|
Jan Mikusiński
Jan Mikusiński (April 3, 1913 Stanisławów – July 27, 1987 Katowice) was a Polish mathematician based at the University of Wrocław known for his pioneering work in mathematical analysis. Mikusiński developed an operational calculus – known as the ''Calculus of Mikusiński'' ( MSC 44A40), which is relevant for solving differential equations. His operational calculus is based upon an algebra of the convolution of functions with respect to the Fourier transform. From the convolution product he goes on to define what in other contexts is called the field of fractions or a quotient field. These ordered pairs of functions Mikusiński calls "operators", the "Mikusiński operators". He is also well known for Mikusinski's cube, the Antosik–Mikusinski theorem, and Mikusinski convolution algebra. A street in Katowice is named after Mikusiński. Selected publications * ''An Introduction to Analysis - From Number to Integral.'' Wiley 1993 * ''The Operational Calculus.'' Pergamon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ivano-Frankivsk
Ivano-Frankivsk ( uk, Іва́но-Франкі́вськ, translit=Iváno-Frankívśk ), formerly Stanyslaviv ( pl, Stanisławów ; german: Stanislau), is a city located in Western Ukraine. It is the administrative centre of Ivano-Frankivsk Oblast and Ivano-Frankivsk Raion. Ivano-Frankivsk hosts the administration of Ivano-Frankivsk urban hromada. Its population is Built in the mid-17th century as a fortress of the Polish Potocki family, Stanisławów was annexed to the Habsburg Empire during the First Partition of Poland in 1772, after which it became the property of the State within the Austrian Empire. The fortress was slowly transformed into one of the most prominent cities at the foothills of the Carpathian Mountains. After World War I, for several months, it served as a temporary capital of the West Ukrainian People's Republic. Following the Peace of Riga in 1921, Stanisławów became part of the Second Polish Republic. After the Soviet invasion of Poland at the ons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1987 Deaths
File:1987 Events Collage.png, From top left, clockwise: The MS Herald of Free Enterprise capsizes after leaving the Port of Zeebrugge in Belgium, killing 193; Northwest Airlines Flight 255 crashes after takeoff from Detroit Metropolitan Airport, killing everyone except a little girl; The King's Cross fire kills 31 people after a fire under an escalator Flashover, flashes-over; The MV Doña Paz sinks after colliding with an oil tanker, drowning almost 4,400 passengers and crew; Typhoon Nina (1987), Typhoon Nina strikes the Philippines; LOT Polish Airlines Flight 5055 crashes outside of Warsaw, taking the lives of all aboard; The USS Stark is USS Stark incident, struck by Iraq, Iraqi Exocet missiles in the Persian Gulf; President of the United States, U.S. President Ronald Reagan gives a famous Tear down this wall!, speech, demanding that Soviet Union, Soviet leader Mikhail Gorbachev tears down the Berlin Wall., 300x300px, thumb rect 0 0 200 200 Zeebrugge disaster rect 200 0 400 200 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1913 Births
Events January * January 5 – First Balkan War: Battle of Lemnos – Greek admiral Pavlos Kountouriotis forces the Turkish fleet to retreat to its base within the Dardanelles, from which it will not venture for the rest of the war. * January 13 – Edward Carson founds the (first) Ulster Volunteer Force, by unifying several existing loyalist militias to resist home rule for Ireland. * January 23 – 1913 Ottoman coup d'état: Ismail Enver comes to power. * January – Stalin (whose first article using this name is published this month) travels to Vienna to carry out research. Until he leaves on February 16 the city is home simultaneously to him, Hitler, Trotsky and Tito alongside Berg, Freud and Jung and Ludwig and Paul Wittgenstein. February * February 1 – New York City's Grand Central Terminal, having been rebuilt, reopens as the world's largest railroad station. * February 3 – The 16th Amendment to the United S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniell Integral
