Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080120190201*-frames in Hilbert modules over pro-C*-algebras110546045ENM. Naroei IraniDepartment of Mathematics, Kerman Branch, Islamic Azad University, Kerman, IranA. NazariDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranJournal Article20180503In this paper, by using the sequence of multipliers, we introduce frames with algebraic bounds in Hilbert pro-$ C^* $-modules. We investigate the relations between frames and $ ast $-frames. Some properties of $ ast $-frames in Hilbert pro-$ C^* $-modules are studied. Also, we show that there exist two differences between $ ast $-frames in Hilbert pro-$ C^* $-modules and Hilbert $ C^* $-modules. Finally, dual $ ast $-frames in Hilbert pro-$ C^* $-modules are presented.http://jlta.iauctb.ac.ir/article_546045_e96bf32e50443e8f6acdb364aca06159.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080120190201Albertson energy and Albertson Estrada index of graphs1124546046ENA. JahanbaniDepartment of Mathematics, Shahrood University of Technology, Shahrood, IranJournal Article20180707Let $G$ be a graph of order $n$ with vertices labeled as $v_1, v_2,dots , v_n$. Let $d_i$ be the degree of the vertex $v_i$ for $i = 1, 2, cdots , n$. The Albertson matrix of $G$ is the square matrix of order $n$ whose $(i, j)$-entry is equal to $|d_i - d_j|$ if $v_i $ is adjacent to $v_j$ and zero, otherwise. The main purposes of this paper is to introduce the Albertson energy and Albertson-Estrada index of a graph, both base on the eigenvalues of the Albertson matrix. Moreover, we establish upper and lower bounds for these new graph invariants and relations between them.http://jlta.iauctb.ac.ir/article_546046_a9e9d6f8e6b5ede19ce15c13c7ad337c.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080120190201On some forms of e*-irresoluteness2539546047ENM. OzkocDepartment of Mathematics, Faculty of Science, Mugla Sitki Kocman University
48000 Mentese-Mugla, Turkey0000-0003-0068-7415K. Sarıkaya AtaseverDepartment of Mathematics, Faculty of Science, Mugla Sitki Kocman University
48000 Mentese-Mugla, TurkeyJournal Article20180712The main goal of this paper is to introduce and study two new class of functions, called weakly $e^*$-irresolute functions and strongly $e^*$-irresolute functions, via the notion of $e^*$-open set defined by Ekici [7]. We obtain several fundamental properties and characterizations of these functions. Moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing topological functions.http://jlta.iauctb.ac.ir/article_546047_1ef1763e9a39324adebbee1e1ee28976.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080120190201System of AQC functional equations in non-Archimedean normed spaces4152546048ENH. MajaniDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, IranJournal Article20180827In 1897, Hensel introduced a normed space which does not have the Archimedean property. During the last three decades theory of non--Archimedean spaces has gained the interest of physicists for their research in particular in problems coming from quantum physics, p--adic strings and superstrings. In this paper, we prove the generalized Hyers--Ulam--Rassias stability for a system of additive, quadratic and cubic functional equations in non--Archimedean normed spaces.http://jlta.iauctb.ac.ir/article_546048_2fdf05eeac66432df83b60a0d4ee321f.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080120190201On a generalization of central Armendariz rings5361546049ENM. SanaeiDepartment of Mathematics, Islamic Azad University, Central Tehran Branch, 13185/768, IranSh. SahebiDepartment of Mathematics, Islamic Azad University, Central Tehran Branch, 13185/768, IranH. H. S. JavadiDepartment of Mathematics and Computer Science, Shahed University, Tehran, IranJournal Article20180901In this paper, some properties of $alpha$-skew Armendariz and central Armendariz rings have been studied by variety of others. We generalize the notions to central $alpha$-skew Armendariz rings and investigate their properties. Also, we show that if $alpha(e)=e$ for each idempotent $e^{2}=e in R$ and $R$ is $alpha$-skew Armendariz, then $R$ is abelian. Moreover, if $R$ is central $alpha$-skew Armendariz, then $R$ is right p.p-ring if and only if $R[x;alpha]$ is right p.p-ring. Then it is proved that if $alpha^{t}=I_{R}$ for some positive integer $t$, $ R $ is central $ alpha $-skew Armendariz if and only if the polynomial ring $ R[x] $ is central $ alpha $-skew Armendariz if and only if the Laurent polynomial ring $R[x,x^{-1}]$ is central $alpha$-skew Armendariz.http://jlta.iauctb.ac.ir/article_546049_b05fa8f6b29802cf5dccd132040d5f9d.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080120190201On $beta-$topological vector spaces6370546091ENS. SharmaDepartment of Mathematics, University of Jammu, JK-18006, IndiaM. RamDepartment of Mathematics, University of Jammu, JK-18006, India.Journal Article20180901We introduce and study a new class of spaces, namely $beta-$topological vector spaces via $beta-$open sets. The relationships among these spaces with some existing spaces are investigated. In addition, some important and useful characterizations of $beta-$topological vector spaces are provided.<br /> http://jlta.iauctb.ac.ir/article_546091_417a50ad8772e4b4ae1129cce46d4286.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080120190201Solving fractional evolution problem in Colombeau algebra by mean generalized fixed point7184546134ENM. ElomariDepartment of Mathematics, Faculty of Sciences and Technics, Beni-Mellal, MoroccoS. MellianiDepartment of Mathematics, Faculty of Sciences and Technics, Beni-Mellal, MoroccoA. TaqbibtDepartment of Mathematics, Faculty of Sciences and Technics, Beni-Mellal, MoroccoS. ChadliDepartment of Mathematics, Faculty of Sciences and Technics, Beni-Mellal, MoroccoJournal Article20180713The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$ for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$, where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself. Here the Caputo fractional derivative $D^{q}_c$ is used instead of the usual derivative. The introduction of locally convex spaces is to use their topology in order to define generalized semigroups and generalized fixed points, then to show our requested result.http://jlta.iauctb.ac.ir/article_546134_8de4872e1cbbac914e7141b51317202c.pdf