theory . Descriptive set theory uses both the notion of forcing from recursion theory as well as set theoretic forcing. Forcing has also been used in model theory but it is common in model theory to define generic mathematics genericity directly without mention of forcing. Intuitions Forcing is equivalent ...for the use of forcing in recursion theory Forcing recursion theory In the mathematical discipline of set theory , forcing is a technique invented by Paul Cohen mathematician Paul Cohen for proving consistency ... . Forcing was considerably reworked and simplified in the 1960s, and has proven to be an extremely ..., but usually much more difficult to apply. Intuitively, forcing consists of expanding the set theoretical universe mathematics universe V to a larger universe V . In this bigger universe ... an expanded membership relation involving the new sets of the form math x,1 math . Forcing is a more ... ramified forcing , is slightly different from the unramified forcing expounded here. Forcing posets A forcing poset is an ordered triple P , , 1 where is a preorder on P , and 1 is a largest element ... with a forcing poset P are the P names . P names are sets of the form u , p u is a P name and p ..., G x . One defines u G u p , p p G , then val u G u , G G . A good example of a forcing poset is Bor ... language is sometimes used with other forcing posets. Countable transitive models and generic filters The key step in forcing is, given a ZFC universe V , to find appropriate G not in V . The resulting ... choose G M . Forcing Given a generic filter G P , one proceeds as follows. The subclass of P names ... of M G to that of M , one works with the forcing language , which is built up like ordinary first ... math u sub 1 sub , , u sub n sub read p forces where p is a condition, is a formula in the forcing ... G is. What is important is that this external definition of the forcing relation p math Vdash math ... by saying the fundamental consistency result is that given a forcing poset P , we may assume ... more details
Wiktionarypar forcingForcing may refer to Forcing set theory , a technique for obtaining proofs in set theory Forcing recursion theory Radiative forcing , the difference between the incoming radiation energy and the outgoing radiation energy in a given climate system Cloud forcing , the difference between the radiation budget components for average cloud conditions and cloud free conditions Forcing magic is when a Illusionist magician forces, or seems to force, someone to make a certain choice. See Card force . Harmonic oscillator Forcing or driving an oscillator at a particular frequency. disambig ... more details
In mathematics, ramified forcing is the original form of forcingmathematicsforcing introduced by harvtxt Cohen 1963 . Ramified forcing starts with a model M of V L , and builds up a larger model M G of Zermelo Fraenkel set theory by adding a generic subset G of a poset to M , by imitating Kurt G del s constructible hierarchy . Dana Scott and Robert M. Solovay Robert Solovay realized that the use of constructible set s was an unnecessary complication, and could be replaced by a simpler construction similar to John von Neumann s construction of the universe as a union of sets R for ordinals . This simplification was originally called unramified forcing harv Shoenfield 1971 , but is now usually just called forcing . As a result, ramified forcing is only rarely used. References Citation last1 Cohen first1 P. J. authorlink Paul Cohen mathematician title Set Theory and the Continuum Hypothesis publisher W. A. Benjamin location Menlo Park, CA year 1966 Citation last1 Cohen first1 Paul J. title The Independence of the Continuum Hypothesis url http links.jstor.org sici?sici 0027 8424 2819631215 2950 3A6 3C1143 3ATIOTCH 3E2.0.CO 3B2 5 year 1963 month 15 journal Proceedings of the National Academy of Sciences of the United States of America volume 50 issue 6 pages 1143 1148 doi 10.1073 pnas.50.6.1143 pmid 16578557 pmc 221287 issn 0027 8424 citation last Shoenfield first J. R. chapter Unramified forcing year 1971 title Axiomatic Set Theory series Proc. Sympos. Pure Math. volume XIII, Part I pages 357 381 publisher Amer. Math. Soc. publication place Providence, R.I. mr 0280359 Category Forcing settheory stub ... more details
