In this paper, we are concerned with a new modification of the well-known (p;q)-Bernstein novel type operators with the gamma integral functions. The direct results demonstrate several aspects of approximations. Such as the rate of convergence theorem using Peetre's K-functional and Korovkin's theorem, which also validates the well-known Voronovskaja's theorem and the convergence theorem for Lipschitz continuous functions.
In this paper, the notion of generalization of pseudo p-closure, denoted by gcl, is introduced and its related properties are investigated. The gcl of subalgebras and pseudo-ideals is discussed. Also, a necessary and sufficient condition for an element to be minimal; and for pseudo BCI-algebra to be nilpotent are given. It is proved that the set of all nilpotent elements of a pseudo BCI-algebra A, denoted by NA, is the least closed pseudo-ideal with the property gcl(NA)=NA. Finally, it is shown that the mentioned notion, as a function, defines a closure operation on pseudo-ideals.
Our focus is on the existence of certain structures and similarities between pseudo slant submanifolds and nearly δ- Lorentzian trans Sasakian manifolds. We examine the geometry of these submanifolds.For a totally umbilical proper-slant submanifold that corresponds to a nearly δ- Lorentzian trans Sasakian manifold, we demonstrate necessary and sufficient conditions. Finally, we talk about the integrability of distributions on approximately δ- Lorentzian trans Sasakian manifold pseudo-slant submanifolds.
In this paper, we begin by introducing the concept of fuzzy partial hyperalgebra and exploring the relationships between congruence relations and strong congruence relations within this framework. We then construct an embedding of any fuzzy partial hyperalgebra into a fuzzy hyperalgebra, ensuring that all congruence relations on the embedded fuzzy partialhyperalgebra can be simultaneously extended to the corresponding fuzzy hyperalgebra.
The purpose of this paper is to introduce and study hyperframes. Where a frame is a generlization of a basis of a vector space, a hyperframe will act as a generalization of a basis in hypervector space. The present research will only considerl hypervector spaces over the reals, viewed as a Krasner hyperfield. In particular, similarity, equivalency, and dual hyperframes are discussed.
Abstract. Let R be a commutative ring with identity and A(R) be the set of all ideals of R with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A∗(R) = A(R)\{(0)} and two distinct vertices I and J are adjacent if and only if IJ = (0). Let G = (V; E) be a graph. A domination set for G is a subset S of V such that every vertex not in S is joined to at least one member of S by some edge. The domination number γ(G) is the minimum cardinality among the dominating sets of G. In this paper, we study and characterize the dominating sets and domination numbers of the annihilating-ideal graph AG(R) for a commutative ring R.
In this paper, we analyze the connection between R-hypermodules and graphs by associating a graph with an R- hypermodule through a normal fuzzy subhypermodule. We investigate the graph's properties, including connectedness, completeness, Eulerian and Hamiltonian characteristics. By defining a regular relation based on the fuzzy subhypermodule, we study how algebraic properties of R-hypermodules induence the associated graph. This work contributes to the understanding of fuzzy algebraic structures and their graphical representations, with potential applications in computer science and network theory.
In this paper, our research sheds new light on generalized ideals, significantly advancing the state of knowledge in ring theory. We introduce an almost δ-primary ideal which unifies an almost prime ideal and an almost primary ideal. We also define and study the concept of a φ-δ-primary ideal in a commutative ring. Some characterizations of almost δ-primary ideal and n-almost δ-primary ideals are proved.
A secure dominating set S ⊆ V is a dominating set of G satisfying the condition that for each u ∈ V \ S, there exists a vertex v ∈ N(u) ∩ S such that (S \ {v}) S {u} is a dominating set of G. The minimum cardinality of a secure dominating set of G is called the secure domination number of G, γs(G). In this paper, we obtain the secure domination number of generalized thorn paths, thorn graphs, and some special graph classes like thorn rod, thorn star and Kragujevac trees, where the generalized thorn paths are important in the study of chemical compounds.
The concept of the Sombor index was extended by Reti et. al. [1] by introducing a pSombor index which can be seen as the p norm of the vector x = (d(u), d(v)) as p → ∞, ∥x∥∞ = max{d(u), d(v)}. Inspired by this, we defined indices namely, Reformulated Inf- Sombor index, Entire Inf-Sombor index, and KG Inf-Sombor index. Also, we present lower and upper bounds by using some graph parameters and obtain exact values of these new topological indices in some graph families. Further, we evaluated the statistical behavior of these indices after computing index values for different types of dendrimers for various growth values k.
The Indu-Bala product of graphs G and H consists of two disjoint copies of the join of G and H such that there is an adjacency between the corresponding vertices in the two copies of H. A vertex subset S of a graph G = (V, E) is said to be a geodetic set if every vertex in G is in some u−v geodesic, where u and v are any two vertices in S. The minimum cardinality of such a set is the geodetic number of G. The vertex subset D of a graph G is said to be a dominating set if every vertex in G is either in D or adjacent to at least one vertex in D. The minimum cardinality of such a set is the domination number of G. In this