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Karl Löwner
Charles Loewner (29 May 1893 – 8 January 1968) was an American mathematician. His name was Karel Löwner in Czech and Karl Löwner in German. Early life and career Karl Loewner was born into a Jewish family in Lany, about 30 km from Prague, where his father Sigmund Löwner was a store owner. Loewner received his Ph.D. from the University of Prague in 1917 under supervision of Georg Pick. One of his central mathematical contributions is the proof of the Bieberbach conjecture in the first highly nontrivial case of the third coefficient. The technique he introduced, the Loewner differential equation, has had far-reaching implications in geometric function theory; it was used in the final solution of the Bieberbach conjecture by Louis de Branges in 1985. Loewner worked at the University of Berlin, University of Prague, University of Louisville, Brown University, Syracuse University and eventually at Stanford University. His students include Lipman Bers, Roger Horn, Adriano ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lány (Kladno District)
Lány is a municipality and village in Kladno District in the Central Bohemian Region of the Czech Republic. It has about 2,300 inhabitants. The main landmark is the Lány Castle, known as the residence of the Czech and Czechoslovak presidents. Tomáš Garrigue Masaryk, the first President of Czechoslovakia, lived here and is buried in Lány cemetery. Administrative division Lány consists of two municipal parts (in brackets population according to the 2021 census): *Lány (2,046) *Vašírov (183) Etymology The word ''lány'' means in Czech language, Czech 'fields' or 'tracts (of land)'. In older times, the word also denoted land belonging to one court (land cultivated by one person in one cultivation period). Geography Lány lies about west of Kladno and west of Prague. Most of the municipality is located in the Křivoklát Highlands and in the Křivoklátsko Protected Landscape Area. The highest point is at above sea level. History The first written mention of Lány is from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loewner Differential Equation
In mathematics, the Loewner differential equation, or Loewner equation, is an ordinary differential equation discovered by Charles Loewner in 1923 in complex analysis and geometric function theory. Originally introduced for studying slit mappings (conformal mappings of the open disk onto the complex plane with a curve joining 0 to ∞ removed), Loewner's method was later developed in 1943 by the Russian mathematician Pavel Parfenevich Kufarev (1909–1968). Any family of domains in the complex plane that expands continuously in the sense of Carathéodory to the whole plane leads to a one parameter family of conformal mappings, called a Loewner chain, as well as a two parameter family of holomorphic univalent self-mappings of the unit disk, called a Loewner semigroup. This semigroup corresponds to a time dependent holomorphic vector field on the disk given by a one parameter family of holomorphic functions on the disk with positive real part. The Loewner semigroup generalizes the no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Matrix
In mathematics, a square matrix is a Matrix (mathematics), matrix with the same number of rows and columns. An ''n''-by-''n'' matrix is known as a square matrix of order Any two square matrices of the same order can be added and multiplied. Square matrices are often used to represent simple linear transformations, such as Shear mapping, shearing or Rotation (mathematics), rotation. For example, if R is a square matrix representing a rotation (rotation matrix) and \mathbf is a column vector describing the Position (vector), position of a point in space, the product R\mathbf yields another column vector describing the position of that point after that rotation. If \mathbf is a row vector, the same transformation can be obtained using where R^ is the transpose of Main diagonal The entries a_ () form the main diagonal of a square matrix. They lie on the imaginary line which runs from the top left corner to the bottom right corner of the matrix. For instance, the main diagonal of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Algebra
Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathematics), matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as line (geometry), lines, plane (geometry), planes and rotation (mathematics), rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to Space of functions, function spaces. Linear algebra is also used in most sciences and fields of engineering because it allows mathematical model, modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagonal Lattice
The hexagonal lattice (sometimes called triangular lattice) is one of the five two-dimensional Bravais lattice types. The symmetry category of the lattice is wallpaper group p6m. The primitive translation vectors of the hexagonal lattice form an angle of 120° and are of equal lengths, : , \mathbf a_1, = , \mathbf a_2, = a. The reciprocal lattice of the hexagonal lattice is a hexagonal lattice in reciprocal space with orientation changed by 90° and primitive lattice vectors of length : g=\frac. Honeycomb point set The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis. The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb point set can be seen as the union of two offset hexagonal lattices. In nature, carbon atoms of the two-dimensional material graphene are arranged in a honeycomb point set. Crystal classes The ''hexagonal lattice'' class names, Schönflies notation, Hermann-Mauguin notation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brown University