Unreferenced stub auto yes date December 2009 In the card game Contract bridge bridge , a forcing bid is any bid that obliges the partner to bid over an intermediate opposing pass. By agreement or tacit understanding, that is, partner must keep the bidding open . Encyclopedia, 161 ... bid Pass ? Here ... represents any beginning of the auction, before the forcing bid bold . Partner is obliged to bid rather than pass, so the forcing bid will not be Glossary of contract bridge terms passedout passed out the auction will return to the forcing bidder . A forcing bid that creates no further obligation is called forcing for one round . A bid that is forcing and promises a rebid creates an obligation on the forcing bidder next round typically, up to some level of the auction . A game forcing bids creates a mutual obligation to continue bidding at least to game level, or to double the opponents. All Bidding system bridge bidding systems utilise forcing bids. For instance, one over one bid s and two over one bid s are all treated as forcing in virtually any bidding system. Also, introducing a new suit at three level is generally treated as forcing provided this bid is made in a non limited hand. The main reason why it is necessary to have certain bids in the system designed as forcing is to allow the partnership to start a dialogue exploring for the right contract. One of the essentials of a good bridge partnership is a thorough understanding and agreement on which bids are forcing. This is no easy territory, as may be exemplified by the fact that in certain auctions even a pass can be forcing see Forcing pass . Some bidding situations for which one is advised to discuss the forcing character non forcing, round forcing or forcing to a specified level with partner responses to preempt ... situations See also Forcing pass References Henry G. Francis, et al., eds., The Official Encyclopedia of Bridge . New York Crown Publishers. 2001. about 900 pages. ISBN 0 943855 44 6. DEFAULTSORT Forcing ... more details
Forcing function can mean In differential calculus, a Forcing function differential equations In interaction design, a behavior shaping constraint , a means of preventing undesirable user input usually made by mistake. disambig ... more details
In the card game contract bridge bridge , a forcing pass is any pass that obliges the partner to bid ... Pass ? Here ... represents any beginning to the auction. The forcing pass bold necessarily occurs directly ... the auction now that is a precondition. The first, direct, forcing pass refers to partner the choice how to act. There is no commitment to accept partner s choice. Indeed, a forcing pass ensures that the auction ... step action by that player. Normally double is natural where pass is forcing. That is, double suggests the current denomination and strain, doubled, as a final contract. Forcing pass is also a synonym ... events When is pass forcing? Here ... act means any beginning to the auction, followed by an opposing ... open themselves because their action is forcing. Then the forcing pass is a moot point and the concept may be considered inapplicable. When their action is not forcing, on the other hand, partnership understanding whether pass is forcing may be vital. Partners should recognize forcing pass situations . Low level forcing pass One family of forcing pass occurs when the partnership auction is already forcing to a particular level and the opponents bid below that level. 1 Hearts 1 Spades 2 Diams 2 Spades Pass Commonly 2 Diams is forcing to 2NT. Then pass over opposing 2 Spades is forcing. Here 2 Diams is natural but the same holds over a conventional call that is forcing. If the convention is a bid forcing only to the next step, such as a Jacoby transfer , then pass is forcing only over a double ... the chosen major. Then pass is forcing it refers the choice of major suit back to the one ... name a strain here diamonds , a direct pass is forcing. Commonly the forcing pass declines to recommend ... level forcing pass ... when it appears that an opposing bid is a sacrifice. 1 Hearts 2 Diams 3 ... sacrifice. Then a direct pass is forcing. It declines to recommend playing 5 Diams doubled and thereby suggests bidding at least 5 Hearts . What is the meaning of a forcing pass followed by 5 Hearts if partner ... more details
In climate science, radiative forcing is loosely defined as the change in net irradiance at atmospheric ... era, it is customary to take the year 1750 as the starting point. A positive forcing more incoming energy tends to warm the system, while a negative forcing more outgoing energy tends to cool it. Possible sources of radiative forcing are changes in insolation incident solar radiation , or the effects .... Because the IPCC regularly assesses the radiative forcing, it also has a more specific technical definition ... of heat by various materials. Any such alteration is a radiative forcing, and causes a new balance .... The term radiative forcing has been used in the IPCC Assessments with a specific technical meaning ... 212.htm ref The exact definition used is The radiative forcing of the surface troposphere system due ... report ar4 syr ar4 syr.pdf ref the IPCC defines it as blockquote Radiative forcing is a measure .... In this report radiative forcing values are for changes relative to preindustrial conditions defined ... forcing is ...the rate of energy change per unit area of the globe as measured at the top of the atmosphere ... 461472a ref In the context of climate change , the term forcing is restricted to changes in the radiation ... . Radiative forcing can be used to estimate a subsequent change in equilibrium surface temperature T sub s sub arising from that radiative forcing via the equation math Delta T s lambda Delta F ... forcing. ref http www.grida.no publications other ipcc tar ?src climate ipcc tar wg1 222.htm ... forcing for doubling CO sub 2 sub , as calculated by radiative transfer code Modtran. Red lines ... forcing for eight times increase of CH sub 4 sub , as calculated by radiative transfer code Modtran. Radiative forcing often measured in watts per square meter can be estimated in different ways for different components. For the case of a change in solar irradiance, the radiative forcing is the change ... pubs crossref 1998 98GL01908.shtml New estimates of radiative forcing due to well mixed greenhouse ... more details
