On the zeros of generalized axially symmetric potentials

On the Domain of Regularity of Generalized Axially Symmetric Potentials

which depends analytically on the two real variables x and y in a domain containing a segment of the singular line y — 0, is uniquely determined by its values on y = 0. In this note we shall consider the following problem: If the function g(z) =u(z, 0) is continued to complex values of z, to what extent does its domain of regularity determine the domain of regularity of u(x, y)? A partial answe...

A double layer potentials for generalized bi-axially symmetric equation

were constructed in R 2 = {(x, y) : x > 0, y > 0} . In the present paper (in case of λ = 0) using the constructed fundamental solutions, a double layer potentials are defined and investigated. Limiting theorems are proved, and integral equations concerning a denseness of potentials of a double layer are found. MSC: Primary 35J15, 35J70.

Generalized Axially Symmetric Potential Theory

Devendra Kumar APPROXIMATION OF GROWTH NUMBERS OF GENERALIZED BI - AXIALLY SYMMETRIC POTENTIALS

The paper deals with growth and approximation of solutions (not necessarily entire) of certain elliptic partial differential equations. These solutions are called Generalized Bi-Axially Symmetric Potentials (GBASP′s). The GBASP′s are taken to be regular in a finite hyperball and influence of the growth of their maximum moduli on the rate of decay of their approximation errors in sup norm is stu...

Chaos in axially symmetric potentials with octupole deformation.

Classical and quantum mechanical results are reported for the single particle motion in a harmonic oscillator potential which is characterized by a quadrupole deformation and an additional octupole deformation. The chaotic character of the motion is strongly dependent on the quadrupole deformation in that for a prolate deformation virtually no chaos is discernible while for the oblate case the ...