Masharov P. The extremum problems on Pompeiu sets

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0405U003585

Thesis Registration Form

0405U003585.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

21-09-2005

Specialized Academic Board

К 11.193.02

Essay

The dissertation is devoted to finding the infimum R(A) of balls radii (or circles radii in R2) B, in which then given set is the Pompeiu set in B, and to investigation of question is A be the Pompeiu set in the ball B with radius R=R(A). The R(A) has been found when A is the circular sector, Reuleaux triangle, wide range of circular segments, lunes, and cylinders in R3. For the other cases of lust sets the estimates of R(A), which improve the well-known estimates, has been found. For Reuleaux triangle, wide range of sectors and segments the second problem is solved.

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