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 ... States of America, Vol. 51, No. 1. Jan. 15, 1964 , pp. 105 110. Category Forcingmathematics ...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, for example ... membership relation involving the new sets of the form math x,1 math . Forcing is a more elaborate ... 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 that satisfies following splitting ... co authors. Associated with a forcing poset P are the P names . P names are sets of the form u , p ... u G u p , p p G , then val u G u , G G . A good example of a forcing poset is Bor I , , I , where I ... used with other forcing posets. Countable transitive models and generic filters The key step in forcing ... is never in M . Forcing Given a generic filter G P , one proceeds as follows. The subclass of P names ... theory of M G to that of M , one works with the forcing language , which is built up like ordinary first ..., is a formula in the forcing language, and the u sub i sub are names, to mean that if G is a generic ... of the forcing relation p math Vdash M,P math is equivalent to an internal definition, defined by transfinite ... u sub 1 sub , , u sub n sub . We define the forcing relation in V by induction on complexity, in which ... more details
Wiktionary 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 , a technique by which a magician forces one outcome from a card draw Forcing, driving a harmonic oscillator at a particular frequency disambiguation ... more details
In the mathematical discipline of set theory , ramified forcing is the original form of forcingmathematicsforcing introduced by harvtxt Cohen 1963 to prove the independence mathematical logic independence of the continuum hypothesis from Zermelo Fraenkel set theory . Ramified forcing starts with a model mvar M of set theory in which the axiom of constructibility , math 1 V L , holds, and then builds up a larger model math M G of Zermelo Fraenkel set theory by adding a generic subset mvar G of a partially ordered set to mvar M , imitating Kurt G del s constructible hierarchy . Dana Scott and Robert M. Solovay Robert Solovay realized that the use of constructible universe 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 math R for ordinals math . Their 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 year 1963 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 jstor 71858 . 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 Forcingmathematics settheory stub ... 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 , a forcing bid is any bid that obliges the partner to bid over an intermediate opposing pass. Owing to the partnership s bidding system or a bridge convention , partner must keep the bidding open ref cite book last1 Francis first1 Henry G., Editor in Chief authorlink1 last2 Truscott first2 Alan F., Executive Editor authorlink2 Alan Truscott last3 Francis first3 Dorthy A., Editor, Sixth Edition authorlink3 title The Official Encyclopedia of Bridge , 6th Edition publisher American Contract Bridge League Memphis, TN series year 2001 doi isbn 0 943855 44 6 Page 161. ref , i.e. not pass, thereby preventing his left hand opponent from ending the auction with a pass and enabling the forcing bidder to bid further. 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, Contract bridge glossary oneoverone ... opening bids are treated as forcing in almost all biding systems. 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 ... are forcing is essential. This is no easy territory, as is exemplified by the fact that in certain auctions even a Forcing pass pass can be forcing . In particular, the following bidding situations require agreement as to their forcing character, i.e. non forcing, round forcing or forcing to a specified ... bid of opener 2NT in competitive bidding situations See also Forcing pass References Reflist DEFAULTSORT Forcing Bid Category Bridge bidding nl Forcerend bod ... more details
In the card game contract bridge bridge , a forcing pass is an agreement or understanding that a pass ... &ndash ? Here ... represents any beginning to the auction. The forcing pass bold necessarily occurs ... to end 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 ... of a two 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 ... competitive events When is pass forcing? Here ... act means any beginning to the auction, followed ... 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 ... that they double the chosen major. Then pass is forcing it refers the choice of major suit back to the one ... does name a strain here diamonds , a direct pass is forcing. Commonly the forcing pass declines ... natural . High level forcing pass ... when it appears that an opposing bid is a sacrifice. 1 Hearts ... 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 ... more details
