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Reversible Turing Machines
Reversibility can refer to: * Time reversibility, a property of some mathematical or physical processes and systems for which time-reversed dynamics are well defined :* Reversible diffusion, an example of a reversible stochastic process * Reversible process (thermodynamics), a process or cycle such that the net change at each stage in the combined entropy of the system and its surroundings is zero * Reversible reaction A reversible reaction is a reaction in which the conversion of reactants to products and the conversion of products to reactants occur simultaneously. : \mathit aA + \mathit bB \mathit cC + \mathit dD A and B can react to form C and D or, in the ..., a chemical reaction for which the position of the chemical equilibrium is very sensitive to the imposed physical conditions; so the reaction can be made to run either forwards or in reverse by changing those conditions * Reversible computing, logical reversibility of a computation; a computational step for which a we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Reversibility
A mathematical or physical process is time-reversible if the dynamics of the process remain well-defined when the sequence of time-states is reversed. A deterministic process is time-reversible if the time-reversed process satisfies the same dynamic equations as the original process; in other words, the equations are invariant or symmetrical under a change in the sign of time. A stochastic process is reversible if the statistical properties of the process are the same as the statistical properties for time-reversed data from the same process. Mathematics In mathematics, a dynamical system is time-reversible if the forward evolution is one-to-one, so that for every state there exists a transformation (an involution) π which gives a one-to-one mapping between the time-reversed evolution of any one state and the forward-time evolution of another corresponding state, given by the operator equation: :U_ = \pi \, U_\, \pi Any time-independent structures (e.g. critical points or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversible Diffusion
In mathematics, a reversible diffusion is a specific example of a reversible stochastic process. Reversible diffusions have an elegant characterization due to the Russian mathematician Andrey Nikolaevich Kolmogorov. Kolmogorov's characterization of reversible diffusions Let ''B'' denote a ''d''-dimensional standard Brownian motion; let ''b'' : R''d'' → R''d'' be a Lipschitz continuous vector field. Let ''X'' : , +∞) × Ω → R''d'' be an Itō diffusion defined on a probability space (Ω, Σ, P) and solving the Itō stochastic differential equation \mathrm X_ = b(X_) \, \mathrm t + \mathrm B_ with square-integrable initial condition, i.e. ''X''0 ∈ ''L''2(Ω, Σ, P; R''d''). Then the following are equivalent: * The process ''X'' is reversible with stationary distribution ''μ'' on R''d''. * There exists a scalar potential Φ : R''d'' & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversible Process (thermodynamics)
In thermodynamics, a reversible process is a process, involving a system and its surroundings, whose direction can be reversed by infinitesimal changes in some properties of the surroundings, such as pressure or temperature. Throughout an entire reversible process, the system is in thermodynamic equilibrium, both physical and chemical, and ''nearly'' in pressure and temperature equilibrium with its surroundings. This prevents unbalanced forces and acceleration of moving system boundaries, which in turn avoids friction and other dissipation. To maintain equilibrium, reversible processes are extremely slow ( ''quasistatic''). The process must occur slowly enough that after some small change in a thermodynamic parameter, the physical processes in the system have enough time for the other parameters to self-adjust to match the new, changed parameter value. For example, if a container of water has sat in a room long enough to match the steady temperature of the surrounding air, for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversible Reaction
A reversible reaction is a reaction in which the conversion of reactants to products and the conversion of products to reactants occur simultaneously. : \mathit aA + \mathit bB \mathit cC + \mathit dD A and B can react to form C and D or, in the reverse reaction, C and D can react to form A and B. This is distinct from a reversible process in thermodynamics. Weak acids and bases undergo reversible reactions. For example, carbonic acid: : H2CO3 (l) + H2O(l) ⇌ HCO3−(aq) + H3O+(aq). The concentrations of reactants and products in an equilibrium mixture are determined by the analytical concentrations of the reagents (A and B or C and D) and the equilibrium constant, ''K''. The magnitude of the equilibrium constant depends on the Gibbs free energy change for the reaction. So, when the free energy change is large (more than about 30 kJ mol−1), the equilibrium constant is large (log K > 3) and the concentrations of the reactants at equilibrium are very small. Such a reac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversible Computing
Reversible computing is any model of computation where the computational process, to some extent, is time-reversible. In a model of computation that uses deterministic transitions from one state of the abstract machine to another, a necessary condition for reversibility is that the relation of the mapping from states to their successors must be one-to-one. Reversible computing is a form of unconventional computing. Due to the unitarity of quantum mechanics, quantum circuits are reversible, as long as they do not "collapse" the quantum states they operate on. Reversibility There are two major, closely related types of reversibility that are of particular interest for this purpose: physical reversibility and logical reversibility. A process is said to be ''physically reversible'' if it results in no increase in physical entropy; it is isentropic. There is a style of circuit design ideally exhibiting this property that is referred to as charge recovery logic, adiabatic circui ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversible Error
In United States law, a reversible error is an error of sufficient gravity to warrant reversal of a judgment on appeal. It is an error by the trier of law (judge), or the trier of fact (the jury, or the judge if it is a bench trial), or malfeasance by one of the trying attorneys, which results in an unfair trial. It is to be distinguished from harmless errors which do not rise to a level which brings the validity of the judgment into question and thus do not lead to a reversal upon appeal. Reversible error criteria A finding of reversible error requires that one or more of the appellant's "substantial rights" be affected, or the evidence in question be of such character as to have affected the outcome of the trial. (See e.g., Montana Petroleum Tank Release Compensation Bd. v. Crumley's, Inc.', 174 P.3d 948 (Mont. 2008).) The criteria for determining what constitutes a "substantial right" is somewhat vague however, being that it varies from case to case, each presenting a slight ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversible Garment
A reversible garment is a garment that can be worn two ways, which differ by turning the garment "inside out". However, there is no true " inside out" to a reversible garment, since either way, it gives a fashionable appearance. Garments that are commonly made reversible include hats, jackets, vests, sweaters, shirts, trousers, and skirts. Reversible garments have some features unlike other types of garments, such as thicker overall fabric (since two fabrics are often sewn together), buttons on both sides (in garments that have buttons), different types of stitching, and no tags. Some ancient shepherd A shepherd or sheepherder is a person who tends, herds, feeds, or guards flocks of sheep. ''Shepherd'' derives from Old English ''sceaphierde (''sceap'' 'sheep' + ''hierde'' 'herder'). ''Shepherding is one of the world's oldest occupations, i ...s had reversible garments, with a warm side that they would wear when the weather was cold, and a cool side when the weather was hot. D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Piaget's Theory Of Cognitive Development
Piaget's theory of cognitive development is a comprehensive theory about the nature and development of human intelligence. It was originated by the Swiss developmental psychologist Jean Piaget (1896–1980). The theory deals with the nature of knowledge itself and how humans gradually come to acquire, construct, and use it. Piaget's theory is mainly known as a developmental stage theory. In 1919, while working at the Alfred Binet Laboratory School in Paris, Piaget "was intrigued by the fact that children of different ages made different kinds of mistakes while solving problems". His experience and observations at the Alfred Binet Laboratory were the beginnings of his theory of cognitive development. He believed that children of different ages made different mistakes because of the “quality rather than quantity” of their intelligence. Piaget proposed four stages to describe the development process of children: sensorimotor stage, pre-operational stage, concrete operational st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
