A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. In this paper, we determine the automorphisms and isomorphisms of connected heptavalent symmetric graphs of order 32p for each prime p. As a result, we get the complete classification of such graphs, and there are two sporadic such graphs with p = 2 and 3.
This study introduces the concepts of intuitionistic Q-fuzzy subalgebras, ideals, and deductive systems in the setting of Hilbert algebras and investigates their fundamental properties and interrelations. The theoretical results are supported by concrete examples and are structured in a way that facilitates understanding of the algebraic-logical framework underlying fuzzy logic extensions. By presenting clear definitions, illustrative cases, and step-by-step reasoning, the paper serves not only as a contribution to the field of abstract algebra but also as a useful learning resource for upper secondary science students beginning to engage with research. The work encourages early exploration of mathematical structures, fosters critical and creative thinking, and promotes accessibility of advanced topics through collaboration across academic levels and institutions.
Prime ideals and their generalizations are fundamental in various research areas, especially in commutative algebra. The study of weakly prime ideals is marked the beginning of this generalization. Subsequent research has further expanded these concepts, with recent attention on weakly 2-prime and S-2-prime ideals. This study aims for new characterizations of weakly S-2-prime ideals, a generalization that includes both weakly 2-prime and S-2-prime ideals. To achieve this goal, we construct an ideal disjoint with a multiplicatively closed subset of commutative rings. We explore several characterizations concerning weakly S-2-prime ideals and investigate this class of ideals in polynomial and formal power series rings. Besides, we examine several new results regarding the trivial extension and amalgamated algebra along an ideal with respect to a ring homomorphism concerning weakly S-2-prime ideals.
Let X be an infinite-dimensional complex Banach space and B(X) be the algebra of all bounded linear operators on X. For T is an element of B(X), and a fixed nonzero complex scalar lambda(0), we denote by E-T({lambda(0)}), the algebraic spectral subspace of T associated with {lambda(0)}. In this paper, we characterize maps phi on B(X) for which whose ranges contain all operators of rank at most two (resp. at most four), and that satisfy E-TS({lambda(0)}) = E-phi(T)phi(S)({lambda(0)}) (resp. ETST({lambda(0)}) = E-phi(T)phi(S)phi(T)({lambda(0)})), for all T, S is an element of B(X).
Soft set theory functions as a flexible mathematical instrument designed to handle uncertain data by aiding in the categorization of universe elements according to predefined parameters. Unlike hypergraphs, semigraphs present a wider interpretation of conventional graphs, allowing for a finer representation of relationships. Through the integration of soft set principles, the notion of soft semigraphs arises, enhancing the adaptability and versatility of semigraphs in addressing uncertainty. This paper sets out to reveal different forms of bipartite soft semigraphs, meticulously examining their varied structures and delving into their inherent characteristics.
In this study we define the radical of the Krasner hypermodules in the subcategory RShmod, then we use short exact sequences in homological algebra for Krasner hypermodules. Besides, by studying the concept of tau-supplements in module theory we will generalize it to the Krasner R-hypermodules by using short exact sequences and a subcategory of RS hmod.
In this paper we present some constructions of the p-biharmonic maps by conformal deformation, we characterize a p-biharmonicity of the first projection and we give many examples of p-biharmonic maps.
In this article, we begin by deriving a unitarily invariant norm inequality for matrices, which is a generalization of the result due to Cao and Wu. Additionally, we introduce a matrix Cauchy-Schwarz inequality for unitarily invariant norms, further generalizing the inequality proposed by Hu.
Graphs are fundamental structures in mathematics and computer science for modeling relationships between objects. This paper studies three hypercompositional structures that are derived from graphs, namely the Path hyperoperation, Simple Path hyperoperation, and Ancestry hyperoperation. These hyperoperations capture complex relationships, offering a robust framework for analyzing intricate connections within graphs. We investigate their properties and provide detailed examples to illustrate their applications.