In climate science, radiative forcing is generally defined as the change in net irradiance between different layers of the Atmosphere of Earth atmosphere . Typically, radiative forcing is quantified at the tropopause in units of watt s per square meter . A positive forcing more incoming energy tends to warm the system, while a negative forcing more outgoing energy tends to cool it. Sources of radiative forcing include changes in insolation incident solar radiation and in concentrations of greenhouse ... is a radiative forcing, and causes a new balance to be reached. In the real world this happens ... right 250px 2005 radiative forcings as estimated by the IPCC. The term radiative forcing has been ... forcing of the surface troposphere system due to the perturbation in or the introduction ... defines it as blockquote Radiative forcing is a measure of the influence a factor has in altering the balance ... of the factor as a potential climate change mechanism. In this report radiative forcing values ... square meter W m sup 2 sup . blockquote In simple terms, radiative forcing is ...the rate of energy ... of climate change , the term forcing is restricted to changes in the radiation balance of the surface ... sensitivity 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 ... is the radiative forcing. ref http www.grida.no publications other ipcc tar ?src climate ipcc tar wg1 ... of CO sub 2 sub . Example calculations Solar Forcing Radiative forcing measured in Watts per ... irradiance i.e., solar forcing , the radiative forcing is simply the change in the average amount ..., or albedo , of the Earth, equal to approximately 0.7. Thus, the solar forcing is the change in the solar ... forcing equal to the change in albedo divided by 4 multiplied by the solar constant . File ModtranRadiativeForcingDoubleCO2.png thumb right 250px Radiative forcing for doubling CO sub 2 sub , as calculated ... 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 publisher Cambridge University Press year 1990 location UK table 3.1 ref If the clouds were removed ... 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 ... to clear sky skies , clouds reduce the global mean radiative forcing due to carbon dioxide CO sub ..., T.J. Wallington, and T.J. Smyth title Radiative forcing of climate by hydrochlorofluorocarbons and hydrofluorocarbons ... Radiative forcing of climate change by CFC 11 and possible CFC replacements. journal J. Geophys. Res ... E.J. Highwood, K.P. Shine, and F. Stordal title New estimates of radiative forcing due to well ... Cloud formation 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 ... high card point s and is non forcing . Opener, with a balanced minimum, may pass the 1NT response ... is forcing for one round if the intervening opponent passes, opener must bid at least once more. This guarantees ... as minimum responder holdings. The forcing notrump is used over major suit major suits only 1NT is always standard and non forcing over the minor suit minor suits . A bid of 1 forcing notrump shows ... holding four spades if the opening bid was 1 heart. As the forcing notrump creates problems of its own, a popular variation that overcomes these is the forcing next step . Opener s rebid Opener ... 18 HCP 3 of a new suit jump shift is natural, normally agreed to be game forcing, and shows about ..., these partnerships rebid 2 Hearts violating rule 1 , or pass if playing Semi forcing notrump Semi forcing notrump . The forcing next step variation discussed below overcomes these problems by allowing ... . This may allow the opponents to get into the bidding at a low level. Playing the forcing notrump ... time. System implications The forcing notrump is required for players using the 2 1 game forcing system ... 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 ... extra values when holding only 3 cards 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 1 Hearts 1 Spades is forcing, with responder having 0 4 spades 1 Hearts 1NT is forcing with responder ... forcing notrump, responder with 5 spades bids 1 Spades over opener s 1 Hearts but if she also has 2 hearts she does not then know whether to rebid 2 Hearts or 2 Spades . In forcing next step, opener ... 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 BridgeHandNWES Label South in 4 spades Lead Lead hearts K 7&thinsp 6&thinsp 5 10&thinsp 8&thinsp 4 A&thinsp 7&thinsp 6&thinsp 5 K&thinsp Q&thinsp 6 A&thinsp 4&thinsp 3&thinsp 2 K&thinsp Q&thinsp J&thinsp 9 8&thinsp 3&thinsp 2 J&thinsp 8 &mdash 7&thinsp 6&thinsp 5&thinsp 3&thinsp 2 K&thinsp 4 A&thinsp 10&thinsp 7&thinsp 5&thinsp 3&thinsp 2 K&thinsp Q&thinsp J&thinsp 10&thinsp 9&thinsp 8 A Q&thinsp J&thinsp 10&thinsp 9 9&thinsp 4 West leads the Hearts K. South takes the Hearts ... Spades A and continues hearts, forcing South to ruff. South has now lost control of the hand. No matter ... 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 ... 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 simple Orbital forcing ... more details
uses see Mathematics disambiguation and Math disambiguation . File Euclid.jpg thumb Euclid , Greek ... . ref Mathematics from Greek language Greek m th ma , knowledge, study, learning is the study ... reasoning often provides insight or predictions. Through the use of abstraction mathematics abstraction and logic al reasoning , mathematics developed from counting , calculation , measurement ... 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 Euclid s Euclid s Elements Elements . Mathematics developed at a relatively slow pace until the Renaissance , when ... of Mathematics 1. Newton and Leibniz , BBC Radio 4 , 27 09 2010. ref Carl Friedrich Gauss 1777 1855 referred to mathematics as the Queen of the Sciences . ref Waltershausen ref Benjamin Peirce 1809 1880 called mathematics the science that draws necessary conclusions . ref Peirce, p. 97. ref David Hilbert said of mathematics We are not speaking here of arbitrariness in any sense. Mathematics is not like ... 