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Spherical Design
A spherical design, part of combinatorial design theory in mathematics, is a finite set of ''N'' points on the ''d''-dimensional unit n-sphere, ''d''-sphere ''Sd'' such that the average value of any polynomial ''f'' of degree ''t'' or less on the set equals the average value of ''f'' on the whole sphere (that is, the integral of ''f'' over ''Sd'' divided by the area or Measure (mathematics), measure of ''Sd''). Such a set is often called a spherical ''t''-design to indicate the value of ''t'', which is a fundamental parameter. The concept of a spherical design is due to Delsarte, Goethals, and Seidel, although these objects were understood as particular examples of cubature formulas earlier. Spherical designs can be of value in approximation theory, in statistics for experimental design, in combinatorics, and in geometry. The main problem is to find examples, given ''d'' and ''t'', that are not too large; however, such examples may be hard to come by. Spherical t-designs have also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Design
Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of ''balance'' and/or ''symmetry''. These concepts are not made precise so that a wide range of objects can be thought of as being under the same umbrella. At times this might involve the numerical sizes of set intersections as in block designs, while at other times it could involve the spatial arrangement of entries in an array as in sudoku grids. Combinatorial design theory can be applied to the area of design of experiments. Some of the basic theory of combinatorial designs originated in the statistician Ronald Fisher's work on the design of biological experiments. Modern applications are also found in a wide gamut of areas including finite geometry, tournament scheduling, lotteries, mathematical chemistry, mathematical biology, algorithm design and analysis, networking, g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Information Theory
Quantum information is the information of the quantum state, state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term. It is an interdisciplinary field that involves quantum mechanics, computer science, information theory, philosophy and cryptography among other fields. Its study is also relevant to disciplines such as cognitive science, psychology and neuroscience. Its main focus is in extracting information from matter at the microscopic scale. Observation in science is one of the most important ways of acquiring information and measurement is required in order to quantify the observation, making this crucial to the scientific method. In quantum mechanics, due to the uncertainty principle, non-commuting Observable, observables cannot be precisely mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Advances In Mathematics
''Advances in Mathematics'' is a peer-reviewed scientific journal covering research on pure mathematics. It was established in 1961 by Gian-Carlo Rota. The journal publishes 18 issues each year, in three volumes. At the origin, the journal aimed at publishing articles addressed to a broader "mathematical community", and not only to mathematicians in the author's field. Herbert Busemann writes, in the preface of the first issue, "The need for expository articles addressing either all mathematicians or only those in somewhat related fields has long been felt, but little has been done outside of the USSR. The serial publication ''Advances in Mathematics'' was created in response to this demand." Abstracting and indexing The journal is abstracted and indexed in: * |
European Journal Of Combinatorics
European, or Europeans, or Europeneans, may refer to: In general * ''European'', an adjective referring to something of, from, or related to Europe ** Ethnic groups in Europe ** Demographics of Europe ** European cuisine, the cuisines of Europe and other Western countries * ''European'', an adjective referring to something of, from, or related to the European Union ** Citizenship of the European Union ** Demographics of the European Union In publishing * ''The European'' (1953 magazine), a far-right cultural and political magazine published 1953–1959 * ''The European'' (newspaper), a British weekly newspaper published 1990–1998 * ''The European'' (2009 magazine), a German magazine first published in September 2009 *''The European Magazine'', a magazine published in London 1782–1826 *''The New European'', a British weekly pop-up newspaper first published in July 2016 Other uses * * Europeans (band), a British post-punk group, from Bristol See also * * * Europe (disam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometriae Dedicata
''Geometriae Dedicata'' is a mathematical journal, founded in 1972, concentrating on geometry and its relationship to topology, group theory and the theory of dynamical systems. It was created on the initiative of Hans Freudenthal in Utrecht, the Netherlands.. It is published by Springer Netherlands. The Editors-in-Chief An editor-in-chief (EIC), also known as lead editor or chief editor, is a publication's editorial leader who has final responsibility for its operations and policies. The highest-ranking editor of a publication may also be titled editor, managing ... are John R. Parker and Jean-Marc Schlenker.Journal website References External links Springer site Mathematics journals Springer Science+Business Media academic journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphs And Combinatorics
