| slovo | definícia |
First-order
(gcide) | First-order \First`-or"der\, a.
decaying at an exponential rate; -- a mathematical concept
applied to various types of decay, such as radioactivity and
chemical reactions.
Note: In first order decay, the amount of material decaying
in a given period of time is directly proportional to
the amount of material remaining. This may be expressed
by the differential equation: dA/dt = -kt where dA/dt
is the rate per unit time at which the quantity (or
concentration) of material (expressed as A) is
increasing, t is the time, and k is a constant. The
minus sign in front of the "kt" assures that the amount
of material remaining will be decreasing as time
progresses. A solution of the differential equation to
give the quantity A shows that: A = e^-kt where e is
the base for natural logarithms. Thus this type of
decay is called exponential decay. In certain chemical
reactions that are in fact second-order, involving two
reactants, the conditions may be chosen in some cases
so that one reactant is vastly in excess of the other,
and its concentration changes very little in the course
of the reaction, so that the reaction rate will be
approximately first order in the more dilute reactant;
such reactions are called pseudo first order.
[PJC] |
first-order
(foldoc) | first-order
Not higher-order.
(1995-03-06)
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| | podobné slovo | definícia |
first-order correlation
(encz) | first-order correlation, n: |
first-order logic
(encz) | first-order logic,predikátová logika prvního řádu [mat.] metan |
First-order
(gcide) | First-order \First`-or"der\, a.
decaying at an exponential rate; -- a mathematical concept
applied to various types of decay, such as radioactivity and
chemical reactions.
Note: In first order decay, the amount of material decaying
in a given period of time is directly proportional to
the amount of material remaining. This may be expressed
by the differential equation: dA/dt = -kt where dA/dt
is the rate per unit time at which the quantity (or
concentration) of material (expressed as A) is
increasing, t is the time, and k is a constant. The
minus sign in front of the "kt" assures that the amount
of material remaining will be decreasing as time
progresses. A solution of the differential equation to
give the quantity A shows that: A = e^-kt where e is
the base for natural logarithms. Thus this type of
decay is called exponential decay. In certain chemical
reactions that are in fact second-order, involving two
reactants, the conditions may be chosen in some cases
so that one reactant is vastly in excess of the other,
and its concentration changes very little in the course
of the reaction, so that the reaction rate will be
approximately first order in the more dilute reactant;
such reactions are called pseudo first order.
[PJC] |
first-order correlation
(wn) | first-order correlation
n 1: a partial correlation in which the effects of only one
variable are removed (held constant) |
first-order logic
(foldoc) | first-order logic
The language describing the truth of
mathematical formulas. Formulas describe properties of
terms and have a truth value. The following are atomic
formulas:
True
False
p(t1,..tn) where t1,..,tn are terms and p is a predicate.
If F1, F2 and F3 are formulas and v is a variable then the
following are compound formulas:
F1 ^ F2 conjunction - true if both F1 and F2 are true,
F1 V F2 disjunction - true if either or both are true,
F1 => F2 implication - true if F1 is false or F2 is
true, F1 is the antecedent, F2 is the
consequent (sometimes written with a thin
arrow),
F1 p). Second-order logic can quantify over functions on
propositions, and higher-order logic can quantify over any
type of entity. The sets over which quantifiers operate are
usually implicit but can be deduced from well-formedness
constraints.
In first-order logic quantifiers always range over ALL the
elements of the domain of discourse. By contrast,
second-order logic allows one to quantify over subsets.
["The Realm of First-Order Logic", Jon Barwise, Handbook of
Mathematical Logic (Barwise, ed., North Holland, NYC, 1977)].
(2005-12-27)
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