In the paper, as a generalization of well-known Hilbert algebras, exchange pre-Hilbert algebras are introduced. Their properties and characterizations are investigated. Some important results and examples are given. Moreover, connections between exchange pre-Hilbert algebras, generalized exchange algebras and BE algebras are presented. Finally, implicative and positive implicative algebras are considered. It is shown that implicative (resp. positive implicative) exchange pre-Hilbert algebras are equivalent to implicative BE algebras with (*) (resp. generalized Hilbert algebras).
In this paper, we introduce the concepts of L-filter and TL-filter as two different generalizations of the notion of fuzzy filter in IL-algebras. We investigate some properties with respect to these concepts. We study the relationship between L-filters and TL-filters. We give some characterizations for filters of IL-algebras by using Lfilters and TL-filters. We present additional conditions so that the notions of L-filter and TL-filter coincide in an IL-algebra.
This article aims to present the concept of hypervaluation on a commutative ternary semihyperring mapped onto an ordered abelian group. It examines various properties of hyperideals within the ternary semihyp erring that correspond to the valuation map. Additionally, the article explores results which are similar to those found in classical valuation rings, but within the framework of hypervalued ternary semihyperrings.
In this paper we introduce the precedence hyperoperation, which constructs a precedence partial hypergroupoid, i.e. a partial hypergroupoid with some special properties. Given a precedence partial hypergroupoid, a precedence graph can be defined and vice versa. Using the precedence partial hypergroupoid of a precedence graph and the Fewer-Descendants-Vertex First algorithm (FDVF algorithm), a process flow diagram is created, which can be used in mixed-model assembly line design.
In this paper, it is proved that if the shape operator of a Hopf hypersurface in complex two-plane Grassmannians G(2)(Cm+2) is Reeb recurrent, it is Reeb parallel. Another recurrent hypersurfaces are also classified.
A subgroup H of a finite group G is said to be semipermutable in G if it is permutable with every subgroup K of G satisfying that (|K|,|H|) = 1. If every subgroup of G is semipermutable in G, then G is said to be a semi-Hamilton group. In this paper, the authors classify the non-semi-Hamilton groups whose proper subgroups are all semi-Hamilton groups.
In this note, particular two-dimensional inequalities dealing with two n-tuples of integer numbers under relatively general assumptions are investigated. Moreover, systems of integers for which the equality holds are completely described.
In this paper, biharmonic pseudo-Riemannian surfaces with diagonalizable shape operetor in pseudo-Riemannian space form N-s(4) (c) are studied. We prove that the surfaces with light-like mean curvature vector field are pseudo-umbilical. For non light-like mean curvature vector field, we show that the pseudo-umbilical surfaces is minimal or H-2 = |c|. Also, we give some sufficient conditions for such surfaces with parallel mean curvature vector field to be minimal.
Let C be a finite group. Recall that a subgroup H is called a TI-subgroup of C if H boolean AND H-g = 1 or H for every element g of C. We call a group C a CTI-group if its every element centralizer is a TI-group. Clearly S-3, A(5), D-7 and Q(8) are all CTI-groups. In this paper, we investigate the structure of a CTI-group C and prove that a CTI-group C is a nilpotent group or a Frobenius group whose complement is either cyclic or the direct product of a cyclic group of odd order and Q(8), or G congruent to PSL(2, 2(n)) with n > 1.
Let G = HK be a finite group, where H and K are proper subgroups of G. A group G is called a mutually N-permutable product of H and K if H permutes with every normal subgroup of K, and K permutes with every normal subgroup of H. In this paper, as a next step of some recently studies, we examine the structural properties of finite group G that is a mutually N-permutable product of two subgroups, with the additional assumption that all maximal subgroups of G are generalized smooth groups.
In this paper, the distance measures between picture fuzzy multisets are proposed as a generalisation of the existing distance measures between picture fuzzy sets. The validity of the transformation from distance measures between PFS to PFMS is carried out using numerical example. Also, an application to medical diagnosis of the proposed distance measures between picture fuzzy multisets is carried out using hypothetical medical database.
