1 1735-4463 ACECR at Tarbiat Modares University 1726 General On Local Antimagic Chromatic Number of Graphs with Cut-vertices Lau Gee-Choon b Shiu Wai-Chee c Ng Ho-Kuen d b Faculty of Computer & Mathematical Sciences, Universiti Teknologi MARA (UiTM) Malaysia c Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong d Department of Mathematics, San José State University, San José CA 95192 USA 1 4 2024 19 1 1 17 16 09 2019 19 02 2022 An edge labeling of a connected graph G = (V, E) is said to be local antimagic if it is a bijection f:E →{1,... ,|E|} such that for any pair of adjacent vertices x and y, f+(x)≠ f+(y), where the induced vertex label f+(x)= ∑ f(e), with e ranging over all the edges incident to x.  The local antimagic chromatic number of G, denoted by Xla(G), is the minimum number of distinct induced vertex labels over all local antimagic labelings of G. In this paper, the sharp lower bound of the local antimagic chromatic number of a graph with cut-vertices given by pendants is obtained. The exact value of the local antimagic chromatic number of many families of graphs with cut-vertices (possibly given by pendant edges) are also determined. Consequently, we partially answered Problem 3.1 in [Local antimagic vertex coloring of a graph, Graphs and Combin., 33, (2017),  275--285].
1729 General Monotone Orbitally Nonexpansive and Cyclic Mappings in Partially Ordered Uniformly Convex Banach Spaces Gabeleh Moosa e Karimi Lotfollah f Vetro Calogero g e Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran f Department of Electrical Engineering, Hamedan University of Technology, Hamedan, Iran g Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy 1 4 2024 19 1 19 33 20 09 2019 26 03 2020 In the setting of uniformly convex Banach spaces equipped with a partially ordered relation, we survey the existence of fixed points for monotone orbitally nonexpansive mappings. In this way, we extend and improve the main results of Alfuraidan and Khamsi [M. R. Alfuraidan, M. A. Khamsi, Proc. Amer. Math. Soc., 146, (2018), 2451-2456]. Examples are given to show the usability of our main conclusions. We also study the existence of an optimal solution for cyclic contractions in such spaces. 1700 General Annihilators of Power Central Values of Generalized Skew Derivations on Lie Ideals Baydar Yarbil Nihan h Argaç Nurcan i h Department of Mathematics, Ege University Bornova, Izmir 35100, Turkey i Department of Mathematics, Ege University Bornova, Izmir 35100, Turkey 1 4 2024 19 1 35 49 21 08 2019 30 06 2021 Let R be a prime ring with center Z(R) and G be a generalized α-derivation of R for  α∈ Aut(R). Let a ∈ R be a nonzero element and n be a fixed positive integer. (i) If aG(x)n ∈ Z(R) for all x ∈ R then aG(x) = 0 for all x ∈ R unless dimCRC = 4. (ii) If aG(x)n ∈ Z(R) for all x ∈ L, where L is a noncommutative Lie ideal of R then aG(x) = 0 for all x ∈ R unless dimCRC = 4. 1372 General Tracial Cyclic Rokhlin Property for Automorphisms of Non-unital Simple C*-algebras Jamali Saeid j j Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran 1 4 2024 19 1 51 62 22 07 2018 23 09 2018 The tracial cyclic Rokhlin property for automorphisms of simple not necessarily unital C*-algebras is investigated. We show that the tracial cyclic Rokhlin property is preserved by going to certain restrictions to subalgebras and taking direct limit or tensor products of actions. We also show that under certain conditions properties such as real rank zero, the tracial rank zero, stable rank one, (tracial) Z-stability, Property (SP), strict comparison on projections are passed to crossed products under automorphisms with the tracial cyclic Rokhlin property. 1746 General Repdigits as Products of Consecutive Pell or Pell–Lucas Numbers Bravo Eric F. k Bravo Jhon J. l k Departamento de Matemáticas, Universidad del Cauca, Calle 5 No. 4–70, Popayán, Colombia l Departamento de Matemáticas, Universidad del Cauca, Calle 5 No. 4–70, Popayán, Colombia 1 4 2024 19 1 63 70 19 10 2019 31 08 2020 A positive integer is called a repdigit if it has only one distinct digit in its decimal expansion. In this paper, we find all repdigits that are products of consecutive Pell or Pell–Lucas numbers. This paper continues previous work which dealt with finding occurrences of repdigits in the Pell and Pell–Lucas sequences. p, li { white-space: pre-wrap; } 1717 General A Study of Metric Spaces of Interval Numbers in n-Sequences Defined by Orlicz Function Tabassum Sabiha m Fatma Ruqaiyya n m