Cloud forcing sometimes described as cloud radiative forcing is, in meteorology , the difference between the radiation budget components for average cloud conditions and cloud free conditions. Much of the interest in cloud forcing relates to its role as a feedback process in the present period of global warming . All global climate model s used for climate change projections include the effects of water vapor and cloud forcing. The models include the effects of clouds on both incoming solar and emitted terrestrial radiation. Clouds increase the global albedo reflection of solar radiation from 15 to 30 , reducing the amount of solar radiation absorbed by the Earth by about 44 W m . This cooling is offset somewhat by the greenhouse effect of clouds which reduces the outgoing longwave radiation by about 31 W m . Thus the net cloud forcing of the radiation budget is a loss of about 13 W m . ref cite book last Intergovernmental Panel on Climate Change title IPCC First Assessment Report.1990 ... up. These numbers should not be confused with the usual radiative forcing concept, which is for the change in forcing related to climate change . Without the inclusion of clouds, water vapor alone ... Water vapour feedback or forcing? publisher RealClimate date 2005 04 06 url http www.realclimate.org ... of clouds reduces the radiative forcing of the greenhouse gases compared to the clear sky forcing. However, the magnitude of the effect due to clouds varies for different greenhouse gases. Relative to clear sky skies , clouds reduce the global mean radiative forcing due to carbon dioxide ... Shine, T.J. Wallington, and T.J. Smyth title Radiative forcing of climate by hydrochlorofluorocarbons ... N. coauthors M.D. Hurley, S. Pinnock, K.P. Shine, and T.J. Wallington title Radiative forcing of climate ... title New estimates of radiative forcing due to well mixed greenhouse gases. journal Geophys. Res. Lett ... reflist 2 Global warming DEFAULTSORT Cloud Forcing Category Climate forcing ... more details
The forcing notrump is a bidding convention bridge convention in the card game of contract bridge bridge ... card point s and is non forcing . Opener, with a balanced minimum, may pass the 1NT response and, if the opponents also pass, that will become the contract. A partnership may agree that this bid is forcing ... as minimum responder holdings. The forcing notrump is used over major suit s only 1NT is always standard and non forcing over the minor suit s. A bid of 1 forcing notrump shows 6 to 12 HCP, denies the ability ... spades if the opening bid was 1 heart. As the forcing notrump imposes a number of problems, a popular variation that overcomes these is the forcing next step . Opener s rebid Opener is forced to bid ... HCP 3 of a new suit jump shift is natural, normally agreed to be game forcing, and shows about 19 ... rebid 2 span style color red span violating rule 1 , or pass if playing Semi forcing notrump Semi forcing notrump . The forcing next step variation discussed below overcomes these problems ... the forcing notrump, however, it is sometimes tactically advantageous to bid 1NT with this hand ... cautious at the same time. System implications The forcing notrump is required for players using the 2 1 game forcing system, but may be used to advantage by other players as well. False preference ... based on 5 of partners minor and invitational values. Semi forcing notrump This section is linked from 2 1 game forcing As a variation, some partnerships choose to play their 1NT response as semi forcing . The rebids and subsequent auctions are the same as with the forcing notrump, except that the opener ... in a newly bid minor. Forcing next step With this approach, the next step bid over the major open is forcing and unspecified. Forcing next step, also known as the Kaplan Inversion, is a mid chart convention in the ACBL. 1 Spades 1NT is forcing, unspecified br 1 Hearts 1 Spades is forcing with responder having 0 4 spades br 1 Hearts 1NT is forcing with responder showing 5 spades. One immediate benefit ... more details
