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Tadeusz Ważewski
Tadeusz Ważewski (24 September 1896 – 5 September 1972) was a Polish mathematician. Ważewski made important contributions to the theory of ordinary differential equations, partial differential equations, control theory and the theory of analytic spaces. He is most famous for applying the topological concept of retract (topology), retract, introduced by Karol Borsuk, to the study of the solutions of differential equations. Biography Ważewski was born in Galicia (Eastern Europe), Galicia on the 24 September 1896 to parents Stanisław Ważewski and Anieli Kozlowskich.He would attend schools in Mielec and Przemyśl before attending the Tarnów County, Tarnow secondary school in 1914. Ważewski went to, originally, study physics at the Jagiellonian University (Kraków, Krakow), but after being convinced by Stanisław Zaremba (mathematician), Stanisław Zaremba, he would change his degree to mathematics. Zaremba helped Tadeusz get a scholarship to study at the University of Pari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chortkiv
Chortkiv ( uk, Чортків; pl, Czortków; yi, ''Chortkov'') is a city in Chortkiv Raion, Ternopil Oblast (province) in western Ukraine. It is the administrative center of the Chortkiv Raion (district), housing the district's local administration buildings. Chortkiv hosts the administration of Chortkiv urban hromada, one of the hromadas of Ukraine. Population: Chortkiv is located in the northern part of the historic region of Galician Podolia on the banks of the Seret River. In the past Chortkiv was the home of many Hasidic Jews; it was a notable shtetl and had a significant number of Jews residing there prior to the Holocaust. Today, Chortkiv is a regional commercial and small-scale manufacturing center. Among its architectural monuments is a fortress built in the 16th and 17th centuries as well as historic wooden churches of the 17th and 18th centuries. History The first historical mention of Chortkiv dates to 1522, when Polish King Sigismund I the Old granted an ow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Space
An analytic space is a generalization of an analytic manifold that allows singularities. An analytic space is a space that is locally the same as an analytic variety. They are prominent in the study of several complex variables, but they also appear in other contexts. Definition Fix a field ''k'' with a valuation. Assume that the field is complete and not discrete with respect to this valuation. For example, this includes R and C with respect to their usual absolute values, as well as fields of Puiseux series with respect to their natural valuations. Let ''U'' be an open subset of ''k''''n'', and let ''f''1, ..., ''f''''k'' be a collection of analytic functions on ''U''. Denote by ''Z'' the common vanishing locus of ''f''1, ..., ''f''''k'', that is, let ''Z'' = . ''Z'' is an analytic variety. Suppose that the structure sheaf of ''U'' is \mathcal_U. Then ''Z'' has a structure sheaf \mathcal_Z = \mathcal_U / \mathcal_Z, where \mathcal_Z is the ideal generated by ''f''1, . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Émile Borel
Félix Édouard Justin Émile Borel (; 7 January 1871 – 3 February 1956) was a French 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 On ... and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability. Biography Borel was born in Saint-Affrique, Aveyron, the son of a Protestant pastor. He studied at the Collège Sainte-Barbe and Lycée Louis-le-Grand before applying to both the École normale supérieure (Paris), École normale supérieure and the École Polytechnique. He qualified in the first position for both and chose to attend the former institution in 1889. That year he also won the concours général, an annual national mathematics competition. After graduating in 1892, he placed first in the agrégati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a dissertation. The degree, abbreviated "Dr. habil." (Doctor habilitatus) or "PD" (for "Privatdozent"), is a qualification for professorship in those countries. The conferral is usually accompanied by a lecture to a colloquium as well as a public inaugural lecture. History and etymology The term ''habilitation'' is derived from the Medieval Latin , meaning "to make suitable, to fit", from Classical Latin "fit, proper, skillful". The degree developed in Germany in the seventeenth century (). Initially, habilitation was synonymous with "doctoral qualification". The term became synonymous with "post-doctoral qualification" in Germany in the 19th century "when holding a doctorate seemed no longer sufficient to guarantee a proficient transfer o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of '' naive set theory''. After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox) various axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly employed as a foundational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Twist (mathematics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity (mathematics), continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopy, homotopies. A property that is invariant under such deformations is a topological property. Basic exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kraków