''Graphs and Combinatorics'' (ISSN 0911-0119, abbreviated ''Graphs Combin.'') is a peer-reviewed academic journal in graph theory, combinatorics, and discrete geometry published by Springer Japan. Its editor-in-chief is Katsuhiro Ota of Keio University. The journal was first published in 1985. Its founding editor in chief was Hoon Heng Teh of Singapore, the president of the Southeast Asian Mathematics Society, and its managing editor was Jin Akiyama. Originally, it was subtitled "An Asian Journal". In most years since 1999, it has been ranked as a second-quartile journal in discrete mathematics and theoretical computer science computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumscribe the ... by SCImago Journal Rank.. References {{reflist Publications established in 1985 Combinatorics jo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomson Problem
The objective of the Thomson problem is to determine the minimum electrostatic potential energy configuration of electrons constrained to the surface of a unit sphere that repel each other with a force given by Coulomb's law. The physicist J. J. Thomson posed the problem in 1904 after proposing an atomic model, later called the plum pudding model, based on his knowledge of the existence of negatively charged electrons within neutrally-charged atoms. Related problems include the study of the geometry of the minimum energy configuration and the study of the large behavior of the minimum energy. Mathematical statement The electrostatic interaction energy occurring between each pair of electrons of equal charges (e_i = e_j = e, with e the elementary charge of an electron) is given by Coulomb's Law, :U_(N)=k_\text. Here, k_\text is the Coulomb constant and r_=, \mathbf_i - \mathbf_j, is the distance between each pair of electrons located at points on the sphere defined by ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Action (mathematics)
In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group ''acts'' on the space or structure. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it. For example, it acts on the set of all triangles. Similarly, the group of symmetries of a polyhedron acts on the vertices, the edges, and the faces of the polyhedron. A group action on a vector space is called a representation of the group. In the case of a finite-dimensional vector space, it allows one to identify many groups with subgroups of , the group of the invertible matrices of dimension over a field . The symmetric group acts on any set wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equiangular Lines
In geometry, a set of lines is called equiangular if all the lines intersect at a single point, and every pair of lines makes the same angle. Equiangular lines in Euclidean space Computing the maximum number of equiangular lines in ''n''-dimensional Euclidean space is a difficult problem, and unsolved in general, though bounds are known. The maximal number of equiangular lines in 2-dimensional Euclidean space is 3: we can take the lines through opposite vertices of a regular hexagon, each at an angle 120 degrees from the other two. The maximum in 3 dimensions is 6: we can take lines through opposite vertices of an icosahedron. It is known that the maximum number in any dimension n is less than or equal to \binom. This upper bound is tight up to a constant factor to a construction by de Caen. The maximum in dimensions 1 through 16 is listed in the ''On-Line Encyclopedia of Integer Sequences'' as follows: :1, 3, 6, 6, 10, 16, 28, 28, 28, 28, 28, 28, 28, 28, 36, 40, ... In particu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Computing
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though current quantum computers may be too small to outperform usual (classical) computers for practical applications, larger realizations are believed to be capable of solving certain computational problems, such as integer factorization (which underlies RSA encryption), substantially faster than classical computers. The study of quantum computing is a subfield of quantum information science. There are several models of quantum computation with the most widely used being quantum circuits. Other models include the quantum Turing machine, quantum annealing, and adiabatic quantum computation. Most models are based on the quantum bit, or "qubit", which is somewhat analogous to the bit in classical computation. A qubit can be in a 1 or 0 quantum s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum T-designs
A quantum t-design is a probability distribution over either pure quantum states or unitary operators which can duplicate properties of the probability distribution over the Haar measure for polynomials of degree t or less. Specifically, the average of any polynomial function of degree t over the design is exactly the same as the average over Haar measure. Here the Haar measure is a uniform probability distribution over all quantum states or over all unitary operators. Quantum t-designs are so called because they are analogous to t-designs in classical statistics, which arose historically in connection with the problem of design of experiments. Two particularly important types of t-designs in quantum mechanics are projective and unitary t-designs. A spherical design is a collection of points on the unit sphere for which polynomials of bounded degree can be averaged over to obtain the same value that integrating over surface measure on the sphere gives. Spherical and projective t-de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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