A forcing defense in contract bridge aims to force declarer to repeatedly ruff the defenders leads. If this can be done often enough, declarer eventually runs out of trumps and may lose control of the hand. A forcing defense is therefore applicable only to contracts played in a trump suit. The defense should try to make declarer ruff in the long trump hand. Unless declarer is playing for a dummy reversal, he usually intends to ruff losers in the short trump hand anyway. If the defense can shorten declarer s trumps sufficiently, it may wind up with more trumps than declarer. In that case, the defense will be able to pull any remaining trumps and run its own winners. A forcing defense is usually begun on the opening lead because the Tempo bridge tempo is often important. It is indicated when The defense knows or suspects that the trump suit is breaking badly for declarer. There is a side suit that declarer will have to ruff. The defense has enough entries that it will be able to continue leading the side suit. The latter requirement means that the forcing defense is seldom attempted against voluntarily bid slams the declaring side normally has so much strength that the defense s opportunities to continue to attack the trump suit are very limited. Example Alfred Sheinwold ref Five Weeks to Winning Bridge, Simon & Schuster, 1959 ref cites this example of a forcing defense to South s contract of 4 Spades BridgeHand 7 6 5 10 8 4 A 7 6 5 K Q 6 A 4 3 2 K Q J 9 8 3 2 J 8 7 6 5 3 2 K 4 A 10 7 5 3 2 K Q J 10 9 8 A Q J 10 9 9 4 West leads the Hearts K. South takes the Hearts A and plans to win five spades, one heart, at least three diamonds and a club. He leads the Spades K, West ducks, and East s club discard discloses the bad trump break. South has no better move than to continue spades, hoping for a defensive error, a winning diamond finesse, or that the hearts block. West ducks ... hearts, forcing South to ruff. South has now lost control of the hand. No matter how South ... more details
Orbital forcing is the effect on climate of slow changes in the tilt of the Earth s axis and shape of the orbit see Milankovitch cycles . These orbital changes change the total amount of sunlight reaching the Earth by up to 25 at mid latitudes from 400 to 500 Wm sup 2 sup at latitudes of 60 degrees . In this context, the term forcing signifies a physical process that affects the Earth s climate. This mechanism is believed to be responsible for the timing of the ice age cycles. A strict application of the Milankovitch theory does not allow the prediction of a sudden ice age rapid being anything under a century or two , since the fastest orbital period is about 20,000 years. The timing of past glacial periods coincides very well with the predictions of the Milankovitch theory, and these effects can be calculated into the future. Overview Image Vostok Petit data.svg thumb right Ice core data. Note length of glacial cycles averages 100,000 years. Blue curve is temperature, green curve is CO sub 2 sub , and red curve is windblown glacial dust loess . Today s date is on the left side of the graph. It is sometimes asserted that the length of the current interglacial temperature peak will be similar to the length of the preceding interglacial peak Eemian Stage Sangamonian Eem Stage , and that therefore we might be nearing the end of this warm period. However, this conclusion is probably mistaken the lengths of previous interglacials were not particularly regular see graphic at right . Berger and Loutre 2002 argue that with or without human perturbations, the current warm climate may last another 50,000 years. The reason is a minimum in the eccentricity of Earth s orbit around the Sun ... of land masses on the Earth s surface are believed to reinforce the orbital forcing effects ... The NOAA page on Climate Forcing Data includes calculated data on orbital variations over the last ... eccentricity Global warming Climate oscillations Category Climate forcing agents ... more details
Dablink Maths and Math redirect here. For other uses of Mathematics or Math , see Mathematics disambiguation ..., Euclid s depiction in works of art depends on the artist s imagination see Euclid . ref Mathematics ... handbook 409 chapters The Future of Mathematics Education.aspx Association for Supervision and Curriculum Development , ascd.org ref ref Keith Devlin Devlin, Keith , Mathematics The Science of Patterns .... ref Through the use of abstraction mathematics abstraction and logic al reasoning , mathematics ... physics motions of physical objects. Practical mathematics has been a human activity for as far back as History of Mathematics written records exist. Logic Rigorous arguments first appeared in Greek mathematics , most notably in Euclid s Elements . Mathematics continued to develop, for example ... naturally or are human creations. The mathematician Benjamin Peirce called mathematics the science ... that as far as the laws of mathematics refer to reality, they are not certain and as far as they are certain, they do not refer to reality. ref name certain Mathematics is used throughout the world ... sciences . Applied mathematics , the branch of mathematics concerned with application of mathematical ... theory . Mathematicians also engage in pure mathematics , or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered. ref Peterson ref Etymology The word mathematics comes from the ancient Greek language ... that English borrowed only the adjective mathematic al and formed the noun mathematics anew ... Dictionary of English Etymology , Oxford English Dictionary , sub mathematics , mathematic , mathematics ref In English, the noun mathematics takes singular verb forms. It is often shortened to maths or, in English speaking North America, math . History Main History of mathematics Image Kapitolinischer ... credited with discovering the Pythagorean theorem . The evolution of mathematics might be seen ... more details
