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Stanisław Zaremba (mathematician)
Stanisław Zaremba (3 October 1863 – 23 November 1942) was a Polish mathematician and engineer.. His research in partial differential equations, applied mathematics and classical analysis, particularly on harmonic functions, gained him a wide recognition. He was one of the mathematicians who contributed to the success of the Polish School of Mathematics through his teaching and organizational skills as well as through his research. Apart from his research works, Zaremba wrote many university textbooks and monographies. He was a professor of the Jagiellonian University (since 1900), member of Academy of Learning (since 1903), co-founder and president of the Polish Mathematical Society (1919). He should not be confused with his son Stanisław Krystyn Zaremba, also a mathematician. Biography Zaremba was born on 3 October 1863 in Romanówka, present-day Ukraine. The son of an engineer, he was educated at a grammar school in Saint Petersburg and studied at the Institute of Techn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Direct Method In The Calculus Of Variations
In mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, introduced by Stanisław Zaremba and David Hilbert around 1900. The method relies on methods of functional analysis and topology. As well as being used to prove the existence of a solution, direct methods may be used to compute the solution to desired accuracy. The method The calculus of variations deals with functionals J:V \to \bar, where V is some function space and \bar = \mathbb \cup \. The main interest of the subject is to find ''minimizers'' for such functionals, that is, functions v \in V such that:J(v) \leq J(u)\forall u \in V. The standard tool for obtaining necessary conditions for a function to be a minimizer is the Euler–Lagrange equation. But seeking a minimizer amongst functions satisfying these may lead to false conclusions if the existence of a minimizer is not established beforehand. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Romanivka, Bereznehuvate Settlement Hromada, Bashtanka Raion, Mykolaiv Oblast
Romanivka ( uk, Рома́нівка russian: Романовка) is a village in Ukraine. It is part of Bashtanka Raion of Mykolaiv Oblast. It belongs to Bereznehuvate settlement hromada, one of the hromadas of Ukraine. Romanivka is the site of an ancient mega-settlement belonging to the Cucuteni–Trypillia culture dating to 3600-3200 BC. The settlement was for the time very large, covering an area of 100 hectares. This proto-city is just one of 2,440 Cucuteni-Trypillia settlements discovered so far in Romania, Moldova and Ukraine. 194 (8%) of these settlements had an area of more than 10 hectares between 5000-2700 B.C. and more than 29 settlements had an area in the range of 100 to 450 hectares. Until 18 July 2020, Romanivka belonged to Bereznehuvate Raion. The raion was abolished that day as part of the administrative reform of Ukraine, which reduced the number of raions of Mykolaiv Oblast to four. The area of Bereznehuvate Raion was merged into Bashtanka Raion. His ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixed Boundary Condition
In mathematics, a mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of the domain where the condition is stated. Precisely, in a mixed boundary value problem, the solution is required to satisfy a Dirichlet or a Neumann boundary condition in a mutually exclusive way on disjoint parts of the boundary. For example, given a solution to a partial differential equation on a domain with boundary , it is said to satisfy a mixed boundary condition if, consisting of two disjoint parts, and , such that , verifies the following equations: :\left. u \_ = u_0and\left. \frac\_ = g, where and are given functions defined on those portions of the boundary. The mixed boundary condition differs from the Robin boundary condition in that the latter requires a linear combination, possibly with pointwise variable coeffici ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saint Petersburg
Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), is the second-largest city in Russia. It is situated on the Neva River, at the head of the Gulf of Finland on the Baltic Sea, with a population of roughly 5.4 million residents. Saint Petersburg is the fourth-most populous city in Europe after Istanbul, Moscow and London, the most populous city on the Baltic Sea, and the world's northernmost city of more than 1 million residents. As Russia's Imperial capital, and a historically strategic port, it is governed as a federal city. The city was founded by Tsar Peter the Great on 27 May 1703 on the site of a captured Swedish fortress, and was named after apostle Saint Peter. In Russia, Saint Petersburg is historically and culturally associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grammar School
A grammar school is one of several different types of school in the history of education in the United Kingdom and other English-speaking countries, originally a school teaching Latin, but more recently an academically oriented secondary school, differentiated in recent years from less academic secondary modern schools. The main difference is that a grammar school may select pupils based on academic achievement whereas a secondary modern may not. The original purpose of medieval grammar schools was the teaching of Latin. Over time the curriculum was broadened, first to include Ancient Greek, and later English and other European languages, natural sciences, mathematics, history, geography, art and other subjects. In the late Victorian era grammar schools were reorganised to provide secondary education throughout England and Wales; Scotland had developed a different system. Grammar schools of these types were also established in British territories overseas, where they have evolv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanisław Krystyn Zaremba (mathematician)
