First-order

First-order
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]


The Collaborative International Dictionary of English. 2000.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • First-order logic — is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less… …   Wikipedia

  • first order of business — UK US noun [C] (plural first orders of business) ► a situation or subject that must be dealt with before anything else: »When the financial situation gets difficult, the first order of business is to define your goals and your priorities …   Financial and business terms

  • first-order languages — first order language …   Philosophy dictionary

  • First-order hold — The first order hold (FOH) is a mathematical model of the practical reconstruction of sampled signals that could be done by a conventional digital to analog converter (DAC) and an analog circuit called an integrator. For the FOH, the signal is… …   Wikipedia

  • First-order control — In control theory, first order control is when a desired result is attempted by adjusting a scalar (first order) control. Such mechanisms, where first order change successfully produces desired results, are called first order mechanisms . First… …   Wikipedia

  • First-order reduction — A first order reduction is a very weak type of reduction between two computational problems in computational complexity theory. A first order reduction is a reduction where each component is restricted to be in the class FO of problems calculable …   Wikipedia

  • First order partial differential equation — In mathematics, a first order partial differential equation is a partial differential equation that involves only first derivatives of the unknown function of n variables. The equation takes the form: F(x 1,ldots,x n,u,u {x 1},ldots u {x n}) =0 …   Wikipedia

  • First-order predicate — A first order predicate (also called a monad) is a predicate that takes only individual(s) constants or variables as argument(s). Compare second order predicate and higher order predicate. ee also*First order predicate calculus *Monadic predicate …   Wikipedia

  • First-order elections — The term first order elections is used by political scientists to the relative importance of certain elections. First order elections are those that are the most important in a nation. In most democracies these are the national parliamentary… …   Wikipedia

  • first-order phase change — pirmosios rūšies fazinis virsmas statusas T sritis fizika atitikmenys: angl. first order phase change; first order phase transition; phase transform of the first kind vok. Phasenumwandlung erster Ordnung, f rus. фазовое превращение первого рода,… …   Fizikos terminų žodynas

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”