CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search In mathematics , the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field . [ 1 ] [ a ] For every vector space there exists a basis, [ b ] and all bases of a vector space have equal cardinality; [ c ] as a result, the dimension of a vector space is uniquely defined. We say V is finite-dimensional if the dimension of V is finite . The dimension of the vector space V over the field F can be written as dim F ( V ) or as [V : F], read "dimension of V over F ". When F can be inferred from context, dim( V ) is typically written. 1 Examples 2 Facts 3 Generalizations 3.1 Trace 4 See also 5 Notes 6 References 7 External links Examples [ edit ] The vector space R 3 has as a basis , and therefore we have dim R ( R 3...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search 11.5 x 200 = 2300 km 28 x 100 = 2800 km 70 x 50 = 3500 km Figure 1. As the length of the measuring stick is scaled smaller and smaller, the total length of the coastline measured increases. A fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured. It has also been characterized as a measure of the space-filling capacity of a pattern that tells how a fractal scales differently from the space it is embedded in; a fractal dimension does not have to be an integer. [ 1 ] [ 2 ] [ 3 ] The essential idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 196...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems . 1 Heighway dragon 1.1 Construction 1.2 [Un]Folding the Dragon 1.2.1 Gray code method 1.3 Dimensions 1.4 Tiling 2 Twindragon 3 Terdragon 4 Lévy dragon 5 Occurrences of the dragon curve in solution sets 6 See also 7 Notes 8 External links Heighway dragon [ edit ] Heighway dragon curve The Heighway dragon (also known as the Harter–Heighway dragon or the Jurassic Park dragon ) was first investigated by NASA physicists John Heighway, Bruce Banks, and William Harter. It was described by Martin Gardner in his Scientific American column Mathematical Games in 1967. Many of its properties were first published by Chandle...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search Learned helplessness is a behaviour in which an organism forced to endure aversive, painful or otherwise unpleasant stimuli, becomes unable or unwilling to avoid subsequent encounters with those stimuli, even if they are escapable. Presumably, the organism has learned that it cannot control the situation and therefore does not take action to avoid the negative stimulus. [ 1 ] Learned helplessness theory is the view that clinical depression and related mental illnesses may result from a perceived absence of control over the outcome of a situation. [ 2 ] Organisms that have been ineffective and less sensitive in determining the consequences of their behaviour are defined as having acquired learned helplessness. [ 3 ] 1 Foundation of research and theory 1.1 Seligman and Maier 1.1.1 ...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search The intimate parts of the human body must, according to Islam , be covered from the sight of others with clothing. Exposing the intimate parts of the body is unlawful in Islam as the Quran tells to cover the genitals, and for adult females, also the breasts. Exposing them is regarded as sin . Precisely which body parts must be covered varies between different schools of Islamic thought. The Quran admonishes Muslim women to dress modestly and cover their breasts and genitals. [ 1 ] The Quran explicitly states that "O wives of the Prophet, you are not like anyone among women" (Quran 33: 32) and as such has separate rules specifically for the wives of the Prophet. [ 2 ] 'Awrah may be exposed for emergencies such as surgery. 1 Etymology 2 In the Quran 3 In the Hadith 4 Differences betw...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search This article needs attention from an expert in Computer science . The specific problem is: disputed definition. WikiProject Computer science (or its Portal ) may be able to help recruit an expert. (August 2013) This article does not cite any references or sources . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . (February 2008) Referential transparency and referential opacity are properties of parts of computer programs . An expression is said to be referentially transparent if it can be replaced with its value without changing the behavior of a program (in other words, yielding a program that has the same effects and output on the same input). The opposite term is referential opaqueness. While ...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search Tidal locking results in the Moon rotating about its axis in about the same time it takes to orbit Earth . Except for libration effects, this results in the Moon keeping the same face turned towards Earth, as seen in the figure on the left. (The Moon is shown in polar view, and is not drawn to scale.) If the Moon were not rotating at all, it would alternately show its near and far sides to Earth, while moving around Earth in orbit, as shown in the figure on the right. Tidal locking (also called gravitational locking or captured rotation ) occurs when the gravitational gradient makes one side of an astronomical body always face another, an effect known as synchronous rotation . For example, the same side of the Moon always faces the Earth . A tidally locked body takes just as long to ro...