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The first-order functions that are provably total in second-order arithmetic are precisely the same as those representable in system F. [4] Almost equivalently, system F is the theory of functionals corresponding to second-order arithmetic in a manner parallel to how Gödel's system T corresponds to first-order arithmetic in the Dialectica ...
Second order approximation, an approximation that includes quadratic terms; Second-order arithmetic, an axiomatization allowing quantification of sets of numbers; Second-order differential equation, a differential equation in which the highest derivative is the second; Second-order logic, an extension of predicate logic
The second-order logic without these restrictions is sometimes called full second-order logic to distinguish it from the monadic version. Monadic second-order logic is particularly used in the context of Courcelle's theorem, an algorithmic meta-theorem in graph theory. The MSO theory of the complete infinite binary tree is decidable.
A typical step response for a second order system, illustrating overshoot, followed by ringing, all subsiding within a settling time.. The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions.
Numerov's method (also called Cowell's method) is a numerical method to solve ordinary differential equations of second order in which the first-order term does not appear. It is a fourth-order linear multistep method. The method is implicit, but can be made explicit if the differential equation is linear.
In signal processing, a digital biquad filter is a second order recursive linear filter, containing two poles and two zeros. "Biquad" is an abbreviation of "biquadratic", which refers to the fact that in the Z domain, its transfer function is the ratio of two quadratic functions:
In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification over sets. [1] It is particularly important in the logic of graphs , because of Courcelle's theorem , which provides algorithms for evaluating monadic second-order formulas over graphs ...
The higher-order counterparts of the major subsystems of second-order arithmetic generally prove the same second-order sentences (or a large subset) as the original second-order systems. [5] For instance, the base theory of higher-order reverse mathematics, called RCA ω 0, proves the same sentences as RCA 0, up to language.