Iranian Journal of Mathematical Sciences and Informatics
Volume:18 Issue: 2, Nov 2023

In this paper, we introduce the notion of hybrid bi-ideals in semigroups and investigate some of their important properties. We also give various equivalent conditions for a semigroup to be regular and hybrid structures to be hybrid bi-ideals of S.

In this paper, we initiate the concept of proximal weak commute mappings and establish some new existence of common best proximity point theorems for this class of mappings. Also, we provide interesting example to illustrate our main results.

Let R be a ring. The ring R is called weakly prime center(WPC ring) if ab∈Z(R) implies that aRb is an ideal of R. In this paper, we prove that every left(right) duo ring is a WPC ring. Also we prove that some classes of rings with nilpotent Jacobson radical are WPC rings. Finally, we prove that a simple ring is a WPC ring if and only if it is a domain.

In this paper, we consider some special Finsler spaces obtained via Randers-β change. First, we find the fundamental metric tensor and Cartan tensor of these metrics. Next, we establish a general formula for the inverse tensor of fundamental metric tensors of these metrics. Finally, we find the necessary and sufficient conditions under which these metrics are projectively flat, and we give examples to support our results.

Let R be a ring. The class of SA-injective right R-modules (SAIR) is introduced as a class of soc-injective right R-modules. Let N be a right R-module. A right R-module M is said to be SA-N-injective if every R-homomorphism from a semi-artinian submodule of N into M extends to N. A module M is called SA- njective, if M is SA-R-injective. We characterize rings over which every right module is SA-injective. Conditions under which the class SAIR is closed under uotient (resp. directsums, pure homomorphic images) are given. The definability of the class SAIR is studied. Finally, relations between SA-injectivity and certain generalizations of injectivity are given.

The basic purpose of this article is to introduce the concept of R - λ - G-contraction by using R-functions, lower semi-continuous functions and digraphs and discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings satisfying such contractions in the setting of metric spaces endowed with a graph. As some consequences of our results, we obtain several recent results in metric spaces and partial metric spaces.

Introducing oil bodies to the industry provided an impetus to know more about the constructive factors. Accordingly, the current article focused on the description of the plant seed caleosins involved in oil body formation. For this purpose, bioinformatics analysis was conducted to identify the putative caleosins. Then, the phylogenetic tree and conserved motifs were extracted from the sequences. Finally, a model sequence was created by WebLogo to indicate all features including secondary structure, post-translational modifications and physicochemical properties. According to the results, the N-terminal region of caleosins owned more length and negative charges. Although the net charge and length of domains have changed over evolutionary time, the members of Brassicaceae had been highly conserved even in the motif sequences. Considering the importance of these two factors in the construction of the oil body, natural selection has probably shaped more stable droplets for lipid storage. However, its confirmation requires more investigation.

A simple graph is said to be cordial if it admits 0-1 labeling that satisfies certain conditions. In this paper we investigate necessary and sufficient conditions for cordial labeling of the corona product between paths and fourth power of paths be cordial.

For a graph G=(V, E) of order n, a Roman {2}-dominating function f: V→E has the property that for every vertex v in V with f(v)=0, either v is adjacent to a vertex assigned 2 under f, or v is adjacent to least two vertices assigned 1 under f. In this paper, we classify all graphs with Roman {2}-domination number belonging to the set {2, 3, 4, n-2, n-1, n}. Furthermore, we obtain some results about Roman {2}-domination number of some graph operations.

The purpose of the paper is to derive some interesting implications associated with some differential inequalities, for certain analytic functions in the open unit disk. Connections to previously well known results are also established.

Let R be a commutative ring with identity and M be an R-module. In this paper, we will introduce the concept of 2-irreducible (resp., strongly 2-irreducible) submodules of M as a generalization of irreducible (resp., strongly irreducible) submodules of M and investigated some properties of these classes of modules.

A difference labeling of a graph G is an injective function f : V (G) → N ∪ {0} together with the weight function f∗ on E(G) given by f∗(uv) = |f(u) - f(v)| for every edge uv in G. The collection of subgraphs induced by the edges of the same weight is a decomposition of G and is called the common weight decomposition of G induced by f. Let ϒf denote the collection of all the paths taken from each member of the common weight decomposition induced by f. A difference labeling f of G is said to be a graphoidal difference labeling if ϒf is an acyclic graphoidal decomposition of G. This paper initiates a study on this concepts.

In this paper, the concept of K-g-frames in Hilbert pro-C∗-modules is introduced, and their basic properties are examined. The conditions under which family of operators can form a K-g-frame on Hilbert pro-C∗-modules are derived. Moreover g-atomic systems in Hilbert proC∗-modules are introduced and their properties are examined.

One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph embedding problem. In this paper we compute the lower bound for dilation and congestion of embedding onto wheel-like networks. Further, we compute the exact dilation of embedding wheellike networks into hypertrees, proving that the lower bound obtained is sharp. Again, we compute the exact congestion of embedding windmill graphs into circulant graphs, proving that the lower bound obtained is sharp. Further, we compute the exact wirelength of embedding wheels and fans into 1,2-fault hamiltonian graphs. Using this we estimate the exact wirelength of embedding wheels and fans into circulant graphs, generalized Petersen graphs, augmented cubes, crossed cubes, Möbius cubes, twisted cubes, twisted n-cubes, locally twisted cubes, generalized twisted cubes, odd-dimensional cube connected cycle, hierarchical cubic networks, alternating group graphs, arrangement graphs, 3-regular planer hamiltonian graphs, star graphs, generalised matching networks, fully connected cubic networks, tori and 1-fault traceable graphs.

In the present paper, we introduce the class Βθ(α,β) consisting of functions f, analytic in the unit disc ∆, normalized by the condition f(0)=0=f'(0)-1 and satisfying the following two-sided inequality α< Re{f'(z)+(1+eiθ)/2 zf''(z)}<β     (z∈∆),where θ∊(-π,π], 0<α<1 and β>1. Integral representation, differential subordination results, coefficient estimates and Fekete-Szegö coefficient functional associated with the k-th (k≥1) root transform [f(zk)]1/k for functions in the class Βθ(α,β), are determined.<betaquad</betaquad

In this paper we show that the category of measurable spaces is closed under coproducts in the category of sets. For an arbitrary ring R, we define measurable and probability right R-modules and we prove that the categories of these new objects are closed under kernels, cokernels and pushouts in the category of right R-modules. We also show that the category of measurable right R-modules is closed under coproducts and products in the category of right R-modules. We end this paper by giving some results about stochastically independence in the category of probability right R-modules.