Brown University is a Private university, private Ivy League research university in Providence, Rhode Island, United States. It is the List of colonial colleges, seventh-oldest institution of higher education in the US, founded in 1764 as the ''College in the English Colony of Rhode Island and Providence Plantations''. One of nine colonial colleges chartered before the American Revolution, it was the first US college to codify that admission and instruction of students was to be equal regardless of the religious affiliation of students. The university is home to the oldest applied mathematics program in the country and oldest engineering program in the Ivy League. It was one of the early doctoral-granting institutions in the U.S., adding masters and doctoral studies in 1887. In 1969, it adopted its Open Curriculum (Brown University), Open Curriculum after student lobbying, which eliminated mandatory Curriculum#Core curriculum, general education distribution requirements. In 197 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Louisville
The University of Louisville (UofL) is a public university, public research university in Louisville, Kentucky, United States. It is part of the Kentucky state university system. Chartered in 1798 as the Jefferson Seminary, it became in the 19th century one of the first municipal college, city-funded public colleges in the United States. The university is mandated by the Kentucky General Assembly to be a "Preeminent Metropolitan Research University". Louisville is Carnegie Classification of Institutions of Higher Education, classified among "R1: Doctoral Universities – Very high research activity". The University of Louisville School of Medicine is touted for the first fully self-contained artificial heart transplant surgery, as well as the first successful hand transplantation in the United States. The University Hospital is also credited with the first civilian ambulance, the nation's first accident services, now known as an emergency department (ED), and one of the first bl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Berlin
The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humboldt, Johann Gottlieb Fichte and Friedrich Daniel Ernst Schleiermacher as the University of Berlin () in 1809, and opened in 1810. From 1828 until its closure in 1945, it was named the (Royal) Friedrich Wilhelm University of Berlin (FWU Berlin; ). During the Cold War, the university found itself in East Berlin and was ''de facto'' split in two when the Free University of Berlin opened in West Berlin. The university received its current name in honour of Alexander and Wilhelm von Humboldt in 1949. The university is divided into nine faculties including its medical school shared with the Freie Universität Berlin. The university has a student enrollment of around 35,000 students, and offers degree programs in some 171 disciplines from und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis De Branges
Louis may refer to: People * Louis (given name), origin and several individuals with this name * Louis (surname) * Louis (singer), Serbian singer Other uses * Louis (coin), a French coin * HMS ''Louis'', two ships of the Royal Navy See also * Derived terms * King Louis (other) * Saint Louis (other) * Louis Cruise Lines * Louis dressing, for salad * Louis Quinze, design style Associated terms * Lewis (other) * Louie (other) * Luis (other) * Louise (other) * Louisville (other) Associated names * * Chlodwig, the origin of the name Ludwig, which is translated to English as "Louis" * Ladislav and László - names sometimes erroneously associated with "Louis" * Ludovic, Ludwig, Ludwick, Ludwik Ludwik () is a Polish given name. Notable people with the name include: * Ludwik Czyżewski, Polish WWII general * Ludwik Fleck (1896–1961), Polish medical doctor and biologist * Ludwik Gintel (1899–1973), Polish- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Function Theory
Geometric function theory is the study of geometric properties of analytic functions. A fundamental result in the theory is the Riemann mapping theorem. Topics in geometric function theory The following are some of the most important topics in geometric function theory: Conformal maps A conformal map is a function which preserves angles locally. In the most common case the function has a domain and range in the complex plane. More formally, a map, : f: U \rightarrow V\qquad with U,V \subset \mathbb^n is called conformal (or angle-preserving) at a point u_0 if it preserves oriented angles between curves through u_0 with respect to their orientation (i.e., not just the magnitude of the angle). Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature. Quasiconformal maps In mathematical complex analysis, a quasiconformal mapping, introduced by and named by , is a homeomorphism between plane domains whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Branges' Theorem
In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane. It was posed by and finally proven by . The statement concerns the Taylor coefficients a_n of a univalent function, i.e. a one-to-one holomorphic function that maps the unit disk into the complex plane, normalized as is always possible so that a_0=0 and a_1=1. That is, we consider a function defined on the open unit disk which is holomorphic and injective ('' univalent'') with Taylor series of the form :f(z)=z+\sum_ a_n z^n. Such functions are called ''schlicht''. The theorem then states that : , a_n, \leq n \quad \textn\geq 2. The Koebe function (see below) is a function for which a_n=n for all n, and it is schlicht, so we cannot find a stricter limit on the absolute value of the nth coefficient. Schlicht functions The normalization ... [...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, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); 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's theorem. The number of known mathematicians grew when Pythagoras of Samos () 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 math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
