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Graded sets, points and numbers.

José A. Herencia (1998)

Mathware and Soft Computing

The basic tool considered in this paper is the so-called graded set, defined on the analogy of the family of α-cuts of a fuzzy set. It is also considered the corresponding extensions of the concepts of a point and of a real number (again on the analogy of the fuzzy case). These new graded concepts avoid the disadvantages pointed out by Gerla (for the fuzzy points) and by Kaleva and Seikkala (for the convergence of sequences of fuzzy numbers).

Green's theorem from the viewpoint of applications

Alexander Ženíšek (1999)

Applications of Mathematics

Making use of a line integral defined without use of the partition of unity, Green’s theorem is proved in the case of two-dimensional domains with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces W 1 , p ( ) H 1 , p ( ) ( 1 p ...

Growth orders occurring in expansions of Hardy-field solutions of algebraic differential equations

John Shackell (1995)

Annales de l'institut Fourier

We consider the asymptotic growth of Hardy-field solutions of algebraic differential equations, e.g. solutions with no oscillatory component, and prove that no ‘sub-term’ occurring in a nested expansion of such can tend to zero more rapidly than a fixed rate depending on the order of the differential equation. We also consider series expansions. An example of the results obtained may be stated as follows.Let g be an element of a Hardy field which has an asymptotic series expansion in x , e x and λ ,...

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