In this paper we introduce and investigate the notion of half cyclically ordered group generalizing the notion of half partially ordered group whose study was begun by Giraudet and Lucas.
In this paper we study Beurling type distributions in the Hankel setting. We consider the space ${\mathcal E}(w)^{\prime }$ of Beurling type distributions on $(0, \infty )$ having upper bounded support. The Hankel transform and the Hankel convolution are studied on the space ${\mathcal E}(w)^{\prime }$. We also establish Paley Wiener type theorems for Hankel transformations of distributions in ${\mathcal E}(w)^{\prime }$.
Some $q$-analysis variants of Hardy type inequalities of the form $$ \int _0^b \bigg (x^{\alpha -1} \int _0^x t^{-\alpha } f(t) {\rm d}_q t \bigg )^{p} {\rm d}_q x \leq C \int _0^b f^p(t) {\rm d}_q t $$ with sharp constant $C$ are proved and discussed. A similar result with the Riemann-Liouville operator involved is also proved. Finally, it is pointed out that by using these techniques we can also obtain some new discrete Hardy and Copson type inequalities in the classical case.
This paper shows that some characterizations of the harmonic majorization of the Martin function for domains having smooth boundaries also hold for cones.
In this paper, we improve the result by Harper on the lower bound of the bandwidth of connected graphs. In addition, we prove that considerating the interior boundary and the exterior boundary when estimating the bandwidth of connected graphs gives the same results.
We use the general Riemann approach to define the Stratonovich integral with respect to Brownian motion. Our new definition of Stratonovich integral encompass the classical Stratonovich integral and more importantly, satisfies the ideal Itô formula without the ''tail'' term, that is, f(Wt) = f(W0) + ∫ t 0 f ′ (Ws) ◦ dWs. Further, the condition on the integrands in this paper is weaker than the classical one.
In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite matrix polynomials is proposed.
Positioned eco-grammar systems (PEG systems, for short) were introduced in our previous papers. In this paper we engage in a new field of research, the hierarchy of PEG systems, namely in the hierarchy of the PEG systems according to the number of agents presented in the environment and according to the number of types of agents in the system.