Kraków (), or Cracow, is the second-largest and one of the oldest cities in Poland. Situated on the Vistula River in Lesser Poland Voivodeship, the city dates back to the seventh century. Kraków was the official capital of Poland until 1596 and has traditionally been one of the leading centres of Polish academic, economic, cultural and artistic life. Cited as one of Europe's most beautiful cities, its Old Town with Wawel Royal Castle was declared a UNESCO World Heritage Site in 1978, one of the first 12 sites granted the status. The city has grown from a Stone Age settlement to Poland's second-most-important city. It began as a hamlet on Wawel Hill and was reported by Ibrahim Ibn Yakoub, a merchant from Cordoba, as a busy trading centre of Central Europe in 985. With the establishment of new universities and cultural venues at the emergence of the Second Polish Republic in 1918 and throughout the 20th century, Kraków reaffirmed its role as a major national academic and a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tarnów County
__NOTOC__ Tarnów County ( pl, powiat tarnowski) is a unit of territorial administration and local government (powiat) in Lesser Poland Voivodeship, southern Poland. It came into being on January 1, 1999, as a result of the Polish local government reforms passed in 1998. Its administrative seat is the city of Tarnów, although the city is not part of the county (it constitutes a separate city county). The county contains seven towns: Tuchów, south of Tarnów, Żabno, north-west of Tarnów, Wojnicz, south-west of Tarnów, Radłów, north-west of Tarnów, Ryglice, south-east of Tarnów, Ciężkowice, south of Tarnów, and Zakliczyn, south-west of Tarnów. The county covers an area of . As of 2006 its total population was 193,549, out of which the population of Tuchów was 6,501, that of Żabno 4,271, that of Wojnicz 3,404, that of Ryglice 2,784, that of Ciężkowice 2,378, that of Zakliczyn 1,556, and the rural population was 176,059 (including approximately 2,800 for the pop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Przemyśl
Przemyśl (; yi, פשעמישל, Pshemishl; uk, Перемишль, Peremyshl; german: Premissel) is a city in southeastern Poland with 58,721 inhabitants, as of December 2021. In 1999, it became part of the Subcarpathian Voivodeship; it was previously the capital of Przemyśl Voivodeship. Przemyśl owes its long and rich history to the advantages of its geographic location. The city lies in an area connecting mountains and lowlands known as the Przemyśl Gate (Brama Przemyska), with open lines of transportation, and fertile soil. It also lies on the navigable San River. Important trade routes that connect Central Europe from Przemyśl ensure the city's importance. The Old Town of Przemyśl is listed as a Historic Monument of Poland. Names Different names in various languages have identified the city throughout its history. Selected languages include: cz, Přemyšl; german: Premissel, Prömsel, Premslen; la, Premislia; uk, Перемишль (Peremyshlj) and (Pshemyslj); ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mielec
Mielec ( yi, מעליץ-Melitz) is the largest city and seat of Mielec County. Mielec is located in south-eastern Poland (Lesser Poland), in the Subcarpathian Voivodeship (Województwo Podkarpackie). The population of Mielec in December 2021 was 59,509. Mielec is an industrial center, with technical and IT schools, craft schools and colleges (providing bachelor's degree and master's degree in several fields of study. Postgraduate studies are also available - e.g. MBA). The city lies within the Special Economic Zone Euro-Park Mielec with access to Mielec Airport and railway. About 15 km north of Mielec runs LHS railway - The transshipment terminal in Wola Baranowska enables the exchange of cargo between the broad gauge and standard gauge railways and trucks. About 20 km south of Mielec runs the A4 motorway. Moreover, the city of Mielec supports a recognizable soccer team - Stal Mielec. The motto of the city is ''Here wings spread!'' in reference to many successful dome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galicia (Eastern Europe)
Galicia ()"Galicia" ''Collins English Dictionary'' ( uk, Галичина, translit=Halychyna ; pl, Galicja; yi, גאַליציע) is a historical and geographic region spanning what is now southeastern Poland and western Ukraine, long part of the Polish–Lithuanian Commonwealth.See also: It covers much of such historic regions as Red Ruthenia (centered on Lviv) and Lesser Poland (centered on Kraków). The name of the region derives from the medieval city of Halych, and was first mentioned in Hungarian historical chronicles in the year 1206 as ''Galiciæ''. The eastern part of the region was controlled by the medieval Kingdom of Galicia a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
