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Hugo Steinhaus
Hugo Dyonizy Steinhaus ( ; ; January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the Jan Kazimierz University in Lwów (now Lviv, Ukraine), where he helped establish what later became known as the Lwów School of Mathematics. He is credited with "discovering" mathematician Stefan Banach, with whom he gave a notable contribution to functional analysis through the Banach–Steinhaus theorem. After World War II Steinhaus played an important part in the establishment of the mathematics department at Wrocław University and in the revival of Polish mathematics from the destruction of the war. Author of around 170 scientific articles and books, Steinhaus has left his legacy and contribution in many branches of mathematics, such as functional analysis, geometry, mathematical logic, and trigonometry. Notably he is regarded as one of the early found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jasło
Jasło is a county town in south-eastern Poland with 36,641 inhabitants, as of 31 December 2012. It is situated in the Subcarpathian Voivodeship (since 1999), and it was previously part of Krosno Voivodeship (1975–1998). It is located in Lesser Poland, in the heartland of the Doły (Pits), and its average altitude is 320 metres above sea level, although there are some hills located within the confines of the city. The Patron Saint of the city is Saint Anthony of Padua. History In the early days of Polish statehood, Jasło was part of the Castellany of Biecz, out of which ''Biecz County'' emerged in the 14th century. A list of rectories, created for collecting tithes, a church in "Jassel" in Zręcin deanery, Kraków diocese, is shown in 1328.Sulimierski, Filip, Bronisław Chlebowski, and Władysław Walewski. ''Słownik Geograficzny Królestwa Polskiego I Innych Krajów Słowiańskich: Warszawa 1880-1902''. Translated by William F. "Fred" Hoffman. Warszawa: BUW. Sekcja Dok ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Juliusz Schauder
Juliusz Paweł Schauder (; 21 September 1899, Lwów, Austria-Hungary – September 1943, Lwów, Occupied Poland) was a Polish mathematician of Jewish origin, known for his work in functional analysis, partial differential equations and mathematical physics. Life and career Born on 21 September 1899 in Lwów, he was drafted into the Austro-Hungarian Army right after his graduation from school and saw action on the Italian front. He was captured and imprisoned in Italy. He entered the university in Lwów in 1919 and received his doctorate in 1923. He got no appointment at the university and continued his research while working as teacher at a secondary school. Due to his outstanding results, he obtained a scholarship in 1932 that allowed him to spend several years in Leipzig and, especially, Paris. In Paris he started a very successful collaboration with Jean Leray. Around 1935 Schauder obtained the position of a senior assistant in the University of Lwów. Schauder, along with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Banach–Steinhaus Theorem
In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered one of the cornerstones of the field. In its basic form, it asserts that for a family of continuous linear operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The theorem was first published in 1927 by Stefan Banach and Hugo Steinhaus, but it was also proven independently by Hans Hahn. Theorem The completeness of X enables the following short proof, using the Baire category theorem. There are also simple proofs not using the Baire theorem . Corollaries The above corollary does claim that T_n converges to T in operator norm, that is, uniformly on bounded sets. However, since \left\ is bounded in operator norm, and the limit operator T is continuous ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Definition, norm, Topological space#Definition, topology, etc.) and the linear transformation, linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous function, continuous, unitary operator, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of variati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lwów School Of Mathematics
The Lwów school of mathematics ( pl, lwowska szkoła matematyczna) was a group of Polish mathematicians who worked in the interwar period in Lwów, Poland (since 1945 Lviv, Ukraine). The mathematicians often met at the famous Scottish Café to discuss mathematical problems, and published in the journal '' Studia Mathematica'', founded in 1929. The school was renowned for its productivity and its extensive contributions to subjects such as point-set topology, set theory and functional analysis. The biographies and contributions of these mathematicians were documented in 1980 by their contemporary Kazimierz Kuratowski in his book ''A Half Century of Polish Mathematics: Remembrances and Reflections''. Members Notable members of the Lwów school of mathematics included: * Stefan Banach * Feliks Barański * Władysław Orlicz * Stanisław Saks * Hugo Steinhaus * Stanisław Mazur * Stanisław Ulam * Józef Schreier * Juliusz Schauder * Mark Kac * Antoni Łomnicki * Stefan Kaczmar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ukraine
