the Faculty of Mathematics and Physics of the University of Warsaw. Supervised by Andrzej Mostowski, he received both a magister degree in mathematics in 1964 and a doctoral degree in mathematics in 1968. He completed habilitation in mathematics in 1972. In 1970–1971, Marek was a postdoctoral researcher at Utrecht University, the Netherlands, where he worked under Dirk van Dalen. In 1967–1968 as well as in 1973–1975, he was a researcher at the Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland. In 1979–1980 and 1982–1983 he worked at the Venezuelan Institute of Scientific Research. In 1976, he was appointed an assistant professor of mathematics at the University of Warsaw. In 1983, he was appointed a professor of computer science at the University of Kentucky. In 1989–1990, he was a visiting professor of mathematics at Cornell University, Ithaca, New York. In 2001–2002, he was a visitor at the Department of Mathematics of the University of California, San Diego. In 2013, Professor Marek was the Chair of the Program Committee of the scientific conference commemorating Andrzej Mostowski's Centennial. == Legacy == === Teaching === He has supervised a number of graduate theses and projects. He was an advisor of 16 doctoral candidates both in mathematics and computer science. In particular, he advised dissertations in mathematics by Małgorzata Dubiel-Lachlan, Roman Kossak, Adam Krawczyk, Tadeusz Kreid, Roman Murawski, Andrzej Pelc, Zygmunt Ratajczyk, Marian Srebrny, and Zygmunt Vetulani. In computer science his students were V. K. Cody Bumgardner, Waldemar W. Koczkodaj, Witold Lipski, Joseph Oldham, Inna Pivkina, Michał Sobolewski [1], Paweł Traczyk, and Zygmunt Vetulani. These individuals have worked in various institutions of higher education in Canada, France, Poland, and the United States. === Mathematics === He investigated a number of areas in the foundations of mathematics, for instance infinitary combinatorics (large cardinals), metamathematics of set theory, the hierarchy of constructible sets, models of second-order arithmetic, the impredicative theory of Kelley–Morse classes. He proved that the so-called Fraïssé conjecture (second-order theories of countable ordinals are all different) is entailed by Gödel's axiom of constructibility. Together with Marian Srebrny, he investigated properties of gaps in a constructible universe. === Computer science === He studied logical foundations of computer science. In the early 1970s, in collaboration with Zdzisław Pawlak, he investigated Pawlak's information storage and retrieval systems, which then was a widely studied concept, especially in Eastern Europe. These systems were essentially single-table relational databases, but unlike Codd's relational databases were bags rather than sets of records. These investigations, in turn, led Pawlak to the concept of rough set, studied by Marek and Pawlak in 1981. The concept of rough set, in computer science, statistics, topology, universal algebra, combinatorics, and modal logic, turned out to be an expressive language for describing, and especially manipulating an incomplete information. === Logic === In the area of nonmonotonic logics, a group of logics related to artificial intelligence, he focused on investigations of Reiter's default logic, and autoepistemic logic of R. Moore. These investigations led to a form of logic programming called answer set programming a computational knowledge representation formalism, studied both in Europe and in the United States. Together with Mirosław Truszczynski, he proved that the problem of existence of stable models of logic programs is NP-complete. In a stronger formalism admitting function symbols, along with Nerode and Remmel he showed that the analogous problem is Σ11-complete. == Publications == V. W. Marek is an author of over 180 scientific papers in the area of foundations of mathematics and of computer science. He was also an editor of numerous proceedings of scientific meetings. Additionally, he authored or coauthored several books. These include: Logika i Podstawy Matematyki w Zadaniach (jointly with Janusz Onyszkiewicz) Logic and Foundations of Mathematics in problems (jointly with Janusz Onyszkiewicz) Analiza Kombinatoryczna (jointly with W. Lipski), Nonmonotonic Logic – Context-dependent Reasoning (jointly with M. Truszczyński), Introduction to Mathematics of Satisfiability. == References == == External links == Personal page of Dr. V.W. Marek at the University of Kentucky Papers online Slides and other scientific materials
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Wikipedia:Victor Zalgaller#0
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Victor (Viktor) Abramovich Zalgaller (Hebrew: ויקטור אבּרמוביץ' זלגלר; Russian: Виктор Абрамович Залгаллер; 25 December 1920 – 2 October 2020) was a Russian-Israeli mathematician in the fields of geometry and optimization. He is best known for the results he achieved on convex polyhedra, linear and dynamic programming, isoperimetry, and differential geometry. == Biography == Zalgaller was born in Parfino, Novgorod Governorate on 25 December 1920. In 1936, he was one of the winners of the Leningrad Mathematics Olympiads for high school students. He started his studies at the Leningrad State University, however, World War II intervened in 1941, and Zalgaller joined the Red Army. He took part in the defence of Leningrad, and in 1945 marched into Germany. He worked as a teacher at the Saint Petersburg Lyceum 239, and received his 1963 doctoral dissertation on polyhedra with the aid of his high school students who wrote the computer programs for the calculation. Zalgaller did his early work under direction of Aleksandr Aleksandrov and Leonid Kantorovich. He wrote joint monographs with both of them. His later monograph Geometric Inequalities (joint with Yuri Burago) is still the main reference in the field. Zalgaller lived in Saint Petersburg most of his life, having studied and worked at the Leningrad State University and the Steklov Institute of Mathematics (Saint Petersburg branch). In 1999, he immigrated to Israel. Zalgaller died on 2 October 2020 at the age of 99. == References == V. A. Aleksandrov, et al. Viktor Abramovich Zalgaller (on his 80th birthday), Russian Mathematical Surveys, Vol. 56 (2001), 1013–1014 (see here for a Russian version). Yu. D. Burago, et al. Viktor Abramovich Zalgaller (on his 80th birthday), J. Math. Sci. (N. Y.) J. Math. Sci. (N.Y.) Vol. 119 (2004), 129–132 (see here for a Russian version). M. Z. Solomyak, A few words about Viktor Abramovich Zalgaller, J. Math. Sci. (N.Y.) Vol. 119 (2004), 138–140. S. S. Kutateladze, A Tribute to the Philanthropist and Geometer. List of papers of V. A. Zalgaller, available here (mostly in Russian). Zalgaller, Victor; Burago, Yuri (February 1988). Geometric Inequalities. Springer Verlag. p. 356pp. ISBN 3-540-13615-0. == External links == Victor Zalgaller at the Mathematics Genealogy Project Intrinsic Geometry of Surfaces — book by A.D Alexandrov and V.A. Zalgaller (AMS Online Book, originally translated in 1967). Personal war memoir (in Russian). Lecture read in 1999 in St.Petersburg, Russia (video, in Russian)
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Wikipedia:Vicumpriya Perera#0
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Vicumpriya Perera (Sinhala: විකුම්ප්රිය පෙරේරා) is a Sri Lankan born mathematician, lyricist, poet and music producer. He has published three books of Sinhala poetry, Mekunu Satahan (Sinhala: මැකුනු සටහන්) in 2001, Paa Satahan (Sinhala: පා සටහන්) in 2013, and Mawbime Suwandha (Sinhala: මව්බිමේ සුවඳ) in 2023. He has written over 200 songs and has produced eleven Sinhala song albums. He currently works as a mathematics professor in Ohio, US. == Life and career == Vicumpriya Perera is originally from Wattala, Sri Lanka. He is a graduate of St. Anthony's College, Wattala and Ananda College, Maradana, Sri Lanka. He received a Bachelor of Science degree in Mathematics with first class honors from University of Colombo, Sri Lanka and continued his graduate studies at Indiana University - Purdue University at Indianapolis. He obtained a doctorate degree from Purdue University in Pure Mathematics with research concentrating on operator algebras and functional analysis in 1993. Vicumpriya Perera lives in Ohio, US, where he has worked as a mathematics professor at Kent State University (Trumbull campus) since 1998. He works in operator algebra, which is an area of pure mathematics. Vicumpriya Perera is a past president of the Ohio Mathematical Association of Two year Colleges (OhioMATYC), the Ohio Affiliate organization of the American Mathematical Association of Two Year Colleges (AMATYC). His term of presidency was from 2021-2023. He also serves as the immediate past president of the Colombo University Faculty of Science Alumni Association - North America (CUFSAA), since the conclusion of his term as President of the Association (2021-2023). == List of albums == The following is a list of the songs albums that Vicumpriya Perera has produced. Vicumpriya Perera was the sole composer of the lyrics of all of them. Siththaruwanani included songs from the sinhala classical musical genre (sarala gee). Instrumentalists for this album consisted of Sri Lankan musicians Mahendra Pasquel, Sarath Fernando, Dhananjaya Somasiri, Janaka Bogoda, Susil Amarasinghe, Rohana Dharmakeerthi, Shelton Wijesekera, and Dilusha Ravindranath. == Other productions == In 2005, Vicumpriya Perera (along with Nalin Jayawardena, and Jaanaka Wimaladharma) produced a compact disc set, Dhammapadaya (Sinhala: ධම්මපදය), under the Lanka Heritage label. The set contained four discs, and consisted of complete the Dhammapada stanzas in the original Pali language followed by the Sinhala translations chanted by venerable Beruwala Siri Sobhitha Thero of the Sri Lanka Buddhist Vihara in Perth, Australia. In 2006, this disc set had an English release called Dhammapada. This version had the original Dhammapada stanzas (again in Pali) followed by the English translations written and rendered by Dr. Gil Fronsdal, director and resident teacher Insight Meditation Center, Redwood City, California, US. In 2012 Vicumpriya Perera (in collaboration with Nalin Jayawardena) produced a Sinhala Audiobook called Kulageyin Kulageyata (Sinhala: කුලගෙයින් කුලගෙයට) under the Lanka Heritage, LLC. The book was written in 2009 by Bhadraji Mahinda Jayatilaka, who provided most of the voice work . The audiobook has a total length of five compact discs, and was published by Sarasavi Publishers, Nugegoda, Sri Lanka. == Notes == == References == == External links == Lyrics of Vicumpriya Perera Vicumpriya Perera music on Google Play Home Page of Insight Meditation Center of Redwood City, CA
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Wikipedia:Vida Dujmović#0
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Vida Dujmović is a Canadian computer scientist and mathematician known for her research in graph theory and graph algorithms, and particularly for graph drawing, for the structural theory of graph width parameters including treewidth and queue number, and for the use of these parameters in the parameterized complexity of graph drawing. She is a professor of electrical engineering & computer science at the University of Ottawa, where she holds the University Research Chair in Structural and Algorithmic Graph Theory. == Education == Dujmović studied telecommunications and computer science as an undergraduate at the University of Zagreb, graduating in 1996. She came to McGill University for graduate study in computer science, earning a master's degree in 2000 and completing her Ph.D. in 2004. Her dissertation, Track Layouts of Graphs, was supervised by Sue Whitesides, and won the 2005 NSERC Doctoral Prize of the Natural Sciences and Engineering Research Council. == Career == She was an NSERC Postdoctoral Fellow at Carleton University, a CRM-ISM Postdoctoral Fellow at McGill University, and a postdoctoral researcher again at Carleton University before finally becoming an assistant professor at Carleton University in 2012. She moved to the University of Ottawa in 2013. == Recognition == In 2023 the University of Ottawa gave her the Glinski Award for Excellence in Research and the University Research Chair in Structural and Algorithmic Graph Theory. Vida Dujmović was an invited speaker at the 9th European Congress of Mathematics. == References == == External links == Home page Vida Dujmović publications indexed by Google Scholar
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Wikipedia:Vieta's formulas#0
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In mathematics, Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. They are named after François Viète (1540-1603), more commonly referred to by the Latinised form of his name, "Franciscus Vieta." == Basic formulas == Any general polynomial of degree n P ( x ) = a n x n + a n − 1 x n − 1 + ⋯ + a 1 x + a 0 {\displaystyle P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{1}x+a_{0}} (with the coefficients being real or complex numbers and an ≠ 0) has n (not necessarily distinct) complex roots r1, r2, ..., rn by the fundamental theorem of algebra. Vieta's formulas relate the polynomial coefficients to signed sums of products of the roots r1, r2, ..., rn as follows: Vieta's formulas can equivalently be written as ∑ 1 ≤ i 1 < i 2 < ⋯ < i k ≤ n ( ∏ j = 1 k r i j ) = ( − 1 ) k a n − k a n {\displaystyle \sum _{1\leq i_{1}<i_{2}<\cdots <i_{k}\leq n}\left(\prod _{j=1}^{k}r_{i_{j}}\right)=(-1)^{k}{\frac {a_{n-k}}{a_{n}}}} for k = 1, 2, ..., n (the indices ik are sorted in increasing order to ensure each product of k roots is used exactly once). The left-hand sides of Vieta's formulas are the elementary symmetric polynomials of the roots. Vieta's system (*) can be solved by Newton's method through an explicit simple iterative formula, the Durand-Kerner method. == Generalization to rings == Vieta's formulas are frequently used with polynomials with coefficients in any integral domain R. Then, the quotients a i / a n {\displaystyle a_{i}/a_{n}} belong to the field of fractions of R (and possibly are in R itself if a n {\displaystyle a_{n}} happens to be invertible in R) and the roots r i {\displaystyle r_{i}} are taken in an algebraically closed extension. Typically, R is the ring of the integers, the field of fractions is the field of the rational numbers and the algebraically closed field is the field of the complex numbers. Vieta's formulas are then useful because they provide relations between the roots without having to compute them. For polynomials over a commutative ring that is not an integral domain, Vieta's formulas are only valid when a n {\displaystyle a_{n}} is not a zero-divisor and P ( x ) {\displaystyle P(x)} factors as a n ( x − r 1 ) ( x − r 2 ) … ( x − r n ) {\displaystyle a_{n}(x-r_{1})(x-r_{2})\dots (x-r_{n})} . For example, in the ring of the integers modulo 8, the quadratic polynomial P ( x ) = x 2 − 1 {\displaystyle P(x)=x^{2}-1} has four roots: 1, 3, 5, and 7. Vieta's formulas are not true if, say, r 1 = 1 {\displaystyle r_{1}=1} and r 2 = 3 {\displaystyle r_{2}=3} , because P ( x ) ≠ ( x − 1 ) ( x − 3 ) {\displaystyle P(x)\neq (x-1)(x-3)} . However, P ( x ) {\displaystyle P(x)} does factor as ( x − 1 ) ( x − 7 ) {\displaystyle (x-1)(x-7)} and also as ( x − 3 ) ( x − 5 ) {\displaystyle (x-3)(x-5)} , and Vieta's formulas hold if we set either r 1 = 1 {\displaystyle r_{1}=1} and r 2 = 7 {\displaystyle r_{2}=7} or r 1 = 3 {\displaystyle r_{1}=3} and r 2 = 5 {\displaystyle r_{2}=5} . == Example == Vieta's formulas applied to quadratic and cubic polynomials: The roots r 1 , r 2 {\displaystyle r_{1},r_{2}} of the quadratic polynomial P ( x ) = a x 2 + b x + c {\displaystyle P(x)=ax^{2}+bx+c} satisfy r 1 + r 2 = − b a , r 1 r 2 = c a . {\displaystyle r_{1}+r_{2}=-{\frac {b}{a}},\quad r_{1}r_{2}={\frac {c}{a}}.} The first of these equations can be used to find the minimum (or maximum) of P; see Quadratic equation § Vieta's formulas. The roots r 1 , r 2 , r 3 {\displaystyle r_{1},r_{2},r_{3}} of the cubic polynomial P ( x ) = a x 3 + b x 2 + c x + d {\displaystyle P(x)=ax^{3}+bx^{2}+cx+d} satisfy r 1 + r 2 + r 3 = − b a , r 1 r 2 + r 1 r 3 + r 2 r 3 = c a , r 1 r 2 r 3 = − d a . {\displaystyle r_{1}+r_{2}+r_{3}=-{\frac {b}{a}},\quad r_{1}r_{2}+r_{1}r_{3}+r_{2}r_{3}={\frac {c}{a}},\quad r_{1}r_{2}r_{3}=-{\frac {d}{a}}.} == Proof == === Direct proof === Vieta's formulas can be proved by considering the equality a n x n + a n − 1 x n − 1 + ⋯ + a 1 x + a 0 = a n ( x − r 1 ) ( x − r 2 ) ⋯ ( x − r n ) {\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{1}x+a_{0}=a_{n}(x-r_{1})(x-r_{2})\cdots (x-r_{n})} (which is true since r 1 , r 2 , … , r n {\displaystyle r_{1},r_{2},\dots ,r_{n}} are all the roots of this polynomial), expanding the products in the right-hand side, and equating the coefficients of each power of x {\displaystyle x} between the two members of the equation. Formally, if one expands ( x − r 1 ) ( x − r 2 ) ⋯ ( x − r n ) {\displaystyle (x-r_{1})(x-r_{2})\cdots (x-r_{n})} and regroup the terms by their degree in x {\displaystyle x} , one gets ∑ k = 0 n ( − 1 ) n − k x k ( ∑ b 1 + ⋯ + b n = k ( ∀ i ) b i ∈ { 0 , 1 } r 1 b 1 ⋯ r n b n ) , {\displaystyle \sum _{k=0}^{n}(-1)^{n-k}x^{k}\left(\sum _{\stackrel {(\forall i)\;b_{i}\in \{0,1\}}{b_{1}+\cdots +b_{n}=k}}r_{1}^{b_{1}}\cdots r_{n}^{b_{n}}\right),} where the inner sum is exactly the k {\displaystyle k} th elementary symmetric function As an example, consider the quadratic f ( x ) = a 2 x 2 + a 1 x + a 0 = a 2 ( x − r 1 ) ( x − r 2 ) = a 2 ( x 2 − x ( r 1 + r 2 ) + r 1 r 2 ) . {\displaystyle f(x)=a_{2}x^{2}+a_{1}x+a_{0}=a_{2}(x-r_{1})(x-r_{2})=a_{2}(x^{2}-x(r_{1}+r_{2})+r_{1}r_{2}).} Comparing identical powers of x {\displaystyle x} , we find a 2 = a 2 {\displaystyle a_{2}=a_{2}} , a 1 = − a 2 ( r 1 + r 2 ) {\displaystyle a_{1}=-a_{2}(r_{1}+r_{2})} and a 0 = a 2 ( r 1 r 2 ) {\displaystyle a_{0}=a_{2}(r_{1}r_{2})} , with which we can for example identify r 1 + r 2 = − a 1 / a 2 {\displaystyle r_{1}+r_{2}=-a_{1}/a_{2}} and r 1 r 2 = a 0 / a 2 {\displaystyle r_{1}r_{2}=a_{0}/a_{2}} , which are Vieta's formula's for n = 2 {\displaystyle n=2} . === Proof by mathematical induction === Vieta's formulas can also be proven by induction as shown below. Inductive hypothesis: Let P ( x ) {\displaystyle {P(x)}} be polynomial of degree n {\displaystyle n} , with complex roots r 1 , r 2 , … , r n {\displaystyle {r_{1}},{r_{2}},{\dots },{r_{n}}} and complex coefficients a 0 , a 1 , … , a n {\displaystyle a_{0},a_{1},\dots ,a_{n}} where a n ≠ 0 {\displaystyle {a_{n}}\neq 0} . Then the inductive hypothesis is that P ( x ) = a n x n + a n − 1 x n − 1 + ⋯ + a 1 x + a 0 = a n x n − a n ( r 1 + r 2 + ⋯ + r n ) x n − 1 + ⋯ + ( − 1 ) n ( a n ) ( r 1 r 2 ⋯ r n ) {\displaystyle {P(x)}={a_{n}}{x^{n}}+{{a_{n-1}}{x^{n-1}}}+{\cdots }+{{a_{1}}{x}}+{{a}_{0}}={{a_{n}}{x^{n}}}-{a_{n}}{({r_{1}}+{r_{2}}+{\cdots }+{r_{n}}){x^{n-1}}}+{\cdots }+{{(-1)^{n}}{(a_{n})}{({r_{1}}{r_{2}}{\cdots }{r_{n}})}}} Base case, n = 2 {\displaystyle n=2} (quadratic): Let a 2 , a 1 {\displaystyle {a_{2}},{a_{1}}} be coefficients of the quadratic and a 0 {\displaystyle a_{0}} be the constant term. Similarly, let r 1 , r 2 {\displaystyle {r_{1}},{r_{2}}} be the roots of the quadratic: a 2 x 2 + a 1 x + a 0 = a 2 ( x − r 1 ) ( x − r 2 ) {\displaystyle {a_{2}x^{2}}+{a_{1}x}+a_{0}={a_{2}}{(x-r_{1})(x-r_{2})}} Expand the right side using distributive property: a 2 x 2 + a 1 x + a 0 = a 2 ( x 2 − r 1 x − r 2 x + r 1 r 2 ) {\displaystyle {a_{2}x^{2}}+{a_{1}x}+a_{0}={a_{2}}{({x^{2}}-{r_{1}x}-{r_{2}x}+{r_{1}}{r_{2}})}} Collect like terms: a 2 x 2 + a 1 x + a 0 = a 2 ( x 2 − ( r 1 + r 2 ) x + r 1 r 2 ) {\displaystyle {a_{2}x^{2}}+{a_{1}x}+a_{0}={a_{2}}{({x^{2}}-{({r_{1}}+{r_{2}}){x}}+{r_{1}}{r_{2}})}} Apply distributive property again: a 2 x 2 + a 1 x + a 0 = a 2 x 2 − a 2 ( r 1 + r 2 ) x + a 2 ( r 1 r 2 ) {\displaystyle {a_{2}x^{2}}+{a_{1}x}+a_{0}={{a_{2}}{x^{2}}-{{a_{2}}({r_{1}}+{r_{2}}){x}}+{a_{2}}{({r_{1}}{r_{2}})}}} The inductive hypothesis has now been proven true for n = 2 {\displaystyle n=2} . Induction step: Assuming the inductive hypothesis holds true for all n ⩾ 2 {\displaystyle n\geqslant 2} , it must be true for all n + 1 {\displaystyle n+1} . P ( x ) = a n + 1 x n + 1 + a n x n + ⋯ + a 1 x + a 0 {\displaystyle {P(x)}={a_{n+1}}{x^{n+1}}+{{a_{n}}{x^{n}}}+{\cdots }+{{a_{1}}{x}}+{{a}_{0}}} By the factor theorem, ( x − r n + 1 ) {\displaystyle {(x-r_{n+1})}} can be factored out of P ( x ) {\displaystyle P(x)} leaving a 0 remainder. Note that the roots of the polynomial in the square brackets are r 1 , r 2 , ⋯ , r n {\displaystyle r_{1},r_{2},\cdots ,r_{n}} : P ( x ) = ( x − r n + 1 ) [ a n + 1 x n + 1 + a n x n + ⋯ + a 1 x + a 0 x − r n + 1 ] {\displaystyle {P(x)}={(x-r_{n+1})}{[{\frac {{a_{n+1}}{x^{n+1}}+{{a_{n}}{x^{n}}}+{\cdots }+{{a_{1}}{x}}+{{a}_{0}}}{x-r_{n+1}}}]}} Factor out a n + 1 {\displaystyle a_{n+1}} , the leading coefficient P ( x ) {\displaystyle P(x)} , from the polynomial in the square brackets: P ( x ) = ( a n + 1 ) ( x − r n + 1 ) [ x n + 1 + a n x n ( a n + 1 ) + ⋯ + a 1 ( a n + 1 ) x + a 0 ( a n + 1 ) x − r n + 1 ] {\displaystyle {P(x)}={(a_{n+{1}})}{(x-r_{n+1})}{[{\frac {{x^{n+1}}+{\frac {{a_{n}}{x^{n}}}{(a_{n+{1}})}}+{\cdots }+{{\frac {a_{1}}{(a_{n+{1}})}}{x}}+{\frac {a_{0}}{(a_{n+{1}})}}}{x-r_{n+1}}}]}} For simplicity sake, allow the coefficients and constant of polynomial be denoted as ζ {\displaystyle \zeta } : P ( x ) = ( a n + 1 ) ( x − r n + 1 ) [ x n + ζ n − 1 x n − 1 + ⋯ + ζ 0 ] {\displaystyle P(x)={(a_{n+1})}{(x-r_{n+1})}{[{x^{n}}+{\zeta _{n-1}x^{n-1}}+{\cdots }+{\zeta _{0}}]}} Using the inductive hypothesis, the polynomial in the square brackets can be rewritten as: P ( x ) = ( a n + 1 ) ( x − r n + 1 ) [ x n − ( r 1 + r 2 + ⋯ + r n ) x n − 1 + ⋯ + ( − 1 ) n ( r 1 r 2 ⋯ r n ) ] {\displaystyle P(x)={(a_{n+1})}{(x-r_{n+1})}{[{x^{n}}-{({r_{1}}+{r_{2}}+{\cdots }+{r_{n}}){x^{n-1}}}+{\cdots }+{{(-1)^{n}}{({r_{1}}{r_{2}}{\cdots }{r_{n}})}}]}} Using distributive property: P ( x ) = ( a n + 1 ) ( x [ x n − ( r 1 + r 2 + ⋯ + r n ) x n − 1 + ⋯ + ( − 1 ) n ( r 1 r 2 ⋯ r n ) ] − r n + 1 [ x n − ( r 1 + r 2 + ⋯ + r n ) x n − 1 + ⋯ + ( − 1 ) n ( r 1 r 2 ⋯ r n ) ] ) {\displaystyle P(x)={(a_{n+1})}{({x}{[{x^{n}}-{({r_{1}}+{r_{2}}+{\cdots }+{r_{n}}){x^{n-1}}}+{\cdots }+{{(-1)^{n}}{({r_{1}}{r_{2}}{\cdots }{r_{n}})}}]}{-r_{n+1}}{[{x^{n}}-{({r_{1}}+{r_{2}}+{\cdots }+{r_{n}}){x^{n-1}}}+{\cdots }+{{(-1)^{n}}{({r_{1}}{r_{2}}{\cdots }{r_{n}})}}]})}} After expanding and collecting like terms: P ( x ) = a n + 1 x n + 1 − a n + 1 ( r 1 + r 2 + ⋯ + r n + r n + 1 ) x n + ⋯ + ( − 1 ) n + 1 ( r 1 r 2 ⋯ r n r n + 1 ) {\displaystyle {\begin{aligned}{P(x)}={{a_{n+1}}{x^{n+1}}}-{a_{n+1}}{({r_{1}}+{r_{2}}+{\cdots }+{r_{n}}+{r_{n+1}}){x^{n}}}+{\cdots }+{{(-1)^{n+1}}{({r_{1}}{r_{2}}{\cdots }{r_{n}}{r_{n+1}})}}\\\end{aligned}}} The inductive hypothesis holds true for n + 1 {\displaystyle n+1} , therefore it must be true ∀ n ∈ N {\displaystyle \forall n\in \mathbb {N} } Conclusion: a n x n + a n − 1 x n − 1 + ⋯ + a 1 x + a 0 = a n x n − a n ( r 1 + r 2 + ⋯ + r n ) x n − 1 + ⋯ + ( − 1 ) n ( r 1 r 2 ⋯ r n ) {\displaystyle {a_{n}}{x^{n}}+{{a_{n-1}}{x^{n-1}}}+{\cdots }+{{a_{1}}{x}}+{{a}_{0}}={{a_{n}}{x^{n}}}-{a_{n}}{({r_{1}}+{r_{2}}+{\cdots }+{r_{n}}){x^{n-1}}}+{\cdots }+{{(-1)^{n}}{({r_{1}}{r_{2}}{\cdots }{r_{n}})}}} By dividing both sides by a n {\displaystyle a_{n}} , it proves the Vieta's formulas true. == History == A method similar to Vieta's formula can be found in the work of the 12th century Islamic mathematician Sharaf al-Din al-Tusi. It is plausible that algebraic advancements made by other Islamic mathematician such as Omar Khayyam, al-tusi, and al-Kashi influenced 16th-century algebraists, with Vieta being the most prominent among them. The formulas were derived by the 16th-century French mathematician François Viète, for the case of positive roots. In the opinion of the 18th-century British mathematician Charles Hutton, as quoted by Funkhouser, the general principle (not restricted to positive real roots) was first understood by the 17th-century French mathematician Albert Girard: ...[Girard was] the first person who understood the general doctrine of the formation of the coefficients of the powers from the sum of the roots and their products. He was the first who discovered the rules for summing the powers of the roots of any equation. == See also == Content (algebra) Descartes' rule of signs Newton's identities Gauss–Lucas theorem Properties of polynomial roots Rational root theorem Symmetric polynomial and elementary symmetric polynomial == Notes == == References == "Viète theorem", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Funkhouser, H. Gray (1930), "A short account of the history of symmetric functions of roots of equations", American Mathematical Monthly, 37 (7), Mathematical Association of America: 357–365, doi:10.2307/2299273, JSTOR 2299273 Vinberg, E. B. (2003), A course in algebra, American Mathematical Society, Providence, R.I, ISBN 0-8218-3413-4 Djukić, Dušan; et al. (2006), The IMO compendium: a collection of problems suggested for the International Mathematical Olympiads, 1959–2004, Springer, New York, NY, ISBN 0-387-24299-6
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Wikipedia:Vigen Malumian#0
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Vigen Malumian (Armenian: Վիգեն Հայկի Մալումյան) (Russian: Виген Гайкович Малумян) (11 March 1932 – 2 February 2013) was an Armenian astrophysicist who specialized in radio galaxies and the radio characteristics of spiral galaxies. He was a prominent scientist at the Byurakan Observatory in Armenia (BAO), a lecturer at the Faculty of Physics at Yerevan State University, and a member of the BAO Scientific Board. Additionally, he was involved in the scientific council responsible for awarding degrees at the Observatory. Malumian was also a member of several international scientific organizations, including the International Astronomical Union (IAU), the European Astronomical Society (EAS), and the Armenian Astronomical Society (ArAS). Malumian graduated in 1954 from the Faculty of Physics and Mathematics at Yerevan State University in Armenia. He began working at the Byurakan Astrophysical Observatory shortly thereafter. From 1955 to 1959, he studied in graduate school and defended his candidate dissertation at Yerevan State University in 1963. His dissertation, titled Results of Observations of Certain Galactic Radio Sources at 33 cm Using High-Resolution Radio Telescopes, was supervised by the renowned radio astronomer Semyon Emanuelovich Khaykin. In 1991, Malumian was awarded a Doctorate of Physical and Mathematical Sciences at the Byurakan Astrophysical Observatory, following his research on Radio Emission from Moderately Active and Weak Radio Galaxies. His work focused on isolated and interacting galaxies, galaxy groups, radio galaxies, quasars, and other radio sources in multiple wavelength domains. Malumian authored more than 90 scientific papers, many of which were widely cited in international scientific literature. He presented his research at numerous international scientific conferences. Malumian was also active within the IAU, where he participated in IAU Symposium 194. He held memberships in various IAU divisions, including Division B Facilities, Technologies, and Data Science, Commission 40 Radio Astronomy (until 2013), and Division X Radio Astronomy (until 2012). == Works == GPS and CSS radio sources Relationship Between Infrared and Radio Emission of Spiral Galaxies Activity Phenomena Observed at Radio Frequences in Spiral Galaxies Radio luminosity of spiral galaxies Relationship between radio luminosity and optical surface brightness of spiral galaxies Radio Emission Spectra of Isolated Spiral Galaxies and Spiral Members of Pairs of Galaxies On the question of radio emission of spiral galaxies in groups of galaxies On the Radio Emission of Spiral Galaxies in Double System of Galaxies Radio Spectrum and Surface Brightness of Radio Galaxies Observations of faint radio galaxies with the RATAN-600 radio telescope Radio luminosities and structure of central regions of spiral galaxies Radio emission of elliptical and lenticular galaxies in groups of galaxies On Enhanced Radio Emission of Spiral Components of Double Galaxies and of Groups of Galaxies RATAN-600 Observations of Faint Bologna Radio Galaxies at 7.6-CM and 3.9-CM Radio Emission of Spiral Galaxies in Groups of Galaxies On the Radio Emission from Interacting Spiral Galaxies Radio emission of isolated single and double galaxies RATAN-600 Observations of another 15 Bologna Radio Galaxies Colors and the Byurakan classification of galaxies RATAN-600 Observations of 15 Bologna Radio Galaxies Investigation of galaxies of high surface brightness at 3.95 GHz Radio Spectra and the Byurakan Classification of Galaxies On the variability of the radio emission of Markarian 421 Observations of Galaxies of High Surface Brightness at 3.66-GHZ - Part One Optical Surface Brightnesses and Radio Luminosities of Galaxies Observations of Galaxies of High Surface Brightness with the Radio Telescope RATAN-600 The break in the radio emission spectrum of Cassiopeia A Radio emission of the galactic nucleus The Radio Spectrum of the Galactic Nucleus Observations of Galactic Plane Near delta = -24deg23' at Wavelength 32.5 cm with High Resolving Power Results of observations of Omega (NGC 6618) nebula made with the large Pulkovo radio telescope at wavelength 32.5 cm The Results of the Observations of Radio Source Sagittarius-A at 32.5 cm Wavelength with High Resolution Power Observation of the Region near the Galactic Center on a Wavelength of 33.3 cm with the Large GAO Radio Telescope == References ==
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Wikipedia:Viggo Brun#0
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Viggo Brun (13 October 1885 – 15 August 1978) was a Norwegian professor, mathematician and number theorist. == Contributions == In 1915, he introduced a new method, based on Legendre's version of the sieve of Eratosthenes, now known as the Brun sieve, which addresses additive problems such as Goldbach's conjecture and the twin prime conjecture. He used it to prove that there exist infinitely many integers n such that n and n+2 have at most nine prime factors, and that all large even integers are the sum of two numbers with at most nine prime factors. He also showed that the sum of the reciprocals of twin primes converges to a finite value, now called Brun's constant: by contrast, the sum of the reciprocals of all primes is divergent. He developed a multi-dimensional continued fraction algorithm in 1919–1920 and applied this to problems in musical theory. He also served as praeses of the Royal Norwegian Society of Sciences and Letters in 1946. == Biography == Brun was born at Lier in Buskerud, Norway. He studied at the University of Oslo and began research at the University of Göttingen in 1910. In 1923, Brun became a professor at the Technical University in Trondheim and in 1946 a professor at the University of Oslo. He retired in 1955 at the age of 70 and died in 1978 (at 92 years-old) at Drøbak in Akershus, Norway. == See also == Brun's theorem Brun-Titchmarsh theorem Brun sieve Sieve theory == Fotnoter == == References == == Other sources == H. Halberstam and H. E. Richert, Sieve methods, Academic Press (1974) ISBN 0-12-318250-6. Gives an account of Brun's sieve. C.J. Scriba, Viggo Brun, Historia Mathematica 7 (1980) 1–6. C.J. Scriba, Zur Erinnerung an Viggo Brun, Mitt. Math. Ges. Hamburg 11 (1985) 271-290 == External links == Brun's Constant Brun's Pure Sieve Viggo Brun personal archive exists at NTN University Library Dorabiblioteket
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Wikipedia:Viggo Stoltenberg-Hansen#0
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Viggo, also spelled Wiggo, is a Nordic male name. There are two main theories about its origins: a latinised form of the Old Norse name Viggeir, which is also found in the form of other Germanic names, such as Ludvig. It stems from old Norse vig-, meaning "battle, fight". a variant of the Icelandic name Vöggur, coming from old Norse 'vöggr', "one who lies in a cradle". People named Viggo include: Viggo Bielefeldt (1851–1909), Danish composer Viggo Brøndal (1887–1942), Danish philologist, professor of Romance languages and literature Viggo Brodersen (1879–1965), Danish composer and pianist Viggo Brun (1885–1978), Norwegian mathematician Viggo Christensen(1880–1967), the first Lord Mayor of Copenhagen Viggo Dibbern (1900–1981), Danish gymnast and Olympic medalist Viggo Fausböll (1821–1908), Danish translator and Indologist Viggo Frederiksen (1916–1993), Danish boxer and Olympic competitor Viggo Hagstrøm (1954–2013), Norwegian legal scholar and educator Viggo Hansteen (1900–1941), Norwegian politician and member of the resistance Viggo Hørup (1841–1902), Danish politician, journalist and agitator Viggo Jensen (1874–1930), Danish weightlifter, shooter, gymnast and Olympic medalist Viggo Jensen (1921–2005), Danish footballer Viggo Jensen (born 1947), Danish footballer Viggo Johansen (1851–1935), Danish painter Viggo Johansen (born 1949), Norwegian journalist and television presenter Viggo Johannessen (1936–2012), Norwegian statistician and civil servant Viggo Kampmann (1910–1976), Prime Minister of Denmark Viggo Larsen (1880–1957), Danish film actor, director and producer Viggo Lindstrøm (1858–1926), Danish actor and theatre director Viggo Mortensen (born 1958), Danish-American actor Viggo Rivad (1922–2016), Danish photographer Viggo Rørup (1903–1971), Danish painter Viggo Stilling-Andersen (1893–1967), Danish fencer Viggo Stoltenberg-Hansen (born 1942), Swedish mathematician and logician Viggo Stuckenberg (1863–1905), Danish poet Viggo Sundmoen (born 1954), Norwegian footballer Viggo Ullmann (1848–1910), Norwegian educator and politician Viggo Venn (born 1989), Norwegian comedian Viggo Widerøe (1904–2002), Norwegian aviator and entrepreneur Viggo Wiehe (1874–1956), Danish actor == References ==
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Wikipedia:Viktor Bunyakovsky#0
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Viktor Yakovlevich Bunyakovsky (Russian: Виктор Яковлевич Буняковский; Ukrainian: Віктор Якович Буняковський, romanized: Viktor Yakovych Buniakovskyi; 16 December [O.S. 4 December] 1804 – 12 December [O.S. 30 November] 1889) was a Russian mathematician, member and later vice president of the Petersburg Academy of Sciences. Bunyakovsky was a mathematician, noted for his work in theoretical mechanics and number theory (see: Bunyakovsky conjecture), and is credited with an early discovery of the Cauchy–Schwarz inequality, proving it for the infinite dimensional case as well as for definite integrals of real-valued functions in 1859, many years prior to Hermann Schwarz's works on the subject. == Biography == Viktor Yakovlevich Bunyakovsky was born in Bar, Podolia Governorate, Russian Empire (now Vinnytsia Oblast, Ukraine) in 1804. Bunyakovsky was a son of Colonel Yakov Vasilievich Bunyakovsky of a cavalry regiment, who was killed in Finland in 1809. == Education == Bunyakovsky obtained his initial mathematical education at the home of his father's friend, Count Alexander Tormasov, in St. Petersburg. In 1820, he traveled with the count's son to a university in Coburg and subsequently to the Sorbonne in Paris to study mathematics. At the Sorbonne, Bunyakovsky had opportunity to attend lectures from Laplace and Poisson. He focused his study and research on mathematics and physics. In 1824, Bunyakovsky received his bachelor's degree from the Sorbonne. Continuing his research, he wrote three doctoral dissertations under Cauchy's supervision by the spring of 1825: The rotary motion in a resistant medium of a set of plates of constant thickness and defined contour around an axis inclined with respect to the horizon; The determination of the radius vector in elliptical motion of planets; and The propagation of heat in solids. He successfully completed his dissertation on theoretical physics, theoretical mechanics and mathematical physics, and obtained his doctorate under Cauchy's supervision. == Scientific and pedagogical work == After the seven years abroad, Bunyakovsky returned to St. Petersburg in 1826 and took up teaching and research, which he pursued for much of his life. In addition to the university courses in analytical mathematics, differential equations, and probability theory, he was also active in preparing syllabi and teaching manuals for Russian schools and military academies. He lectured on mathematics and mechanics at the First Cadet Corps (later the Naval Academy) from 1826 to 1831 and at the Communications Institute in St. Petersburg. From 1828 to 1864, Bunyakovsky was attached to the officer classes at the Naval Academy in St. Petersburg. From 1846 to 1880, Bunyakovsky was a professor at St. Petersburg University in St. Petersburg, Russia. In 1859, Bunyakovsky taught mathematics at St. Petersburg State Railways University, named after Alexander I in St. Petersburg, Russia. Alongside his teaching responsibilities, Bunyakovsky made significant scientific contributions in number theory and probability theory. His other scientific interests included: mathematical physics, condensed matter physics, mathematical analysis, differential equations, actuarial mathematics, and mathematics education with a focus on mathematical terminology. He worked on theoretical mechanics and number theory (see: Bunyakovsky conjecture). He is credited with an early discovery of the Cauchy–Schwarz inequality, proving it for the infinite dimensional case in 1859, many years prior to Hermann Schwarz's research on the subject. Bunyakovsky is an author of Foundations of the mathematical theory of probability (1846). Bunyakovsky published around 150 research papers. == St. Petersburg Academy of Sciences == Bunyakovsky became a member of the precursor organization to the Russian Academy of Sciences. He was named an adjunct in mathematics (7 May 1828), an extraordinary academician (24 March 1830), and an ordinary academician at the physics and mathematics division (8 January 1841). Bunyakovsky was elected to the post of the Vice President of the Russian Academy of Sciences on 8 April 1864 (in fact since 10 August 1863 г.). Bunyakovsky was the Vice President of the St. Petersburg Academy of Sciences for 25 years (8 April 1864 – 26 September 1889). In 1875, the St. Petersburg Academy of Sciences issued a medal and established a prize, bearing Viktor Yakovlevich Bunyakovsky's name, for his outstanding mathematical research. == Scientific contributions == Bunyakovsky wrote around 150 research works and a number of books. Bunyakovsky published his first volume: Lexicon of fundamental and applied mathematics, which was written until letter "D" in Russia in 1839. After Bunyakovsky's death, the manuscripts with other volumes: E, F, G, H, I, J, K, L were found, containing a note by Bunyakovsky's hand: "Do not print, but pass to the Russian Academy of Sciences archive for the researchers, who will continue my Lexicon." The hand-written manuscripts are preserved at the Department of Manuscripts, Library, Russian Academy of Sciences. Foundations of mathematical theory of probability, by Bunyakovsky was published by Imperial Academy of Sciences of St. Petersburg in St. Petersburg in 1846. Bunyakovsky became a world famous scientist after this publication. Bunyakovsky wrote a research article titled: "On possibility of introduction of certain measures of trust to results of some sciences and statistics mainly", which was published in Sovremennik in Russia in 1848. Bunyakovsky published his monograph: "The parallel lines" in which he provided the scientific evidences to the problems in the parallel lines theory in Russia in 1853. Bunyakovsky wrote a research article titled: "Biological researches and their application to man's population in Russia", which was published in "Zapiski Academii Nauk" in Russia in 1873 or 1874. Bunyakovsky printed a research article titled: "On the probability of number of divisions of Russian army in 1883–1885", which was published in Zapiski Academii Nauk in Russia in 1885. Bunyakovsky developed a number of practical applications as far as the probability theory is concerned, publishing his research articles in the Russian magazines Sovremennik and Zhurnal Ministerstava Narodnogo Prosvesheniya. Bunyakovsky made a significant scientific contribution to the problem of the naval department pension fund creation, publishing his research articles in Morskoi Sbornik magazine in 1858. Bunyakovsky formulated an empirical law of deaths in 1869, making it possible to solve the problems on the calculation of both capital insurance and life-time incomes in finances. == Legacy == A street in Bar, Ukraine, is named after Bunyakovsky. The Bunyakovsky International Conference honoring Bunyakovsky's scientific achievements was organized in 2004 in Kyiv, Ukraine. == References == == External links == Bunyakovsky V. Ya., Rotary motion in a resistant medium of a set of plates of constant thickness and defined contour around an axis inclined with respect to the horizon, PhD Thesis no. 1 under Prof. Augustin - Louis Cauchy supervision, École Polytechnique, Paris, France, 1825a. Bunyakovsky V. Ya., Determination of the radius-vector in elliptical motion of planets, PhD Thesis no. 2 under Prof. Augustin - Louis Cauchy supervision, École Polytechnique, Paris, France, 1825b. Bunyakovsky V. Ya., Heat propagation in solids, PhD Thesis no. 3 under Prof. Augustin - Louis Cauchy supervision, École Polytechnique, Paris, France, 1825c. Bunyakovsky V. Ya., Foundations of the mathematical theory of probability, Imperial Academy of Sciences of St. Petersburg, St. Petersburg, Russia, 1846. Bounjakowsky W., «Mémoires de l’Académie des sciences de St-Pétersbourg. 7 série», vol. 1, No. 9, Russia, 1859. «Description of the Celebration of the Doctoral Jubilee of the Vice-President of the Academy of Sciences, Academician Bunyakovsky. 19 May 1875», St. Petersburg, Russia, 1876. Bunyakovsky V. Ya., Liste des travaux mathematiques des Victor Bouniakowsky etc., St. Petersburg, Russia, 1889. Andreev K. A., «V. Y. Bunyakovsky», Kharkov, Russia/Ukraine, 1890. Zhdanov A. M., Bunyakovsky, Viktor Yakovlevich, Brokgauz and Efron Encyclopedia Vocabulary, 86 vols. (82 vols. and 4 additional vols.), St. Petersburg, Russia, 1890. Viktor Yakovlevich Bunyakovsky, Russian Bibliographic Vocabulary, 25 vols., St. Petersburg - Moscow, 1896 - 1918. Dickson L. E., «History of the Theory of Numbers», 3 vols, Washington, D.C., U.S.A., 1919 – 1923. Prudnikov V. E., «On Essays by P. L. Chebyshev, M. V. Ostrogradskii, V. Ya. Bunyakovskii, and I. I. Somov» in the 'Encyclopaedic dictionary,' compiled by Russian scholars and literati, (in Russian), Istor.-Mat. Issled. 6, pp. 223–237, 1953. Prudnikov V. E., «V. Y. Bunyakovsky, Scientist and Teacher», Moscow, Russia, 88 p., 1954. Otradnyh F. P., «V. Ya. Bunyakovskii – Professor in the Petersburg University», (in Russian), Vestnik Leningrad University, 10(5) pp. 49–54, 1955. Melnikov I. G., «Bunyakovsky’s Works on Number Theory», in Research Works of Institute of History of Natural Sciences and Technology, Academy of Sciences of the USSR, 17, pp. 270–286, 1957. Youschkevitch A. P., «History of Mathematics in Russia Before 1917», pp. 296–302, Moscow, Russia, 1968. Viktor Yakovlevich Bunyakovsky, Big Soviet Encyclopedia, Moscow, Russia, 1969. Ermolaeva N. S., «V Ya Bunyakovskii's Doctoral Dissertation», (in Russian), History of Mathematics Research, 29, pp. 241 – 255, 348, 1985. Kirsanov V. S., «V Ya Bunyakovskii's Dissertation and Cauchy's Theory of Residues», (in Russian), History of Mathematics Research, 28, pp. 261–266, 350, 1985. Sheynin O. V., «On V. Ya. Buniakovsky's Work in the Theory of Probability», Archive for History of Exact Sciences, 12, XII, Volume 43, Issue 3, pp. 199–223, 1991. Schreiber P, «The Cauchy–Bunyakovsky–Schwarz Inequality», in Hermann Grassmann, Lieschow, pp. 64–70, 1994, (Greifswald, 1995). Yu F. Zhang, F. X. Bao and X. L. Fu, «The Origin and Development of the Cauchy–Bunyakovskii Inequality», (in Chinese), Qufu Shifan Daxue Xuebao Ziran Kexue Ban 21 (1), pp. 83–86, 1995. «The Bunyakovsky International Conference», Institute of Mathematics of the National Academy of Sciences of Ukraine (NASU), Ministry of Science and Education of Ukraine, National Technical University of Ukraine "KPI", Taras Shevchenko Kyiv National University, Mykhailo Dragomanov National Pedagogical University, Vinnytsia National Technical University, Ukrainian Mathematical Society, Kyiv; Bar, Vinnytsia Region, Ukraine, 16–21 August 2004. Grigorian A. T., «Biography: Bunyakovsky Viktor Yakovlevich», in Complete Dictionary of Scientific Biography, New York, U.S.A., 2008, Encyclopedia.com, 20 July 2014. Viktor Yakovlevich Bunyakovsky, Russian Academy of Sciences, 2015, http://www.ras.ru/win/db/show_per.asp?P=.id-49730.ln-ru . O'Connor, John J.; Robertson, Edmund F., "Viktor Bunyakovsky", MacTutor History of Mathematics Archive, University of St Andrews, 2015.
