Orientation-dependent distribution of the length of a random segment and covariogramJournal of Contemporary Mathematical Analysis - Tập 50 - Trang 90-97 - 2015
A. G. Gasparyan, V. K. Ohanyan
The paper considers a random segment L(ω) in R
n
with fixed direction and length that intersects a given bounded convex body D ⊂ R
n
. We obtain a relationship between the covariogram of D and the distribution of the random variable |L| — the length of L ∩ D. A relationship between the distributi...... hiện toàn bộ
On unbounded divergence sets of series in orthonormal basesJournal of Contemporary Mathematical Analysis - Tập 47 - Trang 234-239 - 2012
D. A. Karagulyan
In this paper we establish a number of theorems providing complete characterizations of divergence sets of general series in orthogonal bases with a localization property.
On the invertible algebras linear over an Abelian groupJournal of Contemporary Mathematical Analysis - Tập 48 - Trang 158-165 - 2013
S. S. Davidov
In this paper using the second order formula, namely the ∀∃(∀)-identities, we characterize some subclasses of the invertible algebras that are linear over an Abelian group and have restrictions on the use of the automorphisms of the corresponding group.
On characterization of extremal sets of differentiation of integrals in ℝ2Journal of Contemporary Mathematical Analysis - Tập 49 - Trang 334-351 - 2014
G. A. Karagulyan, D. A. Karagulyan
The paper considers a question of characterization of the sets of nondifferentiability points of integrals with respect to the bases of rectangles and squares. In particular, a complete characterization of uncertainty sets for the integrals of functions from L
p
(ℝ2), 1 ≤ p ≤ ∞, with respect to the basis of squares is obtained.
Covariogram of a cylinderJournal of Contemporary Mathematical Analysis - Tập 49 - Trang 366-375 - 2014
H. S. Harutyunyan, V. K. Ohanyan
In this paper we establish relationships between the covariogram and the orientation-dependent chord length distribution function of a cylinder and those of its base. Also, we obtain explicit expressions for the covariogram and the orientation-dependent chord length distribution function of a cylinder with cyclic, elliptical and triangular bases.