In mathematics, more specifically in functional analysis, a Banach space is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well defined limit that is within the space.
In physics and mathematics, the dimension of a mathematical space is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces.
MATLAB is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, C#, Java, Fortran and Python.
Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry.
Nicolas Bourbaki is the collective pseudonym of a group of mathematicians. Their aim is to reformulate mathematics on an extremely abstract and formal but self-contained basis in a series of books beginning in 1935. With the goal of grounding all of mathematics on set theory, the group strives for rigour and generality. Their work led to the discovery of several concepts and terminologies still used, and influenced modern branches of mathematics.
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions. A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which does not always equal ; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions.
In mathematics, an arithmetic group is a group obtained as the integer points of an algebraic group, for example They arise naturally in the study of arithmetic properties of quadratic forms and other classical topics in number theory. They also give rise to very interesting examples of Riemannian manifolds and hence are objects of interest in differential geometry and topology. Finally, these two topics join in the theory of automorphic forms which is fundamental in modern number theory.
Sir Simon Kirwan Donaldson, is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds and Donaldson–Thomas theory. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University and a Professor in Pure Mathematics at Imperial College London.
In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions. Its dimension can be clarified as n-honeycomb for a honeycomb of n-dimensional space.
In geometry, a skew polygon is a polygon whose vertices are not all coplanar. Skew polygons must have at least 4 vertices. The interior surface of such a polygon is not uniquely defined.
In mathematics, it is a theorem that there is no analogue of Lebesgue measure on an infinite-dimensional Banach space. Other kinds of measures are therefore used on infinite-dimensional spaces: often, the abstract Wiener space construction is used. Alternatively, one may consider Lebesgue measure on finite-dimensional subspaces of the larger space and consider so-called prevalent and shy sets.
The Black Math Experiment is a band described as a unique blend of 1980s synthpop and new wave music with similarities to “The B-52's crossed with Berlin, The Dead Milkmen, and Talking Heads.” Based in Houston, Texas in 2004, the band is known for their offbeat pop songs with irreverent or strange lyrics. They are known for elaborate live shows that integrate multimedia such as televisions endlessly running odd videos, evangelical-like pamphlets and baptisms, Christmas presents, and a toilet paper cannon, all led by the inexhaustible energy of lead singer Jef With One F. They received notoriety with their song, “You Cannot Kill David Arquette”.
In geometry, a flat is a subset of a Euclidean space that is congruent to a Euclidean space of lower dimension. The flats in two-dimensional space are points and lines, and the flats in three-dimensional space are points, lines, and planes.
Maths Class were a band from the UK that formed in 2006 in Brighton and achieved publicity through their Myspace. They have a wide range of influences and have played extensively around the UK and in Europe. They have also toured Japan in September 2008.
In mathematics, the Bogomolov–Miyaoka–Yau inequality is the inequality
Gopal Prasad is an Indian-American mathematician. His research interests span the fields of Lie groups, their discrete subgroups, algebraic groups, arithmetic groups, geometry of locally symmetric spaces, and representation theory of reductive p-adic groups.
Dipendra Prasad is an Indian mathematician. He is a professor of mathematics at the School of mathematics, Tata Institute of Fundamental Research, Mumbai for the past decade. Earlier, he was at the Harish-Chandra Research Institute in Allahabad for about a decade. He is a number theorist known for his work in the areas of automorphic representations. He is well known for the Gan–Gross–Prasad conjecture.
In geometry, the tritetragonal tiling or alternated octagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbols of {(4,3,3)} or h{8,3}.
Emperor Group is a diversified group of companies founded by Albert Yeung in Hong Kong. Albert Yeung's father, Mr Yeung Shing, opened a watch shop named "Shing On Kee Watch Shop" in 1942, setting the business foundation. Six companies within the Group are listed on the Main Board of The Stock Exchange of Hong Kong. These include Emperor International Holdings Limited, which focuses on real estate investment and property development; Emperor Watch and Jewellery Limited, which specializes in the retail of luxury watches and fine jewellery; Emperor Entertainment Hotel Limited, which concentrates on hotel and gaming businesses in Macau; Emperor Capital Group Limited, which provides a wide range of financial services; and Emperor Culture Group Limited, which principally engages in entertainment, media and cultural development business; and Ulferts International Limited, which is engaged in chain retailing of upmarket European furniture.
arXiv is a repository of electronic preprints approved for posting after moderation, but not full peer review. It consists of scientific papers in the fields of mathematics, physics, astronomy, electrical engineering, computer science, quantitative biology, statistics, mathematical finance and economics, which can be accessed online. In many fields of mathematics and physics, almost all scientific papers are self-archived on the arXiv repository. Begun on August 14, 1991, arXiv.org passed the half-million-article milestone on October 3, 2008, and had hit a million by the end of 2014. By October 2016 the submission rate had grown to more than 10,000 per month.
The bibcode is a compact identifier used by several astronomical data systems to uniquely specify literature references.