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Wikipedia:Viktor Korolev#0
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Viktor Korolev (Russian: Ви́ктор Юрьевич Королёв) (born 1954) is a Russian scientist in the field of mathematical statistics, Professor, Dr. Sc., a professor at the Faculty of Computer Science at the Moscow State University. He defended the thesis «Limit distributions of random sequences with independent random indices and some of their applications» for the degree of Doctor of Physical and Mathematical Sciences (1994). He has authored 27 books and more than 340 scientific articles. == References == == Bibliography == Evgeny Grigoriev (2010). Faculty of Computational Mathematics and Cybernetics: History and Modernity: A Biographical Directory (1 500 экз ed.). Moscow: Publishing house of Moscow University. pp. 314–315. ISBN 978-5-211-05838-5. == External links == Annals of the Moscow University(in Russian) MSU CMC(in Russian) Scientific works of Viktor Korolev Scientific works of Viktor Korolev(in English)
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Wikipedia:Viktor Sadovnichiy#0
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Viktor Antonovich Sadovnichiy (Russian: Виктор Антонович Садовничий; born 3 April 1939) is a Russian mathematician, winner of the 1989 USSR State Prize, and since 1992 the rector of Moscow State University. One of the main opinion leaders in Russia, Sadovnichiy has significant political and social influence. == Biography == Sadovnichiy was born in the village of Krasnopavlovka in Kharkov Oblast (now in Ukraine) to worker Anton Grigoryevich and collective farmer Anna Matveyevna. === Study === After graduating from rural school, Sadovnichiy worked for some time at the Komsomolets coal mine in Gorlovka (Donetsk Oblast) and studied at night school, from which he graduated with honors. In an interview, he said that he planned to enter the Belarusian State Agricultural Academy, but on the advice of a friend, in 1958, he entered the MSU Faculty of Mechanics and Mathematics. In 1963, he graduated with honors with a degree in mathematics. Sadovnichiy was sent to graduate school and graduated in 1966, defending his PhD thesis on 17 March 1967 (topic: "Regularized sums of eigenvalues of general problems for ordinary differential equations"). He was a student of Anatoly Kostyuchenko. After graduate school, he remained as an assistant. === Early career === Sadovnichiy defended his doctoral thesis in 1974 (topic: "On some issues in the theory of ordinary differential equations depending on the spectral parameter"). In 1975, he became Professor. In 1981-1982, he headed the Department of Functional Analysis and Its Applications, MSU Faculty of Computational Mathematics and Cybernetics. Since 1982, Sadovnichiy has been the head of the calculus department of the Faculty of Mechanics and Mathematics. He worked at Moscow State University in the following positions: deputy dean of the Faculty of Mechanics and Mathematics for scientific work, deputy vice-rector, vice-rector (1982-1984), and first vice-rector (1984-1992). === Rectorship of the MSU === On 23 March 1992, Sadovnichiy was elected rector of Moscow State University on an alternative basis and re-elected in 1996, 2001, and 2005 (uncontested). Sadovnichiy has been a corresponding member of the Russian Academy of Sciences since 1994, a full member since 1997, and a member of the Academy's Presidium. In 1989, he was awarded with the USSR State Prize. From 2008 to 2013, he was Vice-President of the Russian Academy of Sciences. Doctor Emeritus of universities worldwide and the author of some 150 works. Sadovnichiy is President of the Russian Union of Rectors (since 1994), President of the Moscow Society of Naturalists (since 2000), and Chairman of the Russian Council of School Olympiads. Member of the Board of Trustees of the Russian Academy of Education. Since 1989, he has been a member of the Council of the Association of Universities of the USSR (since 1992, the Eurasian Association of Universities); since 1992, he has been heading the Association. Sadovnichiy is a member of the editorial board of scientific journals Problem Analysis and Public Management Design, Quantum Computers and Quantum Computing (editor-in-chief), Higher Education in Russia, and Fundamental and Applied Mathematics. Under the scientific supervision of Sadovnichiy, more than 65 candidate's and 15 doctoral dissertations (including scientists from other countries) were prepared. In November 2011, bas-relief portraits of outstanding university rectors were installed in the rotunda of the main building of Moscow State University: Alexander Nesmeyanov, Ivan Petrovsky, and Sadovnichiy. In 2022, he was the lead signature on the Address of the Russian Union of Rectors, which called to support Putin in his invasion of Ukraine. === World financial economic crisis === In their co-authored article “On the Possibilities to Forecast the Current Crisis and its Second Wave” (with Askar Akaev and Andrey Korotayev) in the Russian academic journal “Ekonomicheskaya politika” (December 2010. Issue 6. Pages 39–46 Клиодинамика - математические методы в истории) the three authors published «a forecast of the second wave of the crisis, which suggested that it may start in July — August, 2011». == Honours and awards == Order "For Merit to the Fatherland"; 1st class (April 16, 2019) for his outstanding contribution to the development of national education and many years of research and teaching activities 2nd class (25 January 2005) for outstanding contribution to the development of education and many years of scientific and teaching activities 3rd class (2 April 1999) for services to science, the talent and years of diligent work 4th class (31 March 2009) for the great achievements in science, education and training of qualified specialists Order of the Red Banner of Labour, twice Medal "In Commemoration of the 850th Anniversary of Moscow" Jubilee Medal "In Commemoration of the 100th Anniversary of the Birth of Vladimir Ilyich Lenin" Order of Francysk Skaryna (Belarus) Order of Friendship (Kazakhstan, 1998) Order of Merit (Ukraine); 1st class (26 March 2009) for his outstanding personal contribution to strengthening Russian-Ukrainian cooperation in education and science, and many years of fruitful scientific and social activity 2nd class (6 December 2002) for personal contribution into development of Ukrainian-Russian cooperation, active participation in providing for the Year of Ukraine in the Russian Federation 3rd class (30 March 1999) a significant personal contribution to the development of economic and scientific-technical cooperation between Ukraine and the Russian Federation Sadovnichiy was stripped of his Ukrainian awards on 19 January 2025 by a decree of Ukrainian President Volodymyr Zelenskyy. Commander of the Legion of Honour (France) Order of the Rising Sun, 2nd class (Japan, 2008) - for his contribution to scientific and technical cooperation and deepening understanding between the two countries Order of Holy Prince Daniel of Moscow, 2nd class (Russian Orthodox Church) USSR State Prize (1989) State Prize of the Russian Federation in the field of science and technology (2002) Award of the Government of the Russian Federation (2006, 2011, 2012) Honorary Citizen of Moscow (2008) Honorary Member of the Russian Academy of Education Honorary Member of Russian Academy of Arts == Antisemitism controversy == In the 1970s–1980s, Sadovnichiy held positions of responsibility in the admissions committee for applicants for entrance exams at Moscow State University. Alexander Shen, George Szpiro, and other mathematicians accused Sadovnichiy of being a leading proponent of the discriminatory policy that prevented the mass admission of applicants of Jewish origin to the MSU Faculty of Mechanics and Mathematics. == Public work == In 2004, Sadovnichiy was named “Person of the Year” by Rambler in the “Education and Science” nomination of the “People of the Year” project. In October 2014, the Moscow State University, the Russian Post, and "The Teacher's Newspaper" organized a contest essays among one hundred thousand of Russian high school student on the topic "The person I trust". A few best essays, all of them written about the Russian president Vladimir Putin, were personally presented by Sadovnichiy to president Putin in October 2014. == Political activity == During his studies, Sadovnichiy was engaged in social work, heading the university's student committee and the faculty's Komsomol organization. Throughout his years at MSU, Sadovnichiy was an active member of the Communist Party of the Soviet Union, was a member of the party committees of the Faculty of Mechanics and Mathematics and Moscow State University, and in 1977 became head of the university's party committee. Sadovnichiy said the following about the relation between his political activity and rectorship of the MSU in the early 90s: In his (Yeltsin’s) circle, I was classified as a “red director” - after all, I was a member of the university party committee. And such a person should not become a rector. The rector was to be a reformer. Since December 2002, Sadovnichiy has been a member of the political council of the Moscow regional branch of the United Russia party. He is also a member of the party's Supreme Council. He took part in the elections of deputies to the State Duma of the Russian Federation in 2003, but after that, he refused his mandate as a deputy. On 6 February 2012, for the 2012 Russian presidential election, Sadovnichiy was officially registered as a trusted representative of Russian presidential candidate Vladimir Putin. During the 2018 Russian presidential election, Sadovnichiy was a member of the initiative group that nominated the candidacy of Russian President Vladimir Putin. He was also included in the list of Putin's trusted representatives. On 14 November 2019, the State Duma Committee on Education and Science approved an amendment for adoption in the second reading that will allow President Vladimir Putin to reappoint the rectors of Moscow State University and Saint Petersburg State University an unlimited number of times. On 3 April 2022 Sadovnichiy initiated a letter of the rectors of Russian universities supporting the Russian invasion of Ukraine. The document, signed by Sadovnichiy and co-signed by 304 other rectors of Russian universities, calls, among other things, for the "demilitarization and denazification of Ukraine", for "support [to be given to] the [Russian] army and the president". The letter says that "supporting the patriotism is a duty of the [Russian] universities", and that the "[Russian] universities were always [among the] supporting piers of the [Russian] state". In response for his support of the invasion, he was deprived of honorary doctorates from Ukrainian universities in Kyiv, Kharkiv and Dnipro. On 9 June 2022, Ukraine imposed sanctions on him. == References == Member info: Sadovnichiy, Viktor Antonovich(in Russian), Russian Academy of Sciences. Accessed January 23, 2010 Viktor Antonovich SADOVNICHIY - Rector of Lomonosov Moscow State University. Moscow State University. Accessed January 23, 2010 == External links == Media related to Viktor Sadovnichiy at Wikimedia Commons
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Wikipedia:Viktor Wagner#0
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Viktor Vladimirovich Wagner, also Vagner (Russian: Виктор Владимирович Вагнер) (4 November 1908 – 15 August 1981) was a Russian mathematician, best known for his work in differential geometry and on semigroups. Wagner was born in Saratov and studied at Moscow State University, where Veniamin Kagan was his advisor. He became the first geometry chair at Saratov State University. He received the Lobachevsky Medal in 1937. Wagner was also awarded "the Order of Lenin, the Order of the Red Banner, and the title of Honoured Scientist RSFSR. Moreover, he was also accorded that rarest of privileges in the USSR: permission to travel abroad." Wagner is credited with noting that the collection of partial transformations on a set X forms a semigroup P T X {\displaystyle {\mathcal {PT}}_{X}} which is a subsemigroup of the semigroup B X {\displaystyle {\mathcal {B}}_{X}} of binary relations on the same set X, where the semigroup operation is composition of relations. "This simple unifying observation, which is nevertheless an important psychological hurdle, is attributed by Schein (1986) to V.V. Wagner." == See also == Inverse semigroup Heap == References == B. M. Schein (1981). "Obituary: Viktor Vladimirovich Vagner (1908–1981)". Semigroup Forum. 28: 189–200. doi:10.1007/BF02676643. == External links == Viktor Wagner at the Mathematics Genealogy Project Wagner, V. V. (1952). "Обобщенные группы" [Generalized groups] (PDF). Doklady Akademii Nauk SSSR. 84: 1119–1122. Wagner's Biography – in Russian
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Wikipedia:Vilhelm Bjerknes#0
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Vilhelm Friman Koren Bjerknes ( BYURK-niss, Norwegian: [ˈʋɪlˌhɛlm ˈbjæɾknɛs]; 14 March 1862 – 9 April 1951) was a Norwegian mathematician, meteorologist, and physicist who did much to lay the foundation of the modern practice of weather forecasting. He formulated the primitive equations that are still in use in numerical weather prediction and climate modeling. He founded the so-called Bergen School of Meteorology, which was successful in advancing weather prediction and meteorology in the early 20th century. == Life and career == Born in Christiania (later renamed Oslo), Bjerknes enjoyed an early exposure to fluid dynamics, as assistant to his father, Carl Anton Bjerknes, who had discovered by mathematical analysis the apparent actions at a distance between pulsating and oscillating bodies in a fluid, and their analogy with the electric and magnetic actions at a distance. Apparently no attempt had been made to demonstrate experimentally the theories arrived at by the older professor until Vilhelm Bjerknes, then about 17 or 18 years of age, turned his mathematical knowledge and mechanical abilities to the devising of a series of instruments by which all the well-known phenomena of electricity and magnetism were illustrated and reproduced by spheres and discs and membranes set into rhythmic vibration in a bath containing a viscous fluid such as syrup. These demonstrations formed the most important exhibit in the department of physics at the Exposition Internationale d'Électricité held in Paris in 1881, and aroused greatest interest in the scientific world. Vilhelm Bjerknes became assistant to Heinrich Hertz in Bonn 1890–1891 and made substantial contributions to Hertz' work on electromagnetic resonance. He succeeded in giving the explanation of the phenomenon called "multiple resonance," discovered by Sarasin and De la Rive. Continuing his experiments at the University of Christiania (1891–1892), he proved experimentally the influence which the conductivity and the magnetic properties of the metallic conductors exert upon the electric oscillations, and measured the depth to which the electric oscillations penetrate in metals of different conductivity and magnetic permeability (the "skin effect"). Finally, in 1895 he furnished a complete theory of the phenomenon of electric resonance, involving a method of utilizing resonance experiments for the determination of the wavelengths, and especially of the damping (the logarithmic decrement) of the oscillations in the transmitter and the receiver of the electric oscillations. These methods contributed much to the development of wireless telegraphy. His papers on electric oscillations were published in Annalen der Physik (1891–1895). In 1895, he became professor of applied mechanics and mathematical physics at the Stockholm University where he had been lecturer since 1893. There he elucidated the fundamental interaction between fluid dynamics and thermodynamics. His major contribution was the primitive equations which are used in climate models. It was this work that inspired both V. Walfrid Ekman and Carl-Gustav Arvid Rossby to apply it to large-scale motions in the oceans and atmosphere and to make modern weather forecasting feasible. Bjerknes himself had foreseen the possible applications as early as 1904. This attack upon the meteorological problems from a hydrodynamical point of view was after 1906 supported by the Carnegie Institution of Washington, D.C., of which he became a research associate. Two introductory volumes, Statics and Kinematics, of a greater work, Dynamic Meteorology and Hydrography, were published in 1913 under the auspices of the Institution. In his 1906 work Fields of force, Bjerknes was the first to describe and mathematically derive translational forces on bubbles in an acoustic field, now known as Bjerknes forces. In his Vorlesungen über Hydrodynamische Fernkräfte nach C. A. Bjerknes Theorie (1900–1902) he gave the first complete mathematical and experimental exposition of the discoveries of his father, whose age and excessive self-criticism had prevented him from finishing his work himself. In a later book, Die Kraftfelder (1909), he stated the same theory in a very much generalized form according to methods of his own. In 1907, Bjerknes returned to the Royal Frederick University in Oslo before becoming professor of geophysics at the University of Leipzig in 1912. In 1916, he started the publication Synoptische Darstellung atmosphärischer Zustände über Europa. In 1917, he founded the Geophysical Institute, University of Bergen where he wrote his book On the Dynamics of the Circular Vortex with Applications to the Atmosphere and to Atmospheric Vortex and Wave Motion (1921), and laid the foundation for the Bergen School of Meteorology, which was not a literal school but a school of thought on how the practice of weather forecasting and meteorology should be undertaken. He was the originator of an improved and more scientific weather service, afterwards controlled by his son and collaborator, the meteorologist Jacob Bjerknes (1897–1975). From 1926 to his retirement in 1932, he held a position at the University of Oslo. He was elected a member of the Royal Swedish Academy of Sciences in 1905 and of the Pontifical Academy of Sciences in 1936 and a Fellow of the Royal Society. He was awarded the 1932 Symons Gold Medal of the Royal Meteorological Society. He died of heart problems in Oslo. In 1893, Bjerknes had married Honoria Bonnevie, who in earlier years assisted him much in his scientific work. Their son Jacob Aall Bonnevie Bjerknes also became a meteorologist. The craters Bjerknes on the Moon and Bjerknes on Mars are named in his honor. == References == == Further reading == M.R. Friedman (1989) "Appropriating the weather: Vilhelm Bjerknes and the construction of a modern meteorology". Cornell University Press. Pihl, Mogens (1970–1980). "Bjerknes, Vilhelm Frimann Koren". Dictionary of Scientific Biography. Vol. 2. New York: Charles Scribner's Sons. pp. 167–169. ISBN 978-0-684-10114-9. == External links == Family genealogy
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Wikipedia:Vilmos Totik#0
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Vilmos Totik (Mosonmagyaróvár, March 8, 1954) is a Hungarian mathematician, working in classical analysis, harmonic analysis, orthogonal polynomials, approximation theory, potential theory. He is a professor of the University of Szeged. Since 1989 he is also a part-time professor at the University of South Florida (Tampa). He received the Lester R. Ford Award in 2000 for his expository article A tale of two integrals. He is a corresponding member (1993), member of the Hungarian Academy of Sciences (2001). In 2015 he was elected as a fellow of the American Mathematical Society "for contributions to classical analysis and approximation theory and for exposition." == His books == Z. Ditzian, V. Totik: Moduli of smoothness, Springer Series in Computational Mathematics, 9, Springer-Verlag, New York, 1987. x+227 pp. ISBN 0-387-96536-X Herbert Stahl, Vilmos Totik: General orthogonal polynomials, Encyclopedia of Mathematics and its Applications, 43 Cambridge University Press, Cambridge, 1992. xii+250 pp. ISBN 0-521-41534-9 V. Totik: Weighted approximation with varying weight, Lecture Notes in Mathematics, 1569. Springer-Verlag, Berlin, vi+114 p. (1994). ISBN 3-540-57705-X Edward B. Saff, Vilmos Totik: Logarithmic potentials with external fields, Appendix B by Thomas Bloom. Grundlehren der Mathematischen Wissenschaften 316 Springer-Verlag, Berlin, 1997. xvi+505 pp. ISBN 3-540-57078-0 Péter Komjáth, Vilmos Totik: Problems and Theorems in Classical Set Theory, Springer-Verlag, Berlin, 2006. ISBN 0-387-30293-X Vilmos Totik: Metric Properties of Harmonic Measures, 163 pp, American Mathematical Society, 2006, ISBN 0-8218-3994-2 == References == == External links == Homepage at USF Vilmos Totik at the Mathematics Genealogy Project
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Wikipedia:Vinay V. Deodhar#0
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Vinay Vithal Deodhar (3 December 1948 – 18 January 2015) was a Professor Emeritus in the Department of Mathematics at Indiana University. He worked in the area of algebraic groups and representation theory. == Early life == Deodhar was born in Mumbai (Bombay), India in 1948. == Career == Deodhar earned his Ph.D. from the University of Mumbai in 1974 for his work On Central Extensions of Rational Points of Algebraic Groups done under the supervision of M. S. Raghunathan. After his doctorate, he was invited to join the School of Mathematics of the Tata Institute of Fundamental Research. Simultaneously he was a visiting scholar at the Institute for Advanced Study (IAS) in Princeton during 1975-77 and then a visiting professor at the Australian National University in Canberra. In 1981 he was appointed to a professorship at Indiana University, Bloomington, Indiana, where he remained until his death in 2015. He spent a further period as a visiting scholar at the IAS in 1992-93. == References == == External links == Vinay V. Deodhar at the Mathematics Genealogy Project
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Wikipedia:Vinayak Vatsal#0
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Vinayak Vatsal is a Canadian mathematician working in number theory and arithmetic geometry. == Education == Vatsal received his B.Sc. degree in 1992 from Stanford University and a Ph.D. (thesis title: Iwasawa Theory, modular forms and Artin representations) in 1997 from Princeton University under the supervision of Andrew Wiles who had just completed his proof of Fermat's Last Theorem. He then became a post-doctoral fellow at the University of Toronto. == Career and research == Vatsal joined the faculty at the University of British Columbia in 1999 where he still works today. Vatsal's contributions include his work on the Iwasawa theory of elliptic curves, a field which he approached using novel ideas from ergodic theory. Vatsal has received numerous accolades. He was a Sloan Fellow in 2002–2004 and a recipient of the André Aisenstadt Prize (2004), the Ribenboim Prize (2006) and the Coxeter–James Prize (2007). In 2008, he was an invited speaker at the 2008 International Congress of Mathematicians in Madrid. == Selected publications == Uniform distribution of Heegner Points, Inventiones Mathematicae, Vol. 148, 2002, pp. 1–48 (Proof of a conjecture of Barry Mazur) with Ralph Greenberg Iwasawa Invariants of Elliptic Curves, Inventiones Mathematicae, vol 142, 2000, pp. 17–63 Special values of anticyclotomic L-functions, Duke Mathematical Journal, vol. 116, 2003, pp. 219–261 with C. Cornut Nontriviality of Rankin-Selberg L-functions and CM points, in Burns, Kevin Buzzard, Nekovar (eds), L-functions and Galois Representations, Cambridge University Press, 2007, pp. 121–186 with C. Cornut CM points and quaternion algebras, Documenta Mathematica, volume 10, 2005 == References == == External links == Vinayak Vatsal Homepage at UBC
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Wikipedia:Vincent Reno#0
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Franklin Vincent Reno (14 May 1911 – 1 May 1990) was a mathematician and civilian employee at the United States Army Aberdeen Proving Ground in Maryland in the 1930s. Reno was a member of the "Karl group" of Soviet spies which was being handled by Whittaker Chambers until 1938. Reno confessed in late 1948 to his espionage activities on behalf of the GRU. He is listed as number "118th" in the Gorsky Memo. Reno was sentenced to three years in prison. == Biography == Reno was born in Salt Lake City, to a stock raiser and his wife from "Reno, Idaho" (likely Reno Ranch, Idaho). Reno graduated from Colorado University with "top honors" in mathematics in 1932. He was elected to Phi Beta Kappa in spring 1932 as Victor Reno. While doing graduate studies in astronomy at the University of Virginia in 1935 he joined the Communist Party under the name "Lance Clark." He then took a job at the national office of the Works Progress Administration, after which he resigned to become a Communist Party organizer in Maryland. He began working at Aberdeen Proving Ground in 1937 and continued there until his resignation in 1949. In 1945 he was "given the war department's gold medal for devising a complicated bomb table." He worked on the Norden bombsight and was said to have passed information on this device to Alger Hiss. In 1952 he pleaded guilty to not disclosing his Communist Party when he was being screened for the Aberdeen job. He was sentenced to three years in federal prison. Reno also collaborated with Edward J. McShane of the University of Virginia and John L. Kelley of the University of California on a book called Exterior Ballistics. The judge gave Reno a month's delay in reporting for his sentence so he could finish his work on the book. Reno died in 1990 at age 79. == See also == == References == == Sources == Vassiliev, Alexander (2003), Alexander Vassiliev's Notes on Anatoly Gorsky's December 1948 Memo on Compromised American Sources and Networks, retrieved 2012-04-21
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Wikipedia:Vincenzo Mollame#0
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Vincenzo Mollame (Naples, Kingdom of the Two Sicilies 4 July 1848 – Catania, 23 June 1912) was an Italian mathematician. Mollame was privately tutored by Achille Sanni and then studied Mathematics at the University of Naples Federico II. After obtaining his degree, he became a high-school teacher, first at Benevento and after that at Naples, starting in 1878. He became a professor at the University of Catania in 1880 and remained there for the rest of his career, having retired in 1911, a few months before his death. His research area was the theory of equations and he proved in 1890 that when a cubic polynomial with rational coefficients has three real roots but it is irreducible in Q[x] (the so-called casus irreducibilis), then the roots cannot be expressed from the coefficients using real radicals alone, that is, complex non-real numbers must be involved if one expresses the roots from the coefficients using radicals, probably unaware of the fact that Pierre Wantzel had already proved it in 1843. Molleme's research activity stopped in 1896, due to health problems. Mollame was the author of a textbook on determinants. == Notes == == External links == Short biography (in Italian)
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Wikipedia:Viorel P. Barbu#0
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Viorel P. Barbu (born 14 June 1941) is a Romanian mathematician, specializing in partial differential equations, control theory, and stochastic differential equations. == Biography == He was born in Deleni, Vaslui County, Romania. He attended the Mihail Kogălniceanu High School in Vaslui and then the Costache Negruzzi National College in Iași. Barbu completed his undergraduate degree at the Alexandru Ioan Cuza University of Iași in 1964, and his Ph.D. at the same university in 1969. His doctoral advisor was Adolf Haimovici; his dissertation thesis was titled Regularity Theory of Pseudodifferential Operators. He became a professor at the University of Iași in 1980. In 1993, he was elected a titular member of the Romanian Academy. In 2011 he was awarded the Order of the Star of Romania, Knight rank by President Traian Băsescu. == Bibliography == Some of his books and papers are: Analysis And Control Of Nonlinear Infinite Dimensional Systems Optimization, Optimal Control and Partial Differential Equations Nonlinear semigroups and differential equations in Banach spaces Hamilton-Jacobi Equations on Hilbert Space Stochastic Porous Media Equations Nonlinear Differential Equations of Monotone Types in Banach Spaces Convexity and Optimization in Banach Spaces Optimal Control of Variational Inequalities == References == == External links == Official website Official website
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Wikipedia:Virasena#0
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Acharya Virasena (792-853 CE), also spelt as Veerasena, was a Digambara monk and belonged to the lineage of Acharya Kundakunda. He was an Indian mathematician and Jain philosopher and scholar. He was also known as a famous orator and an accomplished poet. His most reputed work is the Jain treatise Dhavala. The late Dr. Hiralal Jain places the completion of this treatise in 816 AD. Virasena was a noted mathematician. He gave the derivation of the volume of a frustum by a sort of infinite procedure. He worked with the concept of ardhachheda: the number of times a number can be divided by 2. This coincides with the binary logarithm when applied to powers of two, but gives the 2-adic order rather than the logarithm for other integers. Virasena gave the approximate formula C = 3d + (16d+16)/113 to relate the circumference of a circle, C, to its diameter, d. For large values of d, this gives the approximation π ≈ 355/113 = 3.14159292..., which is more accurate than the approximation π ≈ 3.1416 given by Aryabhata in the Aryabhatiya. == Life == Virasena was proficient in astrology, grammar, logic, mathematics and prosody. He wrote Dhavala, a commentary on Jain canon Shatakhandagama. He also started the work on Jayadhavalaa which was completed by his disciples. He was among the jewels of Rashtrakuta Emperor Amoghavarsha. His lineage started with Chandrasena who initiated Aryanandi. Aryanandi initiated Virasena and Jayasena. Virasena initiated six disciples who were Dasharayguru, Jinasena, Vinayasena, Shripal, Padmasena and Devasena. Dasharayguru and Jinasena initiated Gunabhadra who later initiated Lokasena. Vinayasena initiated Kumarasena who started the Kashtha Sangha. == See also == Indian mathematics Umaswami Hemachandra == References == === Citations === === Sources === Jain, Pannalal, ed. (1951), Mahapurana Adipurana of Bhagavata Jinasenacharya, Bharatiya Jnanapitha Jaini, Padmanabh S. (1991), Gender and Salvation: Jaina Debates on the Spiritual Liberation of Women, University of California Press, ISBN 0-520-06820-3 Shah, Natubhai (2004) [First published in 1998], Jainism: The World of Conquerors, vol. I, Motilal Banarsidass, ISBN 81-208-1938-1 == External links == Media related to Virasena at Wikimedia Commons Singh, A. N. "Mathematics of Dhavala". Lucknow University. Translation of part of the Dhavala.
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Wikipedia:Virgil of Salzburg#0
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Virgil (c. 700– 27 November 784), also spelled Vergil, Vergilius, Virgilius, Feirgil or Fearghal, was an Irish priest and early astronomer. He left Ireland around 745, intending to visit the Holy Land; but, like many of his countrymen, he settled in Francia. Virgil served as abbot of Aghaboe, bishop of Ossory and later bishop of Salzburg. He was called "the Apostle of Carinthia" and "the geometer". == Biography == He originated from a noble family of Ireland, where his name was Feirgil or Fearghal, and is said to have been a descendant of Niall of the Nine Hostages. Feirgil was probably educated at the Iona monastery. In Annals of the Four Masters and Annals of Ulster, he is referenced as the Abbot of Aghaboe, in County Laois, where he was known as "the Geometer" because of his knowledge of geography. Around 745, he left Ireland, intending to visit the Holy Land; but, like many of his countrymen, who seemed to have adopted this practice as a work of piety, he settled down in France, where he was received with great favour by Pippin the Younger, who was then Mayor of the Palace under Childeric III of Franconia. He was an adviser to Pippin. He probably used a copy of the Collectio canonum Hibernensis (an Irish collection of canon law) to advise him to receive royal unction in 751, to assist his recognition as king Pippin III after the deposition of Childeric. After spending two years at Cressy, near Compiègne, he went to Bavaria, at the invitation of Duke Odilo, where he founded the monastery of Chiemsee, and within a year or two, was made Abbot of St Peter's Abbey at Salzburg. Among his notable accomplishments was the conversion of the Alpine Slavs to Christianity; he also sent missionaries to Hungary. As Abbot of St Peter's, he clashed with Saint Boniface. A priest having, through ignorance, conferred the Sacrament of Baptism using, in place of the correct formula, the words "Baptizo te in nomine patria et filia et spiritu sancta" (instead of "Baptizo te in nomine patris et filii et spiritus sancti"), Vergilius held that the sacrament had been validly conferred, but Boniface complained to Pope Zachary. The latter, however, decided in favour of Virgil. Later on, Boniface accused Virgil of spreading discord between himself and Duke Odilo of Bavaria and of teaching a doctrine in regard to men descended not from Adam, which was "contrary to the Scriptures". Pope Zachary's decision in this case was that "if it shall be clearly established that he professes belief in another world and other people existing beneath the earth, or in [another] sun and moon there, thou art to hold a council, and deprive him of his sacerdotal rank, and expel him from the church." The treatise in which Virgil expounded his doctrine no longer exists. Two things, however, are certain: first, that there was involved the problem of original sin and the universality of redemption; secondly, that Virgil succeeded in freeing himself from the charge of teaching a doctrine contrary to Scripture. It is likely that Boniface, already biased against Virgil because of the preceding case, misunderstood him, taking it for granted, perhaps, that if there are antipodes, the "other race of men" are not descendants of Adam and were not redeemed by Christ. After the martyrdom of Boniface, Virgil was made Bishop of Salzburg in 766 or 767 and laboured successfully for the upbuilding of his diocese as well as for the spread of Christianity in neighbouring heathen countries, especially in Carinthia. == Veneration == He is venerated as a saint in both the Catholic Church and the Eastern Orthodox Church. In 1233, he was formally canonized by Pope Gregory IX. His doctrine that the earth is a sphere was derived from the teaching of ancient geographers, and his belief in the existence of the antipodes was probably influenced by the accounts which the ancient Irish voyagers gave of their journeys. This, at least, is the opinion of Rettberg (Kirchengesch. Deutschlands, II, 236). === Dedications === Aside from being personally associated with Aghaboe Abbey and Salzburg Cathedral, a number of parishes around the world are dedicated to him, mostly being founded by small populations of far-flung Irish Catholics, like himself. There is a church dedicated to him in Broad Channel, Queens, New York, which merged with another parish in 2008. A parish in Morris Plains, New Jersey, is also dedicated to him. Fittingly for this Irish geometer who predicted antipodes, several churches in the Southern Hemisphere are dedicated to him. St Virgil's College in Hobart, Tasmania is named for him. There was a St Virgilius Church in Balclutha, New Zealand designed by Francis Petre which moved and was re-dedicated to Mary MacKillop, however the new chapel remains dedicated to Virgilius. === Art and culture === A large marble statue of him stands outside the doors of Salzburg Cathedral. A stained-glass window of St Virgil contemplating the antipodes sits in St John's College, University of Sydney. Sebastian Stief painted him amidst Salzburg's construction, Alec Szolomiak painted him, as did Jan Toorop, and Dhiraja McBryde. Yalumba, Australia's oldest family-owned winery, produces a Viognier named Virgilius. == See also == Modestus (Apostle of Carantania) Saint Vergilius of Salzburg, patron saint archive == Notes == == References == == Sources == Laistner, M.L.W. Thought and Letters in Western Europe: A.D. 500 to 900, 2nd. ed. Ithaca: Cornell Univ. Pr., 1955. ISBN 0-8014-9037-5 This article incorporates text from a publication now in the public domain: Turner, William (1912). "St. Vergilius of Salzburg". In Herbermann, Charles (ed.). Catholic Encyclopedia. Vol. 15. New York: Robert Appleton Company. == External links == Media related to Virgilius of Salzburg at Wikimedia Commons Saint Virgilius from the EWTN library
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Wikipedia:Vissarion Alekseyev#0
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Vissarion Grigorievich Alekseyev (Russian: Виссарион Григорьевич Алексеев; 18 June 1866 – 1943) was a Russian mathematician. 1909-1914 and 1917–1918 he was the rector of Tartu University. He was graduated from Moscow University. Since 1891 he worked at Tartu University. In 1920 he moved permanently to Estonia. He died in 1943 in Poland. == References ==
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Wikipedia:Vitaly Khonik#0
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Khonik Vitaly Alexandrovich (Russian: Хоник Виталий Александрович; born 17 December 1955) is a Russian physicist, doctor of physics and mathematics, professor, head of a laboratory researching the physics of non-crystalline materials, and head of the Department of General Physics at Voronezh State Pedagogical University (VSPU). He was born in Kemerovo, USSR. His laboratory collaborates with the Institute of Solid State Physics of the Russian Academy of Sciences, the Institute of Physics of the Slovak Academy of Sciences, the Institut für Materialphysik in Germany and the School of Mechanics and Civil Architecture of Northwestern Polytechical University in China. == Education, academic degrees and titles == 1994 - Professor 1992 - Doctor of Science (physics & mathematics), focusing on solid state physics 1991 - Senior researcher in solid state physics 1983 - Candidate for a doctoral degree in solid state physics 1978 - Graduated from Voronezh Polytechnic Institute (VPI), majoring in solid state physics == Employment history == 2010 to present - Head of the Department of General Physics at VSPU 1992 to 2010 - Professor at VSPU 1992 - Associate professor at VSPU 1991-1992 - Associate professor at VPI 1985-1991 - Senior researcher at VPI 1984-1985 - Junior researcher at VPI 1981-1983 - Doctoral student at VPI 1978-1981 - Engineer and physicist at VPI == Academic awards == Awarded the title "Soros Professor" in 1997, 1998 and 1999. Honored Worker in Higher Professional Education (2011). == International experience == July 2019 - Visiting professor at Northwestern Polytechical University, Xi'an, China July 2018 - Visiting professor at Northwestern Polytechical University, Xi'an, China October 2016 - Visiting professor at the Institute of Physics, Chinese Academy of Sciences, Beijing, China August 2012 - Visiting professor at the department of physics, University of Illinois at Urbana-Champaign, USA May 2009 - Guest professor at the school of materials science, Harbin Institute of Technology, China April 2007 – Guest professor at Roskilde University, Denmark January 2007 to February 2007 – Visiting scholar at the physics department, University of Illinois at Urbana-Champaign, USA January 2006 to March 2006 – Scholar of the Japanese Society for the Promotion of Science (JSPS) at the graduate school of natural science and technology of Kanazawa University, Japan January 2005 to February 2005 – Visiting scholar at the physics department, University of Illinois at Urbana-Champaign, USA April 2003 to August 2003 – Visiting scholar at the physics department, University of Illinois at Urbana-Champaign, USA October 2002 to December 2002 – Scholar of the German Service for Academic Exchanges (DAAD), Technical University Carolo-Wilhelmina, Braunschweig, Germany May 1999 to April 2000 – Associate professor of the mechanical system engineering department, Kanazawa University, Kanazawa, Japan Visiting professor at the Institute of Experimental Physics, Slovak Academy of Sciences, Kosice, Slovakia (two to four week visits in 1996, 1998 and 2001) == International conferences and workshops == Internal Friction and Ultrasonic Attenuation (ICIFUAS, Italy 1993, France 1996, Spain 2002) Mechanical Spectroscopy (Poland 2000) Structure of Non-Crystalline Solids (Czech Republic 1996) 18th International Congress on Glass (USA 1998) Physics of Amorphous Solids: Mechanical Properties and Plasticity (France, Les Houches, March 2010 ) ACAM Workshop on Multiscale Modelling of Amorphous Materials: from Structure to Mechanical Properties (Dublin, Ireland, July 2011) 8th International Discussion Meeting on Relaxations in Complex Systems (Wisla, Poland, July 2017). == Major scientific projects == Ministry of Education and Science of the Russian Federation, No 3.114.2014/К, "Nature of relaxation phenomena in non-crystalline metallic materials - new theoretical concepts and experiments", 2014–2016. Ministry of Education and Science of the Russian Federation, No 3.1310.2017/4.6, "Shear elasticity relaxation as a fundamental basis for the description and prediction of the physical properties of amorphous alloys", 2017–2019. Russian Science Foundation, No 20-62-46003, "Amorphous alloys: a new approach to the understanding of the defect structure and its influence on physical properties", 2020 – present. == References == == External links == "List of papers". hosting.vspu.ac.ru. Retrieved 2020-11-22.
