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Reduction of order (or d’Alembert reduction) is a technique in mathematics for solving second-order linear ordinary differential equations. It is employed when one solution is known and a second linearly independent solution is desired. The method also applies to n -th order equations. In this case the ansatz will yield an (n −1)-th order ...
Model order reduction. Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling, with applications in all areas of mathematical modelling.
Second-order logic. In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. [1] Second-order logic is in turn extended by higher-order logic and type theory. First-order logic quantifies only variables that range over individuals (elements of the domain of discourse ...
In the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences of mathematical logic. There are several variations in the types of logical operation that can be used in these sentences. The first-order logic of graphs concerns sentences in which the ...
e. In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown (s) consists of one (or more) function (s) and involves the derivatives of those functions. [1] The term "ordinary" is used in contrast with partial differential equations ...
Formal definitions. Formally, a binary relation (→) on the set of terms is called a rewrite relation if it is closed under contextual embedding and under instantiation; formally: if l → r implies u [ l σ] p → u [ r σ] p for all terms l, r, u, each path p of u, and each substitution σ. If (→) is also irreflexive and transitive, then ...
Convergence rate definitions. Suppose that the sequence converges to the number . The sequence is said to converge with order to , and with a rate of convergence , if. for some positive constant if and if . [2][4][5] It is not necessary that be an integer. For example, the secant method, when converging to a regular, simple root, has an order ...
A measure of disorder in the universe or of the unavailability of the energy in a system to do work. [7] Entropy and disorder also have associations with equilibrium. [8] Technically, entropy, from this perspective, is defined as a thermodynamic property which serves as a measure of how close a system is to equilibrium—that is, to perfect ...