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Mountain Climbing Problem
In mathematics, the mountain climbing problem is a mathematical problem that considers a two-dimensional mountain range (represented as a continuous function), and asks whether it is possible for two mountaineering, mountain climbers starting at sea level on the left and right sides of the mountain to meet at the summit, while maintaining equal altitudes at all times. It has been shown that when the mountain range has only a finite number of peaks and valleys, it is always possible to coordinate the climbers' movements, but this does not necessarily hold when it has an infinite number of peaks and valleys. This problem was named and posed in this form by , but its history goes back to , who solved a version of it. The problem has been repeatedly rediscovered and solved independently in different contexts by a number of people (see references below). Since the 1990s, the problem was shown to be connected to the weak Fréchet distance of curves in the plane, various planar motion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Undirected Graph
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called '' vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' means that ''A'' owes money to ''B'', then this graph is directed, because owing money is not necessarily reciprocated. Gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The American Mathematical Society
''Proceedings of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. The journal is devoted to shorter research articles. As a requirement, all articles must be at most 15 printed pages. According to the ''Journal Citation Reports'', the journal has a 2018 impact factor of 0.813. Scope ''Proceedings of the American Mathematical Society'' publishes articles from all areas of pure and applied mathematics, including topology, geometry, analysis, algebra, number theory, combinatorics, logic, probability and statistics. Abstracting and indexing This journal is indexed in the following databases: 2011. American Mathematical Society. * [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aequationes Mathematicae
''Aequationes Mathematicae'' is a mathematical journal. It is primarily devoted to functional equations, but also publishes papers in dynamical systems, combinatorics, and geometry. As well as publishing regular journal submissions on these topics, it also regularly reports on international symposia on functional equations and produces bibliographies on the subject. János Aczél founded the journal in 1968 at the University of Waterloo, in part because of the long publication delays of up to four years in other journals at the time of its founding. It is currently published by Springer Science+Business Media, with Zsolt Páles of the University of Debrecen as its editor in chief. János Aczél remains its honorary editor in chief. It is frequently listed as a second-quartile mathematics journal by SCImago Journal Rank The SCImago Journal Rank (SJR) indicator is a measure of the prestige of scholarly journals that accounts for both the number of citations received by a journ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transactions Of The American Mathematical Society
The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of pure and applied mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 printed pages. Its ISSN number is 0002-9947. See also * ''Bulletin of the American Mathematical Society'' * ''Journal of the American Mathematical Society'' * '' Memoirs of the American Mathematical Society'' * '' Notices of the American Mathematical Society'' * ''Proceedings of the American Mathematical Society'' References External links * ''Transactions of the American Mathematical Society''on JSTOR JSTOR ( ; short for ''Journal Storage'') is a digital library of academic journals, books, and primary sources founded in 1994. Originally containing digitized back issues of academic journals, it now encompasses books and other primary source ... American Mathematical Society academic journals Mathematics jo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. The editor-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 editor-in-chief heads all departments of the organization and is held accoun ... is Vadim Ponomarenko ( San Diego State University). The journal gives the Lester R. Ford Award annually to "authors of articles of expository excellence" published in the journal. Editors-in-chief The following persons are or have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semigroup Forum
Semigroup Forum (print , electronic ) is a mathematics research journal published by Springer. The journal serves as a platform for the speedy and efficient transmission of information on current research in semigroup theory. Coverage in the journal includes: * algebraic semigroups, * topological semigroups, * partially ordered semigroups, * semigroups of measures and harmonic analysis on semigroups, * transformation semigroups, and * applications of semigroup theory to other disciplines such as ring theory, category theory, automata, and logic. Semigroups of operators were initially considered off-topic, but began being included in the journal in 1985. Contents Semigroup Forum features survey and research articles. It also contains research announcements, which describe new results, mostly without proofs, of full length papers appearing elsewhere as well as short notes, which detail such information as new proofs, significant generalizations of known facts, comments on unsolv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Composition
In mathematics, the composition operator \circ takes two function (mathematics), functions, f and g, and returns a new function h(x) := (g \circ f) (x) = g(f(x)). Thus, the function is function application, applied after applying to . (g \circ f) is pronounced "the composition of and ". Reverse composition, sometimes denoted f \mapsto g , applies the operation in the opposite order, applying f first and g second. Intuitively, reverse composition is a chaining process in which the output of function feeds the input of function . The composition of functions is a special case of the composition of relations, sometimes also denoted by \circ. As a result, all properties of composition of relations are true of composition of functions, such as #Properties, associativity. Examples * Composition of functions on a finite set (mathematics), set: If , and , then , as shown in the figure. * Composition of functions on an infinite set: If (where is the set of all real numbers) is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interval (mathematics)
In mathematics, a real interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number or positive or negative infinity, indicating the interval extends without a bound. A real interval can contain neither endpoint, either endpoint, or both endpoints, excluding any endpoint which is infinite. For example, the set of real numbers consisting of , , and all numbers in between is an interval, denoted and called the unit interval; the set of all positive real numbers is an interval, denoted ; the set of all real numbers is an interval, denoted ; and any single real number is an interval, denoted . Intervals are ubiquitous in mathematical analysis. For example, they occur implicitly in the epsilon-delta definition of continuity; the intermediate value theorem asserts that the image of an interval by a continuous function is an interval; integrals of real functions are defined over an interval; etc. Interval ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constant Function
In mathematics, a constant function is a function whose (output) value is the same for every input value. Basic properties As a real-valued function of a real-valued argument, a constant function has the general form or just For example, the function is the specific constant function where the output value is . The domain of this function is the set of all real numbers. The image of this function is the singleton set . The independent variable does not appear on the right side of the function expression and so its value is "vacuously substituted"; namely , , , and so on. No matter what value of is input, the output is . The graph of the constant function is a ''horizontal line'' in the plane that passes through the point . In the context of a polynomial in one variable , the constant function is called ''non-zero constant function'' because it is a polynomial of degree 0, and its general form is , where is nonzero. This function has no intersection point with the a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Function
In mathematics, a quadratic function of a single variable (mathematics), variable is a function (mathematics), function of the form :f(x)=ax^2+bx+c,\quad a \ne 0, where is its variable, and , , and are coefficients. The mathematical expression, expression , especially when treated as an mathematical object, object in itself rather than as a function, is a quadratic polynomial, a polynomial of degree two. In elementary mathematics a polynomial and its associated polynomial function are rarely distinguished and the terms ''quadratic function'' and ''quadratic polynomial'' are nearly synonymous and often abbreviated as ''quadratic''. The graph of a function, graph of a function of a real variable, real single-variable quadratic function is a parabola. If a quadratic function is equation, equated with zero, then the result is a quadratic equation. The solutions of a quadratic equation are the zero of a function, zeros (or ''roots'') of the corresponding quadratic function, of which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Path (graph Theory)
In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges). A directed path (sometimes called dipath) in a directed graph is a finite or infinite sequence of edges which joins a sequence of distinct vertices, but with the added restriction that the edges be all directed in the same direction. Paths are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts. See e.g. , , or . cover more advanced algorithmic topics concerning paths in graphs. Definitions Walk, trail, and path * A walk is a finite or infinite sequence of edges which joins a sequence of vertices. : Let be a graph. A finite walk is a sequence of edges for which there is a sequence of vertices such that ''Φ''(''e''''i'') = for . is the ''vertex sequence'' of the walk. The walk is ''closed'' if ''v''1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