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search In functional programming , continuation-passing style ( CPS ) is a style of programming in which control is passed explicitly in the form of a continuation . Gerald Jay Sussman and Guy L. Steele, Jr. coined the phrase in AI Memo 349 (1975), which sets out the first version of the Scheme programming language. [ 1 ] [ 2 ] John C. Reynolds gives a detailed account of the numerous discoveries of continuations. [ 3 ] A function written in continuation-passing style takes an extra argument: an explicit "continuation" i.e. a function of one argument. When the CPS function has computed its result value, it "returns" it by calling the continuation function with this value as the argument. That means that when invoking a CPS function, the calling function is required to supply a procedure to be inv...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search L - notation is an asymptotic notation analogous to big-O notation , denoted as for a bound variable tending to infinity . Like big-O notation, it is usually used to roughly convey the computational complexity of a particular algorithm . It is defined as where c is a positive constant, and is a constant . L-notation is used mostly in computational number theory , to express the complexity of algorithms for difficult number theory problems, e.g. sieves for integer factorization and methods for solving discrete logarithms . The benefit of this notation is that it simplifies the analysis of these algorithms. The expresses the dominant term, and the takes care of everything smaller. When is 0, then is a polynomial function of ln n ; when is 1 then is a fully exponential function...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search In number theory , the general number field sieve ( GNFS ) is the most efficient classical algorithm known for factoring integers larger than 100 digits. Heuristically , its complexity for factoring an integer n (consisting of bits) is of the form (in L-notation ), where ln is the natural logarithm . [ 1 ] It is a generalization of the special number field sieve : while the latter can only factor numbers of a certain special form, the general number field sieve can factor any number apart from prime powers (which are trivial to factor by taking roots). When the term number field sieve ( NFS ) is used without qualification, it refers to the general number field sieve. The principle of the number field sieve (both special and general) can be understood as an improvement to the simpler rat...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search A distributed hash table ( DHT ) is a class of a decentralized distributed system that provides a lookup service similar to a hash table ; ( key , value ) pairs are stored in a DHT, and any participating node can efficiently retrieve the value associated with a given key. Responsibility for maintaining the mapping from keys to values is distributed among the nodes, in such a way that a change in the set of participants causes a minimal amount of disruption. This allows a DHT to scale to extremely large numbers of nodes and to handle continual node arrivals, departures, and failures. DHTs form an infrastructure that can be used to build more complex services, such as anycast , cooperative Web caching , distributed file systems , domain name services , instant messaging , multicast , and also...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search The device mapper is a Linux kernel 's framework for mapping physical block devices onto higher-level virtual block devices . It forms the foundation of LVM2 , software RAIDs , dm-crypt disk encryption, and offers additional features such as file system snapshots . [ 1 ] Device mapper works by passing data from a virtual block device, which is provided by the device mapper itself, to another block device. Data can be also modified in transition, which is performed, for example, in the case of device mapper providing disk encryption or simulation of unreliable behavior. While this article focuses on the Linux kernel's implementation, the device mapper functionality is also available in both NetBSD and DragonFly BSD . [ 2 ] [ 3 ] 1 Usage 2 Features 3 Applications 4 References 5 Ex...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search Adaptive Replacement Cache (ARC) is a page replacement algorithm with better performance [ 1 ] than LRU (Least Recently Used) developed [ 2 ] at the IBM Almaden Research Center . This is accomplished by keeping track of both Frequently Used and Recently Used pages plus a recent eviction history for both. In 2006, IBM was granted a patent for the adaptive replacement cache policy . 1 Summary 1.1 Replacement 2 Deployment 3 References 4 External links 5 See also Summary [ edit ] Basic LRU maintains an ordered list (the cache directory) of resource entries in the cache, with the sort order based on the time of most recent access. New entries are added at the top of the list, after the bottom entry has been evicted. Cache hits move to the top, pushing all other entries down. AR...