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Wikipedia:Vitold Belevitch#0
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Vitold Belevitch (2 March 1921 – 26 December 1999) was a Belgian mathematician and electrical engineer of Russian origin who produced some important work in the field of electrical network theory. Born to parents fleeing the Bolsheviks, he settled in Belgium where he worked on early computer construction projects. Belevitch is responsible for a number of circuit theorems and introduced the now well-known scattering parameters. Belevitch had an interest in languages and found a mathematical derivation of Zipf's law. He also published on machine languages. Another field of interest was transmission lines, where he published on line coupling. He worked on telephone conferencing and introduced the mathematical construct of the conference matrix. == Early life == Belevitch was born 2 March 1921 in Terijoki, Karelia, now incorporated into Russia, but at the time part of Finland. Belevitch's parents were Russian and his mother was an ethnic Pole. They were attempting to flee from their home in Petrograd (St Petersburg) in Russia to escape the Bolshevik revolution, which Belevitch's father opposed. Belevitch's heavily pregnant mother succeeded in crossing the border into Finland and continued on to Helsinki after Vitold was born, where the birth was registered. She headed for Helsinki because her husband's father was principal of the Russian school there. Belevitch's father was arrested before he could follow and was deported to Siberia, where he died without ever seeing his son. In 1926 Belevitch, while still a small child, emigrated with his mother to Belgium. == Education == Belevitch was educated in French in Belgium, until July 1936 at the Notre-Dame de la Paix College at Namur. In 1937, aged 16, he enrolled at the Université Catholique de Louvain where he studied electrical and mechanical engineering, graduating in 1942. Belevitch gained his PhD in applied sciences at the same university in 1945. His sponsor was Charles Lambert Manneback and his second advisor was Wilhelm Cauer, the founder of the field of network synthesis. From 1953 until 1985 Belevitch lectured at the university. He taught circuit theory and other mathematical subjects related to electrical science. In 1960 he became a special professor (buitengewoon hoogleraar). Although Belevitch worked as an electrical engineer, his primary interest was mathematics, especially algebra. There was a tradition in Belgium of the most gifted mathematicians entering engineering rather than pure mathematics or physics. Belevitch showed his mathematical leanings by preferring the use of blackboard and chalk to any audio-visual aids during lectures. He even lectured in this way when presenting the opening lecture to a large audience at an international conference at the IEE in London. == Career == After graduating in 1942, Belevitch joined the Bell Telephone Manufacturing Company (BTMC) in Antwerp, originally part of the International Bell Telephone Company headquartered in Brussels but, along with their other European holdings, sold to International Telephone and Telegraph (ITT) in 1925. At BTMC Belevitch became head of the transmission department. It was here that he came into contact with Wilhelm Cauer who became a great influence on him. Cauer was one of the leading circuit theorists of the day and at the time worked for Mix & Genest in Berlin, a sister company under the ITT umbrella. Cauer died during the Second World War but Belevitch long after continued to consider his works to be the highest authority on matters of circuit theory. From 1951 Belevitch was involved in the design of electronic computers which BTMC were developing for the Belgian government. The purpose of this program was to "catch up" with the advances made in the English-speaking world during the war. It resulted in the construction of the Machine mathématique IRSIA-FNRS. From 1952 Belevitch represented the electrical engineering aspect of this project. In 1955 Belevitch became director of the Belgian Computing Centre (Comité d'Étude et d'Exploitation des Calculateurs Électroniques) in Brussels which operated this computer for the government. Initially, only the 17-rack prototype was operational. One of the first tasks to which it was put was the calculation of Bessel functions. The full 34-rack machine was moved from Antwerp and put into service in 1957. Belevitch used this machine to investigate transcendental functions. In 1963 Belevitch became head of the newly formed Laboratoire de Recherche MBLE (later Philips Research Laboratories Belgium) under the Philips director of research Hendrik Casimir in Eindhoven. This facility specialised in applied mathematics for Philips and was heavily involved in computing research. Belevitch stayed in this post until his retirement in November 1984. Belevitch died on 26 December 1999. He is survived by a daughter, but not his wife. == Works == Belevitch is best known for his contributions to circuit theory, particularly the mathematical basis of filters, modulators, coupled lines, and non-linear circuits. He was on the editorial board of the International Journal of Circuit Theory from its foundation in 1973. He also made major contributions in information theory, electronic computers, mathematics and linguistics. Belevitch dominated international conferences and was prone to asking searching questions of the presenters of papers, often causing them some discomfort. The organiser of one conference at Birmingham University in 1959 made Belevitch the chairman of the session in which the organiser gave his own presentation. It seems he did this to restrain Belevitch from asking questions. Belevitch stopped attending conferences in the mid-1970s with the exception of the IEEE International Symposium on Circuits and Systems in Montreal in 1984 in order to receive the IEEE Centennial Medal. === Circuit theory === ==== Scattering matrix ==== It was in his 1945 dissertation that Belevitch first introduced the important idea of the scattering matrix (called repartition matrix by Belevitch). This work was reproduced in part in a later paper by Belevitch, Transmission Losses in 2n-terminal Networks. Belgium was occupied by Nazi Germany for most of World War II and this prevented Belevitch from any communication with American colleagues. It was only after the war that it was discovered that the same idea, under the scattering matrix name, had independently been used by American scientists developing military radars. The American work by Montgomery, Dicke and Purcell was published in 1948. Belevitch in his work had applied scattering matrices to lumped-element circuits and was certainly the first to do so, whereas the Americans were concerned with the distributed-element circuits used at microwave frequencies in radar. Belevitch produced a textbook, Classical Network Theory, first published in 1968 which comprehensively covered the field of passive one-port, and multiport circuits. In this work he made extensive use of the now-established S parameters from the scattering matrix concept, thus succeeding in welding the field into a coherent whole. The eponymous Belevitch's theorem, explained in this book, provides a method of determining whether or not it is possible to construct a passive, lossless circuit from discrete elements (that is, a circuit consisting only of inductors and capacitors) that represents a given scattering matrix. ==== Telephone conferencing ==== Belevitch introduced the mathematical concept of conference matrices in 1950, so called because they originally arose in connection with a problem Belevitch was working on concerning telephone conferencing. However, they have applications in a range of other fields as well as being of interest to pure mathematics. Belevitch was studying setting up telephone conferencing by connecting together ideal transformers. It turns out that a necessary condition for setting up a conference with n telephone ports and ideal signal loss is the existence of an n×n conference matrix. Ideal signal loss means the loss is only that due to splitting the signal between conference subscribers – there is no dissipation within the conference network. The existence of conference matrices is not a trivial question; they do not exist for all values of n. Values of n for which they exist are always of the form 4k+2 (k integer) but this is not, by itself, a sufficient condition. Conference matrices exist for n of 2, 6, 10, 14, 18, 26, 30, 38 and 42. They do not exist for n of 22 or 34. Belevitch obtained complete solutions for all n up to 38 and also noted that n=66 had multiple solutions. ==== Other work on circuits ==== Belevitch wrote a comprehensive summary of the history of circuit theory. He also had an interest in transmission lines, and published several papers on the subject. They include papers on skin effects and coupling between lines ("crosstalk") due to asymmetry. Belevitch first introduced the great factorization theorem in which he gives a factorization of paraunitary matrices. Paraunitary matrices occur in the construction of filter banks used in multirate digital systems. Apparently, Belevitch's work is obscure and difficult to understand. A much more frequently cited version of this theorem was later published by P. P. Vaidyanathan. === Linguistics === Belevitch was educated in French but continued to speak Russian to his mother until she died. In fact, he was able to speak many languages, and could read even more. He studied Sanskrit and the etymology of Indo-European languages. Belevitch wrote a book on human and machine languages in which he explored the idea of applying the mathematics of information theory to obtain results regarding human languages. The book highlighted the difficulties for machine understanding of language for which there was some naive enthusiasm amongst cybernetics researchers in the 1950s. Belevitch also wrote a paper, On the Statistical Laws of Linguistic Distribution, which gives a derivation for the well-known empirical relationship, Zipf's law. This law, and the more complex Mandelbrot law, provide a relationship between the frequency of word occurrence in languages and the word's rank. In the simplest form of Zipf's law, frequency is inversely proportional to rank. Belevitch expressed a large class of statistical distributions (not only the normal distribution) in terms of rank and then expanded each expression into a Taylor series. In every case Belevitch obtained the remarkable result that a first order truncation of the series resulted in Zipf's law. Further, a second-order truncation of the Taylor series resulted in Mandelbrot's law. This gives some insight into the reason why Zipf's law has been found experimentally to hold in such a wide variety of languages. === Control systems === Belevitch played a part in developing a mathematical test for determining the controllability of linear control systems. A system is controllable if it can be moved from one state to another through the system state space in a finite time by application of control inputs. This test is known as the Popov-Belevitch-Hautus, or PBH, test. There is also a PBH test for determining the observability of a system – that is, the ability to determine the state of a system in finite time solely from the system's own outputs. The PBH test was originally discovered by Elmer G. Gilbert in 1963, but Gilbert's version only applied to systems that could be represented by a diagonalizable matrix. The test was subsequently generalised by Vasile M. Popov (in 1966), Belevitch (in Classical Network Theory, 1968) and Malo Hautus in 1969. == IEEE and honours == Belevitch was a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and was vice-chair of the Benelux section when it was formed in 1959. He was awarded the IEEE Centennial Medal, and in 1993, the Society Award (now called Mac Van Valkenburg Award) of the IEEE Circuits and Systems Society. He was also a member of the North Rhine-Westphalian Academy of Sciences. Belevitch received an honorary doctoral degree in 1975 from the Technical University of Munich, and another from the École Polytechnique Fédérale de Lausanne, Switzerland, in 1978. He was also rewarded with Belgian royal medals. Since 2003, the IEEE Circuits and Systems Society has instituted a Vitold Belevitch award for work in circuit theory. The award is presented biennially at the European Conference on Circuit Theory & Design. == Selected publications == Belevitch was a prolific publisher with around 4000 pages of scientific output. He was publishing throughout his career right up to, and beyond, his retirement in 1984. === Books === Langage des Machines et Langage Humain, Bruxelles: Office de publicité, 1956 OCLC 8998282 (in French). Théorie des Circuits de Télécommunication, Louvain: Librairie Universitaire, 1957 OCLC 3531476 (in French). Théorie des Circuits Nonlinéaires en Régime Alternatif: Redresseurs, Modulateurs, Oscillateurs, Louvain: Uystpruyst, 1959 OCLC 637334683 (in French). Classical Network Theory, San Francisco: Holden-Day, 1968 OCLC 413916. === Journal articles === "Extension of Norton's method of impedance transformation to band-pass filters", Electrical Communication, vol.24, no.1, pp. 59–65, March 1947. "Insertion loss and effective phase shift in composite filters at cut-off frequencies", Electrical Communication, vol.24, no.2, pp. 192–194, June 1947. "Transmission losses in 2n-terminal networks", Journal of Applied Physics, vol.19, No. 7, pp. 636–638, 1948. "Development in the design of filters", Electrical Communication, vol.26, no.1, pp. 84–98, March 1949. "Theory of 2n-terminal networks with application to conference telephony", Electrical Communication, vol.27, no.3, pp. 231–244, September 1950. "Topics in the design of insertion loss filters", IRE Transactions on Circuit Theory, vol.2, iss.4, pp. 337–346, December 1955. "Théorie de l'information et statistique linguistique", Académie Royale de Belgique: Bulletin de la Classe des Sciences, series 5, vol.42, pp. 419–436, 1956. (in French) "On the statistical laws of linguistic distribution", Annales de la Société Scientifique de Bruxelles, vol.3, iss.73, pp. 310–326, 1959 ISSN 0037-959X. (in French) "Summary of the history of circuit theory", Proceedings of the IRE, vol.50, iss.5, pp. 848–855, May 1962. "Factorization of scattering matrices with applications to passive network synthesis", Philips Research Reports, vol.18, pp. 275–317, 1963 ISSN 0031-7918. "Interpolation matrices", Philips Research Reports, vol.25, pp. 337–369, 1970 ISSN 0031-7918. "On the realizability of non-rational positive real functions", International Journal of Circuit Theory and Applications, vol.1, iss.1, pp. 17–30, March 1973. doi:10.1002/cta.4490010105 "Theory of the proximity effect in multiwire cables", Philips Research Reports, vol.32, pp. 16–43, 96-177, 1977 ISSN 0031-7918. "The Gauss hypergeometric ratio as a positive real function", SIAM Journal on Mathematical Analysis, vol.13, pp. 1024–1040, 1982. "Ideal rectifier n-ports are solvable", International Journal of Circuit Theory and Applications, vol.15, iss.2, pp. 171–180, April 1987. doi:10.1002/cta.4490150206 == Notes == == References == == Bibliography == Belevitch, Vitold "Summary of the history of circuit theory", Proceedings of the IRE, vol.50, iss.5, pp. 848–855, May 1962. Chen, Ben M.; Lin, Zongli; Shamash, Yacov Linear Systems Theory: a Structural Decomposition Approach, Boston: Birkhäuser, 2004 ISBN 0-8176-3779-6. Colbourn, Charles J.; Dinitz, Jeffrey H. Handbook of Combinatorial Designs, Boca Raton, Florida: Chapman and Hall/CRC Press, 2007 ISBN 1-58488-506-8. Dutoit, Thierry (ed) "Vitold Belevitch (2 March 1921 - 26 December 1999)", Théorie des Circuits et Traitement du Signal Lab, accessed and archived 21 May 2011. Fettweis, Alfred "In memoriam, Vitold Belevitch", IEEE Transactions on Circuits and Systems, vol.47, iss.5, pp. 613–614, May 2000. Fettweis, Alfred (in Dutoit) "Reminiscing Vitold Belevitch (1921–1999)", European Conference on Circuit Theory and Design 2001, Plenary session, Helsinki. Huurdeman, Anton A. The Worldwide History of Telecommunications, New Jersey: Wiley-IEEE, 2003 ISBN 0-471-20505-2. Kisačanin, Branislav; Agarwal, Gyan C. Linear Control Systems, New York: Kluwer Academic/Plenum Publishers, 2002 ISBN 0-306-46743-7. van Lint, Jacobus Hendricus; Wilson, Richard Michael A Course in Combinatorics, Cambridge: Cambridge University Press, 2001 ISBN 0-521-00601-5. Mols, Sandra; d'Udekem-Gevers, Marie "Disseminating electronics: Bell Telephone and the emergence of electronic computing expertise in post-war Belgium, c.1945–c.1960", History of Telecommunications Conference, 2008, pp. 102–109 Paris: 11–12 September 2008 ISBN 978-1-4244-2530-3. Montgomery, Carol Gray; Dicke, Robert Henry; Purcell, Edward M. Principles of microwave circuits, London: Peter Peregrinus Ltd., 1987 ISBN 0-86341-100-2 (1948 edition is New York: McGraw-Hill, OCLC 2205224). Rockmore, Daniel Nahum; Healy, Dennis M. Modern Signal Processing, Cambridge: Cambridge University Press, 2004 ISBN 0-521-82706-X. Strang, Gilbert; Nguyen, Truong Wavelets and Filter Banks, Wellesley, MA: Wellesley-Cambridge Press 1996 ISBN 0-9614088-7-1. Stinson, Douglas Robert Combinatorial Designs: Constructions and Analysis, New York: Springer, 2004 ISBN 0-387-95487-2. Valkenburg, Mac Elwyn Van Circuit Theory: Foundations and Classical Contributions, Stroudsburg, Pennsylvania: Dowden, Hutchinson & Ross, 1974 ISBN 0-87933-084-8. Vaidyanathan, P. P. Multirate systems and filter banks, Englewood Cliffs, NJ: PTR Prentice Hall, 1993 ISBN 0-13-605718-7. Vandewalle, Joos "In memoriam – Vitold Belevitch", International Journal of Circuit Theory and Applications, vol.28, iss.5, pp. 429–430, September/October 2000. doi:10.1002/1097-007X(200009/10)28:5<429::AID-CTA121>3.0.CO;2-6 de Vries, Marc; Boersma, Kees 80 years of research at the Philips Natuurkundig Laboratorium (1914-1994), Amsterdam University Press, 2005 ISBN 90-8555-051-3. Walker, Mark Science and Ideology: a Comparative History, Routledge, 2003 ISBN 0-415-27122-3. == Further reading == Courtois, P.J. "Vitold Belevitch", éditions académia, ISBN 978-2-8061-0162-4 Courtois, P.J., The Belgian Electronic Mathematical Machine (1951-1962). An Account. In "Randell’s Tales: a Festschrift recognising the contributions of Brian Randell" Cliff Jones & John Lloyd, Ed. Volume 6875 of the Lecture Notes in Computer Science Series. Springer Verlag, 2011. Courtois, P.J., Belevitch, V. (1921-1999). Notice Biographique. Volume X of the "Nouvelle Biographie Nationale de l’Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique ”. Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, 2009, pages 35–42.
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Wikipedia:Vittorio Francesco Stancari#0
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Vittorio Francesco Stancari (1678 – 1709) was a professor of mathematics at the University of Bologna who undertook research into the measurement of sounds, and into optics and hydrostatics. == Career == Vittorio Francesco Stancari was born in Bologna in 1678. In 1698 he became a professor of mathematics at the University of Bologna. Stancari was one of a group of young men at the University who became interested in the techniques of Cartesian geometry and differential calculus, and who engaged in experiments and astronomical observation. Others were Eustachio Manfredi, his brother Gabriele Manfredi and Giuseppe Sentenziola Verzaglia. Of these, Gabriele Manfredi developed the most advanced understanding of mathematics. Stancari was awarded the chair of infinitesimal calculus in Bologna in 1708. He died in Bologna in 1709, aged about 31. == Work == Stancari's dissertations and manuscripts show that he applied Leibnizian calculus to problems of physics, hydrodynamics, meteorology and mechanics. He was also aware of Sir Isaac Newton's Principia Mathematica, and discussed Newton in lectures before the Accademia degli Inquieti in Bologna. Stancari developed a method of measuring the pitch of sound in 1706, using foil that was excited into vibration by rotating toothed wheels. Working in the observatory founded by Count Marsigli, Stancari and Eustachio Manfredi discovered the comet C/1707 W1 in the evening of 25 November 1707. They described it as visible to the naked eye, white, irregular and with a short, faint tail. It had the same apparent size as Jupiter. Stancari experimented with Guillaume Amontons' air thermometer, where air in the bulb pushes up a column of mercury as it expands due to rising temperature. He discovered that the humidity of the air in the bulb had a significant effect on the readings. == Bibliography == == References == Citations Sources
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Wikipedia:Vittorio Grünwald#0
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Vittorio Grünwald (Verona, Italy, 13 June 1855 – Florence, Italy, March 1943) was an Italian professor of mathematics and German language. His father Guglielmo (Willhelm) Grünwald (son of Aronne and Regina) was Hungarian, his mother Fortuna Marini (daughter of Mandolino Marini and Ricca Bassani) was Italian. In 1861 he moved to Hungary with his family, then came back in 1877 to Verona, later in November 1885 they moved to Brescia, and then to Venice. He studied at the Technische Universität Wien, where he graduated in mathematics. After coming back to Italy, he taught mathematics and German language in several schools (such as in Livorno and Venice), and then he settled in Florence. He married Dora Olschky, born in Berlin, and had three kids: Marta Grünwald, Beniamino (Benno) Grünwald, and Emanuele Grünwald. He was a librarian and a teacher at the Rabbinical College of Florence. He died at 88 in Florence, a few months before Nazi's persecutions hit Jewish families in Central Italy. He published several contributions in mathematics, including a seminal work on negative numerical bases. He also published an Italian-German vocabulary. == References == Vittorio Grünwald. Saggio di aritmetica non decimale con applicazioni del calcolo duodecima/e e trigesimale a problemi sui numeri complessi (Verona, 1884) Vittorio Grünwald. Intorno all'aritmetica dei sistemi numerici a base negativa con particolare riguardo al sistema numerico a base negativo-decimale per lo studio delle sue analogie coll'aritmetica ordinaria (decimale), Giornale di Matematiche di Battaglini (1885), 203-221, 367 Vittorio Grünwald and Garibaldi Menotti Gatti, Vocabolario delle lingue Italiana e Tedesca. Ed. Belforte. Gianfranco Di Segni, In ricordo del prof. Vittorio Grünwald, Firenze Ebraica, Anno 25 n. 5, Settembre-Ottobre 2012.
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Wikipedia:Vivek Shende#0
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Vivek Vijay Shende is an American mathematician known for his work on algebraic geometry, symplectic geometry and quantum computing. He is a professor of Quantum Mathematics at Syddansk Universitet while on leave from University of California Berkeley. == Doctoral studies and early career == Shende defended his Ph.D. dissertation "Hilbert schemes of points on integral plane curves" at Princeton University in 2011 under the supervision of Rahul Pandharipande. From 2011 to 2013, he was a Simons Postdoctoral Fellow at MIT mentored by Paul Seidel. Shende joined Berkeley as an assistant professor in 2013 and became an associate professor in 2019. He supervised at least four doctoral degrees at Berkeley. == Awards and accomplishments == In 2021, after moving to Denmark, Shende received sizable grants intended to support the creation of a new research group. The Danish National Research Foundation awarded Shende its DNRF Chair. The Villum Foundation funded Shende's research in mathematical aspects of String theory through the Villum Investigator program. This is one of the largest and most prestigious grants for individual researchers in Denmark. As a Berkeley professor, Shende received the National Science Foundation CAREER Award in 2017 and a Sloan Research Fellowship in Mathematics in 2015. In 2010, Shende proved, together with Martijn Kool and Richard Thomas, the Göttsche conjecture on the universality of formulas counting nodal curves on surfaces, a problem in algebraic geometry whose history stretches back more than a century. During his undergraduate studies at the University of Michigan, he performed computer science research with Igor L. Markov and John P. Hayes. Shende shared in 2004 the IEEE Donald O. Pederson Award in Solid-State Circuits as the lead author of the work on synthesis of reversible logic circuits. This paper proved the existence of reversible circuits that implement certain permutations and developed algorithms for finding such circuits. Shende was also the lead author of the work on synthesis of quantum circuits that developed the quantum Shannon decomposition and algorithms for finding asymptotically optimal quantum circuits that implement a given n {\displaystyle n} -qubit unitary matrix, as well as quantum circuits that construct a given n {\displaystyle n} -qubit quantum state. Shende obtained formulas and algorithms for implementing smallest possible quantum circuits for 2-qubit unitary matrices. For the 3-qubit Toffoli gate, he proved that six CNOT gates are necessary in a circuit that implements it, showing that the widely used six-CNOT decomposition is optimal. These publications are highly cited (per Google Scholar) and their results laid the foundation of compilers for quantum computers. == Mathematics education == Shende taught college-level Calculus, Discrete Mathematics as well as Linear Algebra and Differential Equations courses at Berkeley. In 2021 he cosigned, along with many professional mathematicians, an open letter to Governor Gavin Newsom and other California officials asking to replace the proposed new California Math curriculum framework. The framework was adopted in 2023 despite these objections. == References == == External links == Vivek Shende publications indexed by Google Scholar Vivek Shende at DBLP Bibliography Server
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Wikipedia:Viveka Erlandsson#0
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Viveka Erlandsson is a Swedish mathematician specialising in low-dimensional topology and geometry, and known in particular for extending the work of Maryam Mirzakhani on counting geodesics on hyperbolic manifolds. She is a lecturer at the University of Bristol and in a part position an associate professor at UiT The Arctic University of Norway. == Education and career == Erlandsson earned a bachelor's degree in applied mathematics from San Francisco State University in 2004, and continued at the same university for a master's degree in 2006. She became a lecturer at Baruch College and Hunter College in the City University of New York system, while pursuing a doctorate in mathematics through the Graduate Center of the City University of New York, which she completed in 2013. Her dissertation, The Margulis region in hyperbolic 4-space, was supervised by Ara Basmajian. After postdoctoral research at Aalto University and the University of Helsinki in Finland, she became a lecturer in mathematics at the University of Bristol in 2017. == Book == Erlandsson is the coauthor of the book Geodesic Currents and Mirzakhani’s Curve Counting, with Juan Souto, to be published by Springer in 2022. == Recognition == Erlandsson is the 2021 winner of the Anne Bennett Prize of the London Mathematical Society, given to her "for her outstanding achievements in geometry and topology and her inspirational active role in promoting women mathematicians". She was a 2024 recipient of the Whitehead Prize, "for her outstanding work on curve counting on surfaces" and for her "extraordinary rigidity theorem for bounce sequences associated to billiard tables". == References == == External links == Home page Viveka Erlandsson publications indexed by Google Scholar
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Wikipedia:Viviane Baladi#0
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Viviane Baladi (born 23 May 1963) is a mathematician who works as a director of research at the Centre national de la recherche scientifique (CNRS) in France. Originally Swiss, she has become a naturalized citizen of France. Her research concerns dynamical systems. == Education and career == Baladi earned master's degrees in mathematics and computer science in 1986 from the University of Geneva. She stayed in Geneva for her doctoral studies, finishing a Ph.D. in 1989 under the supervision of Jean-Pierre Eckmann, with a dissertation concerning the zeta functions of dynamical systems. She worked at CNRS beginning in 1990, with a leave of absence from 1993 to 1999 when she taught at ETH Zurich and the University of Geneva. She also spent a year as a professor at the University of Copenhagen in 2012–2013. == Books == She is the author of the book Positive Transfer Operators and Decay of Correlation (Advanced Series in Nonlinear Dynamics 16, World Scientific, 2000) and of Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps: A Functional Approach (Ergebnisse der Mathematik und ihrer Grenzgebiete 68, Springer, 2018). == Recognition == She was an invited speaker at the International Congress of Mathematicians in 2014, speaking in the section on "Dynamical Systems and Ordinary Differential Equations". She became a member of the Academia Europaea in 2018. Baladi was awarded the CNRS Silver Medal in 2019. == References == == External links == Home page Viviane Baladi publications indexed by Google Scholar
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Wikipedia:Vivien Challis#0
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Vivien Joy Challis is an Australian applied mathematician whose research involves topology optimisation through the level-set method and its application to bone implants, piezoelectric metamaterials, and robotics. She is a senior lecturer in applied and computational mathematics at the Queensland University of Technology. == Education and career == Challis has a PhD from the University of Queensland, completed in 2009. Her doctoral dissertation, Multi-Property Topology Optimisation with the Level-Set Method, was jointly supervised by Anthony P. Roberts and Andrew H. Wilkins. She remained at the university as a postdoctoral researcher and lecturer until moving to the Queensland University of Technology as a lecturer in 2019. In 2021, she became a senior lecturer. == Recognition == Challis is the 2024 recipient of the J. H. Michell Medal of ANZIAM. == References == == External links == Vivien Challis publications indexed by Google Scholar
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Wikipedia:Viète's formula#0
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In mathematics, Viète's formula is the following infinite product of nested radicals representing twice the reciprocal of the mathematical constant π: 2 π = 2 2 ⋅ 2 + 2 2 ⋅ 2 + 2 + 2 2 ⋯ {\displaystyle {\frac {2}{\pi }}={\frac {\sqrt {2}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2}}}}{2}}\cdot {\frac {\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}{2}}\cdots } It can also be represented as 2 π = ∏ n = 1 ∞ cos π 2 n + 1 . {\displaystyle {\frac {2}{\pi }}=\prod _{n=1}^{\infty }\cos {\frac {\pi }{2^{n+1}}}.} The formula is named after François Viète, who published it in 1593. As the first formula of European mathematics to represent an infinite process, it can be given a rigorous meaning as a limit expression and marks the beginning of mathematical analysis. It has linear convergence and can be used for calculations of π, but other methods before and since have led to greater accuracy. It has also been used in calculations of the behavior of systems of springs and masses and as a motivating example for the concept of statistical independence. The formula can be derived as a telescoping product of either the areas or perimeters of nested polygons converging to a circle. Alternatively, repeated use of the half-angle formula from trigonometry leads to a generalized formula, discovered by Leonhard Euler, that has Viète's formula as a special case. Many similar formulas involving nested roots or infinite products are now known. == Significance == François Viète (1540–1603) was a French lawyer, privy councillor to two French kings, and amateur mathematician. He published this formula in 1593 in his work Variorum de rebus mathematicis responsorum, liber VIII. At this time, methods for approximating π to (in principle) arbitrary accuracy had long been known. Viète's own method can be interpreted as a variation of an idea of Archimedes of approximating the circumference of a circle by the perimeter of a many-sided polygon, used by Archimedes to find the approximation 223 71 < π < 22 7 . {\displaystyle {\frac {223}{71}}<\pi <{\frac {22}{7}}.} By publishing his method as a mathematical formula, Viète formulated the first instance of an infinite product known in mathematics, and the first example of an explicit formula for the exact value of π. As the first representation in European mathematics of a number as the result of an infinite process rather than of a finite calculation, Eli Maor highlights Viète's formula as marking the beginning of mathematical analysis and Jonathan Borwein calls its appearance "the dawn of modern mathematics". Using his formula, Viète calculated π to an accuracy of nine decimal digits. However, this was not the most accurate approximation to π known at the time, as the Persian mathematician Jamshīd al-Kāshī had calculated π to an accuracy of nine sexagesimal digits and 16 decimal digits in 1424. Not long after Viète published his formula, Ludolph van Ceulen used a method closely related to Viète's to calculate 35 digits of π, which were published only after van Ceulen's death in 1610. Beyond its mathematical and historical significance, Viète's formula can be used to explain the different speeds of waves of different frequencies in an infinite chain of springs and masses, and the appearance of π in the limiting behavior of these speeds. Additionally, a derivation of this formula as a product of integrals involving the Rademacher system, equal to the integral of products of the same functions, provides a motivating example for the concept of statistical independence. == Interpretation and convergence == Viète's formula may be rewritten and understood as a limit expression lim n → ∞ ∏ i = 1 n a i 2 = 2 π , {\displaystyle \lim _{n\rightarrow \infty }\prod _{i=1}^{n}{\frac {a_{i}}{2}}={\frac {2}{\pi }},} where a 1 = 2 a n = 2 + a n − 1 . {\displaystyle {\begin{aligned}a_{1}&={\sqrt {2}}\\a_{n}&={\sqrt {2+a_{n-1}}}.\end{aligned}}} For each choice of n {\displaystyle n} , the expression in the limit is a finite product, and as n {\displaystyle n} gets arbitrarily large, these finite products have values that approach the value of Viète's formula arbitrarily closely. Viète did his work long before the concepts of limits and rigorous proofs of convergence were developed in mathematics; the first proof that this limit exists was not given until the work of Ferdinand Rudio in 1891. The rate of convergence of a limit governs the number of terms of the expression needed to achieve a given number of digits of accuracy. In Viète's formula, the numbers of terms and digits are proportional to each other: the product of the first n terms in the limit gives an expression for π that is accurate to approximately 0.6n digits. This convergence rate compares very favorably with the Wallis product, a later infinite product formula for π. Although Viète himself used his formula to calculate π only with nine-digit accuracy, an accelerated version of his formula has been used to calculate π to hundreds of thousands of digits. == Related formulas == Viète's formula may be obtained as a special case of a formula for the sinc function that has often been attributed to Leonhard Euler, more than a century later: sin x x = cos x 2 ⋅ cos x 4 ⋅ cos x 8 ⋯ {\displaystyle {\frac {\sin x}{x}}=\cos {\frac {x}{2}}\cdot \cos {\frac {x}{4}}\cdot \cos {\frac {x}{8}}\cdots } Substituting x = π/2 in this formula yields 2 π = cos π 4 ⋅ cos π 8 ⋅ cos π 16 ⋯ {\displaystyle {\frac {2}{\pi }}=\cos {\frac {\pi }{4}}\cdot \cos {\frac {\pi }{8}}\cdot \cos {\frac {\pi }{16}}\cdots } Then, expressing each term of the product on the right as a function of earlier terms using the half-angle formula: cos x 2 = 1 + cos x 2 {\displaystyle \cos {\frac {x}{2}}={\sqrt {\frac {1+\cos x}{2}}}} gives Viète's formula. It is also possible to derive from Viète's formula a related formula for π that still involves nested square roots of two, but uses only one multiplication: π = lim k → ∞ 2 k 2 − 2 + 2 + 2 + 2 + ⋯ + 2 ⏟ k square roots , {\displaystyle \pi =\lim _{k\to \infty }2^{k}\underbrace {\sqrt {2-{\sqrt {2+{\sqrt {2+{\sqrt {2+{\sqrt {2+\cdots +{\sqrt {2}}}}}}}}}}}} _{k{\text{ square roots}}},} which can be rewritten compactly as π = lim k → ∞ 2 k 2 − a k , a 1 = 0 , a k = 2 + a k − 1 . {\displaystyle {\begin{aligned}\pi &=\lim _{k\to \infty }2^{k}{\sqrt {2-a_{k}}},\\a_{1}&=0,\\a_{k}&={\sqrt {2+a_{k-1}}}.\end{aligned}}} Many formulae for π and other constants such as the golden ratio are now known, similar to Viète's in their use of either nested radicals or infinite products of trigonometric functions. == Derivation == Viète obtained his formula by comparing the areas of regular polygons with 2n and 2n + 1 sides inscribed in a circle. The first term in the product, 2 / 2 {\displaystyle {\sqrt {2}}/2} , is the ratio of areas of a square and an octagon, the second term is the ratio of areas of an octagon and a hexadecagon, etc. Thus, the product telescopes to give the ratio of areas of a square (the initial polygon in the sequence) to a circle (the limiting case of a 2n-gon). Alternatively, the terms in the product may be instead interpreted as ratios of perimeters of the same sequence of polygons, starting with the ratio of perimeters of a digon (the diameter of the circle, counted twice) and a square, the ratio of perimeters of a square and an octagon, etc. Another derivation is possible based on trigonometric identities and Euler's formula. Repeatedly applying the double-angle formula sin x = 2 sin x 2 cos x 2 , {\displaystyle \sin x=2\sin {\frac {x}{2}}\cos {\frac {x}{2}},} leads to a proof by mathematical induction that, for all positive integers n, sin x = 2 n sin x 2 n ( ∏ i = 1 n cos x 2 i ) . {\displaystyle \sin x=2^{n}\sin {\frac {x}{2^{n}}}\left(\prod _{i=1}^{n}\cos {\frac {x}{2^{i}}}\right).} The term 2n sin(x/2n) goes to x in the limit as n goes to infinity, from which Euler's formula follows. Viète's formula may be obtained from this formula by the substitution x = π/2. == See also == Morrie's law, same identity taking x = 2 n α {\displaystyle x=2^{n}\alpha } on Viète's formula List of trigonometric identities == References == == External links == Viète's Variorum de rebus mathematicis responsorum, liber VIII (1593) on Google Books. The formula is on the second half of p. 30.
