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Forcing (other)
Forcing may refer to: Mathematics and science *Forcing (mathematics), a technique for obtaining independence proofs for set theory *Forcing (recursion theory), a modification of Paul Cohen's original set theoretic technique of forcing to deal with the effective concerns in recursion theory *Forcing, driving a harmonic oscillator at a particular frequency *Cloud forcing, the difference between the radiation budget components for average cloud conditions and cloud-free conditions * Forcing bulbs, the inducement of plants to flower earlier than their natural season *Radiative forcing, the difference between the incoming radiation energy and the outgoing radiation energy in a given climate system Arts, entertainment, and media *Forcing (magic), a technique by which a magician forces one outcome from a card draw * Forcing, several distinct concepts within the game of contract bridge: ** Forcing bid ** Forcing defense ** Forcing notrump ** Forcing pass ** Forcing take-out, an obsolete nam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forcing (mathematics)
In the mathematical discipline of set theory, forcing is a technique for proving consistency and independence results. It was first used by Paul Cohen in 1963, to prove the independence of the axiom of choice and the continuum hypothesis from Zermelo–Fraenkel set theory. Forcing has been considerably reworked and simplified in the following years, and has since served as a powerful technique, both in set theory and in areas of mathematical logic such as recursion theory. Descriptive set theory uses the notions of forcing from both recursion theory and set theory. Forcing has also been used in model theory, but it is common in model theory to define genericity directly without mention of forcing. Intuition Intuitively, forcing consists of expanding the set theoretical universe V to a larger universe V^ . In this bigger universe, for example, one might have many new real numbers, identified with subsets of the set \mathbb of natural numbers, that were not there in the old ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forcing (recursion Theory)
Forcing in computability theory is a modification of Paul Cohen's original set-theoretic technique of forcing to deal with computability concerns. Conceptually the two techniques are quite similar: in both one attempts to build generic objects (intuitively objects that are somehow 'typical') by meeting dense sets. Both techniques are described as a relation (customarily denoted \Vdash) between 'conditions' and sentences. However, where set-theoretic forcing is usually interested in creating objects that meet every dense set of conditions in the ground model, computability-theoretic forcing only aims to meet dense sets that are arithmetically or hyperarithmetically definable. Therefore, some of the more difficult machinery used in set-theoretic forcing can be eliminated or substantially simplified when defining forcing in computability. But while the machinery may be somewhat different, computability-theoretic and set-theoretic forcing are properly regarded as an application of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its Mechanical equilibrium, equilibrium position, experiences a restoring force ''F'' Proportionality (mathematics), proportional to the displacement ''x'': \vec F = -k \vec x, where ''k'' is a positive coefficient, constant. If ''F'' is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude). If a frictional force (Damping ratio, damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction coefficient, the system can: * Oscillate with a frequency lower than in the Damping ratio, undamped case, and an amplitude decreasing with time (Damping ratio, underdamped oscillator). * Decay to the equilibrium p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cloud Forcing
In meteorology, cloud forcing, cloud radiative forcing (CRF) or cloud radiative effect (CRE) is 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. Measuring cloud forcing The following equation calculates this change in the radiation budget at the top of the atmosphere : \Delta R_ = R_ - R_ The net cloud radiative effect can be decomposed into its longwave and shortwave components. This is because net radiation is absorbed solar minus the outgoing longwave radiation shown by the following equations : \Delta R_ = \Delta Q_ - \Delta OLR The first term on the right is the shortwave cloud effect (''Q''abs ) and the second is the longwave effect (OLR). The shortwave cloud effect is calculated by the following equation : \Delta Q_ = (S_o/4) \cdot (1 - \alpha_) - (S_o/4) \cdot (1 - \alpha_) Where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulbs
In botany, a bulb is structurally a short stem with fleshy leaves or leaf basesBell, A.D. 1997. ''Plant form: an illustrated guide to flowering plant morphology''. Oxford University Press, Oxford, U.K. that function as food storage organs during dormancy. (In gardening, plants with other kinds of storage organ are also called "ornamental bulbous plants" or just "bulbs".) Description The bulb's leaf bases, also known as scales, generally do not support leaves, but contain food reserves to enable the plant to survive adverse conditions. At the center of the bulb is a vegetative growing point or an unexpanded flowering shoot. The base is formed by a reduced stem, and plant growth occurs from this basal plate. Roots emerge from the underside of the base, and new stems and leaves from the upper side. Tunicate bulbs have dry, membranous outer scales that protect the continuous lamina of fleshy scales. Species in the genera ''Allium'', ''Hippeastrum'', '' Narcissus'', and ''Tulipa'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radiative Forcing
