Journal of Contemporary Mathematical Analysis
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Orientation-dependent distribution of the length of a random segment and covariogram
Journal of Contemporary Mathematical Analysis - Tập 50 - Trang 90-97 - 2015
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 distribution of |L| and the
orientation-dependent chord length distribution is also obtained. As a
consequence, w...
Uniqueness of series with respect to general Franklin systems
Journal of Contemporary Mathematical Analysis - Tập 44 Số 5 - Trang 271-283 - 2009
Fine properties of functions from Hajłasz–Sobolev classes M α p , p > 0, II. Lusin’s approximation
Journal of Contemporary Mathematical Analysis - Tập 52 - Trang 30-37 - 2017
The present paper is devoted to the Lusin’s approximation of functions from
Hajłasz–Sobolev classes M (X) for p > 0. It is proved that for any f ∈ M (X) and
any ε > 0 there exist an open set O ε ⊂ X with measure less than ε (as a measure
can be taken the corresponding capacity or Hausdorff content) and an
approximating function f ε such that f = f ε on X O ε . Moreover, the correcting
function f ε...
On unbounded divergence sets of series in orthonormal bases
Journal of Contemporary Mathematical Analysis - Tập 47 - Trang 234-239 - 2012
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.
Nonlinear approximation by renormalized trigonometric system
Journal of Contemporary Mathematical Analysis - - 2012
On the invertible algebras linear over an Abelian group
Journal of Contemporary Mathematical Analysis - Tập 48 - Trang 158-165 - 2013
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 ℝ2
Journal of Contemporary Mathematical Analysis - Tập 49 - Trang 334-351 - 2014
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.
Summability of multiple trigonometric Fourier series by linear methods
Journal of Contemporary Mathematical Analysis - - 2012
Covariogram of a cylinder
Journal of Contemporary Mathematical Analysis - Tập 49 - Trang 366-375 - 2014
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.
New Integral Representations for the Fox–Wright Functions and Its Applications II
Journal of Contemporary Mathematical Analysis - Tập 56 - Trang 37-45 - 2021
In this paper our aim is to establish new integral representations for the
Fox–Wright function
$${}_{p}\Psi_{q}[^{(\alpha_{p},A_{p})}_{(\beta_{q},B_{q})}|z]$$ when
$$\mu=\sum_{j=1}^{q}\beta_{j}-\sum_{k=1}^{p}\alpha_{k}+\frac{p-q}{2}=-m,\;\;m\in\mathbb{N}_{0}.$$
In particular, closed-form integral expressions are derived for the four
parameter Wright function under a special restriction on paramete...
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