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Czesław Ryll-Nardzewski
Czesław Ryll-Nardzewski (; 7 October 1926 – 18 September 2015) was a Polish mathematician. Born in Wilno, Second Polish Republic (now Vilnius, Lithuania), he was a student of Hugo Steinhaus. At the age of 26 he became professor at Warsaw University. In 1959, he became a professor at the Wrocław University of Technology. He was the advisor of 18 PhD theses. His main research areas are measure theory, functional analysis, foundations of mathematics and probability theory. Several theorems bear his name: the Ryll-Nardzewski fixed point theorem, “9. Theorem of Ryll-Nardzewski” (p. 171), “(9.6) Theorem (Ryll-Nardzewski)” (p. 174) the Ryll-Nardzewski theorem See Theorem 7.3.1 Cf. (2.10) in model theory, and the Kuratowski and Ryll-Nardzewski measurable selection theorem. See Theorem 6.9.3 on p. 36 and the historical comment on p. 441 He became a member of the Polish Academy of Sciences The Polish Academy of Sciences ( pl, Polska Akademia Nauk, PAN) is a Polish state ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilno
Vilnius ( , ; see also #Etymology and other names, other names) is the capital and List of cities in Lithuania#Cities, largest city of Lithuania, with a population of 592,389 (according to the state register) or 625,107 (according to the municipality of Vilnius). The population of Vilnius's functional urban area, which stretches beyond the city limits, is estimated at 718,507 (as of 2020), while according to the Vilnius territorial health insurance fund, there were 753,875 permanent inhabitants as of November 2022 in Vilnius city and Vilnius district municipalities combined. Vilnius is situated in southeastern Lithuania and is the second-largest city in the Baltic states, but according to the Bank of Latvia is expected to become the largest before 2025. It is the seat of Lithuania's national government and the Vilnius District Municipality. Vilnius is known for the architecture in its Old Town of Vilnius, Old Town, declared a UNESCO World Heritage Site in 1994. The city was #Po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Wilno Voivodeship (1926–1939)
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form "people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural form of pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientists From Vilnius
A scientist is a person who conducts scientific research to advance knowledge in an area of the natural sciences. In classical antiquity, there was no real ancient analog of a modern scientist. Instead, philosophers engaged in the philosophical study of nature called natural philosophy, a precursor of natural science. Though Thales (circa 624-545 BC) was arguably the first scientist for describing how cosmic events may be seen as natural, not necessarily caused by gods,Frank N. Magill''The Ancient World: Dictionary of World Biography'', Volume 1 Routledge, 2003 it was not until the 19th century that the term ''scientist'' came into regular use after it was coined by the theologian, philosopher, and historian of science William Whewell in 1833. In modern times, many scientists have advanced degrees in an area of science and pursue careers in various sectors of the economy such as academia, industry, government, and nonprofit environments.'''' History The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theorists
A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models can be divided into physical models (e.g. a model plane) and abstract models (e.g. mathematical expressions describing behavioural patterns). Abstract or conceptual models are central to philosophy of science, as almost every scientific theory effectively embeds some kind of model of the physical or human sphere. In commerce, "model" can refer to a specific design of a product as displayed in a catalogue or show room (e.g. Ford Model T), and by extension to the sold product itself. Types of models include: Physical model A physical model (most commonly referred to simply as a model but in this context distinguished from a conceptual model) is a smaller or larger physical copy of an object. The object being modelled may be small (fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2015 Deaths
This is a list of deaths of notable people, organised by year. New deaths articles are added to their respective month (e.g., Deaths in ) and then linked here. 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 See also * Lists of deaths by day * Deaths by year {{DEFAULTSORT:deaths by year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1926 Births
