Weakly dissipative semilinear equations of viscoelasticity by Conti M., Pata V.

By Conti M., Pata V.

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If the point c in the domain of f is not a limit point of the domain, then this condition is vacuously true, since x cannot approach c through values not equal c. Thus, for example, every function whose domain is the set of all integers is continuous. We call a function continuous if and only if it is continuous at every point of its domain. More generally, we say that a function is continuous on some subset of its domain if it is continuous at every point of that subset. The notation C(Ω) or C0(Ω) is sometimes used to denote the set of all continuous functions with domain Ω.

Hypergeometric series became an intricate theory, in need of later conceptual arrangement. Lie groups, and in particular their representation theory, explain what a spherical function can be in general; from 1950 onwards substantial parts of classical theory could be recast in terms of Lie groups. Further, work on algebraic combinatorics also revived interest in older parts of the theory. Conjectures of Ian G. Macdonald helped to open up large and active new fields with the typical special function flavour.

Such a function is called non-injective or information-losing. Notice that neither the square root nor the principal square root function is the inverse of x2 because the first is not single-valued, and the second returns -x when x is negative. If the domain and codomain are both the non-negative numbers, or if the domain is the negative numbers, then the function is invertible (by the principal square root) and injective. Inverses in higher mathematics The definition given above is commonly adopted in calculus.

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