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Interval Order
In mathematics, especially order theory, the interval order for a collection of intervals on the real line is the partial order corresponding to their left-to-right precedence relation—one interval, ''I''1, being considered less than another, ''I''2, if ''I''1 is completely to the left of ''I''2. More formally, a countable poset P = (X, \leq) is an interval order if and only if there exists a bijection from X to a set of real intervals, so x_i \mapsto (\ell_i, r_i) , such that for any x_i, x_j \in X we have x_i , a left nesting is an i \in n/math> such that i < i+1 < f(i+1) < f(i) and a right nesting is an |
Interval Order, Hasse Diagram And Interval Realization
Interval may refer to: Mathematics and physics * Interval (mathematics), a range of numbers **Partially ordered set#Intervals, its generalization from numbers to arbitrary partially ordered sets * A statistical level of measurement * Interval estimate * Interval (graph theory) * Space-time interval, the distance between two points in 4-space Arts and entertainment Dramatic arts * Intermission, (British English: interval), a break in a theatrical performance ** ''Entr'acte'', a French term for the same, but used in English often to mean a musical performance played during the break * Interval (play), ''Interval'' (play), a 1939 play by Sumner Locke Elliott * Interval (film), ''Interval'' (film), a 1973 film starring Merle Oberon Music * Interval (music), the relationship in pitch between two notes * Intervals (band), a Canadian progressive metal band * Intervals (See You Next Tuesday album), ''Intervals'' (See You Next Tuesday album), 2008 * Intervals (Ahmad Jamal album), ''Interva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Dimension
In mathematics, the dimension of a partially ordered set (poset) is the smallest number of total orders the intersection of which gives rise to the partial order. This concept is also sometimes called the order dimension or the Dushnik–Miller dimension of the partial order. first studied order dimension; for a more detailed treatment of this subject than provided here, see . Formal definition The dimension of a poset ''P'' is the least integer ''t'' for which there exists a family :\mathcal R=(<_1,\dots,<_t) of s of ''P'' so that, for every ''x'' and ''y'' in ''P'', ''x'' precedes ''y'' in ''P'' if and only if it precedes ''y'' in all of the linear extensions. That is, : An alternative definition of order dimension is the minimal number of |
Topology (journal)
''Topology'' was a peer-reviewed mathematical journal covering topology and geometry. It was established in 1962 and was published by Elsevier. The last issue of ''Topology'' appeared in 2009. Pricing dispute On 10 August 2006, after months of unsuccessful negotiations with Elsevier about the price policy of library subscriptions, the entire editorial board of the journal handed in their resignation, effective 31 December 2006. Subsequently, two more issues appeared in 2007 with papers that had been accepted before the resignation of the editors. In early January the former editors instructed Elsevier to remove their names from the website of the journal, but Elsevier refused to comply, justifying their decision by saying that the editorial board should remain on the journal until all of the papers accepted during its tenure had been published. In 2007 the former editors of ''Topology'' announced the launch of the ''Journal of Topology'', published by Oxford University Press ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Mathematical Psychology
The ''Journal of Mathematical Psychology'' is a peer-reviewed scientific journal established in 1964. It covers all areas of mathematical and theoretical psychology, including sensation and perception, psychophysics, learning and memory, problem solving, judgment and decision-making, and motivation. It is the official journal of the Society for Mathematical Psychology and is published on their behalf by Elsevier. Abstracting and indexing The journal is abstracted and indexed by: According to the ''Journal Citation Reports'', the journal has a 2017 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... of 2.176. References External links * Publications established in 1964 Mathematical and statistical psychology journals Elsevier academic journals Bimonthly j ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIAM Journal On Discrete Mathematics
'' SIAM Journal on Discrete Mathematics'' is a peer-reviewed mathematics journal published quarterly by the Society for Industrial and Applied Mathematics (SIAM). The journal includes articles on pure and applied discrete mathematics. It was established in 1988, along with the ''SIAM Journal on Matrix Analysis and Applications'', to replace the ''SIAM Journal on Algebraic and Discrete Methods''. The journal is indexed by ''Mathematical Reviews'' and Zentralblatt MATH. Its 2009 MCQ was 0.57. According to the ''Journal Citation Reports'', the journal has a 2016 impact factor of 0.755. Although its official ISO abbreviation is ''SIAM J. Discrete Math.'', its publisher and contributors frequently use the shorter abbreviation ''SIDMA''. References External links * Combinatorics journals Publications established in 1988 English-language journals Discrete Mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way ana ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Combinatorial Theory
