As an economic tool market concentration is useful because it reflects the degree of competition in the market. Tirole (1988, p. 247) notes that: Bain's (1956) original concern with market concentration was based on an intuitive relationship between high concentration and collusion. There are game theoretic models of market interaction (e.g. among oligopolists) that predict that an increase in market concentration will result in higher prices and lower consumer welfare even when collusion in the sense of cartelization (i.e. explicit collusion) is absent. Examples are Cournot oligopoly, and ...

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Market concentration, Market concentration - Desirable properties, Market concentration - Examples, Market concentration - Uses, Market concentration - Motivation, Market concentration - Empirical tests, Market concentration - Alternative definition, Market concentration - Further Examples, Market concentration - External link

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A common problem is to find a good notion of a measure on a topological space that is compatible with the topology in some sense. One way to do this is to define a measure on the Borel sets of the topological space. In general there are several problems with this: for example, such a measure may not have a well defined support. Another approach to measure theory is to restrict to locally compact Hausdorff spaces, and only consider the measures that correspond to positive linear functionals on the space of continuous functions with compact su ...

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Radon measure, Radon measure - Motivation, Radon measure - Definitions, Radon measure - Basic properties

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This is a stronger requirement than asking only that M realize all the complete types of the base language; such a model is called weakly saturated. The difference lies in the fact that M may (and likely does) contain points which are "invisible" to the complete theory of M, in the sense that they are not definable. This argument owes its ultimate success to Gödel's completeness theorem, which guarantees that any consistent additional requirements we can add to the theory of M will be satisfiable by some other mo ...

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Saturated model, Saturated model - Definition, Saturated model - Motivation, Saturated model - Examples, Saturated model - Relationship to prime models

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Common uses for mail filters include removal of spam and of computer viruses. A less common use is to inspect outgoing e-mail at some companies to ensure that employees comply with appropriate laws. Users might also employ a mail filter to prioritize messages, and to sort them into folders based on subject matter or other criteria. ...

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Mail filter, Mail filter - Motivation, Mail filter - Users, Mail filter - Customization

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A simplicial set is a categorical (that is, purely algebraic) model capturing those topological spaces which can be built up (or faithfully represented up to homotopy) from simplices and their incidence relations. This is similar to the approach of CW complexes to modeling topological spaces, with the crucial difference that simplicial sets are purely algebraic and do not carry any actual topology (this ...

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Simplicial set, Simplicial set - Motivation, Simplicial set - Formal definition, Simplicial set - Face and degeneracy maps, Simplicial set - The standard n-simplex and the simplex category, Simplicial set - Geometric realization, Simplicial set - Singular set for a space, Simplicial set - Homotopy theory of simplicial sets, Simplicial set - Simplicial objects, Simplicial set - Reference

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The primary motivation behind Mangal's behaviour is attributed to a new type of bullet cartridge used in the Lee-Enfield P-53 rifle introduced in the Bengal Army that year. The cartridge was rumoured to be greased with animal fat (primarily pig and cow fat, which are not consumed by either Hindus or Muslims, the primary religions in the Bengal Army) [1]. The cartidges had to be bitten to remove the cover, and that was abhorrent to the soldiers See also:

Mangal Pandey, Mangal Pandey - Incident, Mangal Pandey - Motivation, Mangal Pandey - The Lee-Enfield Rifle & Cartridge, Mangal Pandey - Consequences, Mangal Pandey - A Different View, Mangal Pandey - Movie, Mangal Pandey - Additional readings

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In The Beatles Anthology, Paul McCartney claims the idea for the movie came from Blackpool Lights tours, where a group of people would take a bus, an accordion player, and get drunk on the way to see the Blackpool Lights. Although it is never fully stated, several scenes in the movie were based on strange ideas the group members had. John Lennon said he came up with one such scene in a dream. He dreamed he was a waiter at a fancy restaurant, and his duty was to continually shovel spaghetti onto a customer's plate. So, in the mo ...