Ukraine ( uk, Україна, Ukraïna, ) is a country in Eastern Europe. It is the second-largest European country after Russia, which it borders to the east and northeast. Ukraine covers approximately . Prior to the ongoing Russian invasion, it was the eighth-most populous country in Europe, with a population of around 41 million people. It is also bordered by Belarus to the north; by Poland, Slovakia, and Hungary to the west; and by Romania and Moldova to the southwest; with a coastline along the Black Sea and the Sea of Azov to the south and southeast. Kyiv is the nation's capital and largest city. Ukraine's state language is Ukrainian; Russian is also widely spoken, especially in the east and south. During the Middle Ages, Ukraine was the site of early Slavic expansion and the area later became a key centre of East Slavic culture under the state of Kievan Rus', which emerged in the 9th century. The state eventually disintegrated into rival regional po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lviv
Lviv ( uk, Львів) is the largest city in western Ukraine, and the seventh-largest in Ukraine, with a population of . It serves as the administrative centre of Lviv Oblast and Lviv Raion, and is one of the main cultural centres of Ukraine. It was named in honour of Leo, the eldest son of Daniel, King of Ruthenia. Lviv emerged as the centre of the historical regions of Red Ruthenia and Galicia in the 14th century, superseding Halych, Chełm, Belz and Przemyśl. It was the capital of the Kingdom of Galicia–Volhynia from 1272 to 1349, when it was conquered by King Casimir III the Great of Poland. From 1434, it was the regional capital of the Ruthenian Voivodeship in the Kingdom of Poland. In 1772, after the First Partition of Poland, the city became the capital of the Habsburg Kingdom of Galicia and Lodomeria. In 1918, for a short time, it was the capital of the West Ukrainian People's Republic. Between the wars, the city was the centre of the Lwów Voivodeship in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lwów
Lviv ( uk, Львів) is the largest city in western Ukraine, and the seventh-largest in Ukraine, with a population of . It serves as the administrative centre of Lviv Oblast and Lviv Raion, and is one of the main cultural centres of Ukraine. It was named in honour of Leo, the eldest son of Daniel, King of Ruthenia. Lviv emerged as the centre of the historical regions of Red Ruthenia and Galicia in the 14th century, superseding Halych, Chełm, Belz and Przemyśl. It was the capital of the Kingdom of Galicia–Volhynia from 1272 to 1349, when it was conquered by King Casimir III the Great of Poland. From 1434, it was the regional capital of the Ruthenian Voivodeship in the Kingdom of Poland. In 1772, after the First Partition of Poland, the city became the capital of the Habsburg Kingdom of Galicia and Lodomeria. In 1918, for a short time, it was the capital of the West Ukrainian People's Republic. Between the wars, the city was the centre of the Lwów Voivodeship in the Se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Göttingen University
Göttingen (, , ; nds, Chöttingen) is a university city in Lower Saxony, central Germany, the capital of the eponymous district. The River Leine runs through it. At the end of 2019, the population was 118,911. General information The origins of Göttingen lay in a village called ''Gutingi, ''first mentioned in a document in 953 AD. The city was founded northwest of this village, between 1150 and 1200 AD, and adopted its name. In medieval times the city was a member of the Hanseatic League and hence a wealthy town. Today, Göttingen is famous for its old university (''Georgia Augusta'', or "Georg-August-Universität"), which was founded in 1734 (first classes in 1737) and became the most visited university of Europe. In 1837, seven professors protested against the absolute sovereignty of the kings of Hanover; they lost their positions, but became known as the "Göttingen Seven". Its alumni include some well-known historical figures: the Brothers Grimm, Heinrich Ewald, Wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Teacher
A teacher, also called a schoolteacher or formally an educator, is a person who helps students to acquire knowledge, competence, or virtue, via the practice of teaching. ''Informally'' the role of teacher may be taken on by anyone (e.g. when showing a colleague how to perform a specific task). In some countries, teaching young people of school age may be carried out in an informal setting, such as within the family (homeschooling), rather than in a formal setting such as a school or college. Some other professions may involve a significant amount of teaching (e.g. youth worker, pastor). In most countries, ''formal'' teaching of students is usually carried out by paid professional teachers. This article focuses on those who are ''employed'', as their main role, to teach others in a ''formal'' education context, such as at a school or other place of ''initial'' formal education or training. Duties and functions A teacher's role may vary among cultures. Teachers may provide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poles
Poles,, ; singular masculine: ''Polak'', singular feminine: ''Polka'' or Polish people, are a West Slavic nation and ethnic group, who share a common history, culture, the Polish language and are identified with the country of Poland in Central Europe. The preamble to the Constitution of the Republic of Poland defines the Polish nation as comprising all the citizens of Poland, regardless of heritage or ethnicity. The majority of Poles adhere to Roman Catholicism. The population of self-declared Poles in Poland is estimated at 37,394,000 out of an overall population of 38,512,000 (based on the 2011 census), of whom 36,522,000 declared Polish alone. A wide-ranging Polish diaspora (the '' Polonia'') exists throughout Europe, the Americas, and in Australasia. Today, the largest urban concentrations of Poles are within the Warsaw and Silesian metropolitan areas. Ethnic Poles are considered to be the descendants of the ancient West Slavic Lechites and other tribes that inhabi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
