Among the many characterizations of the class of Baire one, Darboux real-valued functions of one real variable, the 1907 characterization of Young and the 1997 characterization of Agronsky, Ceder, and Pearson are particularly intriguing in that they yield interesting classes of functions when interpreted in the two-variable setting. We examine the relationship between these two subclasses of the real-valued Baire one defined on the unit square.
We establish two new norm convergence theorems for Henstock-Kurzweil integrals. In particular, we provide a unified approach for extending several results of R. P. Boas and P. Heywood from one-dimensional to multidimensional trigonometric series.
We prove an extension theorem for modular functions on arbitrary lattices and an extension theorem for measures on orthomodular lattices. The first is used to obtain a representation of modular vector-valued functions defined on complemented lattices by measures on Boolean algebras. With the aid of this representation theorem we transfer control measure theorems, Vitali-Hahn-Saks and Nikodým theorems and the Liapunoff theorem about the range of measures to the setting of modular functions on complemented lattices.
Let SP be the set of upper strongly porous at 0 subsets of \mathbb{R}^{+} and let Î(SP) be the intersection of maximal ideals I\subseteq SP. Some characteristic properties of sets E \in Î(SP) are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at 0 subsets of \mathbb{R}^{+} is a proper subideal of Î(SP). Earlier, completely strongly porous sets and some of their properties were studied in the paper V.Bilet, O.Dovgoshey (2013/2014)., Viktoriia Bilet, Oleksiy Dovgoshey, Jürgen Prestin., and Obsahuje seznam literatury
Let $q$ be a positive integer, $\chi $ denote any Dirichlet character $\mod q$. For any integer $m$ with $(m, q)=1$, we define a sum $C(\chi, k, m; q)$ analogous to high-dimensional Kloosterman sums as follows: $$ C(\chi, k, m; q)=\sum _{a_1=1}^{q}{}' \sum _{a_2=1}^{q}{}' \cdots \sum _{a_k=1}^{q}{}' \chi (a_1+a_2+\cdots +a_k+m\overline {a_1a_2\cdots a_k}), $$ where $a\cdot \overline {a}\equiv 1\bmod q$. The main purpose of this paper is to use elementary methods and properties of Gauss sums to study the computational problem of the absolute value $|C(\chi, k, m; q)|$, and give two interesting identities for it.
Archaeometallographic data suggest that there were two technological models in Eastern Europe as early as the Bronze Age–Early Iron Age transition period (9th–7th centuries BC). We link their development to two routes via which knowledge of use of ferrous metals diffused from Anatolia. The first route reached the North Caucasus, the second route passed through Greece and the Balkans to Central and Eastern Europe. and Archeometalografická data naznačují, že již v přechodu mezi dobou bronzovou a ranou dobou železnou (9.–7. stol. př. n. l.) existovaly ve východní Evropě dva technologické modely zpracování železa. Jejich rozvoj spojujeme se dvěma trasami, kterými se znalosti užívání železných kovů z Anatolie rozšířily. První trasa překročila Zakavkazsko, druhá trasa vedla přes Řecko a Balkán do střední a východní Evropy.
The Fibonacci Cube is an interconnection network that gets many desirable properties that are very important in the network design, network stability and applications. The extended Fibonacci Cube is a new network topology. The vulnerability value of a communication network shows the resistance of the network after the disruption of some centres or connection lines until the communication breakdown. In a network, as the number of centres belonging to sub networks changes, the vulnerability of the network also changes and requires greater degrees of stability or less vulnerability. If the communication network is modelled by graph G, the deterministic measures tend to provide a worst-case analysis of some aspects of overall disconnection process. Many graph theoretical parameters have been used in the past to describe the stability of communication networks. There are few parameters such as integrity, neighbour-integrity and tenacity number giving the vulnerability. Also, in the neighbour-integrity, if a station is destroyed, the adjacent stations will be betrayed so that the betrayed stations become useless to network as a whole.
In this paper we study the stability of the Extended Fibonacci Cube using the integrity and neighbour-integrity. We compared the obtained results with the results of the other network topologies. We saw that, for two graphs G1 and G2 that have same number of vertices if k(G1) > k(G2), then I(G1) > I(G2) and NI(G1)< NI(G2).