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After this step we can proceed with the decomposition, measuring the quantity of O 2 that is produced over time because the only form to obtain O 2 is with the N 2 O 5 decomposition. The equation below refers to the decomposition of N 2 O 5 in CCl 4: 2 N 2 O 5 → 4 NO 2 + O 2 (g) And this reaction follows the first order rate law that says:
For a typical second-order reaction with rate equation = [] [], if the concentration of reactant B is constant then = [] [] = ′ [], where the pseudo–first-order rate constant ′ = []. The second-order rate equation has been reduced to a pseudo–first-order rate equation, which makes the treatment to obtain an integrated rate equation much ...
, which is often written as , [5] represents the limiting rate approached by the system at saturating substrate concentration for a given enzyme concentration. The Michaelis constant K m {\displaystyle K_{\mathrm {m} }} is defined as the concentration of substrate at which the reaction rate is half of V {\displaystyle V} . [ 6 ]
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 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.
First-order means that only the first derivative of y appears in the equation, and higher derivatives are absent. Without loss of generality to higher-order systems, we restrict ourselves to first-order differential equations, because a higher-order ODE can be converted into a larger system of first-order equations by introducing extra variables.
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 Verlet method is the second-order integrator with = and coefficients =, =, = =. Since c 1 = 0 {\displaystyle c_{1}=0} , the algorithm above is symmetric in time. There are 3 steps to the algorithm, and step 1 and 3 are exactly the same, so the positive time version can be used for negative time.