



1
Title: On the Properties of Limit and Cluster Points of Real Valued Sequences in the Sense of Porosity
Vol.48(4) (2024) page: 445458
Author(s): M. Kucukaslan and M. Altinok
Abstract: Following the concept of porosity of subsets of natural numbers at infinity, we define notions of porositylimit and porositycluster points for real valued sequences. These new two concepts, which are not equivalent, are compared with the usual limit points of sequences. Also, some topological properties of the sets of all porosity limit (or cluster) points of sequences are investigated.
Keywords: Local upper porosity; Porosity of subsets of natural numbers; Porosity convergence; Porosity limit points; Porosity cluster points. 
2
Title: Nearrings of Functions Determined by a Collection of Invariant Subgroups
Vol.48(4) (2024) page: 459466
Author(s): M.A. Boudreaux, G.A. Cannon, T.R. Palmer and T. R. Troxclair
Abstract: Let $(G, +)$ be a finite group, written additively with identity $0$, but not necessarily abelian. Let $\Gamma = \{H_i\}$ be a nonempty collection of nonzero, proper subgroups of $G$. Then $N = \{f : G \to G\ \ f(0) = 0 \ \hbox{and}\ f(H_i) \subseteq H_i\ \hbox{for all}\ i\}$ is a nearring under pointwise addition and function composition. We determine when $N$ is abelian and distributive, identify the center of $N$, and find necessary and sufficient conditions for the center to be a subnearring of $N$.
Keywords: Abelian; Distributive; Center. 
3
Title: Annihilating and Centralizing Condition of Generalized Derivation in Prime Ring
Vol.48(4) (2024) page: 467476
Author(s): B. Dhara, S. Kar and M. Bera
Abstract: Let $R$ be a prime ring of characteristic different from $2$, $U$ its Utumi ring of quotients and $C$ its extended centroid, $f(x_1,\dots, x_n)$ a multilinear polynomial over $C$ that is noncentralvalued on $R$, $I$ a nonzero ideal of $R$ and $F$ a nonzero generalized derivation of $R$. If for some $0\neq a\in R$,
$$a[F^2(f(r_1,\dots, r_n)),f(r_1,\dots, r_n)]\in C$$ for all $r_1,\dots,r_n\in I$, then one of the following statements holds:
(i) there exists $\lambda \in C$ such that $F(x)= \lambda x$ for all $x\in R$;
(ii) there exists $p \in U$ such that $F(x)= px$ with $p^2 \in C$;
(iii)} there exists $p \in U$ such that $F(x)= xp$ with $p^2 \in C$.
Keywords: Prime ring; Multilinear polynomial; Generalized derivation. 
4
Title: A Study on the Properties of Several Convergent Sequences in Fuzzy Riesz Spaces
Vol.48(4) (2024) page: 477492
Author(s): X. Liu, N. Cheng, J.J. Zhao and J. Dai
Abstract: In this paper, a novel of convergence named the fuzzy uuniform convergence is defined on the basis of the fuzzy order convergence in fuzzy Riesz spaces. The relation between the fuzzy uuniform convergence and the fuzzy order convergence in fuzzy Archimedean Riesz spaces is studied. We also discuss the existence of the fuzzy uuniform limit for the fuzzy uuniform Cauchy sequence in fuzzy Archimedean Riesz Spaces. We give the characterization of fuzzy order completeness in fuzzy Riesz spaces.
Keywords: Fuzzy Riesz spaces; Fuzzy order convergence; Fuzzy uuniformity convergence; Fuzzy order Cauchy sequence. 
5
Title: Estimates for Bilinear PseudoDifferential Operators and Their Commutators on Product of Homogeneous Spaces
Vol.48(4) (2024) page: 493510
Author(s): G.H. Lu and L. Rui
Abstract: In this paper, the authors prove that bilinear pseudodifferential operator $T_{\sigma}$ is bounded from the product of homogeneous Herz spaces $\dot{K}^{\alpha_{1},p_{1}}_{q_{1}}(\mathbb{R}^{n})\times \dot{K}^{\alpha_{2},p_{2}}_{q_{2}}(\mathbb{R}^{n})$ to homogeneous Herz space $\dot{K}^{\alpha,p}_{q}(\mathbb{R}^{n})$, and bounded from the product of homogenous MorreyHerz spaces $M\dot{K}^{\alpha_{1},\lambda_{1}}_{p_{1},q_{1}}(\mathbb{R}^{n})\times M\dot{K}^{\alpha_{2},\lambda_{2}}_{p_{2},q_{2}}(\mathbb{R}^{n})$ to homogeneous MorreyHerz space $M\dot{K}^{\alpha,\lambda}_{p,q}(\mathbb{R}^{n})$. Furthermore, via establishing the sharp maximal estimate for the commutator $[b_{1},b_{2},T_{\sigma}]$ which is generated by $T_{\sigma}$ and $b_{1},b_{2}\in\mathrm{BMO}(\mathbb{R}^{n})$, the boundedness of $[b_{1},b_{2},T_{\sigma}]$ on spaces $\dot{K}^{\alpha,p}_{q}(\mathbb{R}^{n})$ and on spaces $M\dot{K}^{\alpha,\lambda}_{p,q}(\mathbb{R}^{n})$ is also obtained.