Events January * January 3 – Theodoros Pangalos (general), Theodoros Pangalos declares himself dictator in Greece. * January 8 **Abdul-Aziz ibn Saud is crowned King of Kingdom of Hejaz, Hejaz. ** Bảo Đại, Crown Prince Nguyễn Phúc Vĩnh Thuy ascends the throne, the last monarch of Vietnam. * January 12 – Freeman Gosden and Charles Correll premiere their radio program ''Sam 'n' Henry'', in which the two white performers portray two black characters from Harlem looking to strike it rich in the big city (it is a precursor to Gosden and Correll's more popular later program, ''Amos 'n' Andy''). * January 16 – A BBC comic radio play broadcast by Ronald Knox, about a workers' revolution, causes a panic in London. * January 21 – The Belgian Parliament accepts the Locarno Treaties. * January 26 – Scottish inventor John Logie Baird demonstrates a mechanical television system at his London laboratory for members of the Royal Institution and a report ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polish Academy Of Sciences
The Polish Academy of Sciences ( pl, Polska Akademia Nauk, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society of distinguished scholars and a network of research institutes. It was established in 1951, during the early period of the Polish People's Republic following World War II. History The Polish Academy of Sciences is a Polish state-sponsored institution of higher learning, headquartered in Warsaw, that was established by the merger of earlier science societies, including the Polish Academy of Learning (''Polska Akademia Umiejętności'', abbreviated ''PAU''), with its seat in Kraków, and the Warsaw Society of Friends of Learning (Science), which had been founded in the late 18th century. The Polish Academy of Sciences functions as a learned society acting through an elected assembly of leading scholars and research institutions. The Academ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kuratowski And Ryll-Nardzewski Measurable Selection Theorem
In mathematics, the Kuratowski–Ryll-Nardzewski measurable selection theorem is a result from measure theory that gives a sufficient condition for a set-valued function to have a measurable selection function. It is named after the Polish mathematicians Kazimierz Kuratowski and Czesław Ryll-Nardzewski. Many classical selection results follow from this theorem and it is widely used in mathematical economics and optimal control Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and .... Statement of the theorem Let X be a Polish space, \mathcal (X) the Borel σ-algebra of X , (\Omega, \mathcal) a measurable space and \psi a multifunction on \Omega taking values in the set of nonempty closed subsets of X . Suppose that \psi is \mathcal -weakly measurable, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theory
In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mathematical logic), mathematical structure), and their models (those structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be definable set, defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stable theory, stability theory. Compared to other areas of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Omega-categorical Theory
In mathematical logic, an omega-categorical theory is a theory that has exactly one countably infinite model up to isomorphism. Omega-categoricity is the special case κ = \aleph_0 = ω of κ-categoricity, and omega-categorical theories are also referred to as ω-categorical. The notion is most important for countable first-order theories. Equivalent conditions for omega-categoricity Many conditions on a theory are equivalent to the property of omega-categoricity. In 1959 Erwin Engeler, Czesław Ryll-Nardzewski and Lars Svenonius, proved several independently.Rami Grossberg, José Iovino and Olivier Lessmann''A primer of simple theories''/ref> Despite this, the literature still widely refers to the Ryll-Nardzewski theorem as a name for these conditions. The conditions included with the theorem vary between authors.Hodges, Model Theory, p. 341.Rothmaler, p. 200. Given a countable complete first-order theory ''T'' with infinite models, the following are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ryll-Nardzewski Fixed Point Theorem
In functional analysis, a branch of mathematics, the Ryll-Nardzewski fixed-point theorem states that if E is a normed vector space and K is a nonempty convex subset of E that is compact under the weak topology, then every group (or equivalently: every semigroup) of affine isometries of K has at least one fixed point. (Here, a ''fixed point'' of a set of maps is a point that is fixed by each map in the set.) This theorem was announced by Czesław Ryll-Nardzewski. Later Namioka and Asplund gave a proof based on a different approach. Ryll-Nardzewski himself gave a complete proof in the original spirit. Applications The Ryll-Nardzewski theorem yields the existence of a Haar measure on compact groups. See also * Fixed-point theorems * Fixed-point theorems in infinite-dimensional spaces * Markov-Kakutani fixed-point theorem - abelian semigroup of continuous affine self-maps on compact convex set in a topological vector space has a fixed point References * Andrzej Granas and James ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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