A Study of Fuzzy Sequence Spaces

The purpose of this chapter is to introduce and study some new ideal convergence sequence spaces FSJθT, FS0JθT and FS∞JθT on a fuzzy real number F defined by a compact operator T. We investigate algebraic properties like linearity, solidness and monotinicity with some important examples. Further, we also analyze closedness of the subspace and inclusion relations on the said spaces.

Some Algebraic Properties of the Wilson Loop

In this article, some algebraic properties of the Wilson loop have been investigated in a broad manner. These properties include identities, autotopisms, and implications. We use some equivalent conditions to study the behavior of holomorphism of this loop. Under the shadow of this holomorphism, we are able to observe coincident loops.

Subgroup Graphs of Finite Groups

Let G be a fnite group with the set of subgroups of G denoted by S(G), then the subgroup graphs of G denoted by T(G) is a graph which set of vertices is S(G) such that two vertices H, K in S(G) (H not equal to K)are adjacent if either H is a subgroup of K or K is a subgroup of H. In this paper, we introduce the Subgroup graphs T associated with G. We investigate some algebraic properties and combinatorial structures of Subgroup graph T(G) and obtain that the subgroup graph T(G) of G is never bipartite. Further, we show isomorphism and homomorphism of the Subgroup graphs of finite groups. Let be a finite group with the set of subgroups of denoted by , then the subgroup graphs of denoted by is a graph which set of vertices is such that two vertices , are adjacent if either is a subgroup of or is a subgroup of . In this paper, we introduce the Subgroup graphs associated with . We investigate some algebraic properties and combinatorial structures of Subgroup graph and obtain that the subgroup graph of is never bipartite. Further, we show isomorphism and homomorphism of the Subgroup graphs of finite groups.

On Hadamard Product of Hypercomplex Numbers

Certain product rules take various forms in the set of hypercomplex numbers. In this paper, we introduce a new multiplication form of the hypercomplex numbers that will be called «the Hadamard product», inspired by the analogous product in the real matrix space, and investigate some algebraic properties of that, including the norm of inequality. In particular, we extend our new definition and its applications to the complex matrix theory.

On Certain Bounds for Edge Metric Dimension of Zero-Divisor Graphs Associated with Rings

Given a finite commutative unital ring S having some non-zero elements x , y such that x . y = 0 , the elements of S that possess such property are called the zero divisors, denoted by Z S . We can associate a graph to S with the help of zero-divisor set Z S , denoted by ζ S (called the zero-divisor graph), to study the algebraic properties of the ring S . In this research work, we aim to produce some general bounds for the edge version of metric dimension regarding zero-divisor graphs of S . To do so, we will discuss the zero-divisor graphs for the ring of integers ℤ m modulo m , some quotient polynomial rings, and the ring of Gaussian integers ℤ m i modulo m . Then, we prove the general result for the bounds of edge metric dimension of zero-divisor graphs in terms of maximum degree and diameter of ζ S . In the end, we provide the commutative rings with the same metric dimension, edge metric dimension, and upper dimension.

Novel Analysis of Hermite–Hadamard Type Integral Inequalities via Generalized Exponential Type m-Convex Functions

The theory of convexity has a rich and paramount history and has been the interest of intense research for longer than a century in mathematics. It has not just fascinating and profound outcomes in different branches of engineering and mathematical sciences, it also has plenty of uses because of its geometrical interpretation and definition. It also provides numerical quadrature rules and tools for researchers to tackle and solve a wide class of related and unrelated problems. The main focus of this paper is to introduce and explore the concept of a new family of convex functions namely generalized exponential type m-convex functions. Further, to upgrade its numerical significance, we present some of its algebraic properties. Using the newly introduced definition, we investigate the novel version of Hermite–Hadamard type integral inequality. Furthermore, we establish some integral identities, and employing these identities, we present several new Hermite–Hadamard H–H type integral inequalities for generalized exponential type m-convex functions. These new results yield some generalizations of the prior results in the literature.

Intuitionistic fuzzy quasi-interior ideals of semigroups

In this study, it is purposed to introduced the concept of quasi-interior ideal on intuitionistic fuzzy semigroups. The concept introduced is supported with examples and its basic algebraic properties are examined.

On k-Fibonacci hybrid numbers and their matrix representations

In this paper, k-Fibonacci hybrid numbers are defined. Also, some algebraic properties of k-Fibonacci hybrid numbers such as Honsberger identity, Binet Formula, generating functions, d’Ocagne identity, Cassini and Catalan identities are investigated. In addition, we also give 2 × 2 and 4 × 4 representations of the k-Fibonacci hybrid numbers HF_{k,n}.