Wikify date August 2010 In a system of differential equations used to describe a time dependent process, a forcing function is a function that appears in the equations and is only a function of time, not of any of the other variables. ref http depts.washington.edu rfpk training tutorials modeling part8 10.html ref ref http jagger.berkeley.edu pack me132 Section7.pdf ref In effect, it is a constant for each value of t . References reflist Category Mathematics math stub ... more details
Forcing in recursion theory is a modification of Paul Cohen mathematician Paul Cohen s original set theory set theoretic technique of forcing set theory forcing to deal with the effective concerns in recursion theory . Conceptually the two techniques are quite similar, in both one attempts to build generic ... and sentences. However, where set theoretic forcing is usually interested in creating objects that meet every dense set of conditions in the ground model, recursion theoretic forcing only aims ... difficult machinery used in set theoretic forcing can be eliminated or substantially simplified when defining forcing in recursion theory. But while the machinery may be somewhat different recursion theoretic and set theoretic forcing are properly regarded as an application of the same technique ... of forcing A notion of forcing is a set math P math and a partial order on math P math , math succ P math with a greatest element math 0 P math . condition An element in a notion of forcing. We say ... A subset math F math of a notion of forcing math P math is a filter if math p,q in F implies p nmid ... math F math Cohen forcing The notion of forcing math C math where conditions are elements of math 2 omega math and math tau succ C sigma iff sigma supset tau math Note that for Cohen forcing math ... where some recursion theorists reverse the direction of the forcing partial order exchanging math succ P math with math prec P math which is more natural for Cohen forcing but is at odds with the notation used in set theory. Generic objects The intuition behind forcing is that our conditions ... and adds some information of its own. For instance in Cohen forcing the conditions can be viewed ... P math and sentences but first we need to explain the language mathematics that math psi math is a sentence for. However, forcing is a technique not a definition and the language for math psi math will depend ... should express facts about the object we wish to build with our forcing construction. References ... more details
In the mathematical field of set theory , the proper forcing axiom PFA is a significant strengthening of Martin s axiom , where forcing set theory forcing s with the countable chain condition ccc are replaced by proper forcings. Statement A forcing set theory forcing or partially ordered set P is proper if for all regular cardinal regular uncountable cardinal number cardinals math lambda math , forcingmathematicsforcing with P preserves stationary set stationary subsets of math lambda omega math . The proper forcing axiom asserts that if P is proper and D sub &alpha sub is a dense subset of P for each &alpha &omega sub 1 sub , then there is a filter G math subseteq math P such that D sub &alpha sub G is nonempty for all &alpha &omega sub 1 sub . The class of proper forcings, to which PFA can be applied, is rather large. For example, standard arguments show that if P is countable chain condition ccc or &omega closed , then P is proper. If P is a iterated forcing countable support iteration of proper forcings, then P is proper. In general, proper forcings preserve cardinal number math aleph 1 math . Consequences PFA directly implies its version for ccc forcings, Martin s axiom . In Cardinal number cardinal arithmetic , PFA implies math 2 aleph 0 aleph 2 math . PFA implies any two math aleph 1 math dense subsets of R are isomorphic, any two Aronszajn tree s are club isomorphic, and every automorphism of math P omega math fin is trivial. PFA implies that the Singular Cardinals Hypothesis holds. An especially notable consequence proved by John R. Steel is that the axiom of determinacy holds in Constructible universe L R , the smallest inner model containing the real numbers. Another consequence is the failure of square principle s and hence existence of inner models ... comes from PFA. Other forcing axioms The bounded proper forcing axiom BPFA is a weaker variant ... sub 1 sub . Martin s maximum is the strongest possible version of a forcing axiom. Forcing axioms are viable ... more details
