“stability”的概念、定义、翻译、参考文献-科学参考

stability

Computer

A multidiscipline term with a variety of (related) meanings. In numerical analysis it is used with what appears to be a bewildering array of possible prefixes. There are, however, two important basic usages.
Given a well-defined numerical procedure it is important that roundoff errors do not seriously influence the accuracy of the results. This is referred to as numerical stability and depends on the error propagation properties of the procedure.
Discretization methods for the solution of integral and differential equations are based on a subdivision of the region in which the solution is required. Stability here means that perturbations in the data (initial or boundary conditions) have a bounded effect on the solution obtained (ignoring roundoff error) for a given subdivision. The existence of a uniform bound on this effect over all sufficiently fine subdivisions is a necessary condition for the convergence of the method as the subdivision is refined.
In the solution of ordinary differential equations much of the stability theory has been developed in the study of stiff systems of equations. Of great importance to this development was the concept of A-stability introduced by Dahlquist in 1963. A method is A-stable if it produces bounded solutions for the test problem
$y' = q y, y (0) = 1, Re (q) < 0$
for all stepsizes. The trapezoidal rule (see ordinary differential equations) is an example of an A-stable method. Much of the later theory has investigated similar properties for more general test problems.

Electronics and Electrical Engineering

A property of a control system that characterizes how it responds to changes in its inputs or other environmental disturbances, as well as the long-term behaviour of any feedback loops it may contain. A system is stable if any finite input change or disturbance only results in a finite change in output, and any feedback loops do not lead to oscillations or a continually growing output. There are various mathematical techniques for analysing the stability of a system, such as Laplace transforms (see s-domain circuit analysis) and Nyquist plots.

Logic

1. In intuitionistic logic, a property that holds of a formula $φ$ with respect to a theory $T$ precisely when $T ⊢ \neg\neg φ \to φ$ , where $\to$ and $\neg$ are the intuitionistic conditional and negation connectives, respectively.
2. In the field of proof-theoretic semantics, a property holding of a deductive system when for every logical connective, every inference derivable from the grounds under which a connective is introduced remain derivable once the connective has been introduced. This property is essentially the converse of the property of harmony. In some cases, ‘stability’ is defined as the conjunction of harmony with its converse, so that stability of a proof theory is that its introduction and elimination rules can be ‘read off’ one another. Stability of a logical calculus was seen by philosopher Michael Dummett as a necessary condition for the introduction and elimination rules to confer meaning to the logical connectives.

Geology and Earth Sciences

1. Atmospheric condition in which air that is forced to rise tends to return to its pre-existing level in the absence of the uplifting force. If the adiabatic lapse rate of uplifted air is greater than the environmental lapse rate, then the vertically displaced air will become colder than the surrounding air and as its density increases it will tend to sink back. See also instability.
2. In engineering, the resistance of a structure to collapse or sliding, dependent upon the shearing strength of the material.
3. In geochemistry, the state of equilibrium towards which a system will move from any other state under the same conditions.
4. In thermodynamics, the condition when a slight disturbance of temperature, pressure, or composition does not result in the appearance of a new phase.

Geography

The state of a parcel of air which, if displaced vertically, will return to its original position. Thus, if a parcel of air cools more on rising than the air which surrounds it, it becomes denser than its surroundings and therefore sinks. The atmosphere is absolutely stable when the environmental lapse rate is less than both the dry and saturated adiabatic lapse rates. Atmospheric stability is reinforced by inversions. See Peppier (1988) SWS Miscellaneous Publication 104.

单词	stability
释义	stability Computer A multidiscipline term with a variety of (related) meanings. In numerical analysis it is used with what appears to be a bewildering array of possible prefixes. There are, however, two important basic usages. Given a well-defined numerical procedure it is important that roundoff errors do not seriously influence the accuracy of the results. This is referred to as numerical stability and depends on the error propagation properties of the procedure. Discretization methods for the solution of integral and differential equations are based on a subdivision of the region in which the solution is required. Stability here means that perturbations in the data (initial or boundary conditions) have a bounded effect on the solution obtained (ignoring roundoff error) for a given subdivision. The existence of a uniform bound on this effect over all sufficiently fine subdivisions is a necessary condition for the convergence of the method as the subdivision is refined. In the solution of ordinary differential equations much of the stability theory has been developed in the study of stiff systems of equations. Of great importance to this development was the concept of A-stability introduced by Dahlquist in 1963. A method is A-stable if it produces bounded solutions for the test problem $y' = q y, y (0) = 1, Re (q) < 0$ for all stepsizes. The trapezoidal rule (see ordinary differential equations) is an example of an A-stable method. Much of the later theory has investigated similar properties for more general test problems. Electronics and Electrical Engineering A property of a control system that characterizes how it responds to changes in its inputs or other environmental disturbances, as well as the long-term behaviour of any feedback loops it may contain. A system is stable if any finite input change or disturbance only results in a finite change in output, and any feedback loops do not lead to oscillations or a continually growing output. There are various mathematical techniques for analysing the stability of a system, such as Laplace transforms (see s-domain circuit analysis) and Nyquist plots. Logic 1. In intuitionistic logic, a property that holds of a formula $φ$ with respect to a theory $T$ precisely when $T ⊢ \neg\neg φ \to φ$ , where $\to$ and $\neg$ are the intuitionistic conditional and negation connectives, respectively. 2. In the field of proof-theoretic semantics, a property holding of a deductive system when for every logical connective, every inference derivable from the grounds under which a connective is introduced remain derivable once the connective has been introduced. This property is essentially the converse of the property of harmony. In some cases, ‘stability’ is defined as the conjunction of harmony with its converse, so that stability of a proof theory is that its introduction and elimination rules can be ‘read off’ one another. Stability of a logical calculus was seen by philosopher Michael Dummett as a necessary condition for the introduction and elimination rules to confer meaning to the logical connectives. Geology and Earth Sciences 1. Atmospheric condition in which air that is forced to rise tends to return to its pre-existing level in the absence of the uplifting force. If the adiabatic lapse rate of uplifted air is greater than the environmental lapse rate, then the vertically displaced air will become colder than the surrounding air and as its density increases it will tend to sink back. See also instability. 2. In engineering, the resistance of a structure to collapse or sliding, dependent upon the shearing strength of the material. 3. In geochemistry, the state of equilibrium towards which a system will move from any other state under the same conditions. 4. In thermodynamics, the condition when a slight disturbance of temperature, pressure, or composition does not result in the appearance of a new phase. Geography The state of a parcel of air which, if displaced vertically, will return to its original position. Thus, if a parcel of air cools more on rising than the air which surrounds it, it becomes denser than its surroundings and therefore sinks. The atmosphere is absolutely stable when the environmental lapse rate is less than both the dry and saturated adiabatic lapse rates. Atmospheric stability is reinforced by inversions. See Peppier (1988) SWS Miscellaneous Publication 104.
随便看	brackets Brackett series bract bracteole Bradford, William (1590–1657) Bradlaugh, Charles (1833–91) Bradley, Francis Herbert (1846–1924) Bradley, James Bradley, James (1693–1762) Bradley, Omar Nelson (1893–1981) Bradley, Ralph Allen (1923–2001) Bradley–Terry model Bradwardine, Thomas (c.1300–49) bradycardia Brady, Charles, Jr (1951–2006) bradykinin bradymetabolism Brady Plan bradyseism bradytelic evolution Braganza Bragg crystal spectrometer Bragg equation Bragg peak Bragg, Sir William Henry