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Wikipedia:Vladimir Andrunakievich#0
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Vladimir Aleksandrovich Andrunakievich (Russian: Владимир Александрович Андрунакиевич; 3 April 1917 – 22 July 1997) was a Soviet and Moldovan mathematician, known for his work in abstract algebra. He was a doctor of physical and mathematical sciences (1958), academician (1961) and vice-president (1964—1969, 1979—1990) of the Moldavian Soviet Academy of Sciences. Laureate of the State Prize of the Moldavian SSR (1972). Andrunakievich was born in Petrograd. He received his Ph.D. from the Moscow State University in 1947 under the supervision of Aleksandr Gennadievich Kurosh and Otto Schmidt. == Monographs == Radicals of algebras and structure theory (with Iu. M. Ryabukhin). Moscow: Nauka, 1979. Numbers and ideals (with I. D. Chirtoaga). Kishinev: Lumina, 1980. Applied problems of solid mechanics. Kishinev: Ştiinţa, 1985. Modules, algebras and topologies. Kishinev: Ştiinţa, 1988. Constructions of topological rings and modules (with V. I. Arnautov). Kishinev: Ştiinţa, 1988. == Articles == Andrunakievich, Vladimir Aleksandrovich; Ryabukhin, Yuriĭ Mikhaĭlovich (1978). "Complementary and dual torsions". Trudy Mat. Inst. Steklov. 148: 16–26. MR 0558936. == References ==
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Wikipedia:Vladimir Arnold#0
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Vladimir Igorevich Arnold (or Arnol'd; Russian: Влади́мир И́горевич Арно́льд, IPA: [vlɐˈdʲimʲɪr ˈiɡərʲɪvʲɪtɕ ɐrˈnolʲt]; 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to several areas, including geometrical theory of dynamical systems, algebra, catastrophe theory, topology, real algebraic geometry, symplectic geometry, differential equations, classical mechanics, differential-geometric approach to hydrodynamics, geometric analysis and singularity theory, including posing the ADE classification problem. His first main result was the solution of Hilbert's thirteenth problem in 1957 at the age of 19. He co-founded three new branches of mathematics: topological Galois theory (with his student Askold Khovanskii), symplectic topology and KAM theory. Arnold was also known as a popularizer of mathematics. Through his lectures, seminars, and as the author of several textbooks (such as Mathematical Methods of Classical Mechanics) and popular mathematics books, he influenced many mathematicians and physicists. Many of his books were translated into English. His views on education were particularly opposed to those of Bourbaki. == Biography == Vladimir Igorevich Arnold was born on 12 June 1937 in Odesa, Soviet Union (now Odesa, Ukraine). His father was Igor Vladimirovich Arnold (1900–1948), a mathematician. His mother was Nina Alexandrovna Arnold (1909–1986, née Isakovich), a Jewish art historian. While a school student, Arnold once asked his father on the reason why the multiplication of two negative numbers yielded a positive number, and his father provided an answer involving the field properties of real numbers and the preservation of the distributive property. Arnold was deeply disappointed with this answer, and developed an aversion to the axiomatic method that lasted through his life. When Arnold was thirteen, his uncle Nikolai B. Zhitkov, who was an engineer, told him about calculus and how it could be used to understand some physical phenomena. This contributed to sparking his interest for mathematics, and he started to study by himself the mathematical books his father had left to him, which included some works of Leonhard Euler and Charles Hermite. Arnold entered Moscow State University in 1954. Among his teachers there were A. N. Kolmogorov, I. M. Gelfand, L. S. Pontriagin and Pavel Alexandrov. While a student of Andrey Kolmogorov at Moscow State University and still a teenager, Arnold showed in 1957 that any continuous function of several variables can be constructed with a finite number of two-variable functions, thereby solving Hilbert's thirteenth problem. This is the Kolmogorov–Arnold representation theorem. Arnold obtained his PhD in 1961, with Kolmogorov as advisor. After graduating from Moscow State University in 1959, he worked there until 1986 (a professor since 1965), and then at Steklov Mathematical Institute. He became an academician of the Academy of Sciences of the Soviet Union (Russian Academy of Science since 1991) in 1990. Arnold can be said to have initiated the theory of symplectic topology as a distinct discipline. The Arnold conjecture on the number of fixed points of Hamiltonian symplectomorphisms and Lagrangian intersections was also a motivation in the development of Floer homology. In 1999 he suffered a serious bicycle accident in Paris, resulting in traumatic brain injury. He regained consciousness after a few weeks but had amnesia and for some time could not even recognize his own wife at the hospital. He went on to make a good recovery. Arnold worked at the Steklov Mathematical Institute in Moscow and at Paris Dauphine University up until his death. His PhD students include Rifkat Bogdanov, Alexander Givental, Victor Goryunov, Sabir Gusein-Zade, Emil Horozov, Yulij Ilyashenko, Boris Khesin, Askold Khovanskii, Nikolay Nekhoroshev, Boris Shapiro, Alexander Varchenko, Victor Vassiliev and Vladimir Zakalyukin. To his students and colleagues Arnold was known also for his sense of humour. For example, once at his seminar in Moscow, at the beginning of the school year, when he usually was formulating new problems, he said: There is a general principle that a stupid man can ask such questions to which one hundred wise men would not be able to answer. In accordance with this principle I shall formulate some problems. === Death === Arnold died of acute pancreatitis on 3 June 2010 in Paris, nine days before his 73rd birthday. He was buried on 15 June in Moscow, at the Novodevichy Monastery. In a telegram to Arnold's family, Russian President Dmitry Medvedev stated: The death of Vladimir Arnold, one of the greatest mathematicians of our time, is an irretrievable loss for world science. It is difficult to overestimate the contribution made by academician Arnold to modern mathematics and the prestige of Russian science. Teaching had a special place in Vladimir Arnold's life and he had great influence as an enlightened mentor who taught several generations of talented scientists. The memory of Vladimir Arnold will forever remain in the hearts of his colleagues, friends and students, as well as everyone who knew and admired this brilliant man. == Popular mathematical writings == Arnold is well known for his lucid writing style, combining mathematical rigour with physical intuition, and an easy conversational style of teaching and education. His writings present a fresh, often geometric approach to traditional mathematical topics like ordinary differential equations, and his many textbooks have proved influential in the development of new areas of mathematics. The standard criticism about Arnold's pedagogy is that his books "are beautiful treatments of their subjects that are appreciated by experts, but too many details are omitted for students to learn the mathematics required to prove the statements that he so effortlessly justifies." His defense was that his books are meant to teach the subject to "those who truly wish to understand it" (Chicone, 2007). Arnold was an outspoken critic of the trend towards high levels of abstraction in mathematics during the middle of the last century. He had very strong opinions on how this approach—which was most popularly implemented by the Bourbaki school in France—initially had a negative impact on French mathematical education, and then later on that of other countries as well. He was very concerned about what he saw as the divorce of mathematics from the natural sciences in the 20th century. Arnold was very interested in the history of mathematics. In an interview, he said he had learned much of what he knew about mathematics through the study of Felix Klein's book Development of Mathematics in the 19th Century —a book he often recommended to his students. He studied the classics, most notably the works of Huygens, Newton and Poincaré, and many times he reported to have found in their works ideas that had not been explored yet. == Mathematical work == Arnold worked on dynamical systems theory, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics, hydrodynamics and singularity theory. Michèle Audin described him as "a geometer in the widest possible sense of the word" and said that "he was very fast to make connections between different fields". === Hilbert's thirteenth problem === The problem is the following question: can every continuous function of three variables be expressed as a composition of finitely many continuous functions of two variables? The affirmative answer to this general question was given in 1957 by Vladimir Arnold, then only nineteen years old and a student of Andrey Kolmogorov. Kolmogorov had shown in the previous year that any function of several variables can be constructed with a finite number of three-variable functions. Arnold then expanded on this work to show that only two-variable functions were in fact required, thus answering the Hilbert's question when posed for the class of continuous functions. === Dynamical systems === Moser and Arnold expanded the ideas of Kolmogorov (who was inspired by questions of Poincaré) and gave rise to what is now known as Kolmogorov–Arnold–Moser theorem (or "KAM theory"), which concerns the persistence of some quasi-periodic motions (nearly integrable Hamiltonian systems) when they are perturbed. KAM theory shows that, despite the perturbations, such systems can be stable over an infinite period of time, and specifies what the conditions for this are. In 1964, Arnold introduced the Arnold web, the first example of a stochastic web. === Singularity theory === In 1965, Arnold attended René Thom's seminar on catastrophe theory. He later said of it: "I am deeply indebted to Thom, whose singularity seminar at the Institut des Hautes Etudes Scientifiques, which I frequented throughout the year 1965, profoundly changed my mathematical universe." After this event, singularity theory became one of the major interests of Arnold and his students. Among his most famous results in this area is his classification of simple singularities, contained in his paper "Normal forms of functions near degenerate critical points, the Weyl groups of Ak,Dk,Ek and Lagrangian singularities". === Fluid dynamics === In 1966, Arnold published "Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits", in which he presented a common geometric interpretation for both the Euler's equations for rotating rigid bodies and the Euler's equations of fluid dynamics, this effectively linked topics previously thought to be unrelated, and enabled mathematical solutions to many questions related to fluid flows and their turbulence. === Real algebraic geometry === In the year 1971, Arnold published "On the arrangement of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifolds, and the arithmetic of integral quadratic forms", which gave new life to real algebraic geometry. In it, he made major advances in the direction of a solution to Gudkov's conjecture, by finding a connection between it and four-dimensional topology. The conjecture was to be later fully solved by V. A. Rokhlin building on Arnold's work. === Symplectic geometry === The Arnold conjecture, linking the number of fixed points of Hamiltonian symplectomorphisms and the topology of the subjacent manifolds, was the motivating source of many of the pioneer studies in symplectic topology. === Topology === According to Victor Vassiliev, Arnold "worked comparatively little on topology for topology's sake." And he was rather motivated by problems on other areas of mathematics where topology could be of use. His contributions include the invention of a topological form of the Abel–Ruffini theorem and the initial development of some of the consequent ideas, a work which resulted in the creation of the field of topological Galois theory in the 1960s. === Theory of plane curves === According to Marcel Berger, Arnold revolutionized plane curves theory. He developed the theory of smooth closed plane curves in the 1990s. Among his contributions are the introduction of the three Arnold invariants of plane curves: J+, J− and St. === Other === Arnold conjectured the existence of the gömböc, a body with just one stable and one unstable point of equilibrium when resting on a flat surface. Arnold generalized the results of Isaac Newton, Pierre-Simon Laplace, and James Ivory on the shell theorem, showing it to be applicable to algebraic hypersurfaces. == Honours and awards == Lenin Prize (1965, with Andrey Kolmogorov), "for work on celestial mechanics." Crafoord Prize (1982, with Louis Nirenberg), "for their outstanding achievements in the theory of non-linear differential equations." Elected member of the United States National Academy of Sciences in 1983. Foreign Honorary Member of the American Academy of Arts and Sciences (1987) Elected a Foreign Member of the Royal Society (ForMemRS) of London in 1988. Elected member of the American Philosophical Society in 1990. Lobachevsky Prize of the Russian Academy of Sciences (1992) Harvey Prize (1994), "In recognition of his basic contribution to the stability theory of Dynamical Systems, his pioneering work on singularity theory and seminal contributions to analysis and geometry." Dannie Heineman Prize for Mathematical Physics (2001), "for his fundamental contributions to our understanding of dynamics and of singularities of maps with profound consequences for mechanics, astrophysics, statistical mechanics, hydrodynamics and optics." Wolf Prize in Mathematics (2001), "for his deep and influential work in a multitude of areas of mathematics, including dynamical systems, differential equations, and singularity theory." State Prize of the Russian Federation (2007), "for outstanding contribution to development of mathematics." Shaw Prize in mathematical sciences (2008, with Ludwig Faddeev), "for their widespread and influential contributions to Mathematical Physics." The minor planet 10031 Vladarnolda was named after him in 1981 by Lyudmila Georgievna Karachkina. The Arnold Mathematical Journal, published for the first time in 2015, is named after him. The Arnold Fellowships, of the London Institute are named after him. He was a plenary speaker at both the 1974 and 1983 International Congress of Mathematicians in Vancouver and Warsaw, respectively. === Fields Medal omission === Even though Arnold was nominated for the 1974 Fields Medal, one of the highest honours a mathematician could receive, interference from the Soviet government led to it being withdrawn. Arnold's public opposition to the persecution of dissidents had led him into direct conflict with influential Soviet officials, and he suffered persecution himself, including not being allowed to leave the Soviet Union during most of the 1970s and 1980s. == Selected bibliography == 1966: Arnold, Vladimir (1966). "Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits" (PDF). Annales de l'Institut Fourier. 16 (1): 319–361. doi:10.5802/aif.233. 1978: Ordinary Differential Equations, The MIT Press ISBN 0-262-51018-9. 1985: Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. (1985). Singularities of Differentiable Maps, Volume I: The Classification of Critical Points Caustics and Wave Fronts. Monographs in Mathematics. Vol. 82. Birkhäuser. doi:10.1007/978-1-4612-5154-5. ISBN 978-1-4612-9589-1. 1988: Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N. (1988). Arnold, V. I; Gusein-Zade, S. M; Varchenko, A. N (eds.). Singularities of Differentiable Maps, Volume II: Monodromy and Asymptotics of Integrals. Monographs in Mathematics. Vol. 83. Birkhäuser. doi:10.1007/978-1-4612-3940-6. ISBN 978-1-4612-8408-6. S2CID 131768406. 1988: Arnold, V.I. (1988). Geometrical Methods in the Theory of Ordinary Differential Equations. Grundlehren der mathematischen Wissenschaften. Vol. 250 (2nd ed.). Springer. doi:10.1007/978-1-4612-1037-5. ISBN 978-1-4612-6994-6. 1989: Arnold, V.I. (1989). Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics. Vol. 60 (2nd ed.). Springer. doi:10.1007/978-1-4757-2063-1. ISBN 978-1-4419-3087-3. 1989 Арнольд, В. И. (1989). Гюйгенс и Барроу, Ньютон и Гук - Первые шаги математического анализа и теории катастроф. М.: Наука. p. 98. ISBN 5-02-013935-1. 1989: (with A. Avez) Ergodic Problems of Classical Mechanics, Addison-Wesley ISBN 0-201-09406-1. 1990: Huygens and Barrow, Newton and Hooke: Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals, Eric J.F. Primrose translator, Birkhäuser Verlag (1990) ISBN 3-7643-2383-3. 1991: Arnolʹd, Vladimir Igorevich (1991). The Theory of Singularities and Its Applications. Cambridge University Press. ISBN 9780521422802. 1995:Topological Invariants of Plane Curves and Caustics, American Mathematical Society (1994) ISBN 978-0-8218-0308-0 1998: "On the teaching of mathematics" (Russian) Uspekhi Mat. Nauk 53 (1998), no. 1(319), 229–234; translation in Russian Math. Surveys 53(1): 229–236. 1999: (with Valentin Afraimovich) Bifurcation Theory And Catastrophe Theory Springer ISBN 3-540-65379-1 2001: "Tsepniye Drobi" (Continued Fractions, in Russian), Moscow (2001). 2002: "Что такое математика?" (What is mathematics?, in Russian) ISBN 978-5-94057-426-2. 2004: Teoriya Katastrof (Catastrophe Theory, in Russian), 4th ed. Moscow, Editorial-URSS (2004), ISBN 5-354-00674-0. 2004: Vladimir I. Arnold, ed. (15 November 2004). Arnold's Problems (2nd ed.). Springer-Verlag. ISBN 978-3-540-20748-1. 2004: Arnold, Vladimir I. (2004). Lectures on Partial Differential Equations. Universitext. Springer. doi:10.1007/978-3-662-05441-3. ISBN 978-3-540-40448-4. 2007: Yesterday and Long Ago, Springer (2007), ISBN 978-3-540-28734-6. 2013: Arnold, Vladimir I. (2013). Itenberg, Ilia; Kharlamov, Viatcheslav; Shustin, Eugenii I. (eds.). Real Algebraic Geometry. Unitext. Vol. 66. Springer. doi:10.1007/978-3-642-36243-9. ISBN 978-3-642-36242-2. 2014: V. I. Arnold (2014). Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians. American Mathematical Society. ISBN 978-1-4704-1701-7. 2015: Experimental Mathematics. American Mathematical Society (translated from Russian, 2015). 2015: Lectures and Problems: A Gift to Young Mathematicians, American Math Society, (translated from Russian, 2015) 1998: Topological Methods in Hydrodynamics === Collected works === 2010: A. B. Givental; B. A. Khesin; J. E. Marsden; A. N. Varchenko; V. A. Vassilev; O. Ya. Viro; V. M. Zakalyukin (editors). Collected Works, Volume I: Representations of Functions, Celestial Mechanics, and KAM Theory (1957–1965). Springer 2013: A. B. Givental; B. A. Khesin; A. N. Varchenko; V. A. Vassilev; O. Ya. Viro; (editors). Collected Works, Volume II: Hydrodynamics, Bifurcation Theory, and Algebraic Geometry (1965–1972). Springer. 2016: Givental, A.B., Khesin, B., Sevryuk, M.B., Vassiliev, V.A., Viro, O.Y. (Eds.). Collected Works, Volume III: Singularity Theory 1972–1979. Springer. 2018: Givental, A.B., Khesin, B., Sevryuk, M.B., Vassiliev, V.A., Viro, O.Y. (Eds.). Collected Works, Volume IV: Singularities in Symplectic and Contact Geometry 1980–1985. Springer. 2023: Alexander B. Givental, Boris A. Khesin, Mikhail B. Sevryuk, Victor A. Vassiliev, Oleg Ya. Viro (Eds.). Collected Works, Volume VI: Dynamics, Combinatorics, and Invariants of Knots, Curves, and Wave Fronts 1992–1995. Springer. == See also == List of things named after Vladimir Arnold Independent University of Moscow Geometric mechanics == References == == Further reading == Khesin, Boris; Tabachnikov, Serge (Coordinating Editors). "Tribute to Vladimir Arnold", Notices of the American Mathematical Society, March 2012, Volume 59, Number 3, pp. 378–399. Khesin, Boris; Tabachnikov, Serge (Coordinating Editors). "Memories of Vladimir Arnold", Notices of the American Mathematical Society, April 2012, Volume 59, Number 4, pp. 482–502. Boris A. Khesin; Serge L. Tabachnikov (2014). Arnold: Swimming Against the Tide. American Mathematical Society. ISBN 978-1-4704-1699-7. Leonid Polterovich; Inna Scherbak (7 September 2011). "V.I. Arnold (1937–2010)". Jahresbericht der Deutschen Mathematiker-Vereinigung. 113 (4): 185–219. doi:10.1365/s13291-011-0027-6. S2CID 122052411. "Features: "Knotted Vortex Lines and Vortex Tubes in Stationary Fluid Flows"; "On Delusive Nodal Sets of Free Oscillations"" (PDF). EMS Newsletter (96): 26–48. June 2015. ISSN 1027-488X. == External links == V. I. Arnold's web page Personal web page V. I. Arnold lecturing on Continued Fractions A short curriculum vitae On Teaching Mathematics Archived 28 April 2017 at the Wayback Machine, text of a talk from 1997 espousing Arnold's opinions on mathematical instruction Topology of Plane Curves, Wave Fronts, Legendrian Knots, Sturm Theory and Flattenings of Projective Curves Problems from 5 to 15, a text by Arnold for school students, available at the IMAGINARY platform Vladimir Arnold at the Mathematics Genealogy Project S. Kutateladze, Arnold Is Gone В.Б.Демидовичем (2009), МЕХМАТЯНЕ ВСПОМИНАЮТ 2: В.И.Арнольд, pp. 25–58 Author profile in the database zbMATH
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Wikipedia:Vladimir Bening#0
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Vladimir Bening (Russian: Влади́мир Евге́ньевич Бе́нинг) (born 1954) is a Russian mathematician, Professor, Dr.Sc., a professor at the Faculty of Computer Science at the Moscow State University. He defended the thesis «Asymptotic analysis of distributions of some asymptotically efficient statistics in problems of hypothesis testing» for the degree of Doctor of Physical and Mathematical Sciences (1998). Was awarded the title of Professor (2005). Author of 16 books and more than 100 scientific articles. == References == == Literature == Faculty of Computational Mathematics and Cybernetics: History and Modernity: A Biographical Directory (1 500 экз ed.). Moscow: Publishing house of Moscow University. 2010. pp. 296–297. ISBN 978-5-211-05838-5 – via Author-compiler Evgeny Grigoriev. == External links == MSU CMC(in Russian) Scientific works of Vladimir Bening Scientific works of Vladimir Bening(in English)
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Wikipedia:Vladimir Burkov#0
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Vladimir Nikolaevich Burkov (Russian: Владимир Николаевич Бурков; 17 November 1939 – 24 April 2025) was a Russian control theorist and the author of more than four hundred publications on control problems, game theory, and combinatorial optimization. A laureate of the USSR State Prize, of the Prize of the Cabinet Council of the USSR, he was an Honoured Scholar of the Russian Federation. Vladimir Burkov was a vice-president of the Russian Project Management Association (SOVNET) (the Russian branch of International Project Management Association, IPMA), a member of the Russian Academy of Natural Sciences. As a professor at Moscow Institute of Physics and Technology and Head of Laboratory at the V.A. Trapeznikov Institute of Control Sciences of RAS, in the late 1960s he pioneered the theory of active systems (which was a Soviet version of the theory of mechanism design). == Biography == Vladimir Burkov was born on 17 November 1939, in the city of Vologda. In 1963 he graduated from the Moscow Institute of Physics and Technology (MIPT) and was employed by Institute of Automation and Remote Control (since the 1970s it has been known as ICS RAS, V.A. Trapeznikov Institute of Control Sciences of RAS), where he earned his Candidate of Sciences degree in 1966, and became Doctor of Sciences in 1975. In 1981 he earned professorship at the Chair of Control Sciences at MIPT and from 1974 onwards he worked at ICS RAS as a Head of Laboratory 57 "Laboratory of active systems" (until 2019) and a senior research scientist. Married to Elena Burkova, the couple had a daughter Irina, who also earned a doctoral degree for her contributions to control theory. Burkov died at the age of 85 on 24 April 2025. == Contributions to combinatory optimization and project scheduling == Vladimir Burkov's early academic interests were connected with applied problems of combinatorial optimization; in the 1960s he contributed to the boom of project scheduling and network planning, proposed novel models of resource allocation in organizations and in technical systems, solved several extremal graph problems. In particular, Vladimir Burkov proposed a lower-bound estimate of the project makespan in resource-constrained project scheduling problem re-invented in 1998 by A. Mingozzi et al. Two books by Vladimir Burkov, "Network models and control problems" and "Applied problems of graph theory" put forward the problems being intensively studied until now. == Launching theory of active systems == As of the late 1960s, Vladimir Burkov's interests shifted to the studies of the specific nature of the human being as a controlled object (an agent). In 1969 he pursued an idea of the "fairplay principle" (in Russian: принцип открытого управления): plans assigned to selfish agents by the optimal control mechanism must be coordinated with agents' goal functions. Under such an incentive-compatible mechanism, truthtelling is beneficial for agents. The notion of incentive compatibility was independently proposed by Leonid Hurwitz, and later was extended and elaborated by Allan Gibbard, Roger Myerson, and many other researchers. They pioneered the revelation principle, which opened a new era in the studies of economic institutions (mechanism design and contract theory); it was mentioned as the main achievement in 2007's Nobel Memorial Prize in Economic Sciences won by L. Hurwitz, E. Maskin, and R. Myerson. The fairplay principle became the foundation of the newly introduced theory of active systems (a version of mechanism design originating from the USSR), which systematically studied control mechanisms in man-machine systems. In the 1970s the seminal books and articles determined the directions of theory development for many decades to come (some books of the early 2010s are contained in these references:). == Organizational and teaching activities == In 1973 V. Burkov headed the newly created division in the Institute of Automation and Remote Control called "the Sector of Business Games"; in 1974 it was re-organized into the Laboratory 57 "Theory and methods of business games", later renamed to "Laboratory of Active Systems". As of the end of 2016 its staff numbered 28 employees, including 15 Doctors of Sciences and 5 Candidates of Sciences. Over the decades, V. Burkov supervised dozens of thesis works. == Famous followers == Professor Dmitry Novikov, corresponding member of Russian Academy of Sciences (since 2008), was elected a director of ICS RAS on 17 October 2016. == References ==
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Wikipedia:Vladimir Dragović#0
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Vladimir Dragović (born 1967 in Belgrade, SR Serbia) is Professor and Head of the Mathematical Sciences Department at the University of Texas at Dallas. Prior to this he was a Full Research Professor at Serbian Academy of Sciences and Arts, the founder and president of the Dynamical Systems group and co-president of The Centre for Dynamical Systems, Geometry and Combinatorics of the Mathematical Institute of the Serbian Academy of Sciences and Arts. Dragović graduated and received his Doctor of Sciences in Mathematics degree at the Faculty of Mathematics, University of Belgrade, in Belgrade, Serbia, former Socialist Federal Republic of Yugoslavia. Dragović is the author and co-author of numerous books and collections of problems for elementary and secondary schools, as well as special collections of assignments for preparation for mathematics competitions, and mathematics workbooks used as a preparation for admission to faculties. == Education == 1987 B.Sc. in Mathematics, University of Belgrade (graduated in 3 years, instead of 4) 1988–1992 aspirant at Moscow State University, Faculty of Mechanics and Mathematics, Department for Higher Geometry and Topology 1992 Doctor of Sciences in Mathematics, University of Belgrade Thesis: "R-matrices and algebraic curves", advisor: Boris Dubrovin, Moscow State University == Scientific work == Vladimir Dragović is the author of numerous research works in mathematics, mainly focused on algebraic geometric methods in dynamical systems theory. He is the coauthor, along with Milena Radnović, of the book Poncelet Porisms and Beyond. Chairman of the Seminar Mathematical Methods of Mechanics since its founding in 1993. Advisor for four M.Sc. theses and three PhD theses at Department of Mathematics, University of Belgrade. 2001–2007 Member of the Committee for mathematics and mechanics of the Ministry for Science of Serbia 2002–2005 Leader of Project 1643 of the Ministry for Science of Serbia since 2006 Leader of Project 144014 of the Ministry for Science of Serbia since 2005 Leader of the Italian-Serbian project geometry, topology and combinatorics of manifolds and dynamical systems == Visiting Positions == 1999–2000 Department of Mathematics, Kyoto University, Japan 2000–2003 International School for Advanced Studies (SISSA), Trieste, Italy 2008–present University of Lisbon, Portugal 2008 Institute of Advanced Scientific Studies (IHES), Paris, France == Invited lectures and addresses == 2000 ITEF, Moscow, Russia 2004 ICTP, Trieste, Italy 2005 IMPA, Rio de Janeiro, Brazil 2005 ICTP, Trieste, Italy 2006 ICTP, Trieste, Italy 2006 University of Bielsko-Biała, Poland 2007 Montenegrin Academy of Sciences and Arts 2007 SISSA, Trieste, Italy 2007 University of Lisbon, Portugal 2008 Polytechnical University of Catalonia, Barcelona, Spain == Other academic positions and duties == 1992–2007 Special professor (Teacher with special assignments, in special divisions for gifted pupils) in Mathematical Gymnasium Belgrade 2004–2008 Principal, Mathematical Gymnasium Belgrade 1993–1998 Faculty of Mathematics, University of Belgrade; courses: Differential Geometry, several graduate courses 1996–1999 Head of the Committee for mathematical competitions of high school students of Serbia 1996–1999 Department of Philosophy, University of Nis; courses: Differential Geometry, Partial Differential Equations 2003–2008 Department of Sciences and Mathematics, University of Montenegro; courses: Geometry, Analysis and Geometry on Riemann Surfaces, Integrable Dynamical Systems 1, Integrable Dynamical Systems 2 since 2004 regular associate member of ICTP Abdus Salam, Trieste, Italy 2004–2008 head of the Mathematical High School, Belgrade == Awards == 2004 Award of the Union of mathematical societies of Serbia and Montenegro for achievements in mathematical sciences for at most 40-year-old researchers. == References == == External links == Matematička gimnazija prof. Boris Dubrovin, homepage at the International School for Advanced Studies – SISSA – Trieste, Italy Mathematical Institute of Serbian Academy of Sciences and Arts Official Biography of Full Research Professor dr sci Vladimir Dragović, from Mathematical Institute of Serbian Academy of Sciences and Arts
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Wikipedia:Vladimir Entov#0
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Vladimir Markovich Entov (January 8, 1937 – April 10, 2008) was an applied mathematician and physicist. == Biography == During his high school years, Entov won multiple awards at the all-Union Physics Olympiads. In 1954 he graduated from a high school with a Gold Medal (valedictorian). He applied to the Physics Department of the Moscow State University, but was rejected on ideological grounds. The same year he began his study at the Mechanical Department of the Moscow Institute for Oil and Gas. In his second year, he approached Professor I.A. Charny and asked him for a research assignment. This was a beginning of their close personal and scientific friendship, which lasted until the death of Professor Charny. Upon his graduation from the Moscow Institute for Oil and Gas in 1959, Entov began a long-distance course of study at the mathematical department of the Moscow State University, while working in the Institute For Drilling Technology. In 1961 he began his graduate study with Professor I.A.Charny, and in 1965 he successfully defended his dissertation thesis “Non- stationary problems of the non-linear filtration”, earning the title of “Candidate of Science" (roughly equivalent to PhD). Beginning in 1971 and until his death, Entov worked at the Institute for Problems in Mechanics of the Soviet Academy of Science. In 1972 he was awarded the title of Doctor of Sciences for his dissertation thesis "Hydrodynamic theory of filtration of anomalous fluids", completed at the Institute for Problems in Mechanics. In his years at the Institute, Vladimir supervised the theses of 24 Candidates of Science and six Doctors of Science. He worked as a scientific supervisor at the Laboratory of Applied Continuum Mechanics until the last years of his life. In addition, since 1983 he served as a Professor of Applied Mathematics and Computer Modeling of the Moscow Institute of Oil and Gas (now known as the Gubkin Russian State University of Oil and Gas). Since 1993, Vladimir was actively involved in research and teaching activity in France (Institut de Physique du Globe de Paris), the UK (University of Cambridge and University of Oxford), and the USA (WPI, University of Stanford, MIT, UMN). Professor Entov was a Corresponding Member of The Russian Academy of the Natural Sciences, a member of the Russian National Committee for the Theoretical and Applied Mechanics, a member of the International Society for the Interaction of Mechanics and Mathematics, and a member of the editorial board of the European Journal of Applied Mathematics (Cambridge University Press). == Works published (partial list) == Works include: Теория нестационарной фильтрации жидкости и газа // М., "Недра", 1972 (совместно с Г.И.Баренблаттом, В.М.Рыжиком) Гидродинамическая теория фильтрации аномальных жидкостей // М., "Наука", 1975 (совместно с М.Г.Бернадинером) Движение жидкостей и газов в природных пластах // М., "Недра", 1984 (совместно с Г.И.Баренблаттом, В.М.Рыжиком) Гидродинамика в бурении // М., "Недра", 1985 (совместно с А.Х. Мирзаджанзаде) Качественные методы в механике сплошных сред // М., "Наука", 1989 (совместно с Р.В.Гольдштейном) Гидродинамика процессов повышения нефтеотдачи // М., "Недра", 1989 (совместно с А.Ф.Зазовским) Математическая теория целиков остаточной вязкопластичной нефти // Томск, Издательство Томского Университета, 1989 (совместно с В.Н.Панковым и С.В.Панько) Fluids Flow through Natural Rocks // Dordrecht, "Kluwer Academic Publishers", 1990 (with G.I. Barenblatt, V.M.Ryzhik) Qualitative Methods in Continuum Mechanics // New York, "Longman Scientific & Technical", 1994 (with R.V. Goldstein) Mechanics of Continua and Its Application to Gas and Oil Productions // Moscow, "Moscow Nedra", 2008 (with E.V. Glivenko) == References ==
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Wikipedia:Vladimir Gerdt#0
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Vladimir P. Gerdt (21 January 1947 – January 5, 2021) was a Russian mathematician and a full professor at the Joint Institute for Nuclear Research (JINR) where he was the head of the Group of Algebraic and Quantum Computations. His research interests were concentrated in computer algebra, symbolic and algebraic computations, algebraic and numerical analysis of nonlinear differential equations, polynomial equations, applications to mathematics and physics, and quantum computation with over 210 published articles. == Biography == Gerdt, who was born in Engels, earned his MSc in theoretical physics from Saratov State University in 1971, his PhD in theoretical and mathematical physics from JINR in 1976, and his D.Sc. in mathematics and computer science from JINR in 1992. He also did graduate studies in theoretical physics at the Lomonosov Moscow State University (1969-1971). After his MSc he worked as an engineer-programmer (1971-1975) and as a junior researcher (1975-1977) at the JINR Department of Radiation Safety developing software for neutron spectroscopy. In 1977 he moved to the JINR Laboratory of Computing Techniques and Automation renamed in 2000 as Laboratory of Information Technologies for doing research in computer algebra. He worked as a researcher (1977-1980) and as a senior researcher (1980-1983), and since 1983 as the head of the research group on computer algebra, currently the Group of Algebraic and Quantum Computations. Gerdt designed a number of original algorithms and software packages for the investigation of differential equations as well as for the transformation of polynomial and differential systems into the canonical involutive form that alleviates their analysis and the construction of their solutions. In the case of polynomial, differential, and difference systems their involutive form is a Gröbner basis. He was a member of the editorial board of the Journal of Symbolic Computation, the leading international journal specialized in the area of symbolic and algebraic computation, since its foundation in 1985. In 1997 he co-founded the annual international conference Computer Algebra in Scientific Computing with Ernst W. Mayr and since that time was a general chair of this conference. Gerdt was married to Evgenia Almazova and had two sons, Anton and Peter. Gerdt died in 2020 of COVID-19. == Selected works == Gerdt, Vladimir P.; Blinkov, Yuri A. (1998). "Involutive bases of polynomial ideals". Mathematics and Computers in Simulation. 45 (5): 519–541. arXiv:math/9912027. doi:10.1016/s0378-4754(97)00127-4. S2CID 10243294. Gerdt, Vladimir P. Involutive algorithms for computing Gröbner bases. Computational Commutative and Non-Commutative Algebraic Geometry, Amsterdam, IOS Press, 2005. Gerdt, Vladimir P., Yuri A. Blinkov, and Denis A. Yanovich. "Construction of Janet Bases I. Monomial Bases." Computer Algebra in Scientific Computing CASC 2001. Springer Berlin Heidelberg, 2001. 233–247. Gerdt, Vladimir P., Aleksey Y.Zharkov. "Solution of Chew-Low Equations in the Quadratic Approximation", Sov. Theor. Math. Phys. (Teor. Mat. Fiz., 52, 3, 1982, 384–392), 52, 3, 1983, 868–874. Gerdt, Vladimir P., Aleksey Y.Zharkov. "A REDUCE Package for Solving of Ordinary Differential Equations", Proceedings of the Second International Conference on Systems and Techniques of Analytical Computing and Their Applications in Theoretical Physics (Dubna, 21–23 September 1982), JINR D11-83-511, Dubna, 1983, 171–177. Gerdt, Vladimir P., Aleksey Y.Zharkov. "Iterative Method of Construction of General Solution of the Chew-Low Equation", Proceedings of the Second International Conference on Systems and Techniques of Analytical Computing and Their Applications in Theoretical Physics (Dubna, September 21–23, 1982), JINR D11-83-511, Dubna, 1983, 232–241. Gerdt, Vladimir P., Aleksey Y.Zharkov."Cubic Approximation and Local Limitations on the Functional Arbitrariness in the General Solution of the Chew-Low Equations", Sov. Theor. Math. Phys. (Teor. Mat. Fiz., 55, 3, 1983, 469–474), 52, 3, 1983, 626–639. Gerdt, Vladimir P., Aleksey Y.Zharkov. "Methods of Investigating and Solving Differential Equations by Means of Algebraic Computation", In: "Systems for Analytical Transformations in Mechanics", Gorky, 1984, 16–19. == References ==
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Wikipedia:Vladimir Korepin#0
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Vladimir E. Korepin (born 1951) is a professor at the C. N. Yang Institute of Theoretical Physics of the Stony Brook University. Korepin made research contributions in several areas of mathematics and physics. == Educational background == Korepin completed his undergraduate study at Saint Petersburg State University, graduating with a diploma in theoretical physics in 1974. In that same year he was employed by the Mathematical Institute of Academy of Sciences. He worked there until 1989, obtaining his PhD in 1977 under the supervision of Ludwig Faddeev. At the same institution he completed his postdoctoral studies. In 1985, he received a Doctor of Science degree in mathematical physics. == Contributions to physics == Korepin has made contributions to several fields of theoretical physics. Although he is best known for his involvement in condensed matter physics and mathematical physics, he significantly contributed to quantum gravity as well. In recent years, his work has focused on aspects of condensed matter physics relevant for quantum information. === Condensed matter === Among his contributions to condensed matter physics, we mention his studies on low-dimensional quantum gases. In particular, the 1D Hubbard model of strongly correlated fermions, and the 1D Bose gas with delta potential interactions. In 1979, Korepin presented a solution of the massive Thirring model in one space and one time dimension using the Bethe ansatz. In this work, he provided the exact calculation of the mass spectrum and the scattering matrix. He studied solitons in the sine-Gordon model. He determined their mass and scattering matrix, both semiclassically and to one loop corrections. Together with Anatoly Izergin, he discovered the 19-vertex model (sometimes called the Izergin-Korepin model). In 1993, together with A. R. Its, Izergin and N. A. Slavnov, he calculated space, time and temperature dependent correlation functions in the XX spin chain. The exponential decay in space and time separation of the correlation functions was calculated explicitly. === Quantum gravity === In this field, Korepin has worked on the cancellation of ultra-violet infinities in one loop on mass shell gravity. == Contributions to mathematics == In 1982, Korepin introduced domain wall boundary conditions for the six vertex model, published in Communications in Mathematical Physics. The result plays a role in diverse fields of mathematics such as algebraic combinatorics, alternating sign matrices, domino tiling, Young diagrams and plane partitions. In the same paper the determinant formula was proved for the square of the norm of the Bethe ansatz wave function. It can be represented as a determinant of linearized system of Bethe equations. It can also be represented as a matrix determinant of second derivatives of the Yang action. The so-called "Quantum Determinant" was discovered in 1981 by A.G. Izergin and V.E. Korepin. It is the center of the Yang–Baxter algebra. The study of differential equations for quantum correlation functions led to the discovery of a special class of Fredholm integral operators. Now they are referred to as completely integrable integral operators. They have multiple applications not only to quantum exactly solvable models, but also to random matrices and algebraic combinatorics. == Contributions to quantum information and quantum computation == Vladimir Korepin has produced results in the evaluation of the entanglement entropy of different dynamical models, such as interacting spins, Bose gases, and the Hubbard model. He considered models with unique ground states, so that the entropy of the whole ground state is zero. The ground state is partitioned into two spatially separated parts: the block and the environment. He calculated the entropy of the block as a function of its size and other physical parameters. In a series of articles, Korepin was the first to compute the analytic formula for the entanglement entropy of the XX (isotropic) and XY Heisenberg models. He used Toeplitz Determinants and Fisher-Hartwig Formula for the calculation. In the Valence-Bond-Solid states (which is the ground state of the Affleck-Kennedy-Lieb-Tasaki model of interacting spins), Korepin evaluated the entanglement entropy and studied the reduced density matrix. He also worked on quantum search algorithms with Lov Grover. Many of his publications on entanglement and quantum algorithms can be found on ArXiv. In May 2003, Korepin helped organize a conference on quantum and reversible computations in Stony Brook. Another conference was on November 15–18, 2010, entitled the Simons Conference on New Trends in Quantum Computation. == Books == Essler, F. H. L.; Frahm, H., Goehmann, F., Kluemper, A., & Korepin, V. E., The One-Dimensional Hubbard Model. Cambridge University Press (2005). V.E. Korepin, N.M. Bogoliubov and A.G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge University Press (1993). Exactly Solvable Models of Strongly Correlated Electrons. Reprint volume, eds. F.H.L. Essler and V.E. Korepin, World Scientific (1994). == Honours == Korepin's H-index is 68 with over 20431 citations. In 1996 Korepin was elected fellow of the American Physical Society. Fellow of the International Association of Mathematical Physics and the Institute of Physics. Editor of Reviews in Mathematical Physics, the International Journal of Modern Physics and Theoretical and Mathematical Physics. His 60-th birthday was celebrated by Institute of Advanced Studies in Singapore in 2011. == References == == External links == Vladimir Korepin at the Mathematics Genealogy Project Research and achievements Publications on arXiv Korepin on INSPIRE-HEP Faculty webpage Early publications
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Wikipedia:Vladimir Lefebvre#0
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Vladimir Alexandrovich Lefebvre (Влади́мир Алекса́ндрович Лефе́вр, 22 September 1936 in Leningrad, USSR – 9 April 2020) was a mathematical psychologist at the University of California, Irvine. With his wife, V. I. Dubovskaya, Lefebvre left USSR for USA in 1974. He created equations to predict the large-scale consequences of individual actions. Among the parameters in the equations are the self image of the individual and the action as perceived via this self-image. The result is a number expressing the probability that the individual in question will perform a specific action. Lefebvre's mathematical approach to social psychology is often referred to as reflexive theory - presumably due to the 'reflexive' nature of taking into account subjects' self-image(s). Lefebvre developed Reflexive Theory as a military researcher in the former Soviet Union, where he was born and educated prior to coming to the United States. According to Jonathan Farley, a mathematician at Stanford doing applied work on national security issues, Lefebvre's Reflexive Theory was a Soviet alternative to game theory which had been widely adopted by the American defense establishment. Lefebvre created a mathematical theory of ethical cognition. This theory uses a three level structure: the person, the person’ perception and the person’s perception of their communication partner. This theory was used in negotiations by the governments of the US and the Soviet Union during the break-up of the Soviet Union. == References == == External links == The Mathematics of Social Ethics: Reflexive Theory and 'The Torturer's Dilemma' - an introductory overview of 'reflexive theory' (as applied to issues in the War on Terrorism) at Econophysics Blog Vladimir Lefebvre, PhD - Vladimir Lefebvre bio at the Center for Advanced Defense Studies
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Wikipedia:Vladimir Levenshtein#0
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Vladimir Iosifovich Levenshtein (Russian: Влади́мир Ио́сифович Левенште́йн, IPA: [vlɐˈdʲimʲɪr ɨˈosʲɪfəvʲɪtɕ lʲɪvʲɪnˈʂtʲejn] ; 20 May 1935 – 6 September 2017) was a Russian and Soviet scientist who did research in information theory, error-correcting codes, and combinatorial design. Among other contributions, he is known for the Levenshtein distance and a Levenshtein algorithm, which he developed in 1965. He graduated from the Department of Mathematics and Mechanics of Moscow State University in 1958 and worked at the Keldysh Institute of Applied Mathematics in Moscow ever since. He was a fellow of the IEEE Information Theory Society. He received the IEEE Richard W. Hamming Medal in 2006, for "contributions to the theory of error-correcting codes and information theory, including the Levenshtein distance". == Life == Levenshtein graduated from Moscow State University in 1958, where he studied in the faculty of Mechanics and Mathematics. After graduation, he worked at the M.V Keldysh Institute of Applied Mathematics. == Publications == Levenshtein, V. I. (1965), "Binary codes capable of correcting deletions, insertions, and reversals.", Doklady Akademii Nauk SSSR, 163 (4): 845–848 Delsarte, P.; Levenshtein, V. I. (1998), "Association schemes and coding theory", IEEE Transactions on Information Theory, 44 (6): 2477–2504, doi:10.1109/18.720545 V.I. Levenshtein (1960), "On a class of systematic codes", Doklady Akademii Nauk SSSR, 131 (5): 1011–1014 V.I. Levenshtein, Application of Hadamard matrices to a problem in coding theory, Problems of Cybernetics, vol. 5, GIFML, Moscow, 1961, 125–136. V.I. Levenshtein (1961), "Certain properties of code systems", Doklady Akademii Nauk SSSR, 140 (6): 1274–1277 V.I. Levenshtein (1961), "Self-adaptive automata for decoding messages", Doklady Akademii Nauk SSSR, 141 (6): 1320–1323 V.I. Levenshtein (1962), "On the inversion of finite automata", Doklady Akademii Nauk SSSR, 147 (6): 1300–1303 V.I. Levenshtein, On the stable extension of finite automata, Problems of Cybernetics, vol. 10, GIFML, Moscow, 1963, 281–286. V.I. Levenshtein, On some coding systems and self-tuning machines for decoding messages, Problems of Cybernetics, vol. 11, GIFML, Moscow, 1964, 63–121. V.I. Levenshtein, Decoding automata invariant with respect to the initial state, Problems of Cybernetics, vol. 12, GIFML, Moscow, 1964, 125–136. V.I. Levenshtein (1965), "Binary codes with correction for deletions and insertions of the symbol 1", Problemy Peredachi Informatsii, 1 (1): 12–25 V.I. Levenshtein (1965), "On a Method of Solving the Problem of Synchronizing a Chain of Automata in Minimal Time", Problemy Peredachi Informatsii, 1 (4): 20–32 V.I. Levenshtein, Binary codes providing synchronization and correction of errors, Abstracts of short scientific reports of the International Congress of Mathematicians, Section 13, Moscow, 1966, 24. V.I. Levenshtein, Asymptotically optimal binary code with correction of occurrences of one or two adjacent characters, Problems of Cybernetics, vol. 19, Science, Moscow, 1967, 293–298. V.I. Levenshtein, On the redundancy and deceleration of separable coding of natural numbers, Problems of Cybernetics, vol. 20, Nauka, Moscow, 1968, 173–179. V.I. Levenshtein (1968), "On the Synchronization of Two-Way Networks of Automata", Problemy Peredachi Informatsii, 4 (4): 49–62 V.I. Levenshtein (1969), "Bounds for Codes Ensuring Error Correction and Synchronization", Problemy Peredachi Informatsii, 5 (2): 3–13 V.I. Levenshtein (1970), "On the Maximum Number of Words in Codes without Overlapping", Problemy Peredachi Informatsii, 6 (4): 88–90 V.I. Levenshtein (1971), "One Method of Constructing Quasilinear Codes Providing Synchronization in the Presence of Errors", Problemy Peredachi Informatsii, 7 (3): 30–40 V.I. Levenshtein (1971), "Upper-Bound Estimates for Fixed-Weight Codes", Problemy Peredachi Informatsii, 7 (4): 3–12 V.I. Levenshtein (1974), "Minimum Redundancy of Binary Error-Correcting Codes", Problemy Peredachi Informatsii, 10 (2): 26–42 V.I. Levenshtein, Elements of coding theory, In the book. Discrete mathematics and mathematical questions of cybernetics, Nauka, Moscow, 1974, 207–305. V.I. Levenshtein (1975), "Maximal packing density of n-dimensional Euclidean space with equal balls", Matematicheskie Zametki, 18 (2): 301–311. VI Levenshtein, Methods for obtaining bounds in metric problems of coding theory, Proc. of the 1975 IEEE-USSR Joint Workshop on Information Theory, New York, 1976, 126–143. V.I. Levenshtein (1977), "Bounds on the Probability of Undetected Error", Problemy Peredachi Informacii, 13 (1): 3–18 G.A. Kabatiansky; V.I. Levenshtein (1978), "On Bounds for Packings on a Sphere and in Space", Problemy Peredachi Informatsii, 14 (1): 3–25 V.I. Levenshtein, On the choice of polynomials for obtaining boundaries in packaging problems, VII All-Union Conference on the Theory of Coding and Information Transfer, Part II, Moscow - Vilnius, 1978, 103–108. V.I. Levenshtein (1979), "On boundaries for packings in n-dimensional Euclidean space", Doklady Akademii Nauk SSSR, 245 (6): 1299–1303 V.I. Levenshtein (1982), "Bounds of the maximal capacity of a code with a limited scalar product modulus", Doklady Akademii Nauk SSSR, 263 (6): 1303–1308 V.I. Levenshtein, Borders for packaging of metric spaces and some of their applications, Problems of cybernetics, vol. 40, Science, Moscow, 1983, 43–110. VI Levenshtein, Packing of polynomial metric spaces, Third International Workshop on Information Theory, Convolutional codes; multi-user communication, Sochi, 1987, 271–274. V.I. Levenshtein (1989), "On the Straight-Line Bound for the Undetected Error Exponent", Problemy Peredachi Informatsii, 25 (1): 33–37 VI Levenshtein, Perfect deletion-correcting codes as combinatorial designs, Proc. of the Second International Workshop: Algebraic and Combinatorial Coding Theory, Leningrad, USSR, 1990, 137–140. V.I. Levenshtein (1991), "Perfect codes in the metric of deletions and insertions", Diskretnaya Matematika, 3 (1): 3–20. VI Levenshtein, Designs as maximum codes in polynomial metric spaces, Acta Applicandae Mathematicae, vol. 29 (1992), 1-82. VI Levenshtein, Bounds for self-complementary codes and their applications, in Eurocode-92. CISM Courses and Lectures, vol. 339. Springer-Verlag, Wien-New-York, 1993, 159–171. VI Levenshtein, Bounds for codes as solutions of extremum problems for systems of orthogonal polynomials, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Lectures Notes in Computer Science, vol. 673, Springer-Verlag, 1993, 25–42. V.I. Levenshtein; A.J.H. Vinck (1993), "Perfect (d,k)-codes capable of correcting single peak-shifts", IEEE Transactions on Information Theory, 39 (2), IEEE: 656–662, doi:10.1109/18.212300 V.I. Levenshtein (1993), "Packing and Decomposition Problems for Polynomial Association Schemes", European Journal of Combinatorics, 14 (5): 461–477, doi:10.1006/eujc.1993.1049 T. Ericson and VI Levenshtein, Superimposed codes in the Hamming space, IEEE Trans. Inform. Theory, vol. 40, no. 6 (1994), 1882–1893. G. Fasekas and VI Levenshtein, On upper bounds for code distance and covering radius of designs in polynomial metric spaces, J. Combin. Th. Ser. A, vol. 70, no. 2 (1995), 267–288. T. Helleseth, T. Klove, VI Levenshtein, and O. Ytrehus, Bounds on the minimum support weights, IEEE Trans. Inform. Theory, vol. 41, no. 2 (1995), 432–440. VI Levenshtein, Krawtchouk polynomials and universal bounds for codes and designs in Hamming spaces, IEEE Trans. Inform. Theory, vol. 41, no. 5 (1995), 1303–1321. V.I. Levenshtein (1995), "A Simple Proof of the Basic Inequalities for the Fundamental Parameters of Codes in Polynomial Relationship Schemes", Problemy Peredachi Informatsii, 31 (4): 37–50. VI Levenshtein, Reconstructing binary sequences by the minimum number of their subsequences or supersequences of a given length. Proceedings of Fifth Intern. Workshop on Algebr. and Combin. Coding Theory, Sozopol, Bulgaria, June 1–7, 1996, 176–183. VI Levenshtein, Lower bounds on crosscorrelation of codes. Proceedings of IEEE Fourth Intern. Symp on Spread Spectrum Techniques and Appl., Mainz, Germany, September 22–25, 1996, 657–661. VI Levenshtein, Split orthogonal arrays and maximum independent resilient systems of functions, Designs, Codes and Cryptography, vol. 12, no. 2 (1997), 131–160. T. Helleseth, T. Klove, and VI Levenshtein, On the information function of an error-correcting code, IEEE Trans. Inform. Theory, vol. 43, no. 2 (1997), pp. 549–557. V.I. Levenshtein (1997), "Reconstruction of objects from the minimum number of distorted patterns", Doklady Akademii Nauk SSSR, 354 (5): 593–596 P. Delsarte and VI Levenshtein, Association schemes and coding theory, IEEE Trans. Inform. Theory, vol. 44, no. 6 (1998), 2477–2504. VI Levenshtein, Universal bounds for codes and designs, in Handbook of Coding Theory, VS Pless and WC Huffman, Eds., Amsterdam: Elsevier, vol. 1, 499–648, 1998. VI Levenshtein, On designs in compact metric spaces and a universal bound on their size, Discrete Mathematics, vol. 192 (1998), 251–271. VI Levenshtein, On the maximum T-wise independent systems of Boolean functions, Workshop on Coding and Cryptography, Paris, France, 1999, 367–370. VI Levenshtein, Equivalence of Delsarte's bounds for codes and designs in symmetric association schemes and some applications, Discrete Mathematics, vol. 197/198 (1999), 515–536. VI Levenshtein, New lower bounds on aperiodic crosscorrelation of binary codes, IEEE Trans. Inform. Theory, vol. 45, no. 1 (1999), 284–288. IN AND. Levenshtein, On designs in continuous unit cubes, Proceedings of the IV International Conference: Discrete models in the theory of control systems, Moscow State University, MAKS Press, 2000, 62–64. VI Levenshtein, Efficient reconstruction of sequences, IEEE Trans. Inform. Theory, vol. 47, no. 1 (2001), 2-22. VI Levenshtein, Efficient reconstruction of sequences from their subsequences or supersequences, Journal of Combin. Theory, Ser. A, vol. 93, no. 2 (2001), 310–332. T. Berger and VI Levenshtein, Asymptotical efficiency of two-stage testing, IEEE Trans. Inform. Theory, vol. 48, no. 7 (2002), 1741–1749. T. Berger and VI Levenshtein, Application of cover-free codes and combinatorial designs to two-stage testing, Discrete Applied Mathematics. T. Helleseth, T. Klove and VI Levenshtein, Hypercubic 4 and 5-designs from double-error-correcting BCH codes, Designs, Codes and Cryptography. VI Levenshtein, A universal bound for a covering in regular posets and its application to pool testing, Discrete Mathematics. Helleseth, Tor; Kløve, Torleiv; Levenshtein, Vladimir (2005), "Error-correction capability of binary linear codes", IEEE Transactions on Information Theory, 51 (4), IEEE: 1408–1423, doi:10.1109/TIT.2005.844080, S2CID 17840890 VI Levenshtein, Combinatorial problems motivated by comma-free codes, Discrete Mathematics. == See also == Association scheme Bose–Mesner algebra Levenshtein automaton Levenshtein coding == References == == External links == Levenshtein's personal webpage, Internet Archive from July 2023 - in Russian March 2003 pictures of Levenshtein at a professional reception (Internet Archive February 2023). Another (better) picture from the same source "2006 Richard W. Hamming Medal". IEEE. Archived from the original on 2007-09-19.