1992 . ref Albert Einstein 1879 1955 stated that as far as the laws of mathematics refer to reality ... certain Mathematics is used throughout the world as an essential tool in many fields, including natural science , engineering , medicine , and the social sciences . Applied mathematics , the branch of mathematics ... disciplines, such as statistics and game theory . Mathematicians also engage in pure mathematics , or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. ref Peterson ref Etymology The word mathematics comes from the ancient Greek ... . The word mathematics in Greek came to have the narrower and more technical meaning mathematical ... until around 1700, the term mathematics more commonly meant astrology or sometimes astronomy rather ... 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 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 ... how much large cardinal strength comes from PFA. Other forcing axioms The bounded proper forcing ... antichain s of size &omega sub 1 sub . Martin s maximum is the strongest possible version of a forcing axiom. Forcing axioms are viable candidates for extending the axioms of set theory as an alternative ... 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 ... for compatible. Filter A subset math F math of a notion of forcing math P math is a filter ... math F math properly containing math F math Cohen forcing The notion of forcing math C math where ... Note that for Cohen forcing math succ C math is the reverse of the containment relation. This leads to an unfortunate notational confusion where some recursion theorists reverse the direction of the forcing ... forcing but is at odds with the notation used in set theory. Generic objects The intuition behind forcing is that our conditions are finite approximations to some object we wish to build and that math ... forcing the conditions can be viewed as finite approximations to a real and if math tau succ C sigma ... conditions elements of math 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 ... forcing construction. References Melvin Fitting 1981 , Fundamentals of generalized recursion theory ... more details
In mathematics, forcingmathematicsforcing is a method of constructing new models M G of set theory ... Tidbits. Category Forcingmathematics ... that meets every dense subset of P in M . Cohen forcing In Cohen forcing named after Paul Cohen mathematician ... q if p math supseteq math q . This poset satisfies the countable chain condition. Forcing with this poset ... is that does not have cofinality . Grigorieff forcing Grigorieff forcing after Serge Grigorieff destroys a free ultrafilter on &omega Hechler forcing Hechler forcing after Stephen Herman ... h in F . Jockusch Soare forcing a.k.a. forcing with math Pi 0 1 math classes Forcing with math Pi 0 ... 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 ... a given cardinal . If is uncountable then forcing with this poset collapses to . Collapsing ... for fixed cardinals and . Forcing with this poset collapses down to . Levy collapsing If ... . 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 ... of B , and s is contained in t math cup math B . Mathias forcing is named for Adrian Richard David Mathias. Namba forcing Namba forcing after Kanji Namba is used to change the cofinality of ... sequences of ordinals less than sub 2 sub . P is ordered by inclusion. Prikry forcing In Prikry forcing ... 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 ... regular cardinal the number of elements of with p 1 is less than . Radin forcing Radin ... more details
Fourth suit forcing also referred to as fourth suit artificial ref name OEBref OEB 6 167 ref is a contract bridge Glossary of contract bridge terms convention convention that allows responder to create, at his second turn to bid, a forcing bid forcing auction. A bid by responder in the fourth suit, the only remaining unbid suit, is artificial indicating that responder has no appropriate alternate bid, remains interested in the potential for a game contract and asks opener to bid again to show additional features. Opener responds to the fourth suit forcing by in prioritised order Raising of responder s first bid suit with 3 card support, Bidding notrump with values in the fourth suit, Raising the fourth suit with four cards in that suit, Making the most natural rebid possible, lacking any of the above. Fourth suit forcing is minimally forcing for one round and usually forcing to game partnership agreement is required. Whether or not the convention is applicable if the fourth suit bidder is a passed hand is also a matter of partnership agreement there is no consensus amongst experts on the options as to its use being non forcing, forcing, or forcing only after a reverse ref name OEBref ... has no natural forcing rebid, it is a type of game trial bid . Example 1 class wikitable align ... fourth suit forcing , i.e. 2 Hearts , to indicate that he believes they have values for game, that he ... suits. Depending on partnership agreement, this 2 Hearts bid may be either Forcing bid forcing for one round, or forcing to game. Example 2 class wikitable align left North South align center 1 Clubs 1 Hearts align center 1 Spades 2 Diams align center 2 Hearts 2 Spades 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 for slam. Here, the 2 Spades bid ... References reflist WPCBIndex DEFAULTSORT Fourth Suit Forcing Category Bridge conventions nl Vierde ... more details
