Noufaey, Khaled Al
Published in
Open Mathematics

This study provides semi-analytical solutions to the Selkov-Schnakenberg reaction-diffusion system. The Galerkin method is applied to approximate the system of partial differential equations by a system of ordinary differential equations. The steady states of the system and the limit cycle solutions are delineated using bifurcation diagram analysis...

Cabada, Alberto Dimitrov, Nikolay D.
Published in
Open Mathematics

In this paper, a third-order ordinary differential equation coupled to three-point boundary conditions is considered. The related Green’s function changes its sign on the square of definition. Despite this, we are able to deduce the existence of positive and increasing functions on the whole interval of definition, which are convex in a given subin...

Valiullin, Artur R. Valiullin, Albert R.
Published in
Open Mathematics

Greedy expansions with prescribed coefficients were introduced by V. N. Temlyakov in a general case of Banach spaces. In contrast to Fourier series expansions, in greedy expansions with prescribed coefficients, a sequence of coefficients { c n } n = 1 ∞ {\left\{{c}_{n}\right\}}_{n=1}^{\infty } is fixed in advance and does not depend on an expanded ...

Bobkov, Vladimir Tanaka, Mieko
Published in
Open Mathematics

We obtain a generalization of the Picone inequality which, in combination with the classical Picone inequality, appears to be useful for problems with the ( p , q ) (p,q) -Laplace-type operators. With its help, as well as with the help of several other known generalized Picone inequalities, we provide some nontrivial facts on the existence and none...

Han, Yongjie Xiao, Hanyue Chen, Guanggui
Published in
Open Mathematics

In this paper, we define the entropy number in probabilistic setting and determine the exact order of entropy number of finite-dimensional space in probabilistic setting. Moreover, we also estimate the sharp order of entropy number of univariate Sobolev space in probabilistic setting by discretization method.

Badawi, Ayman Rissner, Roswitha
Published in
Open Mathematics

For a partially ordered set ( A , ≤ ) (A,\le ) , let G A {G}_{A} be the simple, undirected graph with vertex set A such that two vertices a ≠ b ∈ A a\ne b\in A are adjacent if either a ≤ b a\le b or b ≤ a b\le a . We call G A {G}_{A} the partial order graph or comparability graph of A. Furthermore, we say that a graph G is a partial order graph if ...

Xiao, Lei Lu, Guoxiang
Published in
Open Mathematics

In this paper, we present a new refinement of Jensen’s inequality with applications in information theory. The refinement of Jensen’s inequality is obtained based on the general functional in the work of Popescu et al. As the applications in information theory, we provide new tighter bounds for Shannon’s entropy and some f-divergences.

Kim, Ju Myung
Published in
Open Mathematics

For a finitely generated tensor norm α \alpha , we investigate the α \alpha -approximation property ( α \alpha -AP) and the bounded α \alpha -approximation property (bounded α \alpha -AP) in terms of some approximation properties of operator ideals. We prove that a Banach space X has the λ \lambda -bounded α p , q {\alpha }_{p,q} -AP ( 1 ≤ p , q ≤ ...

Yu, Xue Lou, Ben Gong
Published in
Open Mathematics

A map is called edge-regular if it is edge-transitive but not arc-transitive. In this paper, we show that a complete graph K n {K}_{n} has an orientable edge-regular embedding if and only if n = p d > 3 n={p}^{d}\gt 3 with p an odd prime such that p d ≡ 3 {p}^{d}\equiv 3 ( mod 4 ) (\mathrm{mod}\hspace{.25em}4) . Furthermore, K p d {K}_{{p}^{d}} has...

Altwaijry, Najla Garayev, Mubariz Guediri, Hocine Baazeem, Amani
Published in
Open Mathematics

We characterize skew-symmetric operators on a reproducing kernel Hilbert space in terms of their Berezin symbols. The solution of some operator equations with skew-symmetric operators is studied in terms of Berezin symbols. We also studied essentially unitary operators via Berezin symbols.