CentralNotice Cowboy Bebop: Tsuioku no Serenade From Wikipedia, the free encyclopedia Jump to: navigation , search For the PlayStation Cowboy Bebop game, see Cowboy Bebop (PlayStation game) . This article needs additional citations for verification . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed. (November 2008) Cowboy Bebop: Tsuioku no Serenade Japanese boxart Developer(s) Banpresto Publisher(s) Bandai Platform(s) PlayStation 2 Release date(s) JP August 25, 2005 [ 1 ] Cancelled (U.S.) Genre(s) Action Mode(s) Single-player Distribution DVD Cowboy Bebop: Tsuioku no Serenade ( カウボーイビバップ 追憶の 夜曲 ( せれなーで ) , Kaubōi Bibappu: Tsuioku no Serenāde ? , lit. "Cowboy Bebop: Serenade of Reminiscence") is a PlayStation 2 action / beat 'em up video game fr...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search This article includes a list of references , related reading or external links , but its sources remain unclear because it lacks inline citations . Please improve this article by introducing more precise citations. (October 2013) The St. Petersburg lottery or St. Petersburg paradox [ 1 ] is a paradox related to probability and decision theory in economics . It is based on a particular (theoretical) lottery game that leads to a random variable with infinite expected value (i.e., infinite expected payoff) but nevertheless seems to be worth only a very small amount to the participants. The St. Petersburg paradox is a situation where a naive decision criterion which takes only the expected value into account predicts a course of action that presumably no actual person would be willing t...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search This article's tone or style may not reflect the encyclopedic tone used on Wikipedia . See Wikipedia's guide to writing better articles for suggestions. (August 2013) The two envelopes problem , also known as the exchange paradox , is a brain teaser , puzzle , or paradox in logic , probability , and recreational mathematics . It is of special interest in decision theory , and for the Bayesian interpretation of probability theory . Historically, it arose as a variant of the necktie paradox . The problem typically is introduced by formulating a hypothetical challenge of the following type: Of two indistinguishable envelopes , each containing money, one contains twice as much as the other. The subject may pick one envelope and keep the money it contains. Having chosen an envelope a...

CentralNotice List of fallacies From Wikipedia, the free encyclopedia Jump to: navigation , search This article may contain improper references to self-published sources . Please help improve it by removing references to unreliable sources , where they are used inappropriately. (October 2014) For specific popular misconceptions, see List of common misconceptions . A fallacy is incorrect argument in logic and rhetoric resulting in a lack of validity , or more generally, a lack of soundness . Fallacies are either formal fallacies or informal fallacies . 1 Formal fallacies 1.1 Propositional fallacies 1.2 Quantification fallacies 1.3 Formal syllogistic fallacies 2 Informal fallacies 2.1 Faulty generalizations 2.2 Red herring fallacies 3 Conditional or questionable fallacies 4 See also 5 References 6 Further reading 7 External links Formal f...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search Cognitive biases are tendencies to think in certain ways that can lead to systematic deviations from a standard of rationality or good judgment, and are often studied in psychology and behavioral economics . Although the reality of these biases is confirmed by replicable research, there are often controversies about how to classify these biases or how to explain them. [ 1 ] Some are effects of information-processing rules (i.e. mental shortcuts), called heuristics , that the brain uses to produce decisions or judgments. Such effects are called cognitive biases . [ 2 ] [ 3 ] Biases in judgment or decision-making can also result from motivation , such as when beliefs are distorted by wishful thinking . Some biases have a variety of cognitive ("cold") or motivational ("hot") explanations. Both...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search For other paradoxes by Joseph Bertrand, see Bertrand's paradox (disambiguation) . Bertrand's box paradox is a classic paradox of elementary probability theory . It was first posed by Joseph Bertrand in his Calcul des probabilités , published in 1889. There are three boxes: a box containing two gold coins, a box containing two silver coins, a box containing one gold coin and one silver coin. After choosing a box at random and withdrawing one coin at random, if that happens to be a gold coin, it may seem that the probability that the remaining coin is gold is 1 ⁄ 2 ; in fact, the probability is actually 2 ⁄ 3 . Two problems that are very similar are the Monty Hall problem and the Three Prisoners problem . These simple but counterintuitive puzzles are used as a standard example in teac...