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Wikipedia:Vladimir Makanin#0
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Vladimir Semyonovich Makanin (Russian: Владимир Семёнович Маканин; 13 March 1937 in Orsk, Orenburg Oblast, RSFSR, Soviet Union – 1 November 2017 in Krasny, Aksaysky District, Rostov Oblast, Russia) was a Russian writer of novels and short stories. == Life == Makanin graduated from the Faculty of Mechanics and Mathematics at Moscow State University and worked as a teacher in the Military Academy until the early 1960s. In 1963 he took the High Courses for Scriptwriters and Film Directors at the Gerasimov Institute of Cinematography, then worked for the publishing house Sovietskiy Pisatel (The Soviet Writer). He published his first book in 1965. In 1985, he became a board member at the Union of Soviet Writers and, two years later, joined the editorial staff at Znamya. He spent most of his later years in Krasny, near Rostov-on-Don. In 2007, he headed the jury for the Big Book award. The following year, he was the recipient. Makanin's writing style may be categorized as realist. His forte lies in depicting the psychological impact of everyday life experiences. == English translations == Antileader, from The New Soviet Fiction, Abbeville Press, NY, 1989. Baize-covered Table with Decanter, Readers International, 1995. Escape Hatch, and The Long Road Ahead, Ardis Publishers, 1996. The Loss, Northwestern University Press, 1998. == Selected bibliography == Straight line (Russian: Прямая линия), 1965 Blue and Red (Голубое и красное), 1975 The Portrait and Around (Портрет и вокруг), 1978 Antileader (Антилидер), 1980 Ancestor (Предтеча), 1982 He and She (Один и одна), 1987 The Underground, or a Hero of Our Time (Андерграунд, или Герой нашего времени), 1999 Asan (Acaн), 2008 == Awards == 1984 Order of the Badge of Honour 1993 Russian Booker Prize for Baize-covered Table with Decanter 1998 Pushkin Prize for his oeuvre 1999 State Prize of the Russian Federation 2001 Italian Premio Penne 2008 Big Book Award for Asan 2012 European Prize for Literature == References ==
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Wikipedia:Vladimir Malanin#0
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Vladimir Vladimirovich Malanin (born August 30, 1942, Sylvensk, Kungursky District, USSR) is a Russian mathematician. Rector, vice-rector and president of Perm University. Head of the Department of Control Processes and Information Security of the Faculty of Mechanics and Mathematics of Perm University. Confidant of Russian President Vladimir Putin in the presidential elections (2000, 2004, 2012). == Biography == From 1960 to 1965, he was studying at the Faculty of Mechanics and Mathematics of Perm University. As one of the best students of Perm University, in the fifth year he had an opportunity to study and internship at the Faculty of Mechanics and Mathematics of the Moscow State University. His dissertation was titled "Some questions of the study of the process of launching an aircraft to a given program". His scientific supervisor was I. F. Vereshchagin. Candidate of Physical and Mathematical Sciences (1970, professor (1991), Doctor of Technical Sciences (2001). From November 1975 to the end of 2011, he was the Head of the Department of Mechanics and Control Processes (since 2006 — the Department of Control Processes and Information Security) of the Faculty of Mechanics and Mathematics of Perm University. From 1983 to 1987, he was a vice-rector for scientific work at Perm University. In March 1987, Malanin was appointed the rector by the decision of the University staff. It was one of the first times in the USSR and the first in the RSFSR when the head of the university in this way. Then he was re-elected to this position four times (in 1992, 1997, 2002, 2007). On January 15, 2010, he was dismissed from the post of rector at his own will. He was elected a President of Perm University. From 2010, he was a member of many scientific and educational Councils, Centers and Associations. Confidant of Russian President Vladimir Putin in the presidential elections (2000, 2004, 2012). Chairman of the Public Council of Perm Krai Police Department (2010–2013), member of Perm Krai Public Chamber (2010–2015). He can speak fluently English and French. == Scientific activities == His research interests are also related to such topics as Computer algebra, Mathematical Modeling in natural sciences, General and Applied Mechanics, methods of Optimization and History of Physical and Mathematical sciences. The longest term direction of scientific research is the solution of problems of optimal flight control of aircraft. He has been developing methods of solid mechanics that use the Rodrigue–Hamilton and Cayley–Klein parameters to describe motion. Since 1975, under the leadership of V. V. Malanin, there have been scientific seminars on dynamical systems at the Department of Mechanics of Perm University. He had scientific internships in 1976 and 1977 at the Sorbonne (France) and in 1999 at Oxford (Great Britain). Under the leadership of V. V. Malanin, there were international and regional conferences, symposiums and seminars in Perm University and other educational and scientific institutions of the Perm Krai. He is the head of research works on grants from CDRF (American Foundation for Civil Research and Development, 2002–2008) and the Russian Foundation for Basic Research (since 2002). He was a scientific consultant of two doctoral dissertations (I. Poloskov, 2004; O. Pensky, 2007). Since 2010, he has been the Chairman of the Doctoral Dissertation Council of Perm University for Physical and Mathematical Sciences and of Perm Regional Branch of the Russian Foundation for Basic Research. He is the author and co-author of more than 440 publications in various fields of science. 139 of them were published in the closed press, 5 scientific manuals for universities, 10 monographs, 5 certificates of official registration of computer programs, 4 certificates of official registration of Database Management Systems, 16 patents and certificates of state registration. Since 2010, he is a member of the National Committee for Theoretical and Applied Mechanics of the Russian Academy of Sciences (2002), the Deputy Chairman of the Scientific and Methodological Council for Theoretical Mechanics of the Ministry of Education and Science of the Russian Federation. == Bibliography == Bugaenko G. A., Malanin V. V., Yakovlev V. I. Fundamentals of classical mechanics: Textbook for universities. Moscow: Higher School, 1999. 367 p. Malanin V. V., Poloskov I. E. Random processes in nonlinear dynamical systems. Analytical and numerical methods of research. Moscow; Izhevsk: Scientific Publishing Centre "Regular and chaotic dynamics", 2001. 160 p. Malanin V. V., Strelkova N. A. The Vietoris method and its application to problems of statistical dynamics and optimal control. Moscow; Izhevsk: Scientific Publishing Centre "Regular and chaotic dynamics", 2002—140 p. Malanin V. V., Strelkova N. A. Optimal control of orientation and helical motion of a rigid body. Moscow; Izhevsk: Scientific Publishing Centre "Regular and chaotic dynamics", 2004. 204 p. Malanin V. V., Poloskov I. E. Methods and practice of analysis of random processes in dynamic systems: textbook. manual. Moscow; Izhevsk: Scientific Publishing Centre "Regular and chaotic dynamics", 2005. 296 p. == Awards and Titles == Award pin "For excellent achievements in work in the field of higher education" (1987). Medal "Veteran of Labour" (1990). Diploma of the Presidium of the Supreme Soviet of the Russian Federation — for the great contribution into the development of Science, Education and Public Education (September 7, 1992). Honored Worker of Science of the Russian Federation (1995). Honorary Worker of Higher Professional Education of the Russian Federation (1996). Order "For Merit to the Fatherland" Fourth Class — for services to the State, many years of conscientious work and a great contribution to strengthening friendship and cooperation between people (2000). Diploma of the laureate in the nomination "Science and education" in the contest "Person of the Year" of Perm European Club (2007). Order "For Merit to the Fatherland" — for merits in the field of education, science and a great contribution to the training of qualified specialists (2008). Certificate of Merit of the Eurasian Association of Universities (2011). Honorary Citizen of Perm (May 22, 2012). Honored Professor of Perm University (2015). Letters of Gratitude from the President of the Russian Federation (March 2000, May 2000, May 2012, December 2012). == References == == Links == Vladimir Malanin // Perm University. Vladimir Vladimirovich Malanin // Kostitsyn V. Rectors of Perm University. 1916—2016. Perm, 2016. 352 P. pp. 241–295. Poloskov I. Great jubilee of a great scientist (to the 70th anniversary of V. V. Malanin) // Perm Scientific Center Herald. № 3—4. pp. 129–145. 2019. Ostapenko E., Yakovlev V. Vladimir Vladimirovich Malanin (to the 75th birthday) // Bulletin of the Perm University. Maths. Mechanics. Informatics. № 3(38) 2017. С. 98–108. Sofin D. M. Vladimir Vladimirovich Malanin. To the 75th Anniversary of the First President of Perm University // Perm City Archive. 2017. UNIVERSUM of Vladimir Malanin
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Wikipedia:Vladimir Mazya#0
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Vladimir Gilelevich Maz'ya (Russian: Владимир Гилелевич Мазья; born 31 December 1937) (the family name is sometimes transliterated as Mazya, Maz'ja or Mazja) is a Russian-born Swedish mathematician, hailed as "one of the most distinguished analysts of our time" and as "an outstanding mathematician of worldwide reputation", who strongly influenced the development of mathematical analysis and the theory of partial differential equations. Mazya's early achievements include: his work on Sobolev spaces, in particular the discovery of the equivalence between Sobolev and isoperimetric/isocapacitary inequalities (1960), his counterexamples related to Hilbert's 19th and Hilbert's 20th problem (1968), his solution, together with Yuri Burago, of a problem in harmonic potential theory (1967) posed by Riesz & Szőkefalvi-Nagy (1955, chapter V, § 91), his extension of the Wiener regularity test to p–Laplacian and the proof of its sufficiency for the boundary regularity. Maz'ya solved Vladimir Arnol'd's problem for the oblique derivative boundary value problem (1970) and Fritz John's problem on the oscillations of a fluid in the presence of an immersed body (1977). In recent years, he proved a Wiener's type criterion for higher order elliptic equations, together with Mikhail Shubin solved a problem in the spectral theory of the Schrödinger operator formulated by Israel Gelfand in 1953, found necessary and sufficient conditions for the validity of maximum principles for elliptic and parabolic systems of PDEs and introduced the so–called approximate approximations. He also contributed to the development of the theory of capacities, nonlinear potential theory, the asymptotic and qualitative theory of arbitrary order elliptic equations, the theory of ill-posed problems, the theory of boundary value problems in domains with piecewise smooth boundary. == Biography == === Life and academic career === Vladimir Maz'ya was born on 31 December 1937 in a Jewish family. His father died in December 1941 at the World War II front, and all four grandparents died during the siege of Leningrad. His mother, a state accountant, chose to not remarry and dedicated her life to him: they lived on her meager salary in a 9 square meters room in a big communal apartment, shared with other four families. As a secondary school student, he repeatedly won the city's mathematics and physics olympiads and graduated with a gold medal. In 1955, at the age of 18, Maz'ya entered the Mathematics and Mechanics Department of Leningrad University. Taking part to the traditional mathematical olympiad of the faculty, he solved the problems for both first year and second year students and, since he did not make this a secret, the other participants did not submit their solutions causing the invalidation of the contest by the jury which therefore did not award the prize. However, he attracted the attention of Solomon Mikhlin who invited him at his home, thus starting their lifelong friendship: and this friendship had a great influence on him, helping him develop his mathematical style more than anyone else. According to Gohberg (1999, p. 2), in the years to come, "Maz'ya was never a formal student of Mikhlin, but Mikhlin was more than a teacher for him. Maz'ya had found the topics of his dissertations by himself, while Mikhlin taught him mathematical ethics and rules of writing, referring and reviewing". More details on the life of Vladimir Maz'ya, from his birth to the year 1968, can be found in his autobiography (Maz'ya 2014). Maz'ya graduated from Leningrad University in 1960. The same year he gave two talks at Smirnov's seminar: their contents were published as a short report in the Proceedings of the USSR Academy of Sciences and later evolved in his "Candidate of Sciences" thesis, "Classes of sets and embedding theorems for function spaces", which was defended in 1962. In 1965 he earned the Doctor of Sciences degree, again from Leningrad University, defending the dissertation "Dirichlet and Neumann problems in Domains with irregular boundaries", when he was only 27. Neither the first nor his second thesis were written under the guidance of an advisor: Vladimir Maz'ya never had a formal scientific adviser, choosing the research problems he worked to by himself. From 1960 up to 1986, he worked as a "research fellow" at the Research Institute of Mathematics and Mechanics of Leningrad University (RIMM), being promoted from junior to senior research fellow in 1965. From 1968 to 1978 he taught at the Leningrad Shipbuilding Institute, where he was awarded the title of "professor" in 1976. From 1986 to 1990 he worked to the Leningrad Section of the Blagonravov Research Institute of Mechanical Engineering of the USSR Academy of Sciences, where he created and directed the Laboratory of Mathematical Models in Mechanics and the Consulting Center in Mathematics for Engineers. In 1978 he married Tatyana Shaposhnikova, a former doctoral student of Solomon Mikhlin, and they have a son, Michael: In 1990, they left the URSS for Sweden, where Prof. Maz'ya obtained the Swedish citizenship and started to work at Linköping University. Currently, he is honorary Senior Fellow of Liverpool University and Professor Emeritus at Linköping University: he is also member of the editorial board of several mathematical journals. === Honors === In 1962 Maz'ya was awarded the "Young Mathematician" prize by the Leningrad Mathematical Society, for his results on Sobolev spaces: he was the first winner of the prize. In 1990 he was awarded an honorary doctorate from Rostock University. In 1999, Maz'ya received the Humboldt Prize. He was elected member of the Royal Society of Edinburgh in 2000, and of the Swedish Academy of Science in 2002. In March 2003, he, jointly with Tatyana Shaposhnikova, was awarded the Verdaguer Prize by the French Academy of Sciences. On 31 August 2004 he was awarded the Celsius Gold Medal, the Royal Society of Sciences in Uppsala's top award, "for his outstanding research on partial differential equations and hydrodynamics". He was awarded the Senior Whitehead Prize by the London Mathematical Society on 20 November 2009. In 2012 he was elected fellow of the American Mathematical Society. On 30 October 2013 he was elected foreign member of the Georgian National Academy of Sciences. Starting from 1993, several conferences have been held to honor him: the first one, held in that year at the University of Kyoto, was a conference on Sobolev spaces. On the occasion of his 60th birthday in 1998, two international conferences were held in his honor: the one at the University of Rostock was on Sobolev spaces, while the other, at the École Polytechnique in Paris, was on the boundary element method. He was invited speaker at the International Mathematical Congress held in Beijing in 2002: his talk is an exposition on his work on Wiener–type criteria for higher order elliptic equations. Other two conferences were held on the occasion of his 70th birthday: "Analysis, PDEs and Applications on the occasion of the 70th birthday of Vladimir Maz'ya" was held in Rome, while the "Nordic – Russian Symposium in honour of Vladimir Maz'ya on the occasion of his 70th birthday" was held in Stockholm. On the same occasion, also a volume of the Proceedings of Symposia in Pure Mathematics was dedicated to him. On the occasion of his 80th birthday, a "Workshop on Sobolev Spaces and Partial Differential Equations" was held on 17–18 May 2018 was held at the Accademia Nazionale dei Lincei to honor him. On the 26–31 May 2019, the international conference "Harmonic Analysis and PDE" was held in his honor at the Holon Institute of Technology. == Work == === Research activity === Because of Maz'ya's ability to give complete solutions to problems which are generally considered as unsolvable, Fichera once compared Maz'ya with Santa Rita, the 14th century Italian nun who is the Patron Saint of Impossible Causes. Maz'ya authored/coauthored more than 500 publications, including 20 research monographs. Several survey articles describing his work can be found in the book (Rossmann, Takáč & Wildenhain 1999a), and also the paper by Dorina and Marius Mitrea (2008) describes extensively his research achievements, so these references are the main ones in this section: in particular, the classification of the research work of Vladimir Maz'ya is the one proposed by the authors of these two references. He is also the author of Seventy (Five) Thousand Unsolved Problems in Analysis and Partial Differential Equations which collects problems he considers to be important research directions in the field ==== Theory of boundary value problems in nonsmooth domains ==== In one of his early papers, Maz'ya (1961) considers the Dirichlet problem for the following linear elliptic equation: (1) L u = ∇ ( A ( x ) ∇ ) u + b ( x ) ∇ u + c ( x ) u = f x ∈ Ω ⊂ R n {\displaystyle {\mathcal {L}}u=\nabla (A(x)\nabla )u+\mathbf {b} (x)\nabla u+c(x)u=f\qquad x\in \Omega \subset \mathbf {R} ^{n}} where Ω is a bounded region in the n–dimensional euclidean space A(x) is a matrix whose first eigenvalue is not less than a fixed positive constant κ > 0 and whose entries are functions sufficiently smooth defined on Ω, the closure of Ω. b(x), c(x) and f(x) are respectively a vector-valued function and two scalar functions sufficiently smooth on Ω as their matrix counterpart A(x). He proves the following a priori estimate (2) ‖ u ‖ L s ( Ω ) ≤ K [ ‖ f ‖ L r ( Ω ) + ‖ u ‖ L ( Ω ) ] {\displaystyle \Vert u\Vert _{L_{s}(\Omega )}\leq K\left[\Vert f\Vert _{L_{r}(\Omega )}+\Vert u\Vert _{L(\Omega )}\right]} for the weak solution u of equation 1, where K is a constant depending on n, s, r κ and other parameters but not depending on the moduli of continuity of the coefficients. The integrability exponents of the Lp norms in Estimate 2 are subject to the relations 1/s ≥ 1/r - 2/n for n/2 > r > 1, s is an arbitrary positive number for r = n/2, the first one of which answers positively to a conjecture proposed by Guido Stampacchia (1958, p. 237). == Selected works == === Papers === Maz'ya, Vladimir G. (1960), Классы областей и теоремы вложения функциональных пространств, Доклады Академии Наук СССР (in Russian), vol. 133, pp. 527–530, MR 0126152, Zbl 0114.31001, translated as Maz'ya, Vladimir G. (1960), "Classes of domains and imbedding theorems for function spaces", Soviet Mathematics - Doklady, vol. 1, pp. 882–885, MR 0126152, Zbl 0114.31001. Maz'ya, Vladimir G. (1961), Некторые оценки решений эллиптических уравнений второго порядка, Доклады Академии Наук СССР (in Russian), vol. 137, pp. 1057–1059, Zbl 0115.08701, translated as Maz'ya, Vladimir G. (1961), "Some estimates for solutions of elliptic second-order equations", Soviet Mathematics - Doklady, vol. 2, pp. 413–415, Zbl 0115.08701. Maz'ya, Vladimir G. (1968), Примеры нерегулярных решений квазилинейных эллиптических уравнений с аналитическими коэффициентами, Функциональный анализ и его приложения (in Russian), vol. 2, no. 3, pp. 53–57, MR 2020860, Zbl 0179.43601, translated in English as Maz'ya, Vladimir G. (1968), "Examples of nonregular solutions of quasilinear elliptic equations with analytic coefficients", Functional Analysis and Its Applications, 2 (3): 230–234, doi:10.1007/BF01076124, MR 2020860, S2CID 121038871, Zbl 0179.43601. Maz'ya, V. G. (1969), "О слабых решениях задач Дирихле и Неймана", Труды Московского математического общества (in Russian), vol. 20, pp. 137–172, MR 0259329, Zbl 0179.43302, translated in English as Maz'ya, Vladimir G. (1971) [1969], "On weak solutions of the Dirichlet and Neumann problems", Transactions of the Moscow Mathematical Society, vol. 20, pp. 135–172, MR 0259329, Zbl 0226.35027. Maz'ya, Vladimir; Shubin, Mikhail (2005), "Discreteness of spectrum and positivity criteria for Schrödinger operators", Annals of Mathematics, 162 (2): 919–942, arXiv:math/0305278, doi:10.4007/annals.2005.162.919, JSTOR 20159932, MR 2183285, S2CID 14741680, Zbl 1106.35043 === Books === Burago, Yuri D.; Maz'ya, Vladimir G. (1967), "Некоторые вопросы теории потенциала и теории функций для областей с нерегулярными границами" [Certain questions of potential theory and function theory for regions with irregular boundaries], Записки научных семинаров ЛОМИ (in Russian), vol. 3, pp. 3–152, MR 0227447, Zbl 0172.14903, translated in English as Burago, Yuri D.; Maz'ya, Vladimir G. (1969), Potential Theory and Function Theory on Irregular Regions, Seminars in Mathematics, V. A. Steklov Mathematical Institute, Leningrad, vol. 3, New York: Consultants Bureau, pp. vii+68, ISBN 9780608100449. Gelman, I. W; Mazja, W. G. (1981), Abschätzungen für Differentialoperatoren im Halbraum [Estimates for differential operators in the half space], Mathematische Lehrbücher und Monogaphien, II. Albeitung: Mathematische Monographien (in German), vol. 54, Berlin: Akademie-Verlag, p. 221, ISBN 978-3-7643-1275-6, MR 0644480, Zbl 0499.47028. A definitive monograph, giving a detailed study of a priori estimates of constant coefficient matrix differential operators defined on ℝn×(0,+∞], with n ≥ 1: translated as Gelman, Igor W; Maz'ya, Vladimir G. (2019) [1981], Estimates for differential operators in half-space, EMS Tracts in Mathematics, vol. 31, translated by Apushkinskaya, Darya, Zurich: European Mathematical Society, pp. xvi+246, doi:10.4171/191, ISBN 978-3-03719-191-0, MR 3889979, S2CID 127027104, Zbl 1447.47007. Maz'ja, Vladimir G. (1985), Sobolev Spaces, Springer Series in Soviet Mathematics, Berlin–Heidelberg–New York: Springer-Verlag, pp. xix+486, doi:10.1007/978-3-662-09922-3, ISBN 978-3-540-13589-0, MR 0817985, Zbl 0692.46023 (also available with ISBN 0-387-13589-8). Maz'ya, Vladimir G.; Shaposhnikova, Tatyana O. (1985), "Theory of multipliers in spaces of differentiable functions", Russian Mathematical Surveys, Monographs and Studies in Mathematics, 23 (3), Boston – London – Melbourne: xiii+344, Bibcode:1983RuMaS..38...23M, doi:10.1070/RM1983v038n03ABEH003484, ISBN 978-0-273-08638-3, MR 0785568, S2CID 250849739, Zbl 0645.46031. Maz'ya, Vladimir G. (1991), "Boundary Integral Equations", in Maz'ya, Vladimir G.; Nikol'skiǐ, S. M. (eds.), Analysis IV, Encyclopaedia of Mathematical Sciences, vol. 27, Berlin–Heidelberg–New York: Springer-Verlag, pp. 127–222, doi:10.1007/978-3-642-58175-5_2, ISBN 978-0-387-51997-5, MR 1098507, Zbl 0780.45002 (also available as ISBN 3-540-51997-1). Maz'ya, Vladimir G.; Poborchi, Sergei V. (1997), Differentiable Functions on Bad Domains, Singapore–New Jersey–London–Hong Kong: World Scientific, pp. xx+481, ISBN 978-981-02-2767-8, MR 1643072, Zbl 0918.46033. Kozlov, Vladimir A.; Maz'ya, Vladimir G.; Rossmann, J. (1997), Elliptic Boundary Value Problems in Domains with Point Singularities, Mathematical Surveys and Monographs, vol. 52, Providence, RI: American Mathematical Society, pp. x+414, ISBN 978-0-8218-0754-5, MR 1469972, Zbl 0947.35004. Maz'ya, Vladimir; Shaposhnikova, Tatyana (1998), Jacques Hadamard, a Universal Mathematician, History of Mathematics, vol. 14, Providence, RI and London: American Mathematical Society and London Mathematical Society, pp. xxv+574, ISBN 978-0-8218-0841-2, MR 1611073, Zbl 0906.01031. There are also two revised and expanded editions: the French translation Maz'ya, Vladimir; Shaposhnikova, Tatyana (January 2005) [1998], Jacques Hadamard, un mathématicien universel, Sciences & Histoire (in French), Paris: EDP Sciences, p. 554, ISBN 978-2-86883-707-3, and the (further revised and expanded) Russian translation Мазья, В. Г.; Шапошникова, Т. О. (2008) [1998], Жак Адамар—легенда математики Жак Адамар Легенда Математики (in Russian), Москва: ИздателЬство МЦНМО, p. 528, ISBN 978-5-94057-083-7. Kozlov, Vladimir; Maz'ya, Vladimir (1999), Differential Equations with Operator Coefficients, Springer Monographs in Mathematics, Berlin–Heidelberg–New York: Springer-Verlag, pp. XV+442, doi:10.1007/978-3-662-11555-8, ISBN 978-3-540-65119-2, MR 1729870, Zbl 0920.35003. Kozlov, Vladimir A.; Maz'ya, Vladimir G.; Movchan, A. B. (1999), Asymptotic Analysis of Fields in Multi-Structures, Oxford Mathematical Monographs, Oxford: Oxford University Press, pp. xvi+282, ISBN 978-0-19-851495-4, MR 1860617, Zbl 0951.35004. Maz'ya, Vladimir G.; Nazarov, Serguei; Plamenevskij, Boris (2000), Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains. Volume I, Operator Theory: Advances and Applications, vol. 110, Birkhäuser Verlag, pp. XXIV+435, ISBN 978-3-7643-6397-0, MR 1779977, Zbl 1127.35300. Maz'ya, Vladimir G.; Nazarov, Serguei; Plamenevskij, Boris (2000), Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains. Volume II, Operator Theory: Advances and Applications, vol. 112, Birkhäuser Verlag, pp. XXIV+323, ISBN 978-3-7643-6398-7, MR 1779978, Zbl 1127.35301. Kozlov, V. A.; Maz'ya, V. G.; Rossmann, Jürgen (2001), Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations, Mathematical Surveys and Monographs, vol. 85, Providence, RI: American Mathematical Society, pp. x+436, ISBN 978-0-8218-2727-7, MR 1788991, Zbl 0965.35003. Kuznetsov, N.; Maz'ya, Vladimir; Vainberg, Boris (2002), Linear Water Waves. A Mathematical Approach, Cambridge: Cambridge University Press, pp. xviii+513, doi:10.1017/CBO9780511546778, ISBN 978-0-521-80853-8, MR 1925354, Zbl 0996.76001. Kresin, Gershon; Maz'ya, Vladimir G. (2007), Sharp Real-Part Theorems. A Unified Approach (PDF), Lecture Notes in Mathematics, vol. 1903, Berlin–Heidelberg–New York City: Springer-Verlag, pp. xvi+140, ISBN 978-3-540-69573-8, MR 2298774, Zbl 1117.30001. Maz'ya, Vladimir; Schmidt, Gunther (2007), Approximate approximations (PDF), Mathematical Surveys and Monographs, vol. 141, Providence, RI: American Mathematical Society, pp. xiv+349, doi:10.1090/surv/141, ISBN 978-0-8218-4203-4, MR 2331734, Zbl 1120.41013. Maz'ya, Vladimir G.; Shaposhnikova, Tatyana O. (2009) [1985], Theory of Sobolev multipliers. With applications to differential and integral operators, Grundlehren der Mathematischen Wissenschaft, vol. 337, Berlin–Heidelberg–New York: Springer-Verlag, pp. xiii+609, ISBN 978-3-540-69490-8, MR 2457601, Zbl 1157.46001. Maz'ya, Vladimir; Rossmann, Jürgen (2010), Elliptic Equations in Polyhedral Domains, Mathematical Surveys and Monographs, vol. 162, Providence, RI: American Mathematical Society, pp. viii+608, doi:10.1090/surv/162, ISBN 978-0-8218-4983-5, MR 2641539, Zbl 1196.35005. Maz'ya, Vladimir G.; Soloviev, Alexander A. (2010), Boundary Integral Equations on Contours with Peaks, Operator Theory: Advances and Applications, vol. 196, Basel: Birkhäuser Verlag, pp. vii+342, doi:10.1007/978-3-0346-0171-9, ISBN 978-3-0346-0170-2, MR 2584276, Zbl 1179.45001. Maz'ya, Vladimir G. (2011) [1985], Sobolev Spaces. With Applications to Elliptic Partial Differential Equations, Grundlehren der Mathematischen Wissenschaften, vol. 342 (2nd revised and augmented ed.), Berlin–Heidelberg–New York: Springer Verlag, pp. xxviii+866, doi:10.1007/978-3-642-15564-2, ISBN 978-3-642-15563-5, MR 2777530, Zbl 1217.46002. Kresin, Gershon; Maz'ya, Vladimir (2012), Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems, Mathematical Surveys and Monographs, vol. 183, Providence, RI: American Mathematical Society, pp. vii+317, doi:10.1090/surv/183, ISBN 978-0-8218-8981-7, MR 2962313, S2CID 118588520, Zbl 1255.35001. Maz'ya, Vladimir (2014), Differential equations of my young years, Basel: Birkhäuser Verlag, pp. xiii+191, doi:10.1007/978-3-319-01809-6, ISBN 978-3-319-01808-9, MR 3288312, Zbl 1303.01002 (also published with ISBN 978-3-319-01809-6). First Russian edition published as Владимир, Мазья (2020), Истории молодого математика, Saint Petersburg: Алетейя, p. 224, ISBN 978-5-00165-068-3. Maz'ya, V. G. (2018), Boundary behavior of solutions to elliptic equations in general domains, EMS Tracts in Mathematics, vol. 30, Zurich: European Mathematical Society, pp. x+431, doi:10.4171/190, ISBN 978-3-03719-190-3, MR 3839287, S2CID 125662951, Zbl 1409.35073 == See also == Function space Multiplication operator Partial differential equation Potential theory Sobolev space == Notes == == References == == External links == Vladimir Mazya at the Mathematics Genealogy Project Professor's Maz'ya's home page
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Wikipedia:Vladimir Miklyukov#0
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Vladimir Michaelovich Miklyukov (Russian: Миклюков, Владимир Михайлович, also spelled Miklioukov or Mikljukov) (8 January 1944 – October 2013) was a Russian educator in mathematics, and head of the Superslow Process workgroup based at Volgograd State University. == Biography == In 1970, as a student of Georgy D. Suvorov at Donetsk National University, he defended his Ph.D. thesis Theory of Quasiconformal Mappings in Space. In 1981 Miklyukov and his family moved to Volgograd. He was transferred to the newly built Volgograd State University where he became chairman of the Department of Mathematical Analysis and Theory of Functions. His scientific research focused on geometrical analysis. At the same time, he was studying zero mean curvature surfaces in Euclidean and pseudo-Euclidean spaces, nonlinear elliptic type partial differential equations and quasiregular mappings of Riemannian manifolds. The main results of that work were related to the following groups of questions: The external geometrical structure of zero mean curvature surfaces in Euclidean and pseudo-euclidean spaces; spacelike tubes and bands of zero mean curvature, their stability and instability with respect to small deformations, their life-time, branches, connections between branch points and Lorentz invariant characteristics of surfaces; Phragmén-Lindelöf type theorems for differential forms; Ahlfors type theorems for differential forms with finite or infinite number of different asymptotic tracts; generalizations of Wiman theorem of forms, applications to quasiregular mappings on manifolds; applications of isoperimetric methods to the Phragmén–Lindelöf principle for quasiregular mappings on manifolds. From 1998-2000 Miklyukov was a visiting professor at Brigham Young University. In 2009 Miklyukov was named a Distinguished Scientist of Russian Federation. == Publications == Miklyukov, Vladimir (2008). Introduction to Nonsmooth Analysis (PDF) (in Russian) (2 ed.). Volgograd: VolSU. ISBN 978-5-9669-0457-9. Archived from the original (PDF) on 2011-07-22. Retrieved 2009-11-16. —— (2007). Geometrical Analysis. Differential Forms, Almost-solutions, Almost Quasiconformal Mappings (PDF) (in Russian). Volgograd: VolSU. ISBN 978-5-9669-0268-1. —— (2006). Introduction to Nonsmooth Analysis. Volgograd: VolSU. ISBN 5-9669-0209-7. —— (2005). Conformal Mapping of Irregular Surfaces and Its Application (PDF) (in Russian). Volgograd: VolSU. ISBN 5-9669-0071-X. Archived from the original (PDF) on 2011-07-22. Retrieved 2009-11-15. Miklyukov, Vladimir; Klyachin, Vladimir A. (2004). Tubes and Bands in Space-Time. Anniversary series: The Scientists of the Volga (in Russian). Volgograd: VolSU. ISBN 5-85534-971-3. == References == == External links == Official website of Milyukov (in Russian) Vladimir Miklyukov's obituary (in Russian)
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Wikipedia:Vladimir Neuvazhaev#0
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Vladimir Emelyanovich Neuvazhaev was born in 1935. He is a Soviet and Russian specialist in the field of computational mathematics, Doctor of Physics and Mathematics (1972), professor (1989), USSR State Prize Laureate (1972), and Honored Scientist of the Russian Federation (2006). == Biography == Neuvazhaev was born on June 30, 1935, in the village of Novodzherelievskaya, Bryukhovetsky District, of Krasnodar territory. In 1956, after graduating from the Faculty of Physics and Mathematics at Rostov State University, he worked in the system of the USSR MSM. In 1956, he was sent to the closed city Chelyabinsk-70 to the All-Russian Scientific Research Institute Of Technical Physics with the appointment of engineer. In 1959, he became senior engineer and group leader, since 1965 - head of department. In 1971, he became Deputy Head of the Mathematical Department for Science at VNIITF. In 1963, he defended his academic degree Candidate of Physical and Mathematical Sciences; in 1986 - Doctor of Physics and Mathematics. In 1996, Chief Researcher of VNIITF, Neuvazhaev's main scientific interests were related to the development of new numerical methods for solving complex problems in continuum mechanics, mathematical modeling processes of occurrence and development of hydrodynamic stability and turbulence in flows of stratified gases and liquids. In 1993, he was a professor at the Department of Computational Mathematics at Chelyabinsk State University and at the Snezhinsk Academy of Physics and Technology. In 1995, he became Academician of the International Informatization Academy. In 1979, he became a member of the editorial board of the Scientific and Technical Collection "Problems of Atomic Science and Technology" (VANT) from the series "Mathematical Modeling of Physical Processes." == Publications == V. E. Neuvazhaev, Gas vacuum exhaustion under power supply law, Academy of Sciences, USSR, 141:5 (1961), 1058–1060 V. E. Neuvazhaev, On the theory of turbulent mixing, Academy of Sciences, USSR, 222:5 (1975), 1053–1056 V. E. Neuvazhaev, V. G. Yakovlev, “Turbulent mixing of the interface in the numerical gas-dynamic calculation,” 440–450 mathnet zmath; U.S.S.R. Comput. Math. Math. Phys., 16:2 (1976), 154–165 V. E. Neuvazhaev, Features of a turbulent mixing model based on the two-component model with different velocities of each component. Separation addition to diffusion models, 7:7 (1995), 3–18 == Awards == Order of Friendship of Peoples (1985) USSR State Prize (1972) Honored Scientist of the Russian Federation (2006) == References == == Further reading == Nikitin V. I.; Kazachenkova G. B., eds. (2009). In orbits of memory: On the founders and creators of the Ural nuclear center. Snezhinsk: VNIITF. ISBN 978-5-902278-35-1.
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Wikipedia:Vladimir Platonov#0
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Vladimir Petrovich Platonov (Belarusian: Уладзімір Пятровіч Платонаў, Uladzimir Piatrovic Platonau; Russian: Влади́мир Петро́вич Плато́нов; born 1 December 1939, Stayki village, Vitebsk Region, Byelorussian SSR) is a Soviet, Belarusian and Russian mathematician. He is an expert in algebraic geometry and topology and member of the Russian Academy of Sciences. From 1992–2004 he worked at research centers in the United States, Canada and Germany. == Education == In 1961 Platonov graduated with highest distinction from Belarusian State University. In 1963 he received his Ph.D. from the Academy of Sciences of Belarus. In 1967, Platonov received his Doctor of Science degree from the Academy of Sciences of USSR. == Career == At age 28 Platonov received a title of full professor at Belarus State. This made him the youngest full professor in the nation's history. In 1972 he became an Academician of the National Academy of Sciences of Belarus and its President (1987–1993). He has been an Academician of the Russian/USSR Academy of Sciences since 1987. He was the Director of the Institute of Mathematics of the Academy of Sciences of Belarus from 1977 to 1992. == Research == His interests are algebra, algebraic geometry and number theory. He solved the Strong approximation problem, developed the reduced K-theory and solved the Tannaka–Artin problem. He solved the Kneser-Tits and Grothendieck problems. Together with F. Grunewald he solved the arithmeticity problem for finite extensions of arithmetic groups and the rigidity problem for arithmetic subgroups of algebraic groups with radical. Platonov solved the rationality problem for spinor varieties and the Dieudonne problem on spinor norms. Platonov was an invited speaker of the International Congresses of Mathematicians in Vancouver (1974), Helsinki (1978) and the European Congress of Mathematicians in Budapest (1996). He is a member of the Canadian Mathematical Society and from 1993 to 2001 was a Professor of the Faculty of Mathematics of the University of Waterloo in Waterloo, Ontario, Canada. He is the author, with Andrei Rapinchuk, of Algebraic Groups and Number Theory. He currently works as a Chief Science Officer of Scientific Research Institute of System Development (NIISI RAN). == Assault conviction == On November 9, 1999, Platonov appeared in court on a bail hearing on a charge of attempted murder for an attack on his wife. He was convicted of assault. The court gave him a conditional sentence of two years. In September 2001, Platonov took early retirement as a professor of the University of Waterloo. == Awards == Order of the Red Banner of Labour 1968: Lenin Komsomol Prize, for a series of works in topological group theory 1978: Lenin Prize in Science and Technology, for a fundamental series of works "Arithmetics of Algebraic Groups and Reduced K-Theory" ("Арифметика алгебраических групп и приведенная К-теория") 1993: Humboldt Prize == See also == List of University of Waterloo people == References ==
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Wikipedia:Vladimir Popov (mathematician)#0
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Vladimir Leonidovich Popov (Russian: Влади́мир Леони́дович Попо́в; born 3 September 1946) is a Russian mathematician working in the invariant theory and the theory of transformation groups. == Education and career == In 1969 he graduated from the Faculty of Mechanics and Mathematics of Moscow State University. In 1972 he received his Candidate of Sciences degree (PhD) with thesis Стабильность действия алгебраических групп и арифметика квазиоднородных многообразий (Stability of the action of algebraic groups and the arithmetic of quasi-homogeneous varieties). In 1984 he received his Russian Doctor of Sciences degree (habilitation) with thesis Группы, образующие, сизигии и орбиты в теории инвариантов (Groups, generators, syzygies and orbits in the theory of invariants). He is a member of the Steklov Institute of Mathematics and a professor of the National Research University – Higher School of Economics. In 1986, he was an invited speaker at the International Congress of Mathematicians (Berkeley, USA), and in 2008–2010 he was a core member of the panel for Section 2, "Algebra" of the Program Committee for the 2010 International Congress of Mathematicians (Hyderabad, India). In 1987 he published a proof of a conjecture of Claudio Procesi and Hanspeter Kraft. In 2006, with Nicole Lemire and Zinovy Reichstein, Popov published a solution to a problem posed by Domingo Luna in 1973. == Awards == In 2012, he was elected a member of the inaugural class of Fellows of the American Mathematical Society which recognizes mathematicians who have made significant contributions to the field. In 2016, he was elected a corresponding member of the Russian Academy of Sciences. == Books == Popov, Vladimir L. (1982). Discrete complex reflection groups. Utrecht: Communications of the Mathematical Institute Rijksuniversiteit Utrecht, Vol. 15. Popov, Vladimir L. (1992). Groups, generators, syzygies, and orbits in invariant theory. Providence RI: Translations of Mathematical Monographs, Vol. 100, Providence RI: Amer. Math. Soc. ISBN 0-8218-4557-8. Popov, V. L.; Vinberg, E. B. (1994). "Invariant Theory". Algebraic Geometry IV. Encyclopaedia of Mathematical Sciences. Vol. 55. Berlin; Heidelberg: Springer. pp. 123–278. doi:10.1007/978-3-662-03073-8_2. ISBN 978-3-642-08119-4. Popov, Vladimir L. (2004). Algebraic transformation groups and algebraic varieties: proceedings of the conference Interesting algebraic varieties arising in algebraic transformation group theory held at the Erwin Schrödinger Institute, Vienna, October 22-26, 2001. Berlin New York: Springer. ISBN 9783540208389. == References == == External links == Personal profile: Vladimir Leonidovich Popov Steklov Institute of Mathematics
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Wikipedia:Vladimir Retakh#0
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Vladimir Solomonovich Retakh (Russian: Ретах Владимир Соломонович; 20 May 1948) is a Russian-American mathematician who made important contributions to Noncommutative algebra and combinatorics among other areas. == Biography == Retakh graduated in 1970 from the Moscow State Pedagogical University. Beginning as an undergraduate Retakh regularly attended lectures and seminars at the Moscow State University most notably the Gelfand seminars. He obtained his PhD in 1973 under the mentorship of Dmitrii Abramovich Raikov. He joined the Gelfand group in 1986. His first position was at the central Research Institute for Engineering Buildings and later obtained his first academic position at the Council for Cybernetics of the Soviet Academy of Sciences in 1989. While at the Council for Cybernetics of the Soviet Academy of Sciences in 1990, Retakh had started working with Gelfand on their new program on Noncommutative determinants. Prior to immigrating to the US in 1993 he also held a position at the Scientific Research Institute of System Development == Research == Retakh's other contributions include: Contributions to the theory of general hypergeometric functions Contributions to the theory of Lie–Massey operators Instigated the study of homotopical properties of categories of extensions based on the Retakh isomorphism Introduction of noncommutative determinants, also known as quasideterminants Introduction of noncommutative symmetric functions The introduction of noncommutative Plücker coordinates Noncommutative integrable systems == Recognition == He was included in the 2019 class of fellows of the American Mathematical Society "for contributions to noncommutative algebra and noncommutative algebraic geometry". == References == Retakh V. (2010). "Israel Moiseevich Gelfand" (PDF). Newsletter of the European Mathematical Society. 63 (76): 25–27. Bibcode:2010PhT....63h..63R. doi:10.1063/1.3480085. ISSN 1027-488X. Gel'fand, I. M.; Graev, M. I.; Retakh, V. S. (1992). "General hypergeometric systems of equations and series of hypergeometric type". Russian Mathematical Surveys. 47 (4): 25–27. "Publications of Vladimir Retakh". Rutgers, The State University of New Jersey. 2011-01-08. Ретах В. (2009-12-25). "Об Израиле Моисеевиче Гельфанде". МЦНМО. Archived from the original on 2010-12-28. Retrieved 2012-04-15. "Ретах Владимир Соломонович: Публикации в базе данных Math-Net.Ru". mathnet.ru – Общероссийский математический портал. Retrieved 2012-04-15. "Israel Moiseevich Gelfand, Part I" (PDF). American Mathematical Society. "Israel Moiseevich Gelfand, Part II" (PDF). American Mathematical Society. "Gelfand Centennial Conference: A View of 21st Century Mathematics, MIT, Cambridge, Massachusetts". 2013. Etingof, Pavel; Retakh, Vladimir S.; Singer, I. M (2013). The Unity of Mathematics. In Honor of the Ninetieth Birthday of I.M. Gelfand.