In mathematics, the Daniell integral is a type of integration that generalizes the concept of more elementary versions such as the Riemann integral to which students are typically first introduced. One of the main difficulties with the traditional formulation of the Lebesgue integral is that it requires the initial development of a workable measure theory before any useful results for the integral can be obtained. However, an alternative approach is available, developed by that does not suffer from this deficiency, and has a few significant advantages over the traditional formulation, especially as the integral is generalized into higher-dimensional spaces and further generalizations such as the Stieltjes integral. The basic idea involves the axiomatization of the integral. Axioms We start by choosing a family H of bounded real functions (called ''elementary functions'') defined over some set X, that satisfies these two axioms: * H is a linear space with the usual operations of add ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convolution Quotient
In mathematics, a space of convolution quotients is a field of fractions of a convolution ring of functions: a convolution quotient is to the operation of convolution as a quotient of integers is to multiplication. The construction of convolution quotients allows easy algebraic representation of the Dirac delta function, integral operator, and differential operator without having to deal directly with integral transforms, which are often subject to technical difficulties with respect to whether they converge. Convolution quotients were introduced by , and their theory is sometimes called ''Mikusiński's operational calculus''. The kind of convolution (f,g)\mapsto f*g with which this theory is concerned is defined by : (f*g)(x) = \int_0^x f(u) g(x-u) \, du. It follows from the Titchmarsh convolution theorem that if the convolution f*g of two functions f,g that are continuous on functions ''ƒ'', ''g'', the pair (''ƒ'', ''g'') has the same convolution quotient ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roman Sikorski
Roman Sikorski (July 11, 1920 – September 12, 1983) was a Polish mathematician. Biography Sikorski was a professor at the University of Warsaw from 1952 until 1982. Since 1962, he was a member of the Polish Academy of Sciences. Sikorski's research interests included: Boolean algebras, mathematical logic, functional analysis, the theory of distributions, measure theory, general topology, and descriptive set theory. Works * ''Boolean Algebras'' (1960) * ''Funkcje rzeczywiste'' (t. 1–2 1958–59) * ''The Mathematics of Metamathematics'' (1963, together with Helena Rasiowa) * ''Rachunek rózniczkowy i całkowy — funkcje wielu zmiennych'' (1967) See also * Warsaw School of Mathematics Warsaw School of Mathematics is the name given to a group of mathematicians who worked at Warsaw, Poland, in the two decades between the World Wars, especially in the fields of logic, set theory, point-set topology and real analysis. They pu ... References * Roman Sikorsk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Katowice
Katowice ( , , ; szl, Katowicy; german: Kattowitz, yi, קאַטעוויץ, Kattevitz) is the capital city of the Silesian Voivodeship in southern Poland and the central city of the Upper Silesian metropolitan area. It is the 11th most populous city in Poland, while its urban area is the most populous in the country and one of the most populous in the European Union. Katowice has a population of 286,960 according to a 31 December 2021 estimate. Katowice is a central part of the Metropolis GZM, with a population of 2.3 million, and a part of a larger Upper Silesian metropolitan area that extends into the Czech Republic and has a population of 5-5.3 million people."''Study on Urban Functions (Project 1.4 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Field Of Fractions
In abstract algebra, the field of fractions of an integral domain is the smallest field in which it can be embedded. The construction of the field of fractions is modeled on the relationship between the integral domain of integers and the field of rational numbers. Intuitively, it consists of ratios between integral domain elements. The field of fractions of R is sometimes denoted by \operatorname(R) or \operatorname(R), and the construction is sometimes also called the fraction field, field of quotients, or quotient field of R. All four are in common usage, but are not to be confused with the quotient of a ring by an ideal, which is a quite different concept. For a commutative ring which is not an integral domain, the analogous construction is called the localization or ring of quotients. Definition Given an integral domain and letting R^* = R \setminus \, we define an equivalence relation on R \times R^* by letting (n,d) \sim (m,b) whenever nb = md. We denote the equivale ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