The ''Journal of Combinatorial Theory'', Series A and Series B, are mathematical journals specializing in combinatorics and related areas. They are published by Elsevier. ''Series A'' is concerned primarily with structures, designs, and applications of combinatorics. ''Series B'' is concerned primarily with graph and matroid theory. The two series are two of the leading journals in the field and are widely known as ''JCTA'' and ''JCTB''. The journal was founded in 1966 by Frank Harary and Gian-Carlo Rota.They are acknowledged on the journals' title pages and Web sites. SeEditorial board of JCTA Originally there was only one journal, which was split into two parts in 1971 as the field grew rapidly. An electronic, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Generating Function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers () by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary series, the ''formal'' power series is not required to converge: in fact, the generating function is not actually regarded as a function, and the "variable" remains an indeterminate. Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general linear recurrence problem. One can generalize to formal power series in more than one indeterminate, to encode information about infinite multi-dimensional arrays of numbers. There are various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series; definitions and examples are given below. Every sequence in principle has a generating function of each type (except t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardinality
In mathematics, the cardinality of a set is a measure of the number of elements of the set. For example, the set A = \ contains 3 elements, and therefore A has a cardinality of 3. Beginning in the late 19th century, this concept was generalized to infinite sets, which allows one to distinguish between different types of infinity, and to perform arithmetic on them. There are two approaches to cardinality: one which compares sets directly using bijections and injections, and another which uses cardinal numbers. The cardinality of a set is also called its size, when no confusion with other notions of size is possible. The cardinality of a set A is usually denoted , A, , with a vertical bar on each side; this is the same notation as absolute value, and the meaning depends on context. The cardinality of a set A may alternatively be denoted by n(A), , \operatorname(A), or \#A. History A crude sense of cardinality, an awareness that groups of things or events compare with other grou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Involution (mathematics)
In mathematics, an involution, involutory function, or self-inverse function is a function that is its own inverse, : for all in the domain of . Equivalently, applying twice produces the original value. General properties Any involution is a bijection. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x \mapsto -x), reciprocation (x \mapsto 1/x), and complex conjugation (z \mapsto \bar z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the Beaufort polyalphabetic cipher. The composition of two involutions ''f'' and ''g'' is an involution if and only if they commute: . Involutions on finite sets The number of involutions, including the identity involution, on a set with elements is given by a recurrence relation found by Heinrich August Rothe in 1800: :a_0 = a_1 = 1 and a_n = a_ + ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fixed Point (mathematics)
A fixed point (sometimes shortened to fixpoint, also known as an invariant point) is a value that does not change under a given transformation. Specifically, in mathematics, a fixed point of a function is an element that is mapped to itself by the function. In physics, the term fixed point can refer to a temperature that can be used as a reproducible reference point, usually defined by a phase change or triple point. Fixed point of a function Formally, is a fixed point of a function if belongs to both the domain and the codomain of , and . For example, if is defined on the real numbers by f(x) = x^2 - 3 x + 4, then 2 is a fixed point of , because . Not all functions have fixed points: for example, , has no fixed points, since is never equal to for any real number. In graphical terms, a fixed point means the point is on the line , or in other words the graph of has a point in common with that line. Fixed-point iteration In numerical analysis, ''fixed-point iter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Complexity
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory. Both areas are highly related, as the complexity of an algorithm is always an upper bound on the complexity of the problem solved by this algorithm. Moreover, for designing efficient algorithms, it is often fundamental to compare the complexity of a specific algorithm to the complexity of the problem to be solved. Also, in most cases, the only thing that is known about the complexity of a problem is that it is lower than the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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