Gonzalez, Ivan Jiu, Lin Moll, Victor H.
Published in
Open Mathematics

The method of brackets, developed in the context of evaluation of integrals coming from Feynman diagrams, is a procedure to evaluate definite integrals over the half-line. This method consists of a small number of operational rules devoted to convert the integral into a bracket series. A second small set of rules evaluates this bracket series and p...

Zhou, Duan-Mei Vu, Hong-Quang
Published in
Open Mathematics

Let A be a square matrix satisfying A 4 = A {A}^{4}=A . We solve the Yang-Baxter-like matrix equation A X A = X A X AXA=XAX to find some solutions, based on analysis of the characteristic polynomial of A and its eigenvalues. We divide the problem into small cases so that we can find the solution easily. Finally, in order to illustrate the results, ...

Feng, Yibin Zhou, Yanping
Published in
Open Mathematics

In this article, the general (p,q)-mixed projection bodies are introduced. Then, some basic properties of the general (p,q)-mixed projection bodies are discussed, and the extreme values of volumes of the general (p,q)-mixed projection bodies and their polar bodies are established.

Wang, Huiwen Li, Fang
Published in
Open Mathematics

In this article, we discuss the nonlinear boundary value problems involving both left Riemann-Liouville and right Caputo-type fractional derivatives. By using some new techniques and properties of the Mittag-Leffler functions, we introduce a formula of the solutions for the aforementioned problems, which can be regarded as a novelty item. Moreover,...

Zhang, Yu Liu, Xinsheng Yu, Yuncai Hu, Hongchang
Published in
Open Mathematics

In this article, an errors-in-variables regression model in which the errors are negatively superadditive dependent (NSD) random variables is studied. First, the Marcinkiewicz-type strong law of large numbers for NSD random variables is established. Then, we use the strong law of large numbers to investigate the asymptotic normality of least square...

Wang, Zhongbi Qin, Chao Lv, Heng Yan, Yanxiong Chen, Guiyun
Published in
Open Mathematics

For a positive integer n and a prime p, let n p {n}_{p} denote the p-part of n. Let G be a group, cd ( G ) \text{cd}(G) the set of all irreducible character degrees of G G , ρ ( G ) \rho (G) the set of all prime divisors of integers in cd ( G ) \text{cd}(G) , V ( G ) = p e p ( G ) | p ∈ ρ ( G ) V(G)=\left\{{p}^{{e}_{p}(G)}|p\in \rho (G)\right\} , w...

Kong, Liang Zhang, Jianhua
Published in
Open Mathematics

In this article, we give a sufficient and necessary condition for every Jordan {g,h}-derivation to be a {g,h}-derivation on triangular algebras. As an application, we prove that every Jordan {g,h}-derivation on τ ( N ) \tau ({\mathscr{N}}) is a {g,h}-derivation if and only if dim 0 + ≠ 1 \dim {0}_{+}\ne 1 or dim H − ⊥ ≠ 1 \dim {H}_{-}^{\perp }\ne 1...

Katz, Mikhail G. Nowik, Tahl
Published in
Open Mathematics

The first paper in systolic geometry was published by Loewner’s student P. M. Pu over half a century ago. Pu proved an inequality relating the systole and the area of an arbitrary metric in the real projective plane. We prove a stronger version of Pu’s systolic inequality with a remainder term.

Ekinci, Gülnaz Boruzanlı Bujtás, Csilla
Published in
Open Mathematics

Let k k be a positive integer and let G G be a graph with vertex set V ( G ) V(G) . A subset D ⊆ V ( G ) D\subseteq V(G) is a k k -dominating set if every vertex outside D D is adjacent to at least k k vertices in D D . The k k -domination number γ k ( G ) {\gamma }_{k}(G) is the minimum cardinality of a k k -dominating set in G G . For any graph G...

Kedim, Imed Berzig, Maher Ajmi, Ahdi Noomen
Published in
Open Mathematics

Consider an ordered Banach space and f , g f,g two self-operators defined on the interior of its positive cone. In this article, we prove that the equation f ( X ) = g ( X ) f(X)=g(X) has a positive solution, whenever f is strictly α \alpha -concave g-monotone or strictly ( − α ) (-\alpha ) -convex g-antitone with g super-homogeneous and surjective...