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Magical Mystery Tour film, Magical Mystery Tour film - Plot, Magical Mystery Tour film - Motivation, Magical Mystery Tour film - Songs, Magical Mystery Tour film - External link

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Extended real number line - Limits. We often wish to describe the behavior of a function f(x), as either the argument x or the function value f(x) get "very big" in some sense. For example, consider the function The graph of this function has a horizontal asymptote of y = 0. Geometrically, as we move farther and farther to the right down the x-axis, the value of 1 / x2 gets closer and ...

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Extended real number line, Extended real number line - Motivation, Extended real number line - Limits, Extended real number line - Measure and integration, Extended real number line - Order and topological properties, Extended real number line - Arithmetic operations, Extended real number line - Algebraic properties, Extended real number line - Miscellaneous

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In general relativity and allied theories, the distribution of the mass, momentum, and stress due to matter and to any non-gravitational fields is described by the energy-momentum tensor (or matter tensor) Tab. However, the Einstein field equation is not very choosy about what kinds of states of matter or nongravitational fields are admissible in a spacetime model. This is both a strength, since a good general theory of gravitation should be maximally independent of any assu ...

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Energy conditions, Energy conditions - Motivation, Energy conditions - Some observable quantities, Energy conditions - Mathematical statement, Energy conditions - Perfect fluids, Energy conditions - A counterexample

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There is a general aesthetic among high energy physicists that the more symmetrical a theory is, the more "beautiful" and "elegant" it is. According to this aesthetic, the Standard Model gauge group, which is the direct product of three groups (modulo some finite group) is "ugly". Also, reasoning in analogy with the 19th-century unification of electricity with magnetism into electromagnetism, and especially the success of the electroweak theory, which utilizes the idea of spontaneous symmetry breaking to unify electromagnetism with the weak ...

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Grand unification theory, Grand unification theory - Motivation, Grand unification theory - Ingredients, Grand unification theory - Proposed theories, Grand unification theory - Current status

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The original software behind CDDB was released under the GNU General Public License, and many people submitted CD information without charging anything, thinking the service would also remain free. The license was later changed however, and some programmers complained that the new licence included certain terms that threatened them in a way they couldn't accept: if one wanted to access CDDB, one was not allowed to access any other CDDB-like database (such as freedb), and any programs using a CDDB lookup had to display a C ...

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Freedb, Freedb - Motivation, Freedb - External link

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If we were to try to create some visual representation of a partially ordered set (S, ≤), how would we proceed? We could begin by first creating a graph, where every node on the graph is an element in S, and every edge (u, v) in that graph would represent the relation u ≤ v. Doing this, and trying to draw the graph, would result in a graph that would be very "busy". In fact, we carry a lot of redundant information in such a graph. Recall the requirements on a partial order: a ≤ ...

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Hasse diagram, Hasse diagram - Examples, Hasse diagram - Motivation, Hasse diagram - Cover relation, Hasse diagram - Finding a good Hasse diagram

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The simplest Lp space is the Euclidean space Rn. The length of a vector is usually given by but this is by no means the only way of defining length. If p is a real number, p≥1, define for any vector . It turns out that this definition indeed satisfies the properties of a length function (or norm), which are that only the length of the zero vector is zero, the length of the vector scales proport ...

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Lp space, Lp space - Motivation, Lp space - l^p spaces, Lp space - Properties of l^p spaces, Lp space - L^p spaces, Lp space - Special cases, Lp space - Relation to l^p spaces, Lp space - Properties of L^p spaces

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Inline expansion is typically used to eliminate the inherent time overhead that occurs in calling a function; it is typically used for functions that execute very quickly, as this overhead is more significant in this case. It also has a space benefit for very small functions, and is an enabling transformation for other optimizations. Without inline functions, however, the programmer has little to no control over which functions are inlined and which are not; the compiler alone makes this decision. Adding this degree of control allows application-specific knowledge, such as frequently executed functions, to be ex ...

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Inline function, Inline function - Motivation, Inline function - Comparison to macros, Inline function - Language support, Inline function - Problems with inline functions, Inline function - Quotes

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Many Germans who supported, fought in, or had otherwise known people lost in the enormously costly war, believed the causes for the German/Austrian involvement in the war were justified. They had hoped it would bring a restoration of past glory and a unified German nation-state. Instead, the war caused the deaths of 1,770,000 German soldiers and 760,000 German civilians, devastated the economy, and brought lo ...