2009 2 1 game forcing Two over one game forcing is a bidding system in modern contract bridge in which ... to bidding at least contract bridge glossary G game . Normal 2 1 game forcing auctions The 2 ... card points are required to respond Forcing notrump 1NT to 1 Spades , or to 1 Hearts if they lack 4 spades. Exceptions to 2 1 game force Some pairs don t play that 1 Diams &ndash 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 bid or double by an opponent. Some pairs play that 2 1 isn t absolutely game forcing the pair ... this possibility. 1NT response forcing or semi forcing for one round Because the two level responses ... 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 the following additional ... a jump raise of a minor suit opening is a weak preemptive bid, while a single raise is strong and forcing ... or more cards Splinter bid s New minor forcing Fourth suit forcing and artificial. Some also utilize Bergen raises . Example sequences 1 Spades &ndash 2 Clubs br 2 Diams &ndash 2 Spades br Forcing to game ... 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 four clubs. 1 Clubs ... 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 At some frequencies the received signal may be weak. To compensate, the magnitude of the zero forcing filter gain 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. Furthermore, the channel may have zeroes in its frequency response that cannot be inverted at all. Gain 0 still equals 0 . This second item is often the more limiting condition. Algorithm If the channel response or transfer function channel transfer ..., in particular 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 ... 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
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 Cite web url http depts.washington.edu rfpk training tutorials modeling part8 10.html title How do Forcing Functions Work? publisher University of Washington Departments ref ref Cite web author Packard A. url http jagger.berkeley.edu pack me132 Section7.pdf format PDF title ME 132 date Spring 2005 publisher University of California, Berkeley page 55 ref In effect, it is a constant for each value of t . References reflist Category Differential equations mathanalysis stub ... more details
Infobox album See Wikipedia WikiProject Albums Name Junius Type EP Artist Junius band Junius Cover Forcingoutthesilencealbumcover.gif Caption Cover Artwork by Michael Repasch Nieves Released January 1, 2004 Recorded Genre Art Rock , Post Rock , Indie Rock Length 20 38 Label Radar Recordings small CDEP small br small RDR 105 small Producer Will Benoit This album Forcing Out the Silence br 2004 Next album Blood is Bright br 2006 Singles Name Forcing Out the Silence Type ep Single 1 Hiding Knives Single 1 date 2004 Forcing Out the Silence is the first extended play EP by American art rock band Junius band Junius . It was originally released by Radar Recordings on January 1, 2004, but was later re released on September 9, 2008 in its original packaging. Background Following the release of Forcing Out the Silence , Junius immediately began touring, playing more than two hundred shows over the duration of around nine months. ref cite web url http www.radarrecordings.com press junius index.htm title Press Resources author publisher Radar Recordings date 2002 2009 accessdate 2011 11 13 ref The band has toured frequently ever since. ref cite web url http www.facebook.com juniusmusic?sk app 4949752878 title Junius Shows Tours date 2011 11 13 accessdate 2011 11 13 publisher Facebook ref Album ratings rev1 EvilSponge rev1score Rating 4 5 ref cite web url http evilsponge.org albums Junius ForcingOutTheSilence.htm title Forcing Out the Silence author PostLibyan publisher EvilSponge year 2005 accessdate 2011 11 12 ref rev2 Decoy Music rev2score Rating 4 5 ref cite web url http www.decoymusic.com reviews junius forcing out the silence title Junius Blood is Bright author Josh Tabbia publisher Decoy Music date 2006 09 29 accessdate 2011 11 12 ref Track listing Track listing all writing Junius band Junius total length 20 38 title1 Elan Vital length1 1 12 title2 Hiding Knives length2 5 27 title3 From the Isle of the Blessed length3 5 05 title4 Elan Fatale length4 2 11 title5 Forcing ou ... 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 used primarily when looking for three card support for a five card major. It shows an unlimited hand with at least invitational values about 11HCP and can be used on hands anywhere from inviting game to slam going it is a forcing bid which asks partner for further information on his shape and strength. In the following auctions, in which the opponents Pass throughout, the rebids by responder are New Minor Forcing. class wikitable align left width 50 Opener width 50 Responder align center 1 Clubs 1 Hearts Spades align center 1NT 2 Diams class wikitable align left width 50 Opener width 50 Responder align center 1 Diams 1 Hearts Spades align center 1NT 2 clubs clear Examples Hands suitable for use of the New Minor Forcing convention are as follows Given the auction 1 Diams &ndash 1 Hearts 1NT &ndash 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 &ndash 1 Spades 1NT &ndash 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 ... New Minor Forcing, the auction 1 Diams &ndash 1 Spades 1NT &ndash 3 Hearts shows a 5 card heart suit and at least 5 spades with a game going hand Without New Minor Forcing you may bid 3 Hearts on something ... can be applied after opener s 2NT rebid, which typically shows 18 19 HCP bid of a new minor is forcing ... Guys New Minor Forcing http www.prairienet.org bridge nmf.htm Karen s Bridge Library Category Bridge ... 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
saved book title Mathematics subtitle An overview cover image Math.svg cover color Mathematics Main article Mathematics Supporting articles History of mathematics Mathematical beauty Mathematical notation Category Wikipedia books on mathematicsMathematics ... more details
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