Iranian Journal of Mathematical Sciences and Informatics
Volume:19 Issue: 1, May 2024

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].

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.

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.

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.

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.
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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.

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.

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.

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.

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].

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.

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.

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.

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.

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.

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.