|
Costa's Surface
In mathematics, Costa's minimal surface or Costa's surface, is an embedded minimal surface discovered in 1982 by the Brazilian mathematician Celso José da Costa. It is also a surface of finite topology, which means that it can be formed by puncturing a compact surface. Topologically, it is a thrice-punctured torus. Until its discovery, the plane, helicoid and the catenoid were believed to be the only embedded minimal surfaces that could be formed by puncturing a compact surface. The Costa surface evolves from a torus, which is deformed until the planar end becomes catenoidal. Defining these surfaces on rectangular tori of arbitrary dimensions yields the Costa surface. Its discovery triggered research and discovery into several new surfaces and open conjectures In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
End (topology)
In topology, a branch of mathematics, the ends of a topological space are, roughly speaking, the connected components of the "ideal boundary" of the space. That is, each end represents a topologically distinct way to move to infinity within the space. Adding a point at each end yields a compactification of the original space, known as the end compactification. The notion of an end of a topological space was introduced by . Definition Let X be a topological space, and suppose that is an ascending sequence of compact subsets of X whose interiors cover X. Then X has one end for every sequence where each U_n is a connected component of X\setminus K_n. The number of ends does not depend on the specific sequence (K_i) of compact sets; there is a natural bijection between the sets of ends associated with any two such sequences. Using this definition, a neighborhood of an end (U_i) is an open set V such that V\supset U_n for some n. Such neighborhoods represent the neighborhood ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as classical antiquity, antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Nikolai Lobachevsky, Lobachevsky. The simplest examples of smooth spaces are the Differential geometry of curves, plane and space curves and Differential geometry of surfaces, surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boletim Da Sociedade Brasileira De Matemática
The ''Bulletin of the Brazilian Mathematical Society'' is a quarterly peer-reviewed scientific journal covering all areas of mathematics. It is the official journal of the Brazilian Mathematical Society and is published on their behalf by Springer Science+Business Media. The journal was established in 1970 as the ''Boletim da Sociedade Brasileira de Matemática'', obtaining its current title in 1989. The editor-in-chief is Daniel Pellegrino ( Universidade Federal da Paraiba). Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. The Impact Factor of a journa ... of 1.177. References External links *{{Official website, https://www.sbm.org.br/en/publicacoes/periodicos/ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Instituto Nacional De Matemática Pura E Aplicada
The ''Instituto Nacional de Matemática Pura e Aplicada'' (National Institute for Pure and Applied Mathematics) is considered to be the foremost research and educational institution of Brazil in the area of mathematics. It is located in the city of Rio de Janeiro, and was formerly known simply as ''Instituto de Matemática Pura e Aplicada'' (IMPA), whose abbreviation remains in use. It is a research and education institution qualified as a Social Organization (SO) under the auspices of the Ministry of Science, Technology, Innovations and Communications (MCTIC) and the Ministry of Education (MEC) of Brazil. Currently located in the Jardim Botânico neighborhood (South Zone) of Rio de Janeiro. IMPA was founded on October 15, 1952. It was the first research unit of the National Research Council (CNPq), a federal funding agency created a year earlier. Its logo is a stylized Möbius strip, reproducing a large sculpture of a Möbius strip on display within the IMPA headquarters. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set (mathematics), set to a set assigns to each element of exactly one element of .; the words ''map'', ''mapping'', ''transformation'', ''correspondence'', and ''operator'' are sometimes used synonymously. The set is called the Domain of a function, domain of the function and the set is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. History of the function concept, Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable function, differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly increased the possible applications of the concept. A f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weierstrass Elliptic Function
In mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions is also referred to as ℘-functions and they are usually denoted by the symbol ℘, a uniquely fancy Cursive, script ''p''. They play an important role in the theory of elliptic functions, i.e., meromorphic functions that are Doubly_periodic_function, doubly periodic. A ℘-function together with its derivative can be used to parameterize elliptic curves and they generate the field of elliptic functions with respect to a given period lattice. Symbol for Weierstrass \wp-function Motivation A Cubic_form, cubic of the form C_^\mathbb=\ , where g_2,g_3\in\mathbb are complex numbers with g_2^3-27g_3^2\neq0, cannot be Rational_variety, rationally parameterized. Yet one still wants to find a way to parameterize it. For the quadric K=\left\; the unit circle, there exists a (non-rational) parameterizatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weierstrass Zeta Function
In mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function. They are named for Karl Weierstrass. The relation between the sigma, zeta, and \wp functions is analogous to that between the sine, cotangent, and squared cosecant functions: the logarithmic derivative of the sine is the cotangent, whose derivative is negative the squared cosecant. Weierstrass sigma function The Weierstrass sigma function associated to a two-dimensional lattice \Lambda\subset\Complex is defined to be the product : \begin \operatorname &= z\prod_\left(1-\frac\right) \exp\left(\frac zw + \frac12\left(\frac zw\right)^2\right) \\ mu&= z\prod_^\infty \left(1 - \frac\right) \exp \end where \Lambda^ denotes \Lambda-\ and (\omega_1,\omega_2) is a ''fundamental pair of periods''. Through careful manipulation of the Weierstrass factorization theorem as it relates also to the sine function, another potentially more manageable inf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjectures
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them. Resolution of conjectures Proof Formal mathematics is based on ''provable'' truth. In mathematics, any number of cases supporting a universally quantified conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample could immediately bring down the conjecture. Mathematical journals sometimes publish the minor results of research teams having extended the search for a counterexample farther than previously done. For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 1012 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catenoid
In geometry, a catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). It is a minimal surface, meaning that it occupies the least area when bounded by a closed space. It was formally described in 1744 by the mathematician Leonhard Euler. Soap film attached to twin circular rings will take the shape of a catenoid. Because they are members of the same associate family of surfaces, a catenoid can be bent into a portion of a helicoid, and vice versa. Geometry The catenoid was the first non-trivial minimal surface in 3-dimensional Euclidean space to be discovered apart from the plane. The catenoid is obtained by rotating a catenary about its directrix. It was found and proved to be minimal by Leonhard Euler Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flower Costa Minimal Surface
Flowers, also known as blooms and blossoms, are the reproductive structures of flowering plants (Flowering plant, angiosperms). Typically, they are structured in four circular levels, called whorls, around the end of a stalk. These whorls include: Sepal, calyx, modified leaves; Petal, corolla, the petals; Stamen, androecium, the male reproductive unit consisting of stamens and pollen; and gynoecium, the female part, containing Style (botany), style and Stigma (botany), stigma, which receives the pollen at the tip of the style, and Ovary (botany), ovary, which contains the ovules. When flowers are arranged in groups, they are known collectively as inflorescences. Floral growth originates at stem tips and is controlled by MADS-box genes. In most plant species flowers are heterospory, heterosporous, and so can produce gamete, sex cells of both sexes. Pollination mediates the transport of pollen to the ovules in the ovaries, to facilitate sexual reproduction. It can occur between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