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Wikipedia:Vladimir Rokhlin Jr.#0
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Vladimir Rokhlin Jr. (born August 4, 1952) is a mathematician and professor of computer science and mathematics at Yale University. He is the co-inventor with Leslie Greengard of the fast multipole method (FMM) in 1985, recognised as one of the top-ten algorithms of the 20th century. In 2008, Rokhlin was elected as a member into the National Academy of Engineering for the development of fast multipole algorithms and their application to electromagnetic and acoustic scattering. == Short biography == Vladimir Rokhlin Jr. was born on August 4, 1952, in Voronezh, USSR (now Russia). In 1973 he received a M.S. in mathematics from the University of Vilnius in Lithuania, and in 1983 a Ph.D. in applied mathematics from Rice University located in Houston, Texas, United States. In 1985 Rokhlin started working at Yale University located in New Haven, Connecticut, United States, where he is now professor of computer science and mathematics. He is the son of Soviet mathematician Vladimir Abramovich Rokhlin. == Awards and honors == Rokhlin has received several awards and honors, including: the Leroy P. Steele Prize for Seminal Contribution to Research from the American Mathematical Society in 2001 (together with Leslie F. Greengard), for their paper describing a new algorithm: the fast multipole method (FMM) the "Rice University Distinguished Alumni Award" in 2001 elected a member of both the U.S. National Academy of Engineering (2008) and the U.S. National Academy of Sciences (1999) the IEEE Honorary Membership in 2006. elected to fellow of the Society for Industrial and Applied Mathematics in 2009 the ICIAM Maxwell Prize from the International Council for Industrial and Applied Mathematics in 2011 The William Benter Prize in Applied Mathematics from the Liu Bie Ju Centre for Mathematical Sciences in 2014 Fellow of the American Academy of Arts and Sciences, 2016 == References == == External links == Vladimir Rokhlin at the Mathematics Genealogy Project
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Wikipedia:Vladimir Smirnov (mathematician)#0
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Vladimir Ivanovich Smirnov (Russian: Влади́мир Ива́нович Смирно́в; 10 June 1887 – 11 February 1974) was a Soviet mathematician who made significant contributions in both pure and applied mathematics, and also in the history of mathematics. Smirnov worked on diverse areas of mathematics, such as complex functions and conjugate functions in Euclidean spaces. In the applied field his work includes the propagation of waves in elastic media with plane boundaries (with Sergei Sobolev) and the oscillations of elastic spheres. His pioneering approach to solving the initial-boundary value problem to the wave equation formed the basis of the spacetime triangle diagram (STTD) technique for wave motion developed by his follower Victor Borisov (also known as the Smirnov method of incomplete separation of variables). Smirnov was a Ph.D. student of Vladimir Steklov. Among his notable students were Sergei Sobolev, Solomon Mikhlin and Nobel prize winner Leonid Kantorovich. Smirnov is also widely known among students for his five volume series (in seven books) A Course in Higher Mathematics (Курс высшей математики) (the first volume was written jointly with Jacob Tamarkin). == References == == External links == Vladimir Smirnov at the Mathematics Genealogy Project O'Connor, John J.; Robertson, Edmund F., "Vladimir Smirnov", MacTutor History of Mathematics Archive, University of St Andrews
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Wikipedia:Vladimir Uspensky (mathematician)#0
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Vladimir Andreyevich Uspensky (Russian: Влади́мир Андре́евич Успе́нский; 27 November 1930 – 27 June 2018) was a Russian mathematician, linguist, writer, doctor of physics and mathematics (1964). He was the author of numerous papers on mathematical logic and linguistics. In addition, he also penned a number of memoir essays. Uspensky initiated a reform of linguistic education in Russia. == Biography == Uspensky graduated in 1952 from the MSU Faculty of Mechanics and Mathematics (Lomonosov Moscow State University). He was a student of Andrey Kolmogorov. He was the head of the Chair of Mathematical Logic and Theory of Algorithms in the MSU Faculty of Mechanics and Mathematics (1995) and one of the founders of the Structural Linguistics branch (now the Theoretical and Applied Linguistics branch) in the MSU Faculty of Philology, where he also taught. He was the author of many books and of over 100 research papers. He prepared 25 candidates and 4 doctors of sciences. His book "The Apology of Mathematics" received in 2010 the “Enlightener" award in the field of natural and exact sciences. He was a distinguished professor at the Moscow State University (1998). His brother Boris Uspenskij is a distinguished Russian philologist and mythographer. == References == V.A. Uspensky. Труды по нематематике. М.: ОГИ, 2002, т. I—II. ISBN 5-94282-087-2 (т.1), ISBN 5-94282-088-0 (т.2) Chapter from the book "Апология математики" V.A. Uspensky: Seven reflections on the themes of philosophy of mathematics V.A. Uspensky: Lecture on mathematics as part of the culture, and the Poincare conjecture == External links == Mathematics Genealogy Project entry MSU home page Dynkin Collection entry with video interviews Russian listing of publications Math-Net.ru list of publications, including video lectures
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Wikipedia:Vladimir Vapnik#0
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Vladimir Naumovich Vapnik (Russian: Владимир Наумович Вапник; born 6 December 1936) is a statistician, researcher, and academic. He is one of the main developers of the Vapnik–Chervonenkis theory of statistical learning and the co-inventor of the support-vector machine method and support-vector clustering algorithms. == Early life and education == Vladimir Vapnik was born to a Jewish family in the Soviet Union. He received his master's degree in mathematics from the Uzbek State University, Samarkand, Uzbek SSR in 1958 and Ph.D in statistics at the Institute of Control Sciences, Moscow in 1964. He worked at this institute from 1961 to 1990 and became Head of the Computer Science Research Department. == Academic career == At the end of 1990, Vladimir Vapnik moved to the USA and joined the Adaptive Systems Research Department at AT&T Bell Labs in Holmdel, New Jersey. While at AT&T, Vapnik and his colleagues did work on the support-vector machine (SVM), which he also worked on much earlier before moving to the USA. They demonstrated its performance on a number of problems of interest to the machine learning community, including handwriting recognition. The group later became the Image Processing Research Department of AT&T Laboratories when AT&T spun off Lucent Technologies in 1996. In 2001, Asa Ben-Hur, David Horn (Israeli physicist), Hava Siegelmann and Vapnik developed Support-Vector Clustering, which enabled the algorithm to categorize inputs without labels—becoming one of the most ubiquitous data clustering applications in use. Vapnik left AT&T in 2002 and joined NEC Laboratories in Princeton, New Jersey, where he worked in the Machine Learning group. He also holds a Professor of Computer Science and Statistics position at Royal Holloway, University of London since 1995, as well as a position as Professor of Computer Science at Columbia University, New York City since 2003. As of February 1, 2021, he has an h-index of 86 and, overall, his publications have been cited 226597 times. His book on "The Nature of Statistical Learning Theory" alone has been cited 91650 times. On November 25, 2014, Vapnik joined Facebook Artificial Intelligence Research (now Meta AI), where he is working alongside his longtime collaborators Jason Weston, Léon Bottou, Ronan Collobert, and Yann LeCun. In 2016, he also joined Peraton Labs. == Honors and awards == Vladimir Vapnik was inducted into the U.S. National Academy of Engineering in 2006. He received the 2005 Gabor Award from the International Neural Network Society, the 2008 Paris Kanellakis Award, the 2010 Neural Networks Pioneer Award, the 2012 IEEE Frank Rosenblatt Award, the 2012 Benjamin Franklin Medal in Computer and Cognitive Science from the Franklin Institute, the 2013 C&C Prize from the NEC C&C Foundation, the 2014 Kampé de Fériet Award, the 2017 IEEE John von Neumann Medal. In 2018, he received the Kolmogorov Medal from University of London and delivered the Kolmogorov Lecture. In 2019, Vladimir Vapnik received BBVA Foundation Frontiers of Knowledge Award. == Selected publications == On the uniform convergence of relative frequencies of events to their probabilities, co-author A. Y. Chervonenkis, 1971 Necessary and sufficient conditions for the uniform convergence of means to their expectations, co-author A. Y. Chervonenkis, 1981 Estimation of Dependences Based on Empirical Data, 1982 The Nature of Statistical Learning Theory, 1995 Statistical Learning Theory (1998). Wiley-Interscience, ISBN 0-471-03003-1. Estimation of Dependences Based on Empirical Data, Reprint 2006 (Springer), also contains a philosophical essay on Empirical Inference Science, 2006 == See also == Alexey Chervonenkis == References == == External links == Photograph of Professor Vapnik Vapnik's brief biography from the Computer Learning Research Centre, Royal Holloway Interview by Lex Fridman
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Wikipedia:Vladimir Varićak#0
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Vladimir Varićak (sometimes also spelled Vladimir Varičak; March 1, 1865 – January 17, 1942) was a Croatian Serb mathematician and theoretical physicist. == Biography == Varićak, an ethnic Serb, was born on March 1, 1865, in the village of Švica near Otočac, Austrian Empire (present-day Croatia). He studied physics and mathematics at the University of Zagreb from 1883 to 1887. He made his PhD in 1889 and got his habilitation in 1895. In 1899 he became professor of mathematics in Zagreb, where he gave lectures until his death in 1942. From 1903 to 1908 he wrote on hyperbolic geometry (or Bolyai–Lobachevskian geometry). In 1910, following a 1909 publication of Sommerfeld, he applied hyperbolic geometry to the special theory of relativity. Sommerfeld, using the imaginary form of Minkowski space, had shown in his 1909 paper that the Einstein formula for combination of velocities is most clearly understandable as a formula for triangular addition on the surface of a sphere of imaginary radius. Varićak reinterpreted this result as showing that rapidity combines by the triangle rule in hyperbolic space. This is a fundamental result for the hyperbolic theory which was demonstrated later by other approaches by Robb (1911) and Borel (1913). The 1910 papers also dealt with several applications of the hyperbolic theory to optics. In 1911 Varićak was invited to speak to the Deutsche Mathematiker-Vereinigung in Karlsruhe on his work. He continued to develop the hyperbolic reinterpretation of Einstein's theory collecting his results in 1924 in a textbook, Darstellung der Relativitätstheorie im drei-dimensionalen Lobatschefskijschen Raume (Relativity in Three-Dimensional Lobachevski Space), now available in English. In the period 1909 to 1913 Varićak had correspondence with Albert Einstein concerning rotation and length contraction where Varićak's interpretations differed from those of Einstein. Concerning length contraction Varićak said that in Einstein's interpretation the contraction is only an "apparent" or a "psychological" phenomenon due to the convention of clock measurements whereas in the Lorentz theory it was an objective phenomenon. Einstein published a brief rebuttal, saying that his interpretation of the contraction was closer to Lorentz's. Walter (1999) re-examined Minkowski's non-Euclidean geometry. He begins by analysis of "the tip of a four-dimensional velocity vector" and notes Minkowski's equations where "both hypersurfaces provide a basis for a well-known model of non-Euclidean space of constant negative curvature, popularized by Helmholtz." In fact it is known as the hyperboloid model of hyperbolic geometry. Walter goes on to say: More than any other mathematician, Varićak devoted himself to the development of the non-euclidean style [of relativity], unfolding Minkowski's image of velocity-vector relations in hyperbolic space, and recapitulating a variety of results in terms of hyperbolic functions. The use of hyperbolic trigonometry was shown by Varićak to entail significant notational advantages. For example, he relayed the interpretation put forth by Hergloz and Klein of the Lorentz transformation as a displacement in hyperbolic space, and indicated simple expressions for proper time and the aberration of light in terms of a hyperbolic argument. Varićak is also known as a high school teacher of Milutin Milanković and of Mileva Marić, the first wife of Einstein, and as a university instructor of Đuro Kurepa. Varićak made scholarly contributions on the life and work of Ruđer Bošković (1711–1787) These are listed in the biography of Kurepa (1965) cited below. Of special interest for the history of relativity is that Varićak also edited and published a little-known 1755 paper of Boscovich in Latin entitled "On absolute motion – if it is possible to distinguish it from relative motion" ("Of Space and Time"). Varićak said that the paper "contains many remarkably clear and radical ideas regarding the relativity of space, time and motion." Although having a Serbian origin and being an Orthodox and later Greek Catholic, he disputed and dismissed the thesis that Ruđer Bošković was a Serb. He was a member of the Yugoslav Academy of Sciences and Arts, the Czech Academy of Sciences, the Serbian Academy of Sciences and Arts, the Croatian Society for Natural Science, and the Yugoslav Mathematical Society. == See also == Ehrenfest paradox == Publications == Varićak, V. (1903), "Bemerkung zu einem Punkte in der Festrede L. Schlesingers über Johann Bolyai", Jahresbericht der Deutschen Mathematiker-Vereinigung (in German), 12: 165–194 Varićak, V. (1908), "Beiträge zur nichteuklidischen Geometrie", Jahresbericht der Deutschen Mathematiker-Vereinigung, 17: 70–83 Varićak, V. (1908) "Zur nichteuklidischen analytischen Geometrie", Proceedings of the International Congress of Mathematicians, Bd. II, SS. 213–26. Varićak, V. (1910), "Anwendung der Lobatschefskijschen Geometrie in der Relativtheorie" , Physikalische Zeitschrift, 11: 93–6 Wikisource translation: Application of Lobachevskian Geometry in the Theory of Relativity Varićak, V. (1910), "Die Relativtheorie und die Lobatschefskijsche Geometrie" , Physikalische Zeitschrift, 11: 287–293 Wikisource translation: The Theory of Relativity and Lobachevskian Geometry Varićak, V. (1910), "Die Reflexion des Lichtes an bewegten Spiegeln" , Physikalische Zeitschrift, 11: 586–587 Wikisource translation: The Reflection of Light at Moving Mirrors Varićak, V. (1911), "Die Interpretation der Relativtheorie in der Lobatschevkijschen Geometrie (Serbian)", Proc. Serb. Acad., 93: 211–255 Varićak, V. (1911), "Zum Ehrenfestschen Paradoxon" , Physikalische Zeitschrift, 12: 169 Wikisource translation: On Ehrenfest's Paradox Varićak, V. (1912), "Über die nichteuklidische Interpretation der Relativtheorie" , Jahresbericht der Deutschen Mathematiker-Vereinigung, 21: 103–127 Wikisource translation: On the Non-Euclidean Interpretation of the Theory of Relativity Varićak, V. (1914), "Bemerkungen zur Relativtheorie" , Bull. Acad. Zagreb (2): 46–64 Varićak, V. (1914), "Beitrag zur nichteuklidischen Interpretation der Relativtheorie" , Bull. Acad. Zagreb (3): 46–49 Varićak, V. (1915), "Über die Transformation des elektromagnetischen Feldes in der Relativtheorie" , Bull. Acad. Zagreb (3): 101–106 Varićak, V. (1915), "Eine Bemerkung zum Dopplerschen Effekt" , Bull. Acad. Zagreb (4): 87–88 Varićak, V.(1924) Darstellung der Relativitatstheorie im drei=dimensionalen Lobatschefskijschen Raume, Zagreb (Narodni Novini); English translation (2007) Relativity in three dimensional Lobachevski Space, A.F. Kracklauer translator ISBN 1-84753-364-7, at Amazon.com. Varićak, V. (1936), "Relativity theory and the Universe", Nature, 137 (3469): 707, Bibcode:1936Natur.137..707V, doi:10.1038/137707b0 A complete list of Varićak's publications on all subjects is given in the following paper: Kurepa D. (1965), "First centenary of the birth of mathematician Vladimir Varićak", Informations Scientifiques, Univ.Belgrade (in Serbian): 61–67 == Notes == == External links == German Wikisource has original text related to this article: Vladimir Varićak Works related to Vladimir Varićak at Wikisource "Vladimir Varićak" at the University of Zagreb
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Wikipedia:Vladimir Zakalyukin#0
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Vladimir Mikhailovich Zakalyukin (in Russian: Владимир Михайлович Закалюкин; 9 July 1951 – 30 December 2011) was a Russian mathematician known for his research on singularity theory, differential equations, and optimal control theory. He obtained his Ph.D. at Moscow State University in 1977 (the thesis: "Lagrangian and Legendrian singularities"). His thesis advisor was Vladimir Arnold. In 2007 he won the MAIK Nauka award for best research publication in Russian. He worked at the Moscow State University, the University of Liverpool, and the Moscow Aviation Institute. == Selected publications == V. M. Zakalyukin, "Lagrangian and Legendrian singularities", Functional Analysis and Its Applications, 1976. V. M. Zakalyukin, "Reconstructions of fronts and caustics depending on a parameter and versality of mappings", Journal of Soviet Mathematics, 1984. V. M. Zakalyukin, "Singularities of Circle-Surface Contacts and Flags", Functional Analysis and Its Applications, 1997. V. V. Goryunov, V. M. Zakalyukin, "Simple symmetric matrix singularities and the subgroups of Weyl groups Aμ, Dμ, Eμ", Mosc. Math. J., 3:2 (2003). J.-P. Gauthier, V. M. Zakalyukin, "On the motion planning problem, complexity, entropy, and nonholonomic interpolation", J. Dyn. Control Syst., 12:3 (2006). == References == == External links == R.I.P. (Independent University of Moscow) R.I.P. (Kevin Houston)
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Wikipedia:Vladimír Palko#0
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Vladimír Palko (born 20 May 1957 in Čuňovo) is a Slovak politician. He is a member of the National Council of the Slovak Republic and former interior minister of Slovakia. On 12 March 2008 he established a new party called Conservative Democrats of Slovakia after he left Christian Democratic Movement in February 2008, due to his scepticism and disappointment about leadership of Pavol Hrušovský. == References == == External links ==
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Wikipedia:Vladimír Šverák#0
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Vladimír Šverák (born 1959) is a Czech mathematician. Since 1990, he has been a professor at the University of Minnesota. Šverák made notable contributions to calculus of variations. Šverák obtained his doctorate from the Charles University in Prague in 1986, under supervision of Jindřich Nečas. He worked on problems in the theory of non-linear elasticity. In 1992, he won an EMS Prize for producing a counterexample to a problem first posed by Charles B. Morrey, Jr. in 1950, whether rank-one convexity implies quasiconvexity. In 1994, Šverák was an Invited Speaker of the International Congress of Mathematicians in Zurich. He was named to the American Academy of Arts and Sciences in 2024. == References == == External links == Vladimír Šverák at the Mathematics Genealogy Project Website at the University of Minnesota
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Wikipedia:Vlastimil Dlab#0
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Vlastimil Dlab (born 5 August 1932) is a Czech-born Canadian mathematician who has worked in Czechoslovakia, Sudan, Australia and especially Canada where he founded and led an influential department of modern mathematics. == Biography == Dlab was born on August 5, 1932, in Bzí, Czechoslovakia, a historical village whose territory currently belongs to Železný Brod. He studied at Charles University in Prague, and worked at the Czechoslovak Academy of Sciences for a while in 1956. At Charles University, he was gradually promoted to associate professor. However. Between 1954 and 1964, he was doing university research in Khartoum in Sudan. Between 1964 and 1965 he returned Prague but the Institute of Advanced Studies in Canberra, Australia attracted him between 1965 and 1968. After the 1968 Warsaw Pact invasion of Czechoslovakia, he wasn't quite embraced with open arms. So in 1971, he left for Ottawa, Canada where he founded and led a department of modern mathematics at Carleton University that has significantly influenced the world of algebra, probability, and statistics. Because his father was ill in the early 1980s, Dlab – as an alien – was allowed to visit Czechoslovakia and he restored his relationship with Charles University. In the late 1980s, he taught some courses again there, and he regained full professorship in 1992. == Academic ancestry and collaborators == Dlab was a postdoctoral student of renowned Czech mathematician Eduard Čech. While in Canada, Dlab worked as the editor-of-chief of mathematical journals and chairman of assorted organizations and institutions. In 1977, he was elected a fellow of the Royal Society of Canada. Claus Michael Ringel was the co-author of some of the most famous academic works by Dlab, such as the 1976 book Indecomposable representations of graphs and algebras. Dlab helped to educate numerous students of mathematics who became successful by themselves. == Teaching of mathematics == In recent years, Dlab was very active in efforts to improve the mathematics education. In the Czech Republic, he's been often quoted as an authority that is skeptical towards modern methods to teach, e.g. the method of Milan Hejný. He emphasizes the key role played by the quality of teachers. == See also == Eduard Čech == References == == External links == Vlastimil Dlab at the Mathematics Genealogy Project Personal web page
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Wikipedia:Vogan diagram#0
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In mathematics, a Vogan diagram, named after David Vogan, is a variation of the Dynkin diagram of a real semisimple Lie algebra that indicates the maximal compact subgroup. Although they resemble Satake diagrams they are a different way of classifying simple Lie algebras. == References == Knapp, Anthony W. (2002), Lie groups beyond an introduction, Progress in Mathematics, vol. 140 (2nd ed.), Boston, MA: Birkhäuser Boston, ISBN 978-0-8176-4259-4, MR 1920389
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Wikipedia:Vojtěch Rödl#0
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Vojtěch Rödl (born 1 April 1949) is a Czech American mathematician, Samuel Candler Dobbs Professor at Emory University. He is noted for his contributions mainly to combinatorics having authored hundreds of research papers. == Academic Background == Rödl obtained his PhD from the School of Mathematics and Physics at Charles University in 1976. His supervisor was Zdeněk Hedrlín. From 1973 to 1987 he lectured at the School of Nuclear and Physical Engineering at the Czech Technical University in Prague. He has held visiting positions in various institutions including McMaster University, University of Waterloo, Bell Laboratories, Microsoft, Charles University, Mathematical Institute of the Czech Academy of Science, Bielefeld University, as well as at Humboldt University in Berlin. He serves on the editorial board of several international journals. He has given lectures at many conferences, including plenary address in 2014 at the International Congress of Mathematicians in Seoul and an invited lecture in 1990 at the International Congress of Mathematicians in Kyoto. He has several joint publications with Paul Erdős, and so has Erdős number one. == Research == Rödl has published more than four hundred papers, mostly in combinatorics. He is mostly known for his contributions to Ramsey theory, extremal problems, and probabilistic combinatorics. == Awards == 1977 – Silver medal of the Union of Czechoslovak Mathematicians and Physicists 1985 – Czechoslovak State prize (jointly with Nesetril) 1996 – Humboldt Prize 2005 – Felber Medal (Czech Technical University) 2011 – Bolzano Medal (Czech Academy of Science) 2012 – Polya Prize (jointly with M.Schacht) 2013 – Neuron Prize 2003 and 2017 Honorary doctorate (Technical University of Liberec and Czech Technical University Prague respectively) In 1983 with P. Frankl he solved a 1000$ problem of Paul Erdős. Since 2010 Rödl has been a Foreign Fellow of the Czech Learned Society. == Books == Nešetřil, Jaroslav; Rödl, Vojtěch, eds. (1991). Mathematics of Ramsey Theory. Algorithms and Combinatorics. Vol. 5. Springer. ISBN 0-387-18191-1. 2012 pbk reprint == See also == Packing in a hypergraph Frankl–Rödl graph Hypergraph removal lemma == References == == External links == Vojtěch Rödl at the Mathematics Genealogy Project "Vojtěch Rödl's home page". Archived from the original on 2021-10-28. Retrieved 2010-10-30.
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Wikipedia:Volodymyr Melnykov#0
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Volodymyr Melnykov (Ukrainian: Володимир Миколайович Мельников; born September 14, 1951) is a Ukrainian poet, writer, songwriter, author of lyrics and music for songs, inventor, composer and public figure, Merited Figure of Arts of Ukraine. == Biography == Volodymyr Melnykov was born on September 14, 1951 in the city of Chernivtsi. In 1974 – graduated from Minsk Higher Air Defense Anti-aircraft Missile Academy (Faculty of Radio Engineering). In 1982 – graduated with honors (gold medal) from Kiev Military Academy of Air Defense of the Land Forces (Faculty of Engineering Management). In 1987 – graduated from Kiev Military Academy of Air Defense of the Land Forces (he graduated from the postgraduate course and defended the dissertation of the candidate of technical sciences). In 1969–1991 – served in the Armed Forces of the USSR (Moscow Air Defense District; Northern Group of Forces, Legnica, Poland; Turkestan Military District, Mary). In 1991 he was awarded the military rank "Colonel" and the scientific title "Associate Professor". Before the collapse of the USSR, he was a senior lecturer of the Kiev Military Air Defense Academy of the Land Forces. In 1992–1995 – served in the Verification Center of the General Staff of the Armed Forces of Ukraine. In 1995–2001, served in the , where before the liquidation of the Inspectorate he was the head of the inspection department for international military cooperation and compliance with international treaties on disarmament and arms control. In late 2001, he retired from military service. Immediately continued his service in the Presidential Administration of Ukraine, where he served as deputy head of the department in the Main Directorate of Judicial Reform, military formations and law enforcement bodies. In 2003 he was transferred to the State Administration of Affairs of the President of Ukraine, where he served until 2005 as the head of the Department for Economic Development. In 2017 he worked in the office of the Writer's Union of Ukraine. == His artistic awards == The winner of the Art Prize of the State Border Guard Service of Ukraine "Emerald Lyra" for the first place in the nomination "Music" (2004) Laureate of the festival of the National Radio of Ukraine for the words to the song "I'm in love with Ukraine" (2013) Winner of the open nationwide song contest "My Dear Mother" (2014) Diploma for creating a cycle of patriotic songs at the All-Ukrainian Song Contest "Premiere of the Song" (2015) Laureate of the International Prize named after Volodymyr Vynnychenko (2019) == His books and inventions == Textbook «Design of mathematical algorithms for the functioning of radio-electronic equipment» (1992) Druziam. Moim Tovarisham. To my friends (2003) Ukraintsi Ne Papuasy (Ukrainians are not Papuans) (2007) (ISBN 978-966-646-089-2) Bezmezna Dolia (Boundless Share) (2014) (ISBN 978-966-288-046-5) == Awards == Polish Bronze Medal on the Watch of Peace (1979) The California State Medal "For Meritorious Service" (1997) Medal For Military Service to Ukraine (2000) Merited Figure of Arts of Ukraine (2004) Honorary Diploma of the Cabinet of Ministers of Ukraine (2004) Jubilee Medal "60 Years of the Armed Forces of the USSR" Jubilee Medal "70 Years of the Armed Forces of the USSR" Medal "For Impeccable Service" (1st class, 2nd class, 3rd class) == Social activity == Responsible Secretary of the Supervisory Board of the National Presidential Orchestra of Ukraine Deputy Chairman of the public organization of the Association of Bukovynes in the city of Kyiv "Bukovina" == References == == External links == Encyclopedia of modern Ukraine about Volodymyr Melnykov, v.20. p.p. 135-136 ISBN 978-966-02-8346-6 Honorable names of Ukraine - elite of the state, v. 4, publishing house «LOGOS UKRAINE», 2017, p.203ISBN 978-966-2457-18-6 V.Melnikov Books in the National Library of Vernadsky About the author Volodymyr Melnykov in the electronic library Rulit Department of Education and Science of the Chernivtsi Regional State Administration about Volodymyr Melnykov Archived 2016-02-03 at the Wayback Machine Website celebrity-birthdays.com about Volodymyr Melnykov Musical-world.com.ua about Volodymyr Melnykov
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Wikipedia:Volodymyr Shcherbyna#0
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Volodymyr Oleksandrovych Shcherbyna (Ukrainian: Володимир Олександрович Щербина; 3 February 1935 – 19 January 2023) was a Ukrainian mathematician and politician. A member of the Democratic Party, he served in the Verkhovna Rada from 1990 to 1994. Shcherbyna died in Kharkiv on 19 January 2023, at the age of 87. == References ==
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Wikipedia:Volterra's function#0
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In mathematics, Volterra's function, named for Vito Volterra, is a real-valued function V defined on the real line R with the following curious combination of properties: V is differentiable everywhere The derivative V ′ is bounded everywhere The derivative is not Riemann-integrable. == Definition and construction == The function is defined by making use of the Smith–Volterra–Cantor set and an infinite number or "copies" of sections of the function defined by f ( x ) = { x 2 sin ( 1 / x ) , x ≠ 0 0 , x = 0. {\displaystyle f(x)={\begin{cases}x^{2}\sin(1/x),&x\neq 0\\0,&x=0.\end{cases}}} The construction of V begins by determining the largest value of x in the interval [0, 1/8] for which f ′(x) = 0. Once this value (say x0) is determined, extend the function to the right with a constant value of f(x0) up to and including the point 1/8. Once this is done, a mirror image of the function can be created starting at the point 1/4 and extending downward towards 0. This function will be defined to be 0 outside of the interval [0, 1/4]. We then translate this function to the interval [3/8, 5/8] so that the resulting function, which we call f1, is nonzero only on the middle interval of the complement of the Smith–Volterra–Cantor set. To construct f2, f ′ is then considered on the smaller interval [0,1/32], truncated at the last place the derivative is zero, extended, and mirrored the same way as before, and two translated copies of the resulting function are added to f1 to produce the function f2. Volterra's function then results by repeating this procedure for every interval removed in the construction of the Smith–Volterra–Cantor set; in other words, the function V is the limit of the sequence of functions f1, f2, ... == Further properties == Volterra's function is differentiable everywhere just as f (as defined above) is. One can show that f ′(x) = 2x sin(1/x) - cos(1/x) for x ≠ 0, which means that in any neighborhood of zero, there are points where f ′ takes values 1 and −1. Thus there are points where V ′ takes values 1 and −1 in every neighborhood of each of the endpoints of intervals removed in the construction of the Smith–Volterra–Cantor set S. In fact, V ′ is discontinuous at every point of S, even though V itself is differentiable at every point of S, with derivative 0. However, V ′ is continuous on each interval removed in the construction of S, so the set of discontinuities of V ′ is equal to S. Since the Smith–Volterra–Cantor set S has positive Lebesgue measure, this means that V ′ is discontinuous on a set of positive measure. By Lebesgue's criterion for Riemann integrability, V ′ is not Riemann integrable. If one were to repeat the construction of Volterra's function with the ordinary measure-0 Cantor set C in place of the "fat" (positive-measure) Cantor set S, one would obtain a function with many similar properties, but the derivative would then be discontinuous on the measure-0 set C instead of the positive-measure set S, and so the resulting function would have a Riemann integrable derivative. == See also == Fundamental theorem of calculus == References == == External links == Wrestling with the Fundamental Theorem of Calculus: Volterra's function Archived 2020-11-23 at the Wayback Machine, talk by David Marius Bressoud Volterra's example of a derivative that is not integrable Archived 2016-03-03 at the Wayback Machine(PPT), talk by David Marius Bressoud
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Wikipedia:Vsevolod Romanovsky#0
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Vsevolod Ivanovich Romanovsky (Russian: Всеволод Иванович Романовский; 4 December 1879, Verny – 6 December 1954, Tashkent) was a Russian, Soviet and Uzbek mathematician, founder of the Tashkent school of mathematics. == Education and career == In 1906 Romanovsky received, under the supervision of Andrey Markov, his doctoral degree from Saint Petersburg University. During 1900–1908 he was a student and then a docent at St. Petersburg University. In 1911–1915 he was a senior lecturer and then professor at the Imperial University of Warsaw, in 1915–1918 a professor at the Imperial University of Warsaw in Rostov-on-Don, and from 1918 a professor of probability and mathematical statistics at what is now called the National University of Uzbekistan (in Tashkent). His doctoral students include Toshmuhammad Sarimsoqov. Romanovsky gained an international reputation for his work in mathematical statistics and probability theory. In 1943 he was made an Academician of the Uzbek Soviet Socialist Republic. The Uzbek Academy of Sciences' Romanovsky Institute of Mathematics is named in his honor. Romanovsky was an Invited Speaker at the ICM in 1928 in Bologna and in 1932 in Zürich. His body was buried in Tashkent in the Botkin Cemetery. == Awards and honors == 1944: Order of Lenin 1948: Stalin Prize of the third class (for the development and introduction of new methods of drawing up the short-term and long-term weather forecasts) 16 January 1950: Order of the Red Banner of Labour 23 August 2004: Order of Outstanding Merit – posthumous award by presidential decree of the Republic of Uzbekistan == Selected works == Романовский В. И. Элементарный курс математической статистики. (Elementary course in mathematical statistics) – М.-Л. Госпланиздат, 1924. Романовский В. И. Элементы теории корреляции. (Elements of correlation theory) 1928 г. – 148 pages. Романовский В. И. Математическая статистика. (Mathematical statistics) – М.-Л. Гос.объед. научно-тех.изд. НКТП СССР. 1938. – 527 pages Романовский В. И. Элементарный курс математической статистики. (Elementary course in mathematical statistics) – М.-Л. Госпланиздат, 1939. – 359 pages Романовский В. И. Введение в анализ. (Introduction to analysis) – Ташкент. Гос.учебно-педагог. изд., 1939. – 436 pages Романовский В. И. О предельных распределениях для стохастических процессов с дискретным временем. (On limiting distributions for stochastic processes with discrete time) – Изд. Среднеаз. Гос. Унив. Ташкент, 1946. – 24 pages Романовский В. И. Применения математической статистики в опытном деле. (Applications of mathematical statistics in the test case) – Гостехиздат, М.-Л.,1947. – 248 pages Романовский В. И. Основные задачи теории ошибок. (The main tasks of the theory of errors) – ОГИЗ. Гостехиздат, М.-Л., 1947. – 116 pages Романовский В. И. Дискретные цепи Маркова. (Discrete Markov chains) – Гостехиздат, М.-Л. 1949. – 436 pages Романовский В. И. Математическая статистика. Кн.1. Основы теории вероятностей и математической статистики. (Mathematical statistics. Book 1. Fundamentals of the theory of probability and mathematical statistics) – Ташкент, 1961. – 637 pages Романовский В. И. Математическая статистика. Кн.2. Оперативные методы математической статистики. (Mathematical statistics. Book 2. Operational methods of mathematical statistics) – Ташкент, 1963. – 794 pages Романовский В. И. Избранные труды. Т.1. (Selected Works. V.1) – Изд-во "Наука" Узб. ССР. Ташкент. 1961. Романовский В. И. Избранные труды. Т.2. (Selected Works. V.2) – Теория вероятностей, статистика и анализ. (Theory of probability, statistics and analysis) Изд-во "Наука" Узб. ССР. Ташкент. 1964. – 390 pages == See also == Romanovski polynomials == References ==
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Wikipedia:Vyacheslav Feodoritov#0
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Vyacheslav Petrovich Feodoritov (Russian: Вячесла́в Петро́вич Феодори́тов)(February 28, 1928 - January 2, 2004), k.N, was a Russian physicist in the former Soviet program of nuclear weapons. He was a co-designer of the first two-stage Soviet thermonuclear device, the RDS-37, and became a chief of laboratory at Arzamas-16, now known as the All-Russian Scientific Research Institute of Experimental Physics. == Early life and career == Feodoritov was born in Sasovo, Ryazan Oblast, 319 km south-east of Moscow. He graduated with honours from the Faculty of Physics and Technology of Moscow State University in 1952. Straight from graduation, he became a researcher in the theoretical sector known as KB-11 in Arzamas-16, which was based in the closed city of Sarov, working under Yakov Zel'dovich. Employees were only allowed leave on officially sanctioned or organised days off work, on trips such as for hunting or fishing. Feodoritov became lost on one such trip and - fearful for his future - was aided in his return by locals (who were well aware of the function of Sarov), later finding from his boss (Andrei Sakharov) that the KGB had been informed and had organised a search party. He worked in this secret institution until the end of his life, starting as a senior laboratory assistant and progressing through to engineer, researcher, head of the research group, senior research fellow and chief of laboratory. He took part in the testing of nuclear weapons and was the scientific lead in a number of tests. Along with his project lead, Yevgeny Zababakhin, and in addition to his work on the RDS-37, he worked on calculations for the core part of the RDS-6s bomb, the first Soviet thermonuclear weapon, and also worked on a design which became the first Soviet serial tactical nuclear weapon, RDS-4. Both devices were successfully completed in 1953. For this work he received the Stalin Prize, third degree and the Medal "For Labour Valour". He also worked on civilian nuclear projects. For further significant theoretical work and following successful weapons testing in 1954 and 1955, leading to a new generation of Soviet nuclear weaponry, he was awarded the Order of the Red Banner of Labour. In 1956, he originated further design improvements which helped lead to a new direction in Soviet nuclear weapons. He was part of the team which developed the RDS-220 thermonuclear weapon, the largest ever tested. With German Goncharov, he worked on the construction scheme of these types of weapons, and with Sakharov he analysed the efficiency of the theoretical model of the RDS-220. He received his PhD in Physical and Mathematical Sciences in 1968. For his role in the projects to develop nuclear weapons he was awarded the State Prize of the USSR in 1973. Later in his career, Feodoritov was one of the compilers of the Atomic Project of the USSR, specifically Documents and materials. Volume II. Atomic bomb. 1945 - 1954 Book 1 (published in 1999). He was honoured for his contributions as a scientist in 2000. In his personal life, he was admired for his humanity and cordiality and was the chair of the parent committees throughout his children's education. He was regarded as a Father Frost figure, referred to as "Uncle Slava" by friends of his children and the children of colleagues. == Awards == Twice laureate of the USSR State Prize/Stalin Prize (1953,1973). Honoured scientist of the Russian Federation (2000) == References ==
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Wikipedia:Václav Benda#0
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Václav Benda (August 8, 1946, Prague – June 2, 1999) was a Czech Roman Catholic activist and intellectual, and mathematician. Under Communist rule in Czechoslovakia, Benda and his wife were rare in that they were devout Roman Catholics among the leadership of the anti-communist dissident organization Charter 77. After the Velvet Revolution, Benda became the head of an organization charged with investigating the former Czechoslovakian secret police and their many informants. The ideas expressed in Benda's iconic essay A Parallel Polis influenced the thought of other dissidents like Vaclav Havel and Lech Walesa. In the 2010s and 2020s, American Paleoconservative writer Rod Dreher and Russian-American writer Masha Gessen have drawn on these events and ideas from Cold War-era eastern Europe in disparate works for popular audience. The first English translation of Benda's collected samizdat essays was published by St. Augustine's Press in 2017. == Life == The son of a lawyer, Benda was president of the Students' Academic Council and obtained a doctorate of Philosophy at Charles University in Prague at age 24. His academic career ended when he refused to join the Communist Party in the early 1970s. As a result of his political activities he experienced harassment from the government and economic exclusion, being forced to work for brief periods in a large number of different jobs. With Benda and his wife Kamila's decision during the Soviet-led invasion of August 1968 not to flee the country, he remained at Charles University. Benda completed his doctorate in theoretical cybernetics in 1975, published works on philosophy and mathematics, and then worked as a computer programmer. Benda was active in the dissident movement against the Czechoslovak Socialist Republic, and in 1977 became a signatory to Charter 77. In 1977, he also wrote a short samizdat essay called "Parallel Polis" (Czech: paralelní polis), calling for his fellow dissidents to abandon hope that the repressive social, economic and political institutions in Czechoslovakia could be changed by protest. Instead, Benda called for new "parallel institutions" to be created, which would be more responsive to human needs and may someday replace the existing corrupt institutions. He argued that as the communist state would drain any efforts at reform, it was better to start new ones than expend energy fighting old ones. The essay was translated into English in 1978. Benda's role as a spokesman for Charter 77 resulted in him being arrested in May 1979 and charged with subverting the state, for which he was imprisoned until 1983. After his release he resumed his role as spokesman. He was also a founder-member of the Committee for the Defense of the Unjustly Prosecuted (VONS). While Benda was imprisoned with Vaclav Havel in Ostrava, they co-wrote a text for the Moscow Helsinki Group in 1980. A devout Roman Catholic, Benda established the Christian Democratic Party in 1989, becoming chairman in 1990. The party later merged with the Civic Democratic Party. Benda's politics were distinct from his former dissident colleagues, and he became an increasingly isolated figure in Czech politics. He was a defender, with qualifications, of former Chilean dictator Augusto Pinochet, a position widely shared in Czech liberal and conservative elite circles. Benda stated that Pinochet had "perhaps, his cruel traits, nevertheless they were answers to the extremely undemocratic and extremely cruel advance at the root of international communism." From June 25 to December 31, 1992, Benda was Chairman of the Chamber of the Nations. From 1991 to 1998, Benda served as head of the Bureau for Investigating the Crimes of Communist Party officials. In 1996, he was elected to the Czech Senate for the Prague 1 district, and held the seat until his death in 1999. == Legacy == Benda's ideas about a Parallel Polis were later revived by a group of scholars at the University of Washington, and a four-story building called Parallel polis has opened in Prague, housing a bitcoin-only cafe, co-working space, makers lab, and "Institute of cryptoanarchy" in Holešovice. In his 2017 book The Benedict Option, author Rod Dreher praised the ideas expressed in Benda's essays and recommended them to American Christians as an example of how to preserve and live their faith in a culture increasingly hostile to it. == References == == Further reading == Edited by F. Flagg Taylor IV (2018), The Long Night of the Watchman: Essays by Vaclav Benda, 1977-1989, St. Augustine's Press
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Wikipedia:Václav Chvátal#0
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Václav (Vašek) Chvátal (Czech: [ˈvaːtslaf ˈxvaːtal]) is a Professor Emeritus in the Department of Computer Science and Software Engineering at Concordia University in Montreal, Quebec, Canada, and a visiting professor at Charles University in Prague. He has published extensively on topics in graph theory, combinatorics, and combinatorial optimization. == Biography == Chvátal was born in 1946 in Prague and educated in mathematics at Charles University in Prague, where he studied under the supervision of Zdeněk Hedrlín. He fled Czechoslovakia in 1968, three days after the Soviet invasion, and completed his Ph.D. in Mathematics at the University of Waterloo, under the supervision of Crispin St. J. A. Nash-Williams, in the fall of 1970. Subsequently, he took positions at McGill University (1971 and 1978–1986), Stanford University (1972 and 1974–1977), the Université de Montréal (1972–1974 and 1977–1978), and Rutgers University (1986–2004) before returning to Montreal for the Canada Research Chair in Combinatorial Optimization at Concordia (2004–2011) and the Canada Research Chair in Discrete Mathematics (2011–2014) till his retirement. == Research == Chvátal first learned of graph theory in 1964, on finding a book by Claude Berge in a Plzeň bookstore and much of his research involves graph theory: His first mathematical publication, at the age of 19, concerned directed graphs that cannot be mapped to themselves by any nontrivial graph homomorphism Another graph-theoretic result of Chvátal was the 1970 construction of the smallest possible triangle-free graph that is both 4-chromatic and 4-regular, now known as the Chvátal graph. A 1972 paper relating Hamiltonian cycles to connectivity and maximum independent set size of a graph, earned Chvátal his Erdős number of 1. Specifically, if there exists an s such that a given graph is s-vertex-connected and has no (s + 1)-vertex independent set, the graph must be Hamiltonian. Avis et al. tell the story of Chvátal and Erdős working out this result over the course of a long road trip, and later thanking Louise Guy "for her steady driving." In a 1973 paper, Chvátal introduced the concept of graph toughness, a measure of graph connectivity that is closely connected to the existence of Hamiltonian cycles. A graph is t-tough if, for every k greater than 1, the removal of fewer than tk vertices leaves fewer than k connected components in the remaining subgraph. For instance, in a graph with a Hamiltonian cycle, the removal of any nonempty set of vertices partitions the cycle into at most as many pieces as the number of removed vertices, so Hamiltonian graphs are 1-tough. Chvátal conjectured that 3/2-tough graphs, and later that 2-tough graphs, are always Hamiltonian; despite later researchers finding counterexamples to these conjectures, it still remains open whether some constant bound on the graph toughness is enough to guarantee Hamiltonicity. Some of Chvátal's work concerns families of sets, or equivalently hypergraphs, a subject already occurring in his Ph.D. thesis, where he also studied Ramsey theory. In a 1972 conjecture that Erdős called "surprising" and "beautiful", and that remains open (with a $10 prize offered by Chvátal for its solution) he suggested that, in any family of sets closed under the operation of taking subsets, the largest pairwise-intersecting subfamily may always be found by choosing an element of one of the sets and keeping all sets containing that element. In 1979, he studied a weighted version of the set cover problem, and proved that a greedy algorithm provides good approximations to the optimal solution, generalizing previous unweighted results by David S. Johnson (J. Comp. Sys. Sci. 1974) and László Lovász (Discrete Math. 1975). Chvátal first became interested in linear programming through the influence of Jack Edmonds while Chvátal was a student at Waterloo. He quickly recognized the importance of cutting planes for attacking combinatorial optimization problems such as computing maximum independent sets and, in particular, introduced the notion of a cutting-plane proof. At Stanford in the 1970s, he began writing his popular textbook, Linear Programming, which was published in 1983. Cutting planes lie at the heart of the branch and cut method used by efficient solvers for the traveling salesman problem. Between 1988 and 2005, the team of David L. Applegate, Robert E. Bixby, Vašek Chvátal, and William J. Cook developed one such solver, Concorde. The team was awarded The Beale-Orchard-Hays Prize for Excellence in Computational Mathematical Programming in 2000 for their ten-page paper enumerating some of Concorde's refinements of the branch and cut method that led to the solution of a 13,509-city instance and it was awarded the Frederick W. Lanchester Prize in 2007 for their book, The Traveling Salesman Problem: A Computational Study. Chvátal is also known for proving the art gallery theorem, for researching a self-describing digital sequence, for his work with David Sankoff on the Chvátal–Sankoff constants controlling the behavior of the longest common subsequence problem on random inputs, and for his work with Endre Szemerédi on hard instances for resolution theorem proving. == Books == Vašek Chvátal (1983). Linear Programming. W.H. Freeman. ISBN 978-0-7167-1587-0.. Japanese translation published by Keigaku Shuppan, Tokyo, 1986. Claude Berge; Vašek Chvátal, eds. (1984). Topics on Perfect Graphs. Amsterdam ; New York : New York: Elsevier North-Holland. ISBN 978-0-444-86587-8. David L. Applegate; Robert E. Bixby; Vašek Chvátal; William J. Cook (2007). The Traveling Salesman Problem: A Computational Study. Princeton University Press. ISBN 978-0-691-12993-8. Vašek Chvátal, ed. (2011). Combinatorial Optimization: Methods and Applications. IOS Press. ISBN 978-1-60750-717-8. Archived from the original on 2017-03-21. Retrieved 2017-03-22. Vašek Chvátal (2021). Discrete Mathematical Charms of Paul Erdős. A Simple Introduction. Cambridge University Press. ISBN 978-1-108-92740-6. == See also == List of University of Waterloo people == References == == External links == Chvátal's website on encs.concordia.ca