In mathematics, forcingmathematicsforcing is a method of constructing new models M G of set theory ... that meets every dense subset of P in M . Cohen forcing In Cohen forcing, named after Paul Cohen mathematician ... and p q if p math supseteq math q . This poset satisfies the countable chain condition. Forcing with this poset ... 2 sub by any cardinal so construct a model where the continuum has size at least . Hechler forcing Hechler forcing is used to show that Martin s axiom implies that every family of less than c functions ... k for all h in E . Jockusch Soare forcing a.k.a. forcing with math Pi 0 1 math classes Forcing with math ... set theory subtrees of math 2 omega math , ordered by inclusion. Iterated forcing Empty section date July 2010 Laver forcing Laver forcing was used by Richard Laver Laver to show that Borel s conjecture ... less than a given cardinal . If is uncountable then forcing with this poset collapses to . Collapsing ... than to for fixed cardinals and . Forcing with this poset collapses down to . Levy collapsing ... all cardinals less than onto , but keeps as the successor to . Magidor forcing Amongst many forcing notions developed by Menachem Magidor Magidor , one of the best known is a generalization of Prikry forcing used to change the cofinality of a cardinal to a given smaller regular cardinal. Mathias forcing AN element of P is a pair consisting of a finite set s of natural numbers and an infinite ... in t math cup math B . Namba forcing Namba forcing is used to change the cofinality of sub 2 sub ... less than sub 2 sub . P is ordered by inclusion. Prikry forcing In Prikry forcing, named ... B . This forcing notion can be used to change to cofinality of while preserving all cardinals. Product forcing Taking a product of forcing conditions is a way of simultaneously forcing all the conditions ... of elements of with p 1 is less than . Radin forcing Radin forcing, a technically involved generalization of Magidor forcing, adds a closed, unbounded subset to some regular cardinal . If ... more details
Unreferenced date December 2009 In the game of Contract bridge bridge , fourth suit forcing also referred to as fourth suit artificial denotes a partnership agreement that allows responder to create a forcing bid forcing auction, at the 2nd turn to bid. Under the fourth suit forcing convention , a bid by either player in the fourth unbid suit is conventional i.e. does not promise any particular holding in the suit bid . It implies that the bidder has no good bid, but nonetheless has something of value, and wishes to continue searching for a contract. It returns the bidding to their partner, and asks them to find a bid or to further describe his her hand. This convention was introduced by the British bridge author Norman Squire , and is adopted by the vast majority of partnerships that play bridge at competitive levels. The fourth suit forcing convention is particularly useful on strong game going hands on which no natural forcing bid is available, hence it is a type of game trial bid . Example A typical 4th suit forcing situation is as follows class wikitable South North 1 Diams 1 Spades 2 Clubs ? North holds Spades A Q 8 6 2 Hearts 8 4 3 Diams Q 7 Clubs A 6 5 After 2 Clubs , North can see there are likely to be sufficient points for game, but he has no good bid He has shown his spade suit fully. To rebid spades would imply a longer or stronger suit than he has. They are not good ... of contract. North instead bids the fourth suit fourth suit forcing 2 Hearts to indicate that he believes ... Hearts bid may be either Forcing bid forcing for one round, or forcing to game level. His partner .... Further details Opener responds to the fourth suit forcing by in prioritised order Raising of responder .... The fourth suit forcing approach in conjunction with the principle of fast arrival allows the partnership to create a forcing bid game forcing auction at low level that leaves ample room to explore ... Spades . DEFAULTSORT Fourth Suit Forcing Category Bridge bidding nl Vierde kleur forcerend bod pl Czwarty ... more details
Unreferenced date July 2009 2 1 game forcing Two over one game forcing is a bidding system in modern ... forcing auctions The 2 1 auctions are 1 Hearts &ndash 2 Clubs , 1 Hearts &ndash 2 Diams , 1 Spades ... bid generally 12 high card points are required to respond Forcing notrump 1NT to 1 Spades , or to 1 ... 2 Clubs is game forcing, although some do. Also, 2 1 game forcing doesn t apply to a passed hand, or if there is an intervening ... game forcing the pair can stop below game only when responder rebids his suit. For example, 1 Hearts ... should discuss this possibility. 