Radiative forcing (or climate forcing) is the change in energy flux in the atmosphere caused by natural or anthropogenic factors of climate change as measured by watts / metre2. It is a scientific concept used to quantify and compare the external drivers of change to Earth's energy balance. System feedbacks and internal variability are related concepts, encompassing other factors that also influence the direction and magnitude of imbalance. Positive radiative forcing means Earth receives more incoming energy from sunlight than it radiates to space. This net gain of energy will cause warming. Conversely, negative radiative forcing means that Earth loses more energy to space than it receives from the sun, which produces cooling. A planet in radiative equilibrium with its parent star and the rest of space can be characterized by net zero radiative forcing and by a planetary equilibrium temperature. Radiative forcing on Earth is meaningfully evaluated at the tropopause and at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forcing (magic)
In stage magic, a force is a method of controlling a choice made by a spectator during a trick. Some forces are performed physically using sleight of hand, such as a trick where a spectator appears to select a random card from a deck but is instead handed a known card by the magician. Other forces use equivocation (or "the magician's choice") to create the illusion of a free decision in a situation where all choices lead to the same outcome. Equivocation Equivocation (or the magician's choice) is a verbal technique by which a magician gives an audience member an apparently free choice but frames the next stage of the trick in such a way that each choice has the same end result. An example of equivocation can be as follows: A performer deals two cards on a table and asks a spectator to select one. If the spectator chooses the card on the left, the performer will hand the card to the spectator. If they pick the card on the right, the performer will take that card as his own and ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contract Bridge
Contract bridge, or simply bridge, is a trick-taking card game using a standard 52-card deck. In its basic format, it is played by four players in two competing partnerships, with partners sitting opposite each other around a table. Millions of people play bridge worldwide in clubs, tournaments, online and with friends at home, making it one of the world's most popular card games, particularly among seniors. The World Bridge Federation (WBF) is the governing body for international competitive bridge, with numerous other bodies governing it at the regional level. The game consists of a number of , each progressing through four phases. The cards are dealt to the players; then the players ''call'' (or ''bid'') in an auction seeking to take the , specifying how many tricks the partnership receiving the contract (the declaring side) needs to take to receive points for the deal. During the auction, partners use their bids to also exchange information about their hands, including o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forcing Bid
In the card game contract bridge, a forcing bid is any 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", 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 bridge bidding systems use forcing bids. For instance, one over one and two over one responses to one-of-a-suit opening bids are treated as forcing in almost all bidding systems. Also, introducing a new suit at three level is generally treated as forcing prov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forcing Defense
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 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 lea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forcing Notrump
The forcing notrump is a bidding convention in the card game of bridge. In Standard American bidding, the response of 1NT to an opening bid of 1 or 1 shows 6 to 9 high card points (HCP) 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'' for one round; if the intervening opponent passes, opener must bid at least once more. This guarantees the responder at least one more opportunity to bid or pass. This mechanism allows the partnership to use the 1NT response for a greater variety of hands: in particular, ''invitational'' as well as ''minimum'' responder holdings. The forcing notrump is used over major suits only; 1NT is always standard and non-forcing over the minor suit In contract bridge the minor suits are diamonds () and clubs (). They are given that name because contracts made in those suits score less (20 per contracted trick) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forcing Pass
In the card game bridge, a forcing pass is an agreement or understanding that a pass call obliges the partner to bid, double, or redouble over an intermediate opposing pass, i.e. partner must "keep the bidding open". : ... – (act) – Pass – (Pass) – ? Here "..." represents any beginning to the auction. The forcing pass (bold) necessarily occurs directly over an opposing bid, double, or redouble (act). After a pass over a pass, the auction might end before partner's turn. In other words, the partnership is committed to act ''somehow'' rather than 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 that the auction will return to the one who issues it, so it may be interpreted as the first half of a two-step action by that player. Normally double is natural where pass is forcing. That is, double suggests t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