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Wikipedia:Václav Hlavatý#0
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Václav Hlavatý (27 January 1894 – 11 January 1969) was a noted Czech-American mathematician, who wrote on the theory of relativity and corresponded extensively with Albert Einstein on the subject. In particular, Hlavatý solved some very difficult equations relating to Einstein's Unified field theory, which was featured in the news media as one of the great scientific achievements of 1953. Einstein himself was reported to have said that if anyone could solve the equations it would be Professor Hlavatý, which proved to be the case. He was born in Louny, Bohemia (now in the Czech Republic) and died in Bloomington, Indiana. He obtained his PhD in 1921 at the Charles University in Prague and during World War II participated in the Prague uprising, but his academic career was mainly at Indiana University, which he joined in 1948, and where he became Professor, later Emeritus, of Mathematics. A special book of mathematical essays was published in his honour. In 1958, he became the first President of the Czechoslovak Society of Arts and Sciences established in Washington DC by intellectuals of Czech and Slovak origin. He was an Invited Speaker of the ICM in 1928 in Bologna and in 1936 in Oslo. In 1931 he married Olga Neumannova, and they had a daughter, Olga. == Some publications == === Articles === Hlavatý, V (1952). "The Elementary Basic Principles of the Unified Theory of Relativity". Proceedings of the National Academy of Sciences of the United States of America. 38 (3): 243–247. Bibcode:1952PNAS...38..243H. doi:10.1073/pnas.38.3.243. PMC 1063539. PMID 16589086. Hlavatý, V (1952). "The Einstein Connection of the Unified Theory of Relativity". Proceedings of the National Academy of Sciences of the United States of America. 38 (5): 415–419. Bibcode:1952PNAS...38..415H. doi:10.1073/pnas.38.5.415. PMC 1063575. PMID 16589114. Hlavatý, V (1952). "The Schrödinger Final Affine Field Laws". Proceedings of the National Academy of Sciences of the United States of America. 38 (12): 1052–1058. Bibcode:1952PNAS...38.1052H. doi:10.1073/pnas.38.12.1052. PMC 1063709. PMID 16589224. Hlavatý, V (1953). "The Spinor Connection in the Unified Einstein Theory of Relativity". Proceedings of the National Academy of Sciences of the United States of America. 39 (6): 501–506. Bibcode:1953PNAS...39..501H. doi:10.1073/pnas.39.6.501. PMC 1063813. PMID 16589296. Hlavatý, V (1953). "Connections Between Einstein's Two Unified Theories of Relativity". Proceedings of the National Academy of Sciences of the United States of America. 39 (6): 507–510. Bibcode:1953PNAS...39..507H. doi:10.1073/pnas.39.6.507. PMC 1063814. PMID 16589297. === Books === Hlavatý, V. (1939). Differentialgeometrie der Kurven und Flächen und Tensorrechnung. Groningen: Noordhoff. Hlavatý, V. (1953). Differential line geometry. Translated by H. Levy. Groningen: Noordhoff. Hlavatý, V. (1957). Geometry of Einstein's Unified Field Theory. Groningen: Noordhoff.{{cite book}}: CS1 maint: publisher location (link) Reprinted as ISBN 978-1-178-77017-9. == References == == External links == Václav Hlavatý at the Mathematics Genealogy Project Václav Hlavatý biography (in Czech) Václav Hlavatý Archived 2012-02-14 at the Wayback Machine biography (in Czech) includes photograph
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Wikipedia:Václav Šimerka#0
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Václav Šimerka (20 December 1819 – 26 December 1887) was a Czech mathematician, priest, physicist and philosopher. He wrote the first Czech text on calculus and is credited for discovering the first seven Carmichael numbers in 1885. == Biography == Šimerka was born on 20 December 1819 in Vysoké Veselí in Bohemia to a family of coopers of businessman Petr Šimerka and his wife Terezie. After attending school in Jičín, he studied in the University of Prague's Faculty of Philosophy from 1839 to 1841. There, he studied mathematics under Jakob Philipp Kulik and astronomy under and practical geometry under Adam Bittner and also obligatory teaching of religion, philosophy, mathematics, Latin philology, natural science, physics, moral philosophy and history. After graduating in Prague, Šimerka studied in the Theological Seminary in Hradec Králové. Šimerka was ordained on 25 July 1845 and then became a chaplain in Žlunice near Jičín. He only spent a short time being a chaplain in Žlunice as he gave up his appointment after disagreements with the pastor there. In 1852, after passing the mathematics teacher qualification exam, he went to Prague to study physics under F. A. Petřina. When he passed the physics qualification exam, he became a substitute teacher at the Piarist gymnasium in České Budějovice but did not attain a permanent appointment there. In 1862, Šimerka requested to return to spiritual administration and then was appointed became parish priest in Slatina nad Zdobnicí and then became a priest in Vraňany from 1866 until 1886. He died in Praskačka on 26 December 1887. == Work == In 1858, his work Die Perioden der quadratischen Zahlformen bei negativen Determinanten was published in the reports of the Vienna Academy of Sciences. The same journal published his article Lösungen zweier Arten von Gleichungen a year later. In 1862, the Royal Czech Society published Přispěvky k neurčité analytice, his contributions to indeterminate analytics. His Die rationalen Dreiecke which deals with the diophantine problem of rational triangles was published in the Archiv der Mathematik und Physik in 1869 and is one of Šimerka's known contributions to the theory of factoring. Šimerka is known for Algebra, čili, počtářství obecné pro vyšší gymnasia, his textbook on algebra published in 1863. Considered as his most important work, his algebra textbook for middle schools was published in three editions. The book's appendix giving an introduction to differential and integral calculus was published separately in 1864 under the title Přídavek k algebra, intended for the more inquisitive students. It is considered the first Czech text on calculus. Šimerka's calculus text presented differential calculus without using the concepts of limits and continuity. His use of differentials is similar to the infinitesimal approach of 17th and 18th century mathematicians. The calculus text focused on explaining the basic knowledge and intuition to teach students to use mathematics in practical tasks. Šimerka was influenced by Johann Friedrich Herbart in his philosophical writings, having referred to the said philosopher in the introduction to his work Síla přesvědčení. Pocus v duchovní mechanice (originally published in Časopis pro pěstování mathematiky a fysiky in 1881, then translated into German in 1883 as Die Kraft der Überzeugung. Ein mathematisch-philosophischer Versuch). In this work, Šimerka set out to indicate the strength of one's belief using numbers between 0 and 1, where a belief of value 0 is an empty mind, increasing to a hunch, then conjecture then hypothesis then ultimately to necessary knowledge for a belief of value 1. Šimerka is quoted to have said "The imperfection of human belief is equal to the product of ignorance of its reasons" (translated from Czech), which arose from his calculations dealing with strength of belief in his 1881 paper. Other results from this paper include "When two conflicting beliefs collide, the weaker suffers more than the stronger" and "The double impact of two counterarguments damages conviction more than the single impact of their consequence". This work was a forerunner of the theory of subjective probability, pre-dating Ramsey's (1931) and Bruno de Finetti's (1937) work on the subject. Due to this, Šimerka was the first Czech mathematician to apply of mathematics in psychology. In 1885, he enumerated the first seven Carmichael numbers, from 561 to 8911, in Zbytky z arithmetické posloupnosti. This was years before Alwin Korselt's criterion hinted at their existence in 1899 and also before Robert Daniel Carmichael's popularized first example in 1912. == Selected works == Šimerka, W. (1858), "Die Perioden der quadratischen Zahlformen bei negativen Determinanten", Sitzungsberichte der Akademie der Wissenschaften Mathematisch-naturwissenschaftliche Klasse, 31 (18): 33–57 Šimerka, W. (1858), "Die Lösungen zweier Arten von Gleichungen", Sitzungsberichte der Akademie der Wissenschaften Mathematisch-naturwissenschaftliche Klasse, 33: 277–284 Šimerka, W. (1859), Die trinären Zahlformen und Zahlwerthe, vol. 38, pp. 390–481 Šimerka, W. (1866), "Die rationalen Dreiecke", Archiv der Mathematik und Physik}, 51: 196–422 Součty celých v lomené arithmetické posloupnosti Řetězové pravidlo u shod Jednočlenná perioda zbytků z mocnin bes předchozích členů… Jednočlenná perioda zbytků z mocnin s pťechcházejícími členy Šimerka, V. (1879), "Poznámka [z teorie čísel]" (PDF), Časopis pro pěstování matematiky a fysiky, 8 (4): 187–188, doi:10.21136/CPMF.1879.123540 Šimerka, V. (1882), "Síla přesvědčení. Pocus v duchovní mechanice" (PDF), Časopis pro pěstování matematiky a fysiky, 11 (2): 75–111, doi:10.21136/CPMF.1882.122070 Šimerka, W. (1885), "Zbytky z arithmetické posloupnosti" (PDF), Časopis pro pěstování matematiky a fysiky, 14 (5): 221–225, doi:10.21136/CPMF.1885.122245 Dampfkessel und Dampfmaschinen und ihre Wartung (Plzeň, 1889) == References == == External links == List of publications from Czech Digital Mathematics Library
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Wikipedia:Věra Kůrková#0
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Věra Kůrková (born 1948) is a Czech mathematician and computer scientist, affiliated with the Institute of Computer Science of the Czech Academy of Sciences. Her research interests include neural networks, computational learning theory, and nonlinear approximation theory. She formulated the abstract concept of a variational norm in 1997 which puts ideas of Maurey, Jones, and Barron into the context of functional analysis. See V. Kůrková, Dimension-independent rates of approximation by neural networks. In: Warwick, K., Karny, M. (eds.) Computer-Intensive Methods in Control and Signal Processing. The Curse of Dimensionality, Birkhauser, Boston, MA, pp. 261–270 (1997). See also F. Girosi and G. Anzellotti, Convergence rates of approximation by translates, MIT Artificial Intelligence Laboratory, AI Memo No. 1288, April 1995, C.B.I.P. Paper No. 73. Kůrková is also known for the concept of quasiorthogonal set which she developed jointly with Robert Hecht-Nielsen and Paul Kainen. Kůrková earned a Ph.D. in 1980 and a habilitation in 1999, both from Charles University. She has been affiliated with the Czech Academy of Sciences since 1990, and she headed the Department of Theoretical Computer Science within the Institute of Computer Science from 2002 to 2008. In 2010, the Czech Academy of Sciences awarded Kůrková the Bernard Bolzano Honorary Medal for Merit in the Mathematical Sciences. As of 2018, Kůrková is president of the European Neural Network Society. For recent work, see V. Kůrková, M. Sanguineti, Classification by sparse neural networks, IEEE Trans Neural Netw Learn Syst. 2019 Jan 10. doi: 10.1109/TNNLS.2018.2888517 [Epub ahead of print] and two chapters in the forthcoming Vladik Kreinovich Festschrift volume published by Springer. == References ==
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Wikipedia:Věra Trnková#0
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Věra Šedivá-Trnková (March 16, 1934 – 27 May 2018) was a Czech mathematician known for her work in topology and in category theory. == Early life and education == Trnková was born on March 16, 1934, in Berehove, then in Czechoslovakia and now in Ukraine; her father was a forester. By the time she was in high school, her family lived in Prague, and she went to Charles University for study in mathematics. There, she worked with Miroslav Katětov on general topology, earning a master's degree in 1957 with the thesis Collectionwise normal and strongly paracompact spaces on strengthened definitions for normal spaces. She continued her work on topology at Charles University as a doctoral student of Eduard Čech, earning a candidate's degree (the Czech equivalent of a Ph.D.) in 1961 with the dissertation Non-F-Topologies. Much later, in 1989, she was also given the Dr.Sc. degree, corresponding to a habilitation. == Later life and career == In 1960, while still a student, Trnková became an assistant professor at Charles University. She was promoted to docent (associate professor), senior researcher, and full professor in 1967, 1986, and 1991, respectively. She became Professor Emeritus in 1999, although she remained active in both teaching and research until a few years before her death on 27 May 2018. == Research == Despite beginning her career working in general topology, Trnková shifted as early as 1962 to category theory. Her work in this area included the study of formal completions of categories, the embeddings of categories into categories of topological spaces, category-theoretic automata theory, and the isomorphism of product objects in categories. She became the author of over 100 research papers and two monographs: Combinatorial, algebraic and topological representations of groups, semigroups and categories (with Aleš Pultr, North-Holland Mathematical Library 22, North-Holland, 1980) Automata and algebras in categories (with Jiří Adámek, Mathematics and its Applications 37, Kluwer, 1990) == References == == External links == Home page (archived 26 March 2015) Věra Trnková on nLab
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Wikipedia:WKB approximation#0
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In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear differential equations with spatially varying coefficients. It is typically used for a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be changing slowly. The name is an initialism for Wentzel–Kramers–Brillouin. It is also known as the LG or Liouville–Green method. Other often-used letter combinations include JWKB and WKBJ, where the "J" stands for Jeffreys. == Brief history == This method is named after physicists Gregor Wentzel, Hendrik Anthony Kramers, and Léon Brillouin, who all developed it in 1926. In 1923, mathematician Harold Jeffreys had developed a general method of approximating solutions to linear, second-order differential equations, a class that includes the Schrödinger equation. The Schrödinger equation itself was not developed until two years later, and Wentzel, Kramers, and Brillouin were apparently unaware of this earlier work, so Jeffreys is often neglected credit. Early texts in quantum mechanics contain any number of combinations of their initials, including WBK, BWK, WKBJ, JWKB and BWKJ. An authoritative discussion and critical survey has been given by Robert B. Dingle. Earlier appearances of essentially equivalent methods are: Francesco Carlini in 1817, Joseph Liouville in 1837, George Green in 1837, Lord Rayleigh in 1912 and Richard Gans in 1915. Liouville and Green may be said to have founded the method in 1837, and it is also commonly referred to as the Liouville–Green or LG method. The important contribution of Jeffreys, Wentzel, Kramers, and Brillouin to the method was the inclusion of the treatment of turning points, connecting the evanescent and oscillatory solutions at either side of the turning point. For example, this may occur in the Schrödinger equation, due to a potential energy hill. == Formulation == Generally, WKB theory is a method for approximating the solution of a differential equation whose highest derivative is multiplied by a small parameter ε. The method of approximation is as follows. For a differential equation ε d n y d x n + a ( x ) d n − 1 y d x n − 1 + ⋯ + k ( x ) d y d x + m ( x ) y = 0 , {\displaystyle \varepsilon {\frac {d^{n}y}{dx^{n}}}+a(x){\frac {d^{n-1}y}{dx^{n-1}}}+\cdots +k(x){\frac {dy}{dx}}+m(x)y=0,} assume a solution of the form of an asymptotic series expansion y ( x ) ∼ exp [ 1 δ ∑ n = 0 ∞ δ n S n ( x ) ] {\displaystyle y(x)\sim \exp \left[{\frac {1}{\delta }}\sum _{n=0}^{\infty }\delta ^{n}S_{n}(x)\right]} in the limit δ → 0. The asymptotic scaling of δ in terms of ε will be determined by the equation – see the example below. Substituting the above ansatz into the differential equation and cancelling out the exponential terms allows one to solve for an arbitrary number of terms Sn(x) in the expansion. WKB theory is a special case of multiple scale analysis. == An example == This example comes from the text of Carl M. Bender and Steven Orszag. Consider the second-order homogeneous linear differential equation ϵ 2 d 2 y d x 2 = Q ( x ) y , {\displaystyle \epsilon ^{2}{\frac {d^{2}y}{dx^{2}}}=Q(x)y,} where Q ( x ) ≠ 0 {\displaystyle Q(x)\neq 0} . Substituting y ( x ) = exp [ 1 δ ∑ n = 0 ∞ δ n S n ( x ) ] {\displaystyle y(x)=\exp \left[{\frac {1}{\delta }}\sum _{n=0}^{\infty }\delta ^{n}S_{n}(x)\right]} results in the equation ϵ 2 [ 1 δ 2 ( ∑ n = 0 ∞ δ n S n ′ ) 2 + 1 δ ∑ n = 0 ∞ δ n S n ′ ′ ] = Q ( x ) . {\displaystyle \epsilon ^{2}\left[{\frac {1}{\delta ^{2}}}\left(\sum _{n=0}^{\infty }\delta ^{n}S_{n}^{\prime }\right)^{2}+{\frac {1}{\delta }}\sum _{n=0}^{\infty }\delta ^{n}S_{n}^{\prime \prime }\right]=Q(x).} To leading order in ϵ (assuming, for the moment, the series will be asymptotically consistent), the above can be approximated as ϵ 2 δ 2 S 0 ′ 2 + 2 ϵ 2 δ S 0 ′ S 1 ′ + ϵ 2 δ S 0 ′ ′ = Q ( x ) . {\displaystyle {\frac {\epsilon ^{2}}{\delta ^{2}}}{S_{0}^{\prime }}^{2}+{\frac {2\epsilon ^{2}}{\delta }}S_{0}^{\prime }S_{1}^{\prime }+{\frac {\epsilon ^{2}}{\delta }}S_{0}^{\prime \prime }=Q(x).} In the limit δ → 0, the dominant balance is given by ϵ 2 δ 2 S 0 ′ 2 ∼ Q ( x ) . {\displaystyle {\frac {\epsilon ^{2}}{\delta ^{2}}}{S_{0}^{\prime }}^{2}\sim Q(x).} So δ is proportional to ϵ. Setting them equal and comparing powers yields ϵ 0 : S 0 ′ 2 = Q ( x ) , {\displaystyle \epsilon ^{0}:\quad {S_{0}^{\prime }}^{2}=Q(x),} which can be recognized as the eikonal equation, with solution S 0 ( x ) = ± ∫ x 0 x Q ( x ′ ) d x ′ . {\displaystyle S_{0}(x)=\pm \int _{x_{0}}^{x}{\sqrt {Q(x')}}\,dx'.} Considering first-order powers of ϵ fixes ϵ 1 : 2 S 0 ′ S 1 ′ + S 0 ′ ′ = 0. {\displaystyle \epsilon ^{1}:\quad 2S_{0}^{\prime }S_{1}^{\prime }+S_{0}^{\prime \prime }=0.} This has the solution S 1 ( x ) = − 1 4 ln Q ( x ) + k 1 , {\displaystyle S_{1}(x)=-{\frac {1}{4}}\ln Q(x)+k_{1},} where k1 is an arbitrary constant. We now have a pair of approximations to the system (a pair, because S0 can take two signs); the first-order WKB-approximation will be a linear combination of the two: y ( x ) ≈ c 1 Q − 1 4 ( x ) exp [ 1 ϵ ∫ x 0 x Q ( t ) d t ] + c 2 Q − 1 4 ( x ) exp [ − 1 ϵ ∫ x 0 x Q ( t ) d t ] . {\displaystyle y(x)\approx c_{1}Q^{-{\frac {1}{4}}}(x)\exp \left[{\frac {1}{\epsilon }}\int _{x_{0}}^{x}{\sqrt {Q(t)}}\,dt\right]+c_{2}Q^{-{\frac {1}{4}}}(x)\exp \left[-{\frac {1}{\epsilon }}\int _{x_{0}}^{x}{\sqrt {Q(t)}}\,dt\right].} Higher-order terms can be obtained by looking at equations for higher powers of δ. Explicitly, 2 S 0 ′ S n ′ + S n − 1 ′ ′ + ∑ j = 1 n − 1 S j ′ S n − j ′ = 0 {\displaystyle 2S_{0}^{\prime }S_{n}^{\prime }+S_{n-1}^{\prime \prime }+\sum _{j=1}^{n-1}S_{j}^{\prime }S_{n-j}^{\prime }=0} for n ≥ 2. === Precision of the asymptotic series === The asymptotic series for y(x) is usually a divergent series, whose general term δn Sn(x) starts to increase after a certain value n = nmax. Therefore, the smallest error achieved by the WKB method is at best of the order of the last included term. For the equation ϵ 2 d 2 y d x 2 = Q ( x ) y , {\displaystyle \epsilon ^{2}{\frac {d^{2}y}{dx^{2}}}=Q(x)y,} with Q(x) <0 an analytic function, the value n max {\displaystyle n_{\max }} and the magnitude of the last term can be estimated as follows: n max ≈ 2 ϵ − 1 | ∫ x 0 x ∗ − Q ( z ) d z | , {\displaystyle n_{\max }\approx 2\epsilon ^{-1}\left|\int _{x_{0}}^{x_{\ast }}{\sqrt {-Q(z)}}\,dz\right|,} δ n max S n max ( x 0 ) ≈ 2 π n max exp [ − n max ] , {\displaystyle \delta ^{n_{\max }}S_{n_{\max }}(x_{0})\approx {\sqrt {\frac {2\pi }{n_{\max }}}}\exp[-n_{\max }],} where x 0 {\displaystyle x_{0}} is the point at which y ( x 0 ) {\displaystyle y(x_{0})} needs to be evaluated and x ∗ {\displaystyle x_{\ast }} is the (complex) turning point where Q ( x ∗ ) = 0 {\displaystyle Q(x_{\ast })=0} , closest to x = x 0 {\displaystyle x=x_{0}} . The number nmax can be interpreted as the number of oscillations between x 0 {\displaystyle x_{0}} and the closest turning point. If ϵ − 1 Q ( x ) {\displaystyle \epsilon ^{-1}Q(x)} is a slowly changing function, ϵ | d Q d x | ≪ Q 2 , [might be Q 3 / 2 ?] {\displaystyle \epsilon \left|{\frac {dQ}{dx}}\right|\ll Q^{2},^{{\text{[might be }}Q^{3/2}{\text{?]}}}} the number nmax will be large, and the minimum error of the asymptotic series will be exponentially small. == Application in non relativistic quantum mechanics == The above example may be applied specifically to the one-dimensional, time-independent Schrödinger equation, − ℏ 2 2 m d 2 d x 2 Ψ ( x ) + V ( x ) Ψ ( x ) = E Ψ ( x ) , {\displaystyle -{\frac {\hbar ^{2}}{2m}}{\frac {d^{2}}{dx^{2}}}\Psi (x)+V(x)\Psi (x)=E\Psi (x),} which can be rewritten as d 2 d x 2 Ψ ( x ) = 2 m ℏ 2 ( V ( x ) − E ) Ψ ( x ) . {\displaystyle {\frac {d^{2}}{dx^{2}}}\Psi (x)={\frac {2m}{\hbar ^{2}}}\left(V(x)-E\right)\Psi (x).} === Approximation away from the turning points === The wavefunction can be rewritten as the exponential of another function S (closely related to the action), which could be complex, Ψ ( x ) = e i S ( x ) ℏ , {\displaystyle \Psi (\mathbf {x} )=e^{iS(\mathbf {x} ) \over \hbar },} so that its substitution in Schrödinger's equation gives: i ℏ ∇ 2 S ( x ) − ( ∇ S ( x ) ) 2 = 2 m ( V ( x ) − E ) , {\displaystyle i\hbar \nabla ^{2}S(\mathbf {x} )-(\nabla S(\mathbf {x} ))^{2}=2m\left(V(\mathbf {x} )-E\right),} Next, the semiclassical approximation is used. This means that each function is expanded as a power series in ħ. S = S 0 + ℏ S 1 + ℏ 2 S 2 + ⋯ {\displaystyle S=S_{0}+\hbar S_{1}+\hbar ^{2}S_{2}+\cdots } Substituting in the equation, and only retaining terms up to first order in ℏ, we get: ( ∇ S 0 + ℏ ∇ S 1 ) 2 − i ℏ ( ∇ 2 S 0 ) = 2 m ( E − V ( x ) ) {\displaystyle (\nabla S_{0}+\hbar \nabla S_{1})^{2}-i\hbar (\nabla ^{2}S_{0})=2m(E-V(\mathbf {x} ))} which gives the following two relations: ( ∇ S 0 ) 2 = 2 m ( E − V ( x ) ) = ( p ( x ) ) 2 2 ∇ S 0 ⋅ ∇ S 1 − i ∇ 2 S 0 = 0 {\displaystyle {\begin{aligned}(\nabla S_{0})^{2}=2m(E-V(\mathbf {x} ))=(p(\mathbf {x} ))^{2}\\2\nabla S_{0}\cdot \nabla S_{1}-i\nabla ^{2}S_{0}=0\end{aligned}}} which can be solved for 1D systems, first equation resulting in: S 0 ( x ) = ± ∫ 2 m ( E − V ( x ) ) d x = ± ∫ p ( x ) d x {\displaystyle S_{0}(x)=\pm \int {\sqrt {2m\left(E-V(x)\right)}}\,dx=\pm \int p(x)\,dx} and the second equation computed for the possible values of the above, is generally expressed as: Ψ ( x ) ≈ C + e + i ℏ ∫ p ( x ) d x | p ( x ) | + C − e − i ℏ ∫ p ( x ) d x | p ( x ) | {\displaystyle \Psi (x)\approx C_{+}{\frac {e^{+{\frac {i}{\hbar }}\int p(x)\,dx}}{\sqrt {|p(x)|}}}+C_{-}{\frac {e^{-{\frac {i}{\hbar }}\int p(x)\,dx}}{\sqrt {|p(x)|}}}} Thus, the resulting wavefunction in first order WKB approximation is presented as, In the classically allowed region, namely the region where V ( x ) < E {\displaystyle V(x)<E} the integrand in the exponent is imaginary and the approximate wave function is oscillatory. In the classically forbidden region V ( x ) > E {\displaystyle V(x)>E} , the solutions are growing or decaying. It is evident in the denominator that both of these approximate solutions become singular near the classical turning points, where E = V(x), and cannot be valid. (The turning points are the points where the classical particle changes direction.) Hence, when E > V ( x ) {\displaystyle E>V(x)} , the wavefunction can be chosen to be expressed as: Ψ ( x ′ ) ≈ C cos ( 1 ℏ ∫ | p ( x ) | d x + α ) | p ( x ) | + D sin ( − 1 ℏ ∫ | p ( x ) | d x + α ) | p ( x ) | {\displaystyle \Psi (x')\approx C{\frac {\cos {({\frac {1}{\hbar }}\int |p(x)|\,dx}+\alpha )}{\sqrt {|p(x)|}}}+D{\frac {\sin {(-{\frac {1}{\hbar }}\int |p(x)|\,dx}+\alpha )}{\sqrt {|p(x)|}}}} and for V ( x ) > E {\displaystyle V(x)>E} , Ψ ( x ′ ) ≈ C + e + i ℏ ∫ | p ( x ) | d x | p ( x ) | + C − e − i ℏ ∫ | p ( x ) | d x | p ( x ) | . {\displaystyle \Psi (x')\approx {\frac {C_{+}e^{+{\frac {i}{\hbar }}\int |p(x)|\,dx}}{\sqrt {|p(x)|}}}+{\frac {C_{-}e^{-{\frac {i}{\hbar }}\int |p(x)|\,dx}}{\sqrt {|p(x)|}}}.} The integration in this solution is computed between the classical turning point and the arbitrary position x'. === Validity of WKB solutions === From the condition: ( S 0 ′ ( x ) ) 2 − ( p ( x ) ) 2 + ℏ ( 2 S 0 ′ ( x ) S 1 ′ ( x ) − i S 0 ″ ( x ) ) = 0 {\displaystyle (S_{0}'(x))^{2}-(p(x))^{2}+\hbar (2S_{0}'(x)S_{1}'(x)-iS_{0}''(x))=0} It follows that: ℏ ∣ 2 S 0 ′ ( x ) S 1 ′ ( x ) ∣ + ℏ ∣ i S 0 ″ ( x ) ∣≪∣ ( S 0 ′ ( x ) ) 2 ∣ + ∣ ( p ( x ) ) 2 ∣ {\textstyle \hbar \mid 2S_{0}'(x)S_{1}'(x)\mid +\hbar \mid iS_{0}''(x)\mid \ll \mid (S_{0}'(x))^{2}\mid +\mid (p(x))^{2}\mid } For which the following two inequalities are equivalent since the terms in either side are equivalent, as used in the WKB approximation: ℏ ∣ S 0 ″ ( x ) ∣≪∣ ( S 0 ′ ( x ) ) 2 ∣ 2 ℏ ∣ S 0 ′ S 1 ′ ∣≪∣ ( p ′ ( x ) ) 2 ∣ {\displaystyle {\begin{aligned}\hbar \mid S_{0}''(x)\mid \ll \mid (S_{0}'(x))^{2}\mid \\2\hbar \mid S_{0}'S_{1}'\mid \ll \mid (p'(x))^{2}\mid \end{aligned}}} The first inequality can be used to show the following: ℏ ∣ S 0 ″ ( x ) ∣≪∣ ( p ( x ) ) ∣ 2 1 2 ℏ | p ( x ) | | d p 2 d x | ≪ | p ( x ) | 2 λ | d V d x | ≪ | p | 2 m {\displaystyle {\begin{aligned}\hbar \mid S_{0}''(x)\mid \ll \mid (p(x))\mid ^{2}\\{\frac {1}{2}}{\frac {\hbar }{|p(x)|}}\left|{\frac {dp^{2}}{dx}}\right|\ll |p(x)|^{2}\\\lambda \left|{\frac {dV}{dx}}\right|\ll {\frac {|p|^{2}}{m}}\\\end{aligned}}} where | S 0 ′ ( x ) | = | p ( x ) | {\textstyle |S_{0}'(x)|=|p(x)|} is used and λ ( x ) {\textstyle \lambda (x)} is the local de Broglie wavelength of the wavefunction. The inequality implies that the variation of potential is assumed to be slowly varying. This condition can also be restated as the fractional change of E − V ( x ) {\textstyle E-V(x)} or that of the momentum p ( x ) {\textstyle p(x)} , over the wavelength λ {\textstyle \lambda } , being much smaller than 1 {\textstyle 1} . Similarly it can be shown that λ ( x ) {\textstyle \lambda (x)} also has restrictions based on underlying assumptions for the WKB approximation that: | d λ d x | ≪ 1 {\displaystyle \left|{\frac {d\lambda }{dx}}\right|\ll 1} which implies that the de Broglie wavelength of the particle is slowly varying. === Behavior near the turning points === We now consider the behavior of the wave function near the turning points. For this, we need a different method. Near the first turning points, x1, the term 2 m ℏ 2 ( V ( x ) − E ) {\displaystyle {\frac {2m}{\hbar ^{2}}}\left(V(x)-E\right)} can be expanded in a power series, 2 m ℏ 2 ( V ( x ) − E ) = U 1 ⋅ ( x − x 1 ) + U 2 ⋅ ( x − x 1 ) 2 + ⋯ . {\displaystyle {\frac {2m}{\hbar ^{2}}}\left(V(x)-E\right)=U_{1}\cdot (x-x_{1})+U_{2}\cdot (x-x_{1})^{2}+\cdots \;.} To first order, one finds d 2 d x 2 Ψ ( x ) = U 1 ⋅ ( x − x 1 ) ⋅ Ψ ( x ) . {\displaystyle {\frac {d^{2}}{dx^{2}}}\Psi (x)=U_{1}\cdot (x-x_{1})\cdot \Psi (x).} This differential equation is known as the Airy equation, and the solution may be written in terms of Airy functions, Ψ ( x ) = C A Ai ( U 1 3 ⋅ ( x − x 1 ) ) + C B Bi ( U 1 3 ⋅ ( x − x 1 ) ) = C A Ai ( u ) + C B Bi ( u ) . {\displaystyle \Psi (x)=C_{A}\operatorname {Ai} \left({\sqrt[{3}]{U_{1}}}\cdot (x-x_{1})\right)+C_{B}\operatorname {Bi} \left({\sqrt[{3}]{U_{1}}}\cdot (x-x_{1})\right)=C_{A}\operatorname {Ai} \left(u\right)+C_{B}\operatorname {Bi} \left(u\right).} Although for any fixed value of ℏ {\displaystyle \hbar } , the wave function is bounded near the turning points, the wave function will be peaked there, as can be seen in the images above. As ℏ {\displaystyle \hbar } gets smaller, the height of the wave function at the turning points grows. It also follows from this approximation that: 1 ℏ ∫ p ( x ) d x = U 1 ∫ x − a d x = 2 3 ( U 1 3 ( x − a ) ) 3 2 = 2 3 u 3 2 {\displaystyle {\frac {1}{\hbar }}\int p(x)dx={\sqrt {U_{1}}}\int {\sqrt {x-a}}\,dx={\frac {2}{3}}({\sqrt[{3}]{U_{1}}}(x-a))^{\frac {3}{2}}={\frac {2}{3}}u^{\frac {3}{2}}} === Connection conditions === It now remains to construct a global (approximate) solution to the Schrödinger equation. For the wave function to be square-integrable, we must take only the exponentially decaying solution in the two classically forbidden regions. These must then "connect" properly through the turning points to the classically allowed region. For most values of E, this matching procedure will not work: The function obtained by connecting the solution near + ∞ {\displaystyle +\infty } to the classically allowed region will not agree with the function obtained by connecting the solution near − ∞ {\displaystyle -\infty } to the classically allowed region. The requirement that the two functions agree imposes a condition on the energy E, which will give an approximation to the exact quantum energy levels.The wavefunction's coefficients can be calculated for a simple problem shown in the figure. Let the first turning point, where the potential is decreasing over x, occur at x = x 1 {\displaystyle x=x_{1}} and the second turning point, where potential is increasing over x, occur at x = x 2 {\displaystyle x=x_{2}} . Given that we expect wavefunctions to be of the following form, we can calculate their coefficients by connecting the different regions using Airy and Bairy functions. Ψ V > E ( x ) ≈ A e 2 3 u 3 2 u 4 + B e − 2 3 u 3 2 u 4 Ψ E > V ( x ) ≈ C cos ( 2 3 u 3 2 − α ) u 4 + D sin ( 2 3 u 3 2 − α ) u 4 {\displaystyle {\begin{aligned}\Psi _{V>E}(x)\approx A{\frac {e^{{\frac {2}{3}}u^{\frac {3}{2}}}}{\sqrt[{4}]{u}}}+B{\frac {e^{-{\frac {2}{3}}u^{\frac {3}{2}}}}{\sqrt[{4}]{u}}}\\\Psi _{E>V}(x)\approx C{\frac {\cos {({\frac {2}{3}}u^{\frac {3}{2}}-\alpha )}}{\sqrt[{4}]{u}}}+D{\frac {\sin {({\frac {2}{3}}u^{\frac {3}{2}}-\alpha )}}{\sqrt[{4}]{u}}}\\\end{aligned}}} ==== First classical turning point ==== For U 1 < 0 {\displaystyle U_{1}<0} ie. decreasing potential condition or x = x 1 {\displaystyle x=x_{1}} in the given example shown by the figure, we require the exponential function to decay for negative values of x so that wavefunction for it to go to zero. Considering Bairy functions to be the required connection formula, we get: Bi ( u ) → − 1 π 1 u 4 sin ( 2 3 | u | 3 2 − π 4 ) where, u → − ∞ Bi ( u ) → 1 π 1 u 4 e 2 3 u 3 2 where, u → + ∞ {\displaystyle {\begin{aligned}\operatorname {Bi} (u)\rightarrow -{\frac {1}{\sqrt {\pi }}}{\frac {1}{\sqrt[{4}]{u}}}\sin {\left({\frac {2}{3}}|u|^{\frac {3}{2}}-{\frac {\pi }{4}}\right)}\quad {\textrm {where,}}\quad u\rightarrow -\infty \\\operatorname {Bi} (u)\rightarrow {\frac {1}{\sqrt {\pi }}}{\frac {1}{\sqrt[{4}]{u}}}e^{{\frac {2}{3}}u^{\frac {3}{2}}}\quad {\textrm {where,}}\quad u\rightarrow +\infty \\\end{aligned}}} We cannot use Airy function since it gives growing exponential behaviour for negative x. When compared to WKB solutions and matching their behaviours at ± ∞ {\displaystyle \pm \infty } , we conclude: A = − D = N {\displaystyle A=-D=N} , B = C = 0 {\displaystyle B=C=0} and α = π 4 {\displaystyle \alpha ={\frac {\pi }{4}}} . Thus, letting some normalization constant be N {\displaystyle N} , the wavefunction is given for increasing potential (with x) as: Ψ WKB ( x ) = { − N | p ( x ) | exp ( − 1 ℏ ∫ x x 1 | p ( x ) | d x ) if x < x 1 N | p ( x ) | sin ( 1 ℏ ∫ x x 1 | p ( x ) | d x − π 4 ) if x 2 > x > x 1 {\displaystyle \Psi _{\text{WKB}}(x)={\begin{cases}-{\frac {N}{\sqrt {|p(x)|}}}\exp {(-{\frac {1}{\hbar }}\int _{x}^{x_{1}}|p(x)|dx)}&{\text{if }}x<x_{1}\\{\frac {N}{\sqrt {|p(x)|}}}\sin {({\frac {1}{\hbar }}\int _{x}^{x_{1}}|p(x)|dx-{\frac {\pi }{4}})}&{\text{if }}x_{2}>x>x_{1}\\\end{cases}}} ==== Second classical turning point ==== For U 1 > 0 {\displaystyle U_{1}>0} ie. increasing potential condition or x = x 2 {\displaystyle x=x_{2}} in the given example shown by the figure, we require the exponential function to decay for positive values of x so that wavefunction for it to go to zero. Considering Airy functions to be the required connection formula, we get: Ai ( u ) → 1 2 π 1 u 4 e − 2 3 u 3 2 where, u → + ∞ Ai ( u ) → 1 π 1 u 4 cos ( 2 3 | u | 3 2 − π 4 ) where, u → − ∞ {\displaystyle {\begin{aligned}\operatorname {Ai} (u)\rightarrow {\frac {1}{2{\sqrt {\pi }}}}{\frac {1}{\sqrt[{4}]{u}}}e^{-{\frac {2}{3}}u^{\frac {3}{2}}}\quad {\textrm {where,}}\quad u\rightarrow +\infty \\\operatorname {Ai} (u)\rightarrow {\frac {1}{\sqrt {\pi }}}{\frac {1}{\sqrt[{4}]{u}}}\cos {\left({\frac {2}{3}}|u|^{\frac {3}{2}}-{\frac {\pi }{4}}\right)}\quad {\textrm {where,}}\quad u\rightarrow -\infty \\\end{aligned}}} We cannot use Bairy function since it gives growing exponential behaviour for positive x. When compared to WKB solutions and matching their behaviours at ± ∞ {\displaystyle \pm \infty } , we conclude: 2 B = C = N ′ {\displaystyle 2B=C=N'} , D = A = 0 {\displaystyle D=A=0} and α = π 4 {\displaystyle \alpha ={\frac {\pi }{4}}} . Thus, letting some normalization constant be N ′ {\displaystyle N'} , the wavefunction is given for increasing potential (with x) as: Ψ WKB ( x ) = { N ′ | p ( x ) | cos ( 1 ℏ ∫ x x 2 | p ( x ) | d x − π 4 ) if x 1 < x < x 2 N ′ 2 | p ( x ) | exp ( − 1 ℏ ∫ x 2 x | p ( x ) | d x ) if x > x 2 {\displaystyle \Psi _{\text{WKB}}(x)={\begin{cases}{\frac {N'}{\sqrt {|p(x)|}}}\cos {({\frac {1}{\hbar }}\int _{x}^{x_{2}}|p(x)|dx-{\frac {\pi }{4}})}&{\text{if }}x_{1}<x<x_{2}\\{\frac {N'}{2{\sqrt {|p(x)|}}}}\exp {(-{\frac {1}{\hbar }}\int _{x_{2}}^{x}|p(x)|dx)}&{\text{if }}x>x_{2}\\\end{cases}}} ==== Common oscillating wavefunction ==== Matching the two solutions for region x 1 < x < x 2 {\displaystyle x_{1}<x<x_{2}} , it is required that the difference between the angles in these functions is π ( n + 1 / 2 ) {\displaystyle \pi (n+1/2)} where the π 2 {\displaystyle {\frac {\pi }{2}}} phase difference accounts for changing cosine to sine for the wavefunction and n π {\displaystyle n\pi } difference since negation of the function can occur by letting N = ( − 1 ) n N ′ {\displaystyle N=(-1)^{n}N'} . Thus: ∫ x 1 x 2 2 m ( E − V ( x ) ) d x = ( n + 1 / 2 ) π ℏ , {\displaystyle \int _{x_{1}}^{x_{2}}{\sqrt {2m\left(E-V(x)\right)}}\,dx=(n+1/2)\pi \hbar ,} Where n is a non-negative integer. This condition can also be rewritten as saying that: The area enclosed by the classical energy curve is 2 π ℏ ( n + 1 / 2 ) {\displaystyle 2\pi \hbar (n+1/2)} . Either way, the condition on the energy is a version of the Bohr–Sommerfeld quantization condition, with a "Maslov correction" equal to 1/2. It is possible to show that after piecing together the approximations in the various regions, one obtains a good approximation to the actual eigenfunction. In particular, the Maslov-corrected Bohr–Sommerfeld energies are good approximations to the actual eigenvalues of the Schrödinger operator. Specifically, the error in the energies is small compared to the typical spacing of the quantum energy levels. Thus, although the "old quantum theory" of Bohr and Sommerfeld was ultimately replaced by the Schrödinger equation, some vestige of that theory remains, as an approximation to the eigenvalues of the appropriate Schrödinger operator. ==== General connection conditions ==== Thus, from the two cases the connection formula is obtained at a classical turning point, x = a {\displaystyle x=a} : N | p ( x ) | sin ( 1 ℏ ∫ x a | p ( x ) | d x − π 4 ) ⟹ − N | p ( x ) | exp ( 1 ℏ ∫ a x | p ( x ) | d x ) {\displaystyle {\frac {N}{\sqrt {|p(x)|}}}\sin {\left({\frac {1}{\hbar }}\int _{x}^{a}|p(x)|dx-{\frac {\pi }{4}}\right)}\Longrightarrow -{\frac {N}{\sqrt {|p(x)|}}}\exp {\left({\frac {1}{\hbar }}\int _{a}^{x}|p(x)|dx\right)}} and: N ′ | p ( x ) | cos ( 1 ℏ ∫ x a | p ( x ) | d x − π 4 ) ⟸ N ′ 2 | p ( x ) | exp ( − 1 ℏ ∫ a x | p ( x ) | d x ) {\displaystyle {\frac {N'}{\sqrt {|p(x)|}}}\cos {\left({\frac {1}{\hbar }}\int _{x}^{a}|p(x)|dx-{\frac {\pi }{4}}\right)}\Longleftarrow {\frac {N'}{2{\sqrt {|p(x)|}}}}\exp {\left(-{\frac {1}{\hbar }}\int _{a}^{x}|p(x)|dx\right)}} The WKB wavefunction at the classical turning point away from it is approximated by oscillatory sine or cosine function in the classically allowed region, represented in the left and growing or decaying exponentials in the forbidden region, represented in the right. The implication follows due to the dominance of growing exponential compared to decaying exponential. Thus, the solutions of oscillating or exponential part of wavefunctions can imply the form of wavefunction on the other region of potential as well as at the associated turning point. === Probability density === One can then compute the probability density associated to the approximate wave function. The probability that the quantum particle will be found in the classically forbidden region is small. In the classically allowed region, meanwhile, the probability the quantum particle will be found in a given interval is approximately the fraction of time the classical particle spends in that interval over one period of motion. Since the classical particle's velocity goes to zero at the turning points, it spends more time near the turning points than in other classically allowed regions. This observation accounts for the peak in the wave function (and its probability density) near the turning points. Applications of the WKB method to Schrödinger equations with a large variety of potentials and comparison with perturbation methods and path integrals are treated in Müller-Kirsten. == Examples in quantum mechanics == Although WKB potential only applies to smoothly varying potentials, in the examples where rigid walls produce infinities for potential, the WKB approximation can still be used to approximate wavefunctions in regions of smoothly varying potentials. Since the rigid walls have highly discontinuous potential, the connection condition cannot be used at these points and the results obtained can also differ from that of the above treatment. === Bound states for 1 rigid wall === The potential of such systems can be given in the form: V ( x ) = { V ( x ) if x ≥ x 1 ∞ if x < x 1 {\displaystyle V(x)={\begin{cases}V(x)&{\text{if }}x\geq x_{1}\\\infty &{\text{if }}x<x_{1}\\\end{cases}}} where x 1 < x 2 {\textstyle x_{1}<x_{2}} . Finding wavefunction in bound region, ie. within classical turning points x 1 {\textstyle x_{1}} and x 2 {\textstyle x_{2}} , by considering approximations far from x 1 {\textstyle x_{1}} and x 2 {\textstyle x_{2}} respectively we have two solutions: Ψ WKB ( x ) = A | p ( x ) | sin ( 1 ℏ ∫ x x 1 | p ( x ) | d x + α ) {\displaystyle \Psi _{\text{WKB}}(x)={\frac {A}{\sqrt {|p(x)|}}}\sin {\left({\frac {1}{\hbar }}\int _{x}^{x_{1}}|p(x)|dx+\alpha \right)}} Ψ WKB ( x ) = B | p ( x ) | cos ( 1 ℏ ∫ x x 2 | p ( x ) | d x + β ) {\displaystyle \Psi _{\text{WKB}}(x)={\frac {B}{\sqrt {|p(x)|}}}\cos {\left({\frac {1}{\hbar }}\int _{x}^{x_{2}}|p(x)|dx+\beta \right)}} Since wavefunction must vanish near x 1 {\textstyle x_{1}} , we conclude α = 0 {\textstyle \alpha =0} . For airy functions near x 2 {\textstyle x_{2}} , we require β = − π 4 {\textstyle \beta =-{\frac {\pi }{4}}} . We require that angles within these functions have a phase difference π ( n + 1 / 2 ) {\displaystyle \pi (n+1/2)} where the π 2 {\displaystyle {\frac {\pi }{2}}} phase difference accounts for changing sine to cosine and n π {\displaystyle n\pi } allowing B = ( − 1 ) n A {\displaystyle B=(-1)^{n}A} . 1 ℏ ∫ x 1 x 2 | p ( x ) | d x = π ( n + 3 4 ) {\displaystyle {\frac {1}{\hbar }}\int _{x_{1}}^{x_{2}}|p(x)|dx=\pi \left(n+{\frac {3}{4}}\right)} Where n is a non-negative integer. Note that the right hand side of this would instead be π ( n − 1 / 4 ) {\displaystyle \pi (n-1/4)} if n was only allowed to non-zero natural numbers. Thus we conclude that, for n = 1 , 2 , 3 , ⋯ {\textstyle n=1,2,3,\cdots } ∫ x 1 x 2 2 m ( E − V ( x ) ) d x = ( n − 1 4 ) π ℏ {\displaystyle \int _{x_{1}}^{x_{2}}{\sqrt {2m\left(E-V(x)\right)}}\,dx=\left(n-{\frac {1}{4}}\right)\pi \hbar } In 3 dimensions with spherically symmetry, the same condition holds where the position x is replaced by radial distance r, due to its similarity with this problem. === Bound states within 2 rigid wall === The potential of such systems can be given in the form: V ( x ) = { ∞ if x > x 2 V ( x ) if x 2 ≥ x ≥ x 1 ∞ if x < x 1 {\displaystyle V(x)={\begin{cases}\infty &{\text{if }}x>x_{2}\\V(x)&{\text{if }}x_{2}\geq x\geq x_{1}\\\infty &{\text{if }}x<x_{1}\\\end{cases}}} where x 1 < x 2 {\textstyle x_{1}<x_{2}} . For E ≥ V ( x ) {\textstyle E\geq V(x)} between x 1 {\textstyle x_{1}} and x 2 {\textstyle x_{2}} which are thus the classical turning points, by considering approximations far from x 1 {\textstyle x_{1}} and x 2 {\textstyle x_{2}} respectively we have two solutions: Ψ WKB ( x ) = A | p ( x ) | sin ( 1 ℏ ∫ x x 1 | p ( x ) | d x ) {\displaystyle \Psi _{\text{WKB}}(x)={\frac {A}{\sqrt {|p(x)|}}}\sin {\left({\frac {1}{\hbar }}\int _{x}^{x_{1}}|p(x)|dx\right)}} Ψ WKB ( x ) = B | p ( x ) | sin ( 1 ℏ ∫ x x 2 | p ( x ) | d x ) {\displaystyle \Psi _{\text{WKB}}(x)={\frac {B}{\sqrt {|p(x)|}}}\sin {\left({\frac {1}{\hbar }}\int _{x}^{x_{2}}|p(x)|dx\right)}} Since wavefunctions must vanish at x 1 {\textstyle x_{1}} and x 2 {\textstyle x_{2}} . Here, the phase difference only needs to account for n π {\displaystyle n\pi } which allows B = ( − 1 ) n A {\displaystyle B=(-1)^{n}A} . Hence the condition becomes: ∫ x 1 x 2 2 m ( E − V ( x ) ) d x = n π ℏ {\displaystyle \int _{x_{1}}^{x_{2}}{\sqrt {2m\left(E-V(x)\right)}}\,dx=n\pi \hbar } where n = 1 , 2 , 3 , ⋯ {\textstyle n=1,2,3,\cdots } but not equal to zero since it makes the wavefunction zero everywhere. === Quantum bouncing ball === Consider the following potential a bouncing ball is subjected to: V ( x ) = { m g x if x ≥ 0 ∞ if x < 0 {\displaystyle V(x)={\begin{cases}mgx&{\text{if }}x\geq 0\\\infty &{\text{if }}x<0\\\end{cases}}} The wavefunction solutions of the above can be solved using the WKB method by considering only odd parity solutions of the alternative potential V ( x ) = m g | x | {\displaystyle V(x)=mg|x|} . The classical turning points are identified x 1 = − E m g {\textstyle x_{1}=-{E \over mg}} and x 2 = E m g {\textstyle x_{2}={E \over mg}} . Thus applying the quantization condition obtained in WKB: ∫ x 1 x 2 2 m ( E − V ( x ) ) d x = ( n odd + 1 / 2 ) π ℏ {\displaystyle \int _{x_{1}}^{x_{2}}{\sqrt {2m\left(E-V(x)\right)}}\,dx=(n_{\text{odd}}+1/2)\pi \hbar } Letting n odd = 2 n − 1 {\textstyle n_{\text{odd}}=2n-1} where n = 1 , 2 , 3 , ⋯ {\textstyle n=1,2,3,\cdots } , solving for E {\textstyle E} with given V ( x ) = m g | x | {\displaystyle V(x)=mg|x|} , we get the quantum mechanical energy of a bouncing ball: E = ( 3 ( n − 1 4 ) π ) 2 3 2 ( m g 2 ℏ 2 ) 1 3 . {\displaystyle E={\left(3\left(n-{\frac {1}{4}}\right)\pi \right)^{\frac {2}{3}} \over 2}(mg^{2}\hbar ^{2})^{\frac {1}{3}}.} This result is also consistent with the use of equation from bound state of one rigid wall without needing to consider an alternative potential. === Quantum Tunneling === The potential of such systems can be given in the form: V ( x ) = { 0 if x < x 1 V ( x ) if x 2 ≥ x ≥ x 1 0 if x > x 2 {\displaystyle V(x)={\begin{cases}0&{\text{if }}x<x_{1}\\V(x)&{\text{if }}x_{2}\geq x\geq x_{1}\\0&{\text{if }}x>x_{2}\\\end{cases}}} where x 1 < x 2 {\textstyle x_{1}<x_{2}} . Its solutions for an incident wave is given as ψ ( x ) = { A exp ( i p 0 x ℏ ) + B exp ( − i p 0 x ℏ ) if x < x 1 C | p ( x ) | exp ( − 1 ℏ ∫ x 1 x | p ( x ) | d x ) if x 2 ≥ x ≥ x 1 D exp ( i p 0 x ℏ ) if x > x 2 {\displaystyle \psi (x)={\begin{cases}A\exp({ip_{0}x \over \hbar })+B\exp({-ip_{0}x \over \hbar })&{\text{if }}x<x_{1}\\{\frac {C}{\sqrt {|p(x)|}}}\exp {(-{\frac {1}{\hbar }}\int _{x_{1}}^{x}|p(x)|dx)}&{\text{if }}x_{2}\geq x\geq x_{1}\\D\exp({ip_{0}x \over \hbar })&{\text{if }}x>x_{2}\\\end{cases}}} where the wavefunction in the classically forbidden region is the WKB approximation but neglecting the growing exponential. This is a fair assumption for wide potential barriers through which the wavefunction is not expected to grow to high magnitudes. By the requirement of continuity of wavefunction and its derivatives, the following relation can be shown: | D | 2 | A | 2 = 4 ( 1 + a 1 2 / p 0 2 ) a 1 a 2 exp ( − 2 ℏ ∫ x 1 x 2 | p ( x ′ ) | d x ′ ) {\displaystyle {\frac {|D|^{2}}{|A|^{2}}}={\frac {4}{(1+{a_{1}^{2}}/{p_{0}^{2}})}}{\frac {a_{1}}{a_{2}}}\exp \left(-{\frac {2}{\hbar }}\int _{x_{1}}^{x_{2}}|p(x')|dx'\right)} where a 1 = | p ( x 1 ) | {\displaystyle a_{1}=|p(x_{1})|} and a 2 = | p ( x 2 ) | {\displaystyle a_{2}=|p(x_{2})|} . Using J ( x , t ) = i ℏ 2 m ( ψ ∗ ∇ ψ − ψ ∇ ψ ∗ ) {\textstyle \mathbf {J} (\mathbf {x} ,t)={\frac {i\hbar }{2m}}(\psi ^{*}\nabla \psi -\psi \nabla \psi ^{*})} we express the values without signs as: J inc. = ℏ 2 m ( 2 p 0 ℏ | A | 2 ) {\textstyle J_{\text{inc.}}={\frac {\hbar }{2m}}({\frac {2p_{0}}{\hbar }}|A|^{2})} J ref. = ℏ 2 m ( 2 p 0 ℏ | B | 2 ) {\textstyle J_{\text{ref.}}={\frac {\hbar }{2m}}({\frac {2p_{0}}{\hbar }}|B|^{2})} J trans. = ℏ 2 m ( 2 p 0 ℏ | D | 2 ) {\textstyle J_{\text{trans.}}={\frac {\hbar }{2m}}({\frac {2p_{0}}{\hbar }}|D|^{2})} Thus, the transmission coefficient is found to be: T = | D | 2 | A | 2 = 4 ( 1 + a 1 2 / p 0 2 ) a 1 a 2 exp ( − 2 ℏ ∫ x 1 x 2 | p ( x ′ ) | d x ′ ) {\displaystyle T={\frac {|D|^{2}}{|A|^{2}}}={\frac {4}{(1+{a_{1}^{2}}/{p_{0}^{2}})}}{\frac {a_{1}}{a_{2}}}\exp \left(-{\frac {2}{\hbar }}\int _{x_{1}}^{x_{2}}|p(x')|dx'\right)} where p ( x ) = 2 m ( E − V ( x ) ) {\textstyle p(x)={\sqrt {2m(E-V(x))}}} , a 1 = | p ( x 1 ) | {\displaystyle a_{1}=|p(x_{1})|} and a 2 = | p ( x 2 ) | {\displaystyle a_{2}=|p(x_{2})|} . The result can be stated as T ∼ e − 2 γ {\textstyle T\sim ~e^{-2\gamma }} where γ = ∫ x 1 x 2 | p ( x ′ ) | d x ′ {\textstyle \gamma =\int _{x_{1}}^{x_{2}}|p(x')|dx'} . == See also == == References == === Further reading === Child, M. S. (1991). Semiclassical mechanics with molecular applications. Oxford: Clarendon Press. ISBN 0-19-855654-3. Fröman, N.; Fröman, P.-O. (1965). JWKB Approximation: Contributions to the Theory. Amsterdam: North-Holland. Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-111892-7. Hall, Brian C. (2013), Quantum Theory for Mathematicians, Graduate Texts in Mathematics, vol. 267, Springer, Bibcode:2013qtm..book.....H, ISBN 978-1461471158 Liboff, Richard L. (2003). Introductory Quantum Mechanics (4th ed.). Addison-Wesley. ISBN 0-8053-8714-5. Olver, Frank William John (1974). Asymptotics and Special Functions. Academic Press. ISBN 0-12-525850-X. Razavy, Mohsen (2003). Quantum Theory of Tunneling. World Scientific. ISBN 981-238-019-1. == External links == Fitzpatrick, Richard (2002). "The W.K.B. Approximation". (An application of the WKB approximation to the scattering of radio waves from the ionosphere.)