1NT response forcing or semi forcing for one round Because ... or 1 Spades opening is Forcing bid forcing for one round and is used among other things for weaker hands containing low ranking suits. Since the 1NT response is forcing, hands with a three card limit raise can start with 1NT and later jump support partner. See Forcing notrump for additional details. Some pairs play a variant in which the 1NT response to 1 Hearts or 1 Spades is Forcing notrump Semi forcing notrump semi forcing . Other 2 1 features Use of the 2 1 system usually implies at least ... raise is strong and forcing for one round Jacoby transfer s over 1NT opening Jacoby 2NT , showing strong support with 4 or more cards Splinter bid s New minor forcing Fourth suit forcing and artificial ... Spades br Forcing to game, with original spade support and good club suit. This is different from standard .... 1 Spades &ndash 2 Clubs br 2 Spades &ndash 2NT. br Forcing to game, with balanced hand and a good club suit. 1 Spades &ndash 2 Clubs br 2 Diams &ndash 3 Clubs br Forcing, unless the partnership has agreed that this is an exception to the 2 1 rule. 1 Diams &ndash 2 Clubs br Forcing for one round only as in Standard American , except in the variant of 2 1 where this sequence is game forcing as well. 1 Clubs &ndash 2 Clubs br Forcing for one round 10 high card points points or more with at least ... shows a very strong hand and is unequivocally forcing. However, since such hands do not occur with great ... more details
Orphan date February 2009 unreferenced date June 2008 Zero Forcing Equalizer refers to a form of linear equalization algorithm used in telecommunications communication systems which inverts the frequency response of the channel. This form of equalizer was first proposed by Robert Lucky . The Zero Forcing Equalizer applies the inverse of the channel to the received signal, to restore the signal before the channel. It has many useful applications. For example, it is studied heavily for IEEE 802.11n MIMO where knowing the channel allows recovery of the two or more streams which will be received on top of each other on each antenna. The name Zero Forcing corresponds to bringing down the intersymbol interference ISI to zero in a noise free case. This will be useful when ISI is significant compared to noise. For a channel with frequency response math F f math the zero forcing equalizer math C f math is constructed by math C f 1 F f math . Thus the combination of channel and equalizer gives a flat frequency response and linear phase math F f C f 1 math . In reality, zero forcing equalization does not work in most applications, for the following reasons Even though the channel impulse response has finite length, the impulse response of the equalizer needs to be infinitely long The channel may have zeroes in its frequency response that cannot be inverted At some frequencies, may be very small. To compensate, grows very large. As a consequence, any noise added after the channel gets boosted by a large factor and destroys the overall signal to noise ratio. The third item is often the most important one. Algorithm If the channel response or transfer function channel transfer function for a particular channel is H s then the input signal is multiplied by the Multiplicative inverse reciprocal ... the intersymbol interference ISI . The zero forcing equalizer removes all ISI, and is ideal when the channel is noiseless. However, when the channel is noisy, the zero forcing equalizer will amplify ... more details
Competition law Third line forcing is a form of exclusive dealing involving the supply of goods or services on the condition that the purchaser buys goods or services from a particular third party, or a refusal to supply because the purchaser will not agree to that condition. Third line forcing is strictly prohibited by the Australian Trade Practices Act 1974 . ref cite web url http www.accc.gov.au content index.phtml itemId 259608 fromItemId 3669 h3 40 title Anti competitive conduct and restrictive trade practices work Australian Competition and Consumer Commission ACCC ref References reflist External links http www.findlaw.com.au article 6686.htm Australian Competition & Consumer Commission v IMB Group Pty Ltd Category Anti competitive behaviour law stub econ stub ... more details
New Minor Forcing often abbreviated NMF , is a bridge convention in which responder s bid of a previously unbid minor over a no trump rebid by opener generally 1NT is artificial and is primarily used when looking for three card support for your five card major and shows at least invitational values about 11HCP but is unlimited. It asks partner for clarification of shape and strength and it can be used on hands anywhere from inviting game to slam going. For example, with the opponents silent, 1 Clubs 1 Hearts Spades 1NT 2 Diams NMF 1 Diams 1 Hearts Spades 1NT 2 Clubs NMF Examples of suitable hands for NMF Given the auction 1 Diams 1 Hearts 1NT 2 Clubs NMF BridgeHandInline Ax KQxxx Qxx xxx interested in either a game or part score, in either hearts or notrump BridgeHandInline Axx AKxx AQxxx J expecting to play a slam, possibly a grand slam, in either diamonds or notrump BridgeHandInline Ax KQJ10x xx AQJx there s no rule that you can t actually have the suit you bid Given the auction 1 Clubs 