Department of Applied Mathematics, Aligarh Muslim University, Aligarh-202002, India n Department of Applied Mathematics, Aligarh Muslim University, Aligarh-202002, India 1 4 2024 19 1 71 83 05 09 2019 30 03 2022 In recent years, a variety of work has been done in the field of single, double and triple sequences. Study on n-tuple sequence is new in this field. The main interest of this paper is to explore the idea of n-tuple sequences x = (xi_1,i_2,...,i_n) in metric spaces. We introduce the concept of n-sequence space of interval number and discussed its arithmetic properties. Furthermore, we combined the concept of Orlicz function, statistical convergence, interval number and n-sequence to construct some new nsequence spaces and discussed their properties. Some suitable examples for these spaces have been constructed. 1723 General Unification of Generalized Open Sets with Respect to an Ideal Boonpok Chawalit o o Mathematics and Applied Mathematics Research Unit Department of Mathematics, Faculty of Science, Mahasarakham University Mahasarakham, 44150, Thailand 1 4 2024 19 1 85 93 14 09 2019 19 05 2020 This paper deals with the concepts of Iµ-g-closed sets, Iµ-semi-open sets and Iµ-semi-preopen sets in ideal topological spaces and investigate several properties of these sets. Some characterizations of Iµ -regular spaces and Iµ-normal spaces are discussed. 1691 Special Finite Groups with Specific Number of 2-Engelizers Khoshtarash Raheleh p Rajabzadeh Moghaddam Mohammad Reza Rostamyari Mohammad Amin p Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran Department of Mathematics, Khayyam University, Mashhad, Iran Department of Mathematics, Khayyam University, Mashhad, Iran 1 4 2024 19 1 95 105 31 07 2019 10 02 2021 In 2016, the second and third authors introduced the notion of 2-Engelizer of the element x in a given group G and denoted the set of all 2-Engelizers in G by E2(G). They also constructed the possible values of |E2(G)| [Bull. Korean Math. Soc., 53(3), (2016), 657-665]. In the present paper, we classify all non 2-Engel finite groups G, when |E2(G)| = 4, 5. 1704 Special New Characterizations of Semisimple Alternative Algebras Boulmane Said Department of Economic Sciences and Management Moulay Ismail University, Polydisciplinary Faculty, Errachidia-Morocco 1 4 2024 19 1 107 115 26 08 2019 20 04 2020 We give some new characterizations of semisimple alternative algebras among the pseudo-Euclidean alternative algebras. These charcterizations are based on the index of a pseudo Euclidean alternative algebra, operators of Casimir type and representations of alternative algebras. 1718 General A Parametric $ F_4 $ Algorithm Dehghani Darmain Mahdi Hashemi Amir Department of Mathematics, Technical and Vocational University (TVU), Tehran, Iran Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran 1 4 2024 19 1 117 133 07 09 2019 28 12 2020 In this paper, we present a parametric F4 algorithm (socalled PF4) which can be considered as a generalization of Faugére’s F4 algorithm [8] to polynomial ideals with parametric coefficients. Our approach is based on the F4 algorithm, Montes DisPGB algorithm [21] and the parametric linear algebra method developed in [6]. The PF4 algorithm takes as input a parametric polynomial ideal and two monomial orderings on the variables and the parameters and returns a Gröbner system of the ideal with respect to a compatible elimination product of the given monomial orderings. We have implemented our new algorithm in Maple and give timings to compare its performance with those of (our implementation) of the Kapur et al. algorithm [16] and the DisPGB algorithm [21]. 1714 General Approximating Fixed Points of Operators Satisfying the ($B_{gamma,mu}$) Condition Ullah Kifayat Abbas Mujahid Ahmad Junaid Ahmad Fayyaz Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat-28420, Khyber Pakhtunkhwa, Pakistan Department of Mathematics, Government College University, Lahore 54000, Pakistan Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad - 44000, Pakistan Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat-28420, Khyber Pakhtunkhwa, Pakistan 1 4 2024 19 1 135 148 02 09 2019 04 03 2023 Suppose C is any nonempty subset of a Banach space X. A mapping T : C → C is said to satisfy condition (Bγ,µ) if there exists γ ∈ [0, 1] and µ ∈ [0, 1 /2 ] with 2µ ≤ γ such that for each two elements x, y ∈ C, γ||x - T x|| ≤ ||x - y|| + µ||y - T y|| implies ||T x - T y|| ≤ (1 - γ)||x - y|| + µ(||x - T y|| + ||y - T x||). In this research, we suggest some convergence results for these mappings under a up-to-date iterative process in a Banach space setting. Our results are new and improve some known results of the literature. 