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A Dynkin system (or λ-system) is a collection of subsets of that contains and is closed under complement and under countable unions of disjoint subsets. Dynkin's π-λ theorem says, if P {\displaystyle P} is a π-system and D {\displaystyle D} is a Dynkin system that contains P , {\displaystyle P,} then the σ-algebra σ ( P ) {\displaystyle ...
In physics, a sigma model is a field theory that describes the field as a point particle confined to move on a fixed manifold. This manifold can be taken to be any Riemannian manifold , although it is most commonly taken to be either a Lie group or a symmetric space .
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics , science , and engineering for representing complex concepts and properties in a concise ...
Series are represented by an expression like + + +, or, using capital-sigma summation notation, [8] =. The infinite sequence of additions expressed by a series cannot be explicitly performed in sequence in a finite amount of time.
In mathematics, a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. The set of the solutions of such a system is a differential algebraic variety , and corresponds to an ideal in a differential algebra of differential ...
Two linear systems using the same set of variables are equivalent if each of the equations in the second system can be derived algebraically from the equations in the first system, and vice versa. Two systems are equivalent if either both are inconsistent or each equation of each of them is a linear combination of the equations of the other one.
In quantum field theory, a nonlinear σ model describes a field Σ which takes on values in a nonlinear manifold called the target manifold T.The non-linear σ-model was introduced by Gell-Mann & Lévy (1960, section 6), who named it after a field corresponding to a spinless meson called σ in their model. [1]