1 Spades 1NT 2 Diams NMF BridgeHandInline Axxxx KQx Axxx J planning to force to game, in either spades or notrump BridgeHandInline Axxxx KQx x Axxx looking for spade support because if partner has three it may play better than no trump, and clubs may also be an option BridgeHandInline AKxxx KQxx x Axx unsure for the right denomination to play, the hand could play game in spades, hearts, no trump or clubs When playing this convention, jump rebids by responder are typically played as invitational, as NMF can be used with hands wishing to force to game. For example, on the auction above, a 3 Hearts ... in game, but only in hearts. If you re playing New Minor Forcing, the auction 1 Diams 1 Spades 1NT 3 Hearts shows a 5 card heart suit and at least 5 spades with a game going hand Without New Minor Forcing ... can be applied after opener s 2NT rebid, which typically shows 18 19 HCP bid of a new minor is forcing ... Bridge Guys New Minor Forcing http www.prairienet.org bridge nmf.htm Karen s Bridge Library Category ... more details
Zero forcing or Null Steering precoding is a spatial signal processing by which the multiple antenna transmitter can null multiuser interference signals in wireless wireless communications . Regularized zero forcing precoding is enhanced processing to consider the impact on a background noise and unknown user Interference communication interference ref cite journal author B. C. B. Peel, B. M. Hochwald, and A. L. Swindlehurst title A vector perturbation technique for near capacity multiantenna multiuser communication Part I channel inversion and regularization journal IEEE Trans. Commun. pages 195 202 volume 53 date Jan. 2005 doi 10.1109 TCOMM.2004.840638 ref , where the background noise and the unknown user interference can be emphasized in the result of known interference signal nulling. In particular, Null Steering is a method of beamforming for narrowband signal processing signals where we want to have a simple way of compensating delays of receiving signals from a specific source at different elements of the antenna array. In general to make use of the antenna arrays, we better to sum and average the signals coming to different elements, but this is only possible when delays are equal. Otherwise we first need to compensate the delays and then to sum them up. To reach this goal, we may only add the weighted version of the signals with appropriate weight values. We do this in such a way that the frequency domain output of this weighted sum produces a zero result. This method is called null steering. The generated weights are of course related to each other and this relation is a function of delay and central working frequency of the source. Performance of Zero forcing Precoding If the transmitter knows the downlink channel state information CSI perfectly, ZF precoding can achieve almost the system capacity when the number of users is large. On the other hand, with limited ... zero forcing with perfect feedback and with limited feedback, i.e.,, math Delta R R ZF R FB leq ... more details
In mathematics , let A be a set and let &le be a binary relation on A . Then a subset B of A is said to be cofinal if it satisfies the following condition For every a &isin A , there exists some b &isin B such that a &le b . This definition is most commonly applied when A is a partially ordered set or directed set under the relation &le . Also, the notion of cofinal is sometimes applied to objects other than subsets, e.g. a cofinal function mathematics function &fnof X &rarr A is a function whose range mathematics range &fnof X is a cofinal subset of A Cofinal subsets are very important in the theory of directed sets and net mathematics nets , where &ldquo subnet mathematics cofinal subnet &rdquo is the appropriate generalization of &ldquo subsequence &rdquo . They are also important in order theory , including the theory of cardinal numbers , where the minimum possible cardinality of a cofinal subset of A is referred to as the cofinality of A . A subset B of A is said to be coinitial or dense in the sense of Forcingmathematicsforcing if it satisfies the following condition For every a &isin A , there exists a b &isin B such that b &le a . This is the Duality order theory order theoretic dual to the notion of cofinal subset. Properties Every partially ordered set is cofinal in itself. If B is a cofinal subset of a poset A and C is a cofinal subset of B with the partial ordering of A restricted to B , then C is also a cofinal subset of A . For a partially ordered set with maximal element s, every cofinal subset must contain all maximal element s. For a partially ordered set with greatest element , a subset is cofinal if and only if it contains that greatest element. Partially ordered sets without greatest element or maximal elements admit disjoint cofinal subsets. For example, the even and odd natural number s form disjoint cofinal subsets of the set of all natural numbers. If a partially ... more details
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