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142 (number)
142 (one hundred ndforty-two) is the natural number following 141 and preceding 143. In mathematics There are 142 connected functional graphs on four labeled vertices, 142 planar graphs with 6 unlabeled vertices, and 142 partial involutions on five elements. See also * The year AD 142 Year 142 ( CXLII) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known in the Roman Empire as the Year of the Consulship of Pactumeius and Quadratus (or, less frequently, y ... or 142 BC * List of highways numbered 142 * References {{DEFAULTSORT:142 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
141 (number)
141 (one hundred ndforty-one) is the natural number following 140 and preceding 142. In mathematics 141 is: *a centered pentagonal number. *the sum of the sums of the divisors of the first 13 positive integers. *the second ''n'' to give a prime Cullen number (of the form ''n''2''n'' + 1). *an undulating number in base 10, with the previous being 131, and the next being 151. *the sixth hendeca gonal (11-gonal) number. *a semiprime: a product of two prime numbers, namely 3 and 47. Since those prime factors are Gaussian primes, this means that 141 is a Blum integer. * a Hilbert prime In the military * The Lockheed C-141 Starlifter was a United States Air Force military strategic airlifter * K-141 ''Kursk'' was a Russian nuclear cruise missile submarine, which sank in the Barents Sea on 12 August 2000 * was a United States Navy ship during World War II * was a United States Navy during World War II * was a United States Navy during World War II * was a United States Navy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
143 (number)
143 (one hundred ndforty-three) is the natural number following 142 and preceding 144. In mathematics 143 is the sum of seven consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31). But this number is never the sum of an integer and its base 10 digits, making it a self number. Every positive integer is the sum of at most 143 seventh powers (see Waring's problem). 143 is the difference in the first exception to the pattern shown below: :3^2+4^2=5^2 :3^3+4^3+5^3=6^3 :3^4+4^4+5^4+6^4=7^4-143. In the military * Vickers Type 143 was a British single-seat fighter biplane in 1929 * United States Air Force 143d Airlift Wing airlift unit at Quonset Point, Rhode Island * was a United States Navy during World War II * was a United States Navy during World War II * was a United States Navy during World War II * was a United States Navy in World War II * was a United States Navy patrol boat * was a United States Navy during the Cuban Missile Crisis * was a United States Navy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudoforest
In graph theory, a pseudoforest is an undirected graphThe kind of undirected graph considered here is often called a multigraph or pseudograph, to distinguish it from a simple graph. in which every connected component has at most one cycle. That is, it is a system of vertices and edges connecting pairs of vertices, such that no two cycles of consecutive edges share any vertex with each other, nor can any two cycles be connected to each other by a path of consecutive edges. A pseudotree is a connected pseudoforest. The names are justified by analogy to the more commonly studied trees and forests. (A tree is a connected graph with no cycles; a forest is a disjoint union of trees.) Gabow and Tarjan. attribute the study of pseudoforests to Dantzig's 1963 book on linear programming, in which pseudoforests arise in the solution of certain network flow problems.. Pseudoforests also form graph-theoretic models of functions and occur in several algorithmic problems. Pseudoforests ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planar Graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points. Every graph that can be drawn on a plane can be drawn on the sphere as well, and vice versa, by means of stereographic projection. Plane graphs can be encoded by combinatorial maps or rotation systems. An equivalence class of topologically equivalent drawings on the sphere, usually with additional assumptions such as the absence of isthmuses, is called a pl ... [...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] |
AD 142
Year 142 ( CXLII) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known in the Roman Empire as the Year of the Consulship of Pactumeius and Quadratus (or, less frequently, year 895 '' Ab urbe condita''). The denomination 142 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Emperor Antoninus Pius orders the construction of the Antonine Wall. The wall stretches 39 miles (63 km), from Old Kilpatrick in West Dunbartonshire on the Firth of Clyde, to Carriden near Bo'ness on the Firth of Forth (Scotland). The Romans build 19 forts and smaller fortlets (milecastles), to protect the border against the Caledonians. * Municipal doctors are named throughout the Roman Empire. Asia * First year of the ''Hanan'' era of the Chinese Han Dynasty. * The Chinese Taoist alchemist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
142 BC
__NOTOC__ Year 142 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Calvus and Servilianus (or, less frequently, year 612 ''Ab urbe condita''). The denomination 142 BC for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Syria * Diodotus Tryphon seizes the throne of the Seleucid Empire. Roman Republic * The first stone bridge over the Tiber river is completed. Judea * Simon Maccabaeus succeeds his brother Jonathan as High Priest of Judea until 135 BC. Births * Ptolemy IX, Egyptian pharaoh (d. 81 BC __NOTOC__ Year 81 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Decula and Dolabella (or, less frequently, year 673 '' Ab urbe condita''). The denomination 81 BC for this year has been ...) References {{DEFAULTSORT:142 Bc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Highways Numbered 142
The following highways are numbered 142: Cambodia * National Road 142 (Cambodia) Canada * Nova Scotia Highway 142 * Prince Edward Island Route 142 Costa Rica * National Route 142 Japan * Japan National Route 142 * Fukuoka Prefectural Route 142 * Nara Prefectural Route 142 Malaysia * Malaysia Federal Route 142 United States * Alabama State Route 142 * Arkansas Highway 142 * California State Route 142 * Colorado State Highway 142 * Connecticut Route 142 * Florida State Road 142 (pre-1945) (former) ** County Road 142 (Jefferson County, Florida) ** County Road 142 (Leon County, Florida) * Georgia State Route 142 * Illinois Route 142 ** Illinois Route 142A (former) * Indiana State Road 142 * Iowa Highway 142 (former) * Kentucky Route 142 * Louisiana Highway 142 * Maine State Route 142 * Maryland Route 142 (former) * Massachusetts Route 142 * M-142 (Michigan highway) * Missouri Route 142 * Nevada State Route 142 (former) * New Hampshire Route 142 * New Mexico Stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