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Dolchstosslegende, Dolchstosslegende - Motivation, Dolchstosslegende - Origins, Dolchstosslegende - Related concepts outside of Weimar Germany, Dolchstosslegende - Sources

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The class P, typically taken to consist of all the "tractable" problems for a sequential computer, contains the class NC, which consists of those problems which can be efficiently solved on a parallel computer. This is because parallel computers can be simulated on a sequential machine. It is not known whether NC=P. In other words, it is not known whether there are any tractable problems that are inherently sequential. Just as it is widely suspected that P does not equal NP, so it is w ...

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P-complete, P-complete - Motivation, P-complete - P-complete problems, P-complete - Problems not known to be P-complete

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The terrorists were said to be motivated by a sense of alienation and frustration with their situation in South Africa, as well as religious beliefs similar to Christian Identity, which asserted their God-given right to rule the nation. They subsequently issued further threats, asserting that there would be further "surprises" in store. One of the group's aims was to assassinate Nelson Mandela and [14] possibly restore apartheid to South Africa, (although some have suggested that their aim was to start a race war and "kick the blacks out of the country", while others have asserted that the ...

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2002 Soweto bombings, 2002 Soweto bombings - Background, 2002 Soweto bombings - The bombs, 2002 Soweto bombings - Investigation and trial, 2002 Soweto bombings - Motivation, 2002 Soweto bombings - Aftermath

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As a motivating example, consider the problem of finding an 'a' in an array of n elements, given that half are 'a's and the other half are 'b's. The obvious approach is to look at each element of the array, but this would take very long (n/2 operations) if the array were ordered as 'b's first followed by 'a's. There is a similar drawback with checking in the reverse order, or checking every second element. In fact, with any strategy at all in which the order in which the elements will be checked is fixed, i.e, a deterministic a ...

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Randomized algorithm, Randomized algorithm - Motivation, Randomized algorithm - Complexity, Randomized algorithm - Applications

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The Speak Mandarin Campaign (SMC) was launched in 1979 by then Prime Minister Lee Kuan Yew. The motivation was to discourage the use of various Chinese dialects by the Chinese Singaporeans and to encourage the speaking of Mandarin as a common language among the Chinese population. The campaign aims to [1]: simplify the language environment and understanding amongst Chinese Singaporeans. improve communication and understanding amongst Chinese Singaporeans. create a Mandarin-speaking environment conducive to the successful imple ...

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Speak Mandarin Campaign, Speak Mandarin Campaign - Motivation, Speak Mandarin Campaign - History, Speak Mandarin Campaign - Implementation, Speak Mandarin Campaign - Criticism

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The techniques are widely used by engineers designing or analysing devices that interact with fluid, such as vehicles, pumps, chemical apparatus or ventilation systems. There are numerous commercial software packages to solve the Navier Stokes Equations. Examples of such commercial packages include the following (alphabetically listed): AVL/FIRE, CFD-ACE+, CFD-FASTRAN, CFX by ANSYS Inc., Coolit, FLUENT, KIVA, NUMECA, Phoenics, and STAR-CD. Other software packages serve as add-ons or complementary products to CFD tools. These include FieldView for post-proc ...

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Computational fluid dynamics, Computational fluid dynamics - Methodology, Computational fluid dynamics - Discretization methods, Computational fluid dynamics - Turbulence Models, Computational fluid dynamics - Solution algorithms, Computational fluid dynamics - Motivation, Computational fluid dynamics - Software

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In the English-speaking world, a reductionist view of family history prevails: the family historian's chief motivation is to improve self-esteem. Until the late 19th century, family histories were almost exclusively of interest to persons who had obtained their wealth or rank by inheritance. Such groups ranged from European aristocrats to New Zealand Maori, who recite whakapapa (genealogies) as an affirmation of identity. Ancestry for such groups was a source of status. Other people, who had inherited nothing, might, in extreme cases, suppre ...

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Family history, Family history - Introduction, Family history - Motivation, Family history - The single family history, Family history - Conducting a Project, Family history - Benefits, Family history - External link

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