Keywords: Bilinear pseudodifferential operator; Commutator; Space $\mathrm{BMO}(\mathbb{R}^{n})$; Homogeneous Herz space; Homogeneous MorreyHerz space. 
6
Title: An Extension of the BanachSteinhaus Theorem for Sargent Spaces
Vol.48(4) (2024) page: 511516
Author(s): W.L. Ng and P.Y. Lee
Abstract: We prove a special case of the BanachSteinhaus theorem for Sargent spaces, making use of the HahnBanach theorem and bypassing the proof by Sargent which requires the Baire category theorem.
Keywords: BanachSteinhaus theorem; Sargent spaces; HahnBanach theorem; HenstockKurzweil integral. 
7
Title: Darboux Associate Curves of Timelike Curves in $\mathbb{E}_{1}^{3}$
Vol.48(4) (2024) page: 517530
Author(s): U. Ozturk and G.A. Mahmood Mahmood
Abstract: In this paper, we introduce $k$directional Darboux curves of a given timelike curve $\alpha $ lying on a timelike surface in Minkowski $3$space $\mathbb{E}_{1}^{3}$ as the integral curves of some vector fields generated by the Darboux frame along the curve. The relationships of such associate curves are given including the relationship of their curvatures. By using these curves, we give a new approach to classifying some special curves such as helices, and slant helices.
Keywords: Direction curves; General helix; Slant helix; Darboux frame; Minkowski space. 
8
Title: On Order Prime Divisor Graphs of Finite Groups II
Vol.48(4) (2024) page: 531551
Author(s): M.K. Sen, S.K. Maity and S. Das
Abstract: In [3], we defined and studied the order prime divisor graph $\mathscr{PD}(G)$ of a finite group $G$. In this paper, we also study several properties of the order prime divisor graph of a finite group. Also, we discuss the order prime divisor graph for direct product of finite groups. We characterize some graph theoretic properties of $\mathscr{PD}(\mathbb{Z}_{n})$, $\mathscr{PD}(Q_{4n})$, $\mathscr{PD}(Q_{2^{n+1}})$, $\mathscr{PD}(SD_{2^n})$.
Keywords: Dicyclic group; Generalized quaternion group; Semidihedral group; Petersen graph; Maximal planar graph; Chordal graph. 
9
Title: $\iota$Open and $(\iota)$Open Sets in Topological Spaces
Vol.48(4) (2024) page: 553568
Author(s): H. Shanmugapriya and K. Sivakamasundari
Abstract: The primary goal of this study is to propose the concept of an operation $\iota$ on $\delta$preopen subsets in topological spaces. Here we defined the concepts of $\iota$open sets, $\iota$regular spaces and some topological properties such as $\iota$closure, $\iota$interior, $closure_\iota$ of sub sets and $\iota$derived were analysed. $\iotag.$closed sets and $\iotaT_{1/2}$ spaces were studied. And a new set called $(\iota)$open sets are studied along with its properties.
Keywords: $\iota$Open sets; $\iota$Regular spaces; $\iota$Closure; $\iota$Interior; $Closure_\iota$; $\iota$Derived; $\iota g.$Closed sets; $\iotaT_{1/2}$ and $(\iota)$open sets. 
10
Title: SemiBrouwerian Almost Distributive Lattices
Vol.48(4) (2024) page: 569578
Author(s): V.V.V.S.S.P.S. Srikanth, S. Ramesh, M.V. Ratnamani and K.P. Shum
Abstract: We define a semiBrouwerian almost distributive lattice as a description of a semiBrouwerian algebra in the category of almost distributive lattices and derive a number of algebraic properties on them. We obtain a few equivalent conditions for an almost distributive lattice to become a semiBrouwerian almost distributive lattice. Finally we identify a class of pseudocomplemented lattices and a class of semiBrouwerian algebras in a semiBrouwerian almost distributive lattice.
Keywords: Principal ideal; Almost distributive lattice; Heyting algebra; SemiBrouwerian algebra; Heyting almost distributive lattice. 
11
Title: Equality of Power Graphs, Enhanced Power Graphs and Commuting Graphs on Semigroups
Vol.48(4) (2024) page: 579595
Author(s): Y.H. Wang, X. Lu and X.Y. Guo
Abstract: This paper focuses on three kinds of graphs built from semigroups: power graphs, enhanced power graphs and commuting graphs. Let $S$ be a semigroup constructed in a prescribed way from a semigroup $T$. We show in particular instances that pairs of these graphs built over $S$ coincide precisely when the same pairs built over $T$ coincide. This is true, for example, when $S$ is a completely simple semigroup and $T$ is a maximal subgroup. We give several other instances of this phenomenon. In addition, we give counterexamples to show that equality for an arbitrary pair of these three graphs does not always pass between semigroups and their maximal subgroups.
Keywords: Completely simple semigroup; A semilattice of semigroups; Power graph; Enhanced power graph; Commuting graph. 
11 Records!