Stanisław Krystyn Zaremba (August 15, 1903, in Cracow – January 14, 1990, in Aberystwyth, Wales) was a Polish climber, mountaineer and mathematician. He was the son of Stanisław Zaremba (1863–1942), also a mathematician. Zaremba is known for his contributions to low-discrepancy sequences, low-discrepancy sets of points, and their application to Quasi-Monte Carlo methods for numerical integration. He is one of the namesakes of the Hlawka–Zaremba formula in the theory of low-discrepancy sequences. Education and career Zaremba studied mathematics at the Jagiellonian University (1921-1924, 1926-1929) and in Paris (1924–26). After his studies he was an assistant at Vilnius University and since 1936 he was an associate professor at Jagiellonian University. He then worked as a lecturer in Stalinabad (nowadays Dushanbe in Tajikistan), England, Wales, United States and Canada, eventually settling in Wales, where he died in 1990. He visited Poland well into his old age, lectur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polish Mathematical Society
The Polish Mathematical Society ( pl, Polskie Towarzystwo Matematyczne) is the main professional society of Polish mathematicians and represents Polish mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). History The society was established in Kraków, Poland on 2 April 1919 . It was originally called the Mathematical Society in Kraków, the name was changed to the Polish Mathematical Society on 21 April 1920. It was founded by 16 mathematicians, Stanisław Zaremba, Franciszek Leja, Alfred Rosenblatt, Stefan Banach and Otto Nikodym were among them. Ever since its foundation, the society's main activity was to bring mathematicians together by means of organizing conferences and lectures. The second main activity is the publication of its annals ''Annales Societatis Mathematicae Polonae'', consisting of: * Series 1''Commentationes Mathematicae'' * Series 2Wiadomości Matematyczne("Mathematical News"), in Polish * Series 3: ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academy Of Learning
Academy of Learning ( pl, Akademia Umiejętności; AU) was a primary Polish scientific institution during the annexation of Poland established in 1871. It was founded in Kraków as a continuation of the ''Kraków Scientific Society'' (''Towarzystwo Naukowe Krakowskie''). The institution began activity two years later, in 1873. At first, it focused on scholars from Kraków, however, it soon expanded its activity to Polish scholars from all annexed territories, along with Polish emigration. Its main goals were to organize, support and conduct learning, plus represent Polish scientists and scholars from all over the world. AU changed its statute and in 1919 began activity as the Polish Academy of Learning The Polish Academy of Arts and Sciences or Polish Academy of Learning ( pl, Polska Akademia Umiejętności), headquartered in Kraków and founded in 1872, is one of two institutions in contemporary Poland having the nature of an academy of scie ... (''Polska Akademia Umiejętno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monograph
A monograph is a specialist work of writing (in contrast to reference works) or exhibition on a single subject or an aspect of a subject, often by a single author or artist, and usually on a scholarly subject. In library cataloging, ''monograph'' has a broader meaning—that of a nonserial publication complete in one volume (book) or a definite number of volumes. Thus it differs from a serial or periodical publication such as a magazine, academic journal, or newspaper. In this context only, books such as novels are considered monographs.__FORCETOC__ Academia The English term "monograph" is derived from modern Latin "monographia", which has its root in Greek. In the English word, "mono-" means "single" and "-graph" means "something written". Unlike a textbook, which surveys the state of knowledge in a field, the main purpose of a monograph is to present primary research and original scholarship ascertaining reliable credibility to the required recipient. This research is prese ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polish School Of Mathematics
The Polish School of Mathematics was the mathematics community that flourished in Poland in the 20th century, particularly during the Interbellum between World Wars I and II. Overview The Polish School of Mathematics subsumed: *the Lwów School of Mathematics - mostly focused on functional analysis; *the Warsaw School of Mathematics - mostly focused on set theory, mathematical logic and topology; and *the Kraków School of Mathematics - mostly focused on differential equations, analytic functions, differential geometry. Nomenclature Poland's mathematicians provided a name to Polish notation and Polish space. Background It has been debated what stimulated the exceptional efflorescence of mathematics in Poland after World War I. Important preparatory work had been done by the Polish "Positivists" following the disastrous January 1863 Uprising. The Positivists extolled science and technology, and popularized slogans of "organic work" and "building from the foundations." I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Functions
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U \to \mathbb R, where is an open subset of that satisfies Laplace's equation, that is, : \frac + \frac + \cdots + \frac = 0 everywhere on . This is usually written as : \nabla^2 f = 0 or :\Delta f = 0 Etymology of the term "harmonic" The descriptor "harmonic" in the name harmonic function originates from a point on a taut string which is undergoing harmonic motion. The solution to the differential equation for this type of motion can be written in terms of sines and cosines, functions which are thus referred to as ''harmonics''. Fourier analysis involves expanding functions on the unit circle in terms of a series of these harmonics. Considering higher dimensional analogues of the harmonics on the unit ''n''-sphere, one arrives at the spherical harmonics. These functions satisfy Laplace's equation and over time "harmonic" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, an infinite geometric sum is implicit in Zeno's paradox of the dichotomy. (St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