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search This article includes a list of references , related reading or external links , but its sources remain unclear because it lacks inline citations . Please improve this article by introducing more precise citations. (February 2012) The paradoxes of material implication are a group of formulae which are truths of classical logic , but which are intuitively problematic. One of these paradoxes is the paradox of entailment . The root of the paradoxes lies in a mismatch between the interpretation of the validity of logical implication in natural language, and its formal interpretation in classical logic, dating back to George Boole 's algebraic logic. In classical logic, implication describes conditional if-then statements using a truth-functional interpretation, i.e. "p implies q" is de...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search This article has multiple issues. Please help improve it or discuss these issues on the talk page . This article needs additional citations for verification . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed. (November 2010) This section does not cite any references or sources . Please help improve this section by adding citations to reliable sources . Unsourced material may be challenged and removed . (November 2010) Quine's paradox is a paradox concerning truth values , attributed to Willard Van Orman Quine . It is related to the liar paradox as a problem, and it purports to show that a sentence can be paradoxical even if it is not self-referring and does not use demonstratives or...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search This is a list of paradoxes , grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. Because of varying definitions of the term paradox , some of the following are not considered to be paradoxes by everyone. This list collects only scenarios that have been called a paradox by at least one source and have their own article. Although considered paradoxes, some of these are based on fallacious reasoning, or incomplete/faulty analysis. Informally, the term is often used to describe a counter-intuitive result. 1 Logic 1.1 Self-reference 1.2 Vagueness 2 Mathematics 2.1 Statistics 2.2 Probability 2.3 Infinity and infinitesimals 2.4 Geometry and topology 3 Decision theory 4 Physics 4.1 Astrophysics 4.2 Classical mechanics 4.3 Cos...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search In philosophy and logic , the liar paradox or liar's paradox is the statement "this sentence is false". Trying to assign to this statement a classical binary truth value leads to a contradiction . If "this sentence is false" is true, then the sentence is false, but then if "this sentence is false" is false, then the sentence is true, and so on. 1 History 2 Explanation of the paradox and variants 3 Possible resolutions 3.1 Alfred Tarski 3.2 Arthur Prior 3.3 Saul Kripke 3.4 Jon Barwise and John Etchemendy 3.5 Dialetheism 3.6 Non-cognitivism 4 Logical structure of the liar paradox 5 Applications 5.1 Gödel's First Incompleteness Theorem 6 In popular culture 7 See also 8 Notes 9 References 10 External links History [ edit ] The Epimenides paradox (circa 600 BC) has...

CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search Hudson Dusters Founder Circular Jack Kid Yorke Goo Goo Knox Founding location Lower East Side, New York Years active 1890s-1910s Territory Manhattan Ethnicity Irish-American Membership 200 (est.) Criminal activities Burglary , armed robbery , street muggings , assault , narcotics . Rivals Boodle Gang Marginals Pearl Buttons Fashion Plates Gopher Gang The Hudson Dusters was a New York City street gang during the early twentieth century. Formed in the late 1890s by "Circular Jack", "Kid Yorke", and "Goo Goo Knox", the gang began operating from an apartment house on Hudson Street . Knox, a former member of the Gopher Gang , had fled after a failed attempt to gain leadership of the gang from then leader, Marty Brennan. However the two gangs later became all...

CentralNotice Symmetric multiprocessing From Wikipedia, the free encyclopedia Jump to: navigation , search This article has multiple issues. Please help improve it or discuss these issues on the talk page . This article is outdated . Please update this article to reflect recent events or newly available information. (November 2010) This article needs additional citations for verification . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed. (November 2012) Diagram of a symmetric multiprocessing system Symmetric multiprocessing ( SMP ) involves a symmetric multiprocessor system hardware and software architecture where two or more identical processors connect to a single, shared main memory , have full access to all I/O devices, and are controlled by a single ...