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A Symbolic Test-Function for Describing Electromagnetic Interaction

100%
Toma C.
Waves, Wavelets and Fractals
|
2016
|
tom 2
|
nr 1
EN
This paper presents a symbolic test-function defined on a restricted interval for describing the electromagnetic interaction. An exponential function with the exponent represented by the inverse of a differential operator is put in correspondence with a test function defined on a restricted interval. The lateral limits of this function at the edge of this interval are either zero (when the variable is considered in closer proximity inside this interval) or infinity (when the variable is considered in closer proximity outside this interval). By substituting with a differential operator these edges (stable points) can be put in correspondence with the wave function of charged particles. In a similar manner, the maximum of this function (an unstable point) can be put in correspondence with an electromagnetic propagating wave. As a consequence, the electromagnetic interaction can be described by particles with eigenvalues of differential operators confined within a restricted interval (similar to wavelets presenting a non-zero amplitude on limited space-time intervals).
2
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Successive derivatives and finite expansions involving the H-function of one and more variables

75%
Joshi C., Joshi N.
Annales Polonici Mathematici
|
1997
|
tom 67
|
nr 1
15-29
EN
Certain results including the successive derivatives of the H-function of one and more variables are established. These remove the limitations of Ławrynowicz's (1969) formulas and as a result extend the results of Skibiński [13] and various other authors. As an application some finite expansion formulas are also established, which reduce to hypergeometric functions of one and more variables that are of common interest.
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