1743 General A Note on Acyclic Coloring of Strong Product of Graphs Babu P Shanas A V Chithra Department of Mathematics, National Institute of Technology, Calicut, Kerala, India-673601 Department of Mathematics, National Institute of Technology, Calicut, Kerala, India-673601 1 4 2024 19 1 149 160 08 10 2019 27 02 2022 A vertex coloring of a graph G is called acyclic if no two adjacent vertices have the same color and no cycle in G is bichromatic. The acyclic chromatic number a(G) of a graph G is the least number of colors in an acyclic coloring of G. In this paper, we obtain bound for the acyclic chromatic number of the strong product of a tree and a graph. An exact value for the acyclic chromatic number of the strong product of two trees is derived. Further observations are made on the upper bound for the strong product of three paths. 1443 General Multiresolution Analysis on Sobolev Space over Local Fields of Positive Characteristic and Characterization of Scaling Function Pathak Ashish Kumar Dileep Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India Department of Applied Science and Humanities (Mathematics), GL Bajaj Institute of Technology and Management, Greater Noida-201306, India 1 4 2024 19 1 161 174 26 10 2018 25 02 2024 A general concept of wavelets and multiresolution analysis on Sobolev space over local fields of positive characteristic (Hs(K)) is given. A characterization of the scaling functions associated with an MRA is also given. 1750 General Darbo Type Best Proximity Point Results via R-function using Measure of Noncompactness with an Application Patle Pradip Ramesh Patel Deepesh Kumar Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur-440010, India Department of Mathematics School of Advanced Sciences, VIT-AP University, Amravati-522237, Andhra Pradesh 1 4 2024 19 1 175 192 25 10 2019 05 05 2021 The concept of measure of noncompactness (MNC) allows us to select an important class of mappings which are more general than compact operators. The proposed work exploits the axiomatic definitio of MNC and introduces the notion of relatively nonexpansive cyclic (noncyclic) SR-condensing operators along with the aid of SR-functions. The first phase of the paper concentrates on establishing the best proximity point (pair) theorems for such operators. The main results in this manuscript extend and generalize several state of art literature on Darbo type fixed point results. In the second phase, proposed results are applied to show the actuality of optimum solutions for system of second order differential equations with two initial conditions. 1757 General Fourier Method For an Existence of Quasilinear Inverse Pseudo-Parabolic Equation Baglan Irem Kanca Fatma Mishra Vishnu Narayan Mishra Department of Mathematics, Kocaeli University, Kocaeli 41380, Turkey Department of Computer Engineering, Fenerbahce University, Istanbul, Turkey Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India 1 4 2024 19 1 193 209 06 11 2019 22 04 2023 In this work, the inverse quasi-linear pseudo-parabolic problem was investigated. We demonstrated the solution by the Fourier approximation. The inverse problem was first examined by linearizing and then used implicit finite difference schema for the numerical solution. 1758 General First and Second Order Optimality Conditions using Approximations for Fractional Multiobjective Bilevel Problems under Fractional Constraints Lahoussine Lafhim LASMA Laboratory, Faculty of Sciences Dhar El Mehrez, Sidi Mohammed Ben Abdelah University, Department of Mathematics, Fes, Morocco 1 4 2024 19 1 211 232 07 11 2019 16 01 2022 In this paper, first and second order optimality conditions using the concept of approximations are developed for an optimistic fractional multiobjective bilevel problem with non-convex lower level problem. Our idea is based on using the properties of approximations in nonsmooth analysis and a separation theorem in convex analysis. All over the article, the data is assumed to be continuous but not necessarily Lipschitz. 2647 General ABSTRACTS IN PERSIAN Vol. 19, No. 1 in this Volume The Name of Authors Academic Center for Education, Culture and Research (ACECR) 1 4 2024 19 1 233 249 13 06 2024 13 06 2024 Please see the full text contains the Persian abstracts of this volume.