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Wikipedia:Wacław Marzantowicz#0
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Wacław Bolesław Marzantowicz is a Polish mathematician known for his contributions in number theory and topology. He was President of the Polish Mathematical Society from 2014 to 2019. == Biography == In 1967 he became the finalist of the 18th Mathematical Olympiad. In 1972, he graduated in mathematics at Adam Mickiewicz University in Poznań. He obtained his doctorate in Institute of Mathematics of the Polish Academy of Sciences in 1977, based on the work Lefschetz Numbers of Maps Commuting with an Action of a Group written under the direction Kazimierz Gęba. He got habilitation there in 1991, based on the work Invariant topology methods used in variational problems. From 1993 to 1996, he was the director of the Institute of Mathematics University of Gdańsk. Since 1996, he has been working at Faculty of Mathematics and Computer Science at the Adam Mickiewicz University in Poznań, where he heads the Department of Geometry and Topology. In 2002 he received the title of professor of mathematics. References to his papers can be found in mathematical databases. From 1993 to 1996, he was the president of the Gdańsk Branch of the Polish Mathematical Society (PMS) and then its vice president (2011–2013). Since 2014, he has been the president of the Polish Mathematical Society. == Honours and awards == Since 1995, he has been a member of the Scientific Council of the Juliusz Schauder Center for Nonlinear Studies at Nicolaus Copernicus University in Toruń, of which he was the Chairman from 2012 to 2018. He has served multiple terms on the Mathematics Committee of the Polish Academy of Sciences (PAN), including the term 2024-2027. From 2016 to 2019, he was a representative of the Polish Mathematical Society (PTM) in the international mathematical cooperation program Silk-Road, conducted by the Chinese Mathematical Society. From 2010 to 2020, he represented PTM on the Council of the European Mathematical Society (EMS), and for the term 2021-2023, he was elected as a representative of individual members of EMS to this council. He became the joint recipient of the Stefan Banach Prize of the Polish Mathematical Society (alongside Jerzy Jezierski). == Further reading == Jerzy Jezierski; Wacław Marzantowicz, Homotopy methods in topological fixed and periodic points theory. Topological Fixed Point Theory and Its Applications, 3. Springer, Dordrecht, 2006. xii+319 pp. ISBN 978-1-4020-3930-0; ISBN 1-4020-3930-1, doi:10.1007/1-4020-3931-X. Złota księga nauk ekonomicznych, prawnych i ścisłych 2005, wyd. Gliwice 2005, p. 205 == References ==
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Wikipedia:Wadim Zudilin#0
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Wadim Zudilin (Вадим Валентинович Зудилин) is a Russian mathematician and number theorist who is active in studying hypergeometric functions and zeta constants. He studied under Yuri V. Nesterenko and worked at Moscow State University, the Steklov Institute of Mathematics, the Max Planck Institute for Mathematics and the University of Newcastle, Australia. He now works at the Radboud University Nijmegen, the Netherlands. He has reproved Apéry's theorem that ζ(3) is irrational, and expanded it. Zudilin proved that at least one of the four numbers ζ(5), ζ(7), ζ(9), or ζ(11) is irrational. For that accomplishment, he won the Distinguished Award of the Hardy-Ramanujan Society in 2001. With Doron Zeilberger, Zudilin improved upper bound of irrationality measure for π, which as of November 2022 is the current best estimate. == References == == External links == Wadim Zudilin's homepage Wadim Zudilin's research profile Wadim Zudilin's list of published works Wadim Zudilin at the Mathematics Genealogy Project
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Wikipedia:Waleed Al-Salam#0
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Waleed Al-Salam (born 15 July 1926 in Baghdad, Iraq – died 14 April 1996 in Edmonton, Canada) was a mathematician who introduced Al-Salam–Chihara polynomials, Al-Salam–Carlitz polynomials, q-Konhauser polynomials, and Al-Salam–Ismail polynomials. He was a Professor Emeritus at the University of Alberta. Born in Iraq, Baghdad, Al-Salam received his bachelor's degree in engineering physics (1950) and M.A. in mathematics (1951) from University of California Berkeley. He completed his education at Duke, receiving his Ph.D. for his dissertation on Bessel polynomials (1958). == References == Chihara, Theodore Seio; Ismail, Mourad E. H. (1998), "In memoriam: Waleed Al-Salam (July 15, 1926–April 13, 1996)", Journal of Approximation Theory, 95 (2): 153–160, doi:10.1006/jath.1998.3301, ISSN 0021-9045, MR 1652868 Ismail, Mourad E. H. (1999), "Waleed Al-Salam, 1926–1996", in Diejen, Jan Felipe van; Vinet, Luc (eds.), Algebraic methods and q-special functions. Proceedings of the workshop dedicated to the memory of Waleed Al-Salam held at the Université de Montréal, Montréal, QC, May 21–26, 1996, CRM Proc. Lecture Notes, vol. 22, Providence, R.I.: American Mathematical Society, pp. ix–xi, ISBN 978-0-8218-2026-1, MR 1726825 == External links == Waleed Al-Salam 1926-1996 Waleed Al-Salam at the Mathematics Genealogy Project
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Wikipedia:Walk-regular graph#0
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In graph theory, a walk-regular graph is a simple graph where the number of closed walks of any length ℓ {\displaystyle \ell } from a vertex to itself does only depend on ℓ {\displaystyle \ell } but not depend on the choice of vertex. Walk-regular graphs can be thought of as a spectral graph theory analogue of vertex-transitive graphs. While a walk-regular graph is not necessarily very symmetric, all its vertices still behave identically with respect to the graph's spectral properties. == Equivalent definitions == Suppose that G {\displaystyle G} is a simple graph. Let A {\displaystyle A} denote the adjacency matrix of G {\displaystyle G} , V ( G ) {\displaystyle V(G)} denote the set of vertices of G {\displaystyle G} , and Φ G − v ( x ) {\displaystyle \Phi _{G-v}(x)} denote the characteristic polynomial of the vertex-deleted subgraph G − v {\displaystyle G-v} for all v ∈ V ( G ) . {\displaystyle v\in V(G).} Then the following are equivalent: G {\displaystyle G} is walk-regular. A k {\displaystyle A^{k}} is a constant-diagonal matrix for all k ≥ 0. {\displaystyle k\geq 0.} Φ G − u ( x ) = Φ G − v ( x ) {\displaystyle \Phi _{G-u}(x)=\Phi _{G-v}(x)} for all u , v ∈ V ( G ) . {\displaystyle u,v\in V(G).} == Examples == The vertex-transitive graphs are walk-regular. The semi-symmetric graphs are walk-regular. The distance-regular graphs are walk-regular. More generally, any simple graph in a homogeneous coherent algebra is walk-regular. A connected regular graph is walk-regular if: It has at most four distinct eigenvalues. It is triangle-free and has at most five distinct eigenvalues. It is bipartite and has at most six distinct eigenvalues. == Properties == A walk-regular graph is necessarily a regular graph. Complements of walk-regular graphs are walk-regular. Cartesian products of walk-regular graphs are walk-regular. Categorical products of walk-regular graphs are walk-regular. Strong products of walk-regular graphs are walk-regular. In general, the line graph of a walk-regular graph is not walk-regular. == k-walk-regular graphs == A graph is k {\displaystyle k} -walk-regular if for any two vertices v {\displaystyle v} and w {\displaystyle w} of distance at most k , {\displaystyle k,} the number of walks of length ℓ {\displaystyle \ell } from v {\displaystyle v} to w {\displaystyle w} depends only on k {\displaystyle k} and ℓ {\displaystyle \ell } . For k = 0 {\displaystyle k=0} these are exactly the walk-regular graphs. In analogy to walk-regular graphs generalizing vertex-transitive graphs, 1-walk-regular graphs can be thought of as generalizing symmetric graphs, that is, graphs that are both vertex- and edge-transitive. For example, the Hoffman graph is 1-walk-regular but not symmetric. If k {\displaystyle k} is at least the diameter of the graph, then the k {\displaystyle k} -walk-regular graphs coincide with the distance-regular graphs. In fact, if k ≥ 2 {\displaystyle k\geq 2} and the graph has an eigenvalue of multiplicity at most k {\displaystyle k} (except for eigenvalues d {\displaystyle d} and − d {\displaystyle -d} , where d {\displaystyle d} is the degree of the graph), then the graph is already distance-regular. == References == == External links == Chris Godsil and Brendan McKay, Feasibility conditions for the existence of walk-regular graphs.
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Wikipedia:Wallis Professor of Mathematics#0
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The Wallis Professorship of Mathematics is a chair in the Mathematical Institute of the University of Oxford. It was established in 1969 in honour of John Wallis, who was Savilian Professor of Geometry at Oxford from 1649 to 1703. == List of Wallis Professors of Mathematics == 1969 to 1985: John Kingman 1985 to 1997: Simon Donaldson 1999 to 2022: Terence Lyons 2022 to date: Massimiliano Gubinelli == See also == List of professorships at the University of Oxford == References ==
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Wikipedia:Walter Craig (mathematician)#0
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Walter L. Craig (1953 – January 18, 2019) was a United States born Canadian mathematician and a Canada Research Chair in Mathematical Analysis and Applications at McMaster University, Hamilton, Ontario. == Personal life == Craig was born in State College, Pennsylvania in 1953. His father, a professor at Pennsylvania State University transferred to University of California, Berkeley, where Craig and his siblings were raised starting in 1959. Craig was the son of the logician William Craig and the husband of mathematician Deirdre Haskell. == Education == Craig attended the University of California at Berkeley and, after spending two years performing as a jazz musician, returned there to graduate with a bachelor's degree in mathematics in 1977. Craig earned his Ph.D. from New York University - Courant Institute in 1981; his dissertation, A Bifurcation Theory for Periodic Dissipative Wave Equations, was supervised by Louis Nirenberg. == Career == After stints at the California Institute of Technology, Stanford University, and Brown University, Craig moved to McMaster University in Hamilton, Ontario, Canada in 2000. His research topics included nonlinear partial differential equations, infinite dimensional Hamiltonian systems, Schrödinger operators and spectral theory, water waves, general relativity, and cosmology. In 2007, he was made a Fellow of the Royal Society of Canada; he was awarded a Killam Fellowship in 2009. In 2013, he became one of the inaugural Fellows of the American Mathematical Society. He served as Director of the Fields Institute from 2013 to 2015. == References ==
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Wikipedia:Walter Davis Lambert#0
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Walter Davis Lambert (January 12, 1879 – October 27, 1968) was an American geodesist. Known for his mathematics work with the U.S. Coast and Geodetic Survey as well as at multiple educational institutions, he was elected to the National Academy of Sciences in 1949—that same year, he won the William Bowie Medal and the Department of Commerce Gold Medal. == Biography == Lambert was born in West New Brighton, New York on January 12, 1879, with English ancestry. He attended a public school as well as the Friends Seminary, and later matriculated at Harvard University. In 1900, he graduated with a Bachelor of Arts degree; in 1901 he received a Master of Arts degree, also from Harvard. From 1901 to 1902, he was an instructor in mathematics at Purdue University. In the following two years, he taught math and astronomy at the University of Maine. In 1904, he accepted an offer to work for the U.S. Coast and Geodetic Survey as a mathematician. He worked on a part-time basis for some time while instructing math and pursuing postgraduate studies at the University of Pennsylvania. After becoming full-time again in 1911, he travelled to Washington, D.C. to work for the survey. He served in World War I—in 1917, he was commissioned as a first lieutenant in the U.S. Army, serving in France with the 101st Engineering Regiment, and returning to the Coast and Geodetic Survey in 1919, after the war. During this time he became more involved in the International Association of Geodesy. In 1929, Lambert wrote back and forth with Beno Gutenberg about the international participation of the Deutsche Geophysikalische Gesellschaft. Later, Lambert served as president of the association from 1946 to 1951. To honor him, he was made honorary president for the rest of his life. He had retired from the survey in 1949. Post-retirement, he was involved in geodesy at Ohio State University; for his contributions, the university awarded him an honorary Doctor of Science degree in 1957. He died on October 27, 1968, in Washington, D.C. == Notes == == References == == Further reading == Tardi, Pierre (January 20, 1969). "Notice nécrologique sur Walter Davis Lambert, Correspondant de la Section de Géographie et Navigation" (PDF). Vie Académique. C. R. Acad. Sci. 268: 32–33. Available via Gallica. == External links == National Academy of Sciences profile Niels Bohr Library & Archives portrait
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Wikipedia:Walter Eugene Clark#0
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Walter Eugene Clark (September 8, 1881 – September 30, 1960), was an American philologist. He was the second Wales Professor of Sanskrit at Harvard University and editor of the volumes 38-44 of the Harvard Oriental Series. He translated the Aryabhatiya of Aryabhata with critical notes which was published in 1930, by the University of Chicago Press. == Education == Clark was born on September 8, 1881, in Digby, Nova Scotia, and came to the United States in 1883. Clark received his A.B. in 1903, A.M. in 1904 from Harvard. After receiving his Doctorate from Harvard in 1906, with the dissertation titled "Quid de rebus Indicis scirent Graeci prisci quaeritur" he went to Germany to Berlin to receive further training under the Indologist Richard Pischel. He joined the "Department of Comparative Philology" at University of Chicago as the "Instructor in Sanskrit". In 1915, he was promoted to Assistant Professor of the "Department of Comparative Philology, General Linguistics, and Indo-Iranian Philology" and from 1923 to 1927 as Associate Professor of Sanskrit. In 1927 he became the Wales Professor of Sanskrit at Harvard. He held the position until his retirement in 1950. He was the editor of the volumes 38-44 of the Harvard Oriental Series after Charles Lanman. He was a member of the American Oriental Society, the American Academy of Arts and Sciences, the Linguistic Society of America, the Royal Asiatic Society, and the Société Asiatique. Among his other positions he was appointed the second Master of the Kirkland House (1935–46) on September 1, 1935, succeeding Edward A. Whitney. == Bibliography == Walter Eugene Clark (1933). India. Open Court Publishing Company. == References == == External links == Walter Eugene Clark at the Database of Classical Scholars
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Wikipedia:Walter Gautschi#0
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Walter Gautschi (; GOW-chee; born December 11, 1927) is a Swiss-born American mathematician, writer and professor emeritus of Computer science and Mathematics at Purdue University in West Lafayette, Indiana. He is primarily known for his contributions to numerical analysis and has authored over 200 papers in his area and published four books. == Early life and education == Gautschi was born December 11, 1927, in Basel, Switzerland, to Heinrich Gautschi (1901-1975). His paternal family originally hailed from Reinach. His patrilineal uncle, Adolf Eduard Gautschi, was a custodian and landscape painter. He had one twin brother Werner (1927-1959). He completed a Ph.D. in mathematics from the University of Basel on the thesis Analyse graphischer Integrationsmethoden advised by Alexander Ostrowski and Andreas Speiser (1953). == Career == Since then, he did postdoctoral work as a Janggen-Pöhn Research, Fellow at the Istituto Nazionale per le Applicazioni del Calcolo in Rome (1954) and at the Harvard Computation Laboratory (1955). He had positions at the National Bureau of Standards (1956–59), the American University in Washington, D.C., the Oak Ridge National Laboratory (1959–63) before joining Purdue University where he has worked from 1963 to 2000 and now being professor emeritus. He has been a Fulbright Scholar at the Technical University of Munich (1970) and held visiting appointments at the University of Wisconsin–Madison (1976), Argonne National Laboratory, the Wright-Patterson Air Force Base, ETH Zurich (1996-2001), the University of Padova (1997), and the University of Basel (2000). As well-known (e.g. Gerhard Wanner, Geneva c. 2011 and the well-known first-hand sources and subsequent reports such as Math. Intelligencer, etc), one of Gautschi's most important contributions on numerical simulation of special functions offered evidence and confidence to de Branges's tour-de-force attack on the elusive Bieberbach conjecture on the magnitude of coefficients of schlicht functions, which hitherto received only slow, difficult and partial progress by work of Bieberbach, Loewner, Gabaredian and Schiffer. == Personal life == In 1960, Gautschi married Erika, who was previously married to his twin brother Werner (1927-1959). Werner was also an academic professor and lecturer and emigrated to the United States with his wife in 1956. After his sudden death, Erika returned to Switzerland, while being pregnant with her child to Basel where she met Walter and married him in 1960. They had three daughters; Theresa (1961-2018), married Ainsworth, two children; Emily Ainsworth (b. 1994) and Keith (b. 1997), formerly of Camas, Washington. Doris (b. 1965) Caroline Cari (b. 1969) Through his predeceased twin brother, he has stepson/nephew, Thomas (b. 1960). Gautschi still resides in West Lafayette, Indiana. == Books == Colloquium approximatietheorie, MC Syllabus 14, Mathematisch Centrum Amsterdam, 1971. With H. Bavinck and G. M. Willems Numerical analysis: an introduction, Birkhäuser, Boston, 1997; 2nd edition, 2012. Orthogonal polynomials: computation and approximation, Oxford University Press, Oxford, 2004. Walter Gautschi, Selected Works with Commentaries, Springer Science & Business Media, 2013, 3 vols., Brezinski, Claude, and Ahmed Sameh, eds. volume 1; volume 2; volume 3 Orthogonal polynomials in MATLAB: exercises and solutions, SIAM, Philadelphia, 2016. == Surveys == Gander, W., & Gautschi, W. (2000). Adaptive quadrature—revisited. BIT Numerical Mathematics, 40(1), 84–101. Gautschi, W. (1996). Orthogonal polynomials: applications and computation. Acta Numerica, 5, 45–119. Gautschi, W. (1981). A survey of Gauss-Christoffel quadrature formulae. In EB Christoffel (pp. 72-147). Birkhäuser, Basel. Gautschi, W. (1967). Computational aspects of three-term recurrence relations. SIAM Review, 9(1), 24–82. == References == == External links == Publications by Walter Gautschi at ResearchGate Walter Gautschi at DBLP Bibliography Server
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Wikipedia:Walter Hayman#0
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Walter Kurt Hayman FRS (formerly Haymann; 6 January 1926 – 1 January 2020) was a British mathematician known for contributions to complex analysis. He was a professor at Imperial College London. == Life and work == Hayman was born in Cologne, Germany, the son of Roman law professor Franz Haymann (1874-1947) and Ruth Therese Hensel, daughter of mathematician Kurt Hensel. He was a great-grandson of acclaimed composer Fanny Mendelssohn. Because of his Jewish heritage, he left Germany, then under Nazi rule, alone by train in 1938. He continued his schooling at Gordonstoun School, and later at St John's College, Cambridge under John Edensor Littlewood and his doctoral advisor Mary Cartwright. He taught at King's College, Newcastle, and the University of Exeter. In 1947, he married Margaret Riley Crann after they met at a Quaker meeting. Together, they founded the British Mathematical Olympiad. The pair had three daughters, including the peace activist Carolyn Hayman and the filmmaker Sheila Hayman. He is known for his asymptotic results in Bieberbach conjecture in 1955, and for Hayman's alternatives in Nevanlinna Theory. His work with Wolfgang Fuchs gave a solution to an inverse problem of the Nevanlinna theory for entire functions, predating David Drasin's 1976 work. == Honours and awards == Hayman was elected to the Royal Society in 1956 and of the Finnish Academy of Science and Letters in 1978: he was elected "Foreign member" of the Accademia dei Lincei on 16 December 1985. In 1992 he received an honorary doctorate from the Faculty of Mathematics and Science at Uppsala University, Sweden In 1995 he was awarded the De Morgan Medal by the London Mathematical Society. In 2008, an issue of the Journal Computational Methods and Function Theory was dedicated to him on the occasion of his 80th birthday. == Selected publications == === Papers === Hayman, W. K. (1952), "Functions with values in a given domain", Proceedings of the American Mathematical Society, 3 (3): 428–432, doi:10.1090/S0002-9939-1952-0049323-9, MR 0049323, Zbl 0048.31402. Hayman, W. K. (1974), "The local growth of power series: a survey of the Wiman-Valiron method", Canadian Mathematical Bulletin, 17 (3): 317–358, CiteSeerX 10.1.1.433.7629, doi:10.4153/CMB-1974-064-0, MR 0385095, Zbl 0314.30021. Hayman, W. K.; Rossi, J. F. (1984), "Characteristic, maximum modulus and value distribution", Transactions of the American Mathematical Society, 284 (2): 651–664, doi:10.1090/S0002-9947-1984-0743737-2, MR 0743737, Zbl 0547.30023. Hayman, Walter K. (1993), "A problem on Fourier series arising from an Isoperimetric inequality", in Ricci, Paolo Emilio (ed.), Problemi attuali dell'analisi e della fisica matematica. Atti del simposio internazionale dedicato a Gaetano Fichera nel suo 70o compleanno. Taormina, 15–17 ottobre 1992, Roma: Dipartimento di Matematica Università di Roma La Sapienza – Aracne Editrice, pp. 119–125, MR 1249093, Zbl 0851.42009. Hayman, W. K. (2002), "Univalent and Multivalent Functions", in Kuhnau, Reiner (ed.), Geometric Function Theory, Handbook of Complex Analysis, vol. 1, Amsterdam: North-Holland, pp. 1–36, ISBN 978-0-444-82845-3, MR 1966188, Zbl 1069.30018. === Books === Hayman, W. K. (1964), Meromorphic functions, Oxford Mathematical Monographs, Oxford: Clarendon Press, pp. XIV+191, MR 0164038, Zbl 0115.06203. Hayman, W. K. (1967), Research Problems in Function Theory, London: Athlone Press, pp. vii+56. Hayman, W. K.; Kennedy, P. B. (1976), Subharmonic functions. Volume 1, London Mathematical Society Monographs, vol. 9, London–New York: Academic Press, pp. XVII+284, ISBN 978-0-12-334801-2, MR 0460672, Zbl 0419.31001. Hayman, W. K. (1988), Subharmonic functions. Volume 2, London Mathematical Society Monographs, vol. 20, London: Academic Press, pp. xiii+875, ISBN 978-0-12-334802-9, MR 1049148, Zbl 0699.31001. Hayman, W. K. (1994) [1958], Multivalent functions, Cambridge Tracts on Mathematics, vol. 110 (Second ed.), Cambridge: Cambridge University Press, pp. xii+263, ISBN 978-0-521-46026-2, MR 1310776, Zbl 0904.30001. Hayman, W. K. (2014), My Life and Functions, Logic Press, pp. iv+138, ISBN 978-1-326-03020-9 Hayman, W. K.; Lingham, E. F. (2019), Research Problems in Function Theory - Fiftieth Anniversary Edition, Problem Books in Mathematics, Springer, pp. VIII+284, ISBN 978-3-030-25164-2 == Notes == == References == == External links == O'Connor, John J.; Robertson, Edmund F., "Walter Hayman", MacTutor History of Mathematics Archive, University of St Andrews Walter Hayman at the Mathematics Genealogy Project Obituary at the London Mathematical Society
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Wikipedia:Walter Murray Wonham#0
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Walter Murray Wonham (1934 – May 14, 2023) was a Canadian control theorist and professor at the University of Toronto. He focused on multi-variable geometric control theory, stochastic control and stochastic filters, and the control of discrete event systems from the standpoint of mathematical logic and formal languages. == Education == Wonham attended a boys' school and preferred individual to team sports, taking up sailing and tennis. He obtained his bachelor's degree in engineering physics from McGill University in 1956 and a doctorate in stochastic control from the University of Cambridge in 1961. == Career == In the 1960s, he worked at Purdue University's Control and Information Systems Laboratory, Martin Marietta's Research Institute for Advanced Studies (RIAS) in Baltimore, Brown University's Department of Applied Mathematics, and in the Office for Control Theory and Applications of NASA's Electronics for Research Center, where he developed a geometric theory of multivariable control with A. Stephen Morse. In 1968, Wonham proved a separation theorem for controls in a more general cost functional class with many technical assumptions and restrictions. Wonham returned to Canada in 1970, after fifteen years away, and joined the University of Toronto as an associate professor in the Faculty of Electrical Engineering. Being with the university's Control Theory Group as a full professor since 1972, he served as Dean of Engineering and Applied Sciences at the University of Toronto between 1992 and 1996. He was made university professor in 1996 and appointed University Professor Emeritus upon his retirement in 2000. Wonham and his student Bruce Francis first articulated the internal model principle in 1976, which is a good regulator restricted to the ordinary differential equations subset of control theory. As an explicit formulation of the Conant and Ashby good regulator theorem, it stands in contrast to classical control where the classical feedback loop fails to explicitly model the controlled system (although the classical controller may contain an implicit model). In 1987, Wonham and Peter Ramadge introduced supervisory control theory as a method for automatically synthesizing supervisors that restrict the behavior of a plant such that as much as possible of the given specifications are fulfilled. Wonham authored and co-authored about seventy-five research papers, as well as the book Linear Multivariable Control: A Geometric Approach. He was a Fellow of the Royal Society of Canada and the Institute of Electrical and Electronics Engineers (IEEE). He was an Honorary Professor of the Beijing University of Aeronautics and Astronautics and a Foreign Member of the (U.S.) National Academy of Engineering. == Death == Wonham died on May 14, 2023, at the age of 88. == Selected works == Linear multivariable control: a geometric approach. Springer 1979 Supervisor Localization: A Top-Down Approach to Distributed Control of Discrete-Event Systems. Springer 2016 Supervisory Control of Discrete-Event Systems. Springer 2019 == References == == External links == Official personal webpage hosted by University of Toronto University Professor Emeritus W. Murray Wonham – Past & Future Mathematics Genealogy Project profile
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Wikipedia:Walter Warwick Sawyer#0
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Walter Warwick Sawyer (or W. W. Sawyer; April 5, 1911 – February 15, 2008) was a mathematician, mathematics educator and author, who taught on several continents. == Life and career == Walter Warwick Sawyer was born in St. Ives, Hunts, England on April 5, 1911. He attended Highgate School in London. He was an undergraduate at St. John's College, Cambridge, obtaining a BA in 1933 and specializing in quantum theory and relativity. He was an assistant lecturer in mathematics from 1933 to 1937 at University College, Dundee and from 1937 to 1944 at University of Manchester. In 1940 he met Betty [Hilda Elizabeth Crowther] and within two weeks, they were married. In 1943 their one child, daughter Anne Elizabeth, was born. 1943 was also the year that Sawyer's publishing career began with the book Mathematician's Delight published by Pelican Books, the non-fiction imprint of Penguin Books founded by Allen Lane and V. K. Krishna Menon. From 1945 to 1947, he was the head of mathematics at Leicester College of Technology. In 1948 Sawyer became the first head of the mathematics department of what is now the University of Ghana. From 1951 to 1956, he was at Canterbury College (now the University of Canterbury in New Zealand). He left Canterbury College to become an associate professor at the University of Illinois, where he worked from winter 1957 through June 1958. While there, he criticized the New Math movement, which included criticism of the people who had hired him. From 1958 to 1965, he was a professor of mathematics at Wesleyan University, where he edited Mathematics Student Journal. In the fall of 1965 he became a professor at the University of Toronto, appointed to both the College of Education and the Department of Mathematics. He retired in 1976. Sawyer was the author of some 11 books. He is probably best known for his semi-popular works Mathematician's Delight and Prelude to Mathematics. Both of these have been translated into many languages. Mathematician's Delight was still in print 65 years after it was written. Some mathematicians have credited these books with helping to inspire their choice of a career. Sawyer died on February 15, 2008, at the age of 96. He is survived by a daughter, Anne León (Artist) and granddaughter, Anita León (Educator). == Partial bibliography == Mathematician's Delight, (Penguin, 1943), is probably his best known book. Mathematics in Theory and Practice, (Odhams, 1952) Prelude to Mathematics (Penguin, 1955) Designing and Making, (Blackwell, 1957) A Concrete Approach to Abstract Algebra, (Freeman, 1959) What Is Calculus About?, (Yale University, 1961) Vision in Elementary Mathematics, (Penguin, 1964) A Path to Modern Mathematics, (Penguin, 1966) Search for Pattern, (Penguin, 1970) An Engineering Approach to Linear Algebra, (Cambridge University Press, 1972) A First Look at Numerical Functional Analysis, (Oxford University Press, 1978) == Notes == == External links == Sawyer, Walter Warwick; Mark Alder (2001). "Professor Warwick Sawyer". Retrieved 21 August 2009. Walter Warwick Sawyer information and materials
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Wikipedia:Walter Whiteley#0
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Walter John Whiteley is a professor in the department of mathematics and statistics at York University in Canada. He specializes in geometry and mathematics education, and is known for his expertise in structural rigidity and rigidity matroids. == Education and career == Whiteley graduated from Queen's University in 1966. He earned his Ph.D. in 1971 from the Massachusetts Institute of Technology, with a dissertation titled Logic and Invariant Theory supervised by Gian-Carlo Rota. He worked as an instructor at Champlain College Saint-Lambert, with a joint appointment in mathematics and humanities, from 1972 until he joined the York University faculty in 1992. == Awards and honours == In 2009, Whiteley won the Adrien Pouliot Award of the Canadian Mathematical Society for his contributions to mathematics education. In August 2014, the Fields Institute at the University of Toronto hosted a workshop on rigidity theory and spatial reasoning, "inspired by the distinguished career of Professor Walter Whiteley". == Selected publications == Roth, B.; Whiteley, W. (1981), "Tensegrity frameworks", Transactions of the American Mathematical Society, 265 (2): 419–446, doi:10.2307/1999743, JSTOR 1999743, MR 0610958. Connelly, Robert; Whiteley, Walter (1996), "Second-order rigidity and prestress stability for tensegrity frameworks", SIAM Journal on Discrete Mathematics, 9 (3): 453–491, CiteSeerX 10.1.1.145.3168, doi:10.1137/S0895480192229236, MR 1402190. Whiteley, Walter (1996), "Some matroids from discrete applied geometry", Matroid theory (Seattle, WA, 1995), Contemporary Mathematics, vol. 197, Providence, RI: American Mathematical Society, pp. 171–311, doi:10.1090/conm/197/02540, ISBN 978-0-8218-0508-4, MR 1411692. Whiteley, Walter (1997), "Rigidity and scene analysis", Handbook of discrete and computational geometry, CRC Press Ser. Discrete Math. Appl., CRC, Boca Raton, FL, pp. 893–916, MR 1730205. Eren, T.; Goldenberg, O.K.; Whiteley, W.; Yang, Y.R.; Morse, A.S.; Anderson, B.D.O.; Belhumeur, P.N. (2004), "Rigidity, computation, and randomization in network localization", Proceedings of the Twenty-Third Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE INFOCOM 2004), Vol. IV, vol. 4, pp. 2673–2684, doi:10.1109/infcom.2004.1354686, ISBN 0-7803-8355-9, S2CID 5674760. Aspnes, J.; Eren, T.; Goldenberg, D.K.; Morse, A.S.; Whiteley, W.; Yang, Y.R.; Anderson, B.D.O.; Belhumeur, P.N. (2006), "A theory of network localization", IEEE Transactions on Mobile Computing, 5 (12): 1663–1678, CiteSeerX 10.1.1.138.2248, doi:10.1109/tmc.2006.174, S2CID 2911118. Connelly, Robert; Weiss, Asia Ivić; Whiteley, Walter, eds. (2014). Rigidity and Symmetry. New York: Springer. ISBN 9781493907809. OCLC 941174259. == References == == External links == Home page
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