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The limiting reagent (or limiting reactant or limiting agent) in a chemical reaction is a reactant that is totally consumed when the chemical reaction is completed. [1][2] The amount of product formed is limited by this reagent, since the reaction cannot continue without it. If one or more other reagents are present in excess of the quantities ...
Stoichiometry. A stoichiometric diagram of the combustion reaction of methane. Stoichiometry (/ ˌstɔɪkiˈɒmɪtri /) is the relationship between the weights of reactants and products before, during, and following chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equals the ...
Double operator integral. In functional analysis, double operator integrals (DOI) are integrals of the form. where is a bounded linear operator between two separable Hilbert spaces , are two spectral measures, where stands for the set of orthogonal projections over , and is a scalar-valued measurable function called the symbol of the DOI.
In mathematical analysis, Fubini's theorem characterizes the conditions under which it is possible to compute a double integral by using an iterated integral. It was introduced by Guido Fubini in 1907. The theorem states that if a function is Lebesgue integrable on a rectangle , then one can evaluate the double integral as an iterated integral ...
In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in (the real-number plane) are called double integrals, and integrals of a function of three variables over a region ...
Wallis's integrals can be evaluated by using Euler integrals: Euler integral of the first kind: the Beta function: for Re (x), Re (y) > 0. Euler integral of the second kind: the Gamma function: for Re (z) > 0. If we make the following substitution inside the Beta function: we obtain:
Lebesgue–Stieltjes integrals, named for Henri Leon Lebesgue and Thomas Joannes Stieltjes, are also known as Lebesgue–Radon integrals or just Radon integrals, after Johann Radon, to whom much of the theory is due. They find common application in probability and stochastic processes, and in certain branches of analysis including potential theory.
Rate-determining step. In chemical kinetics, the overall rate of a reaction is often approximately determined by the slowest step, known as the rate-determining step (RDS or RD-step[1] or r/d step[2][3]) or rate-limiting step. For a given reaction mechanism, the prediction of the corresponding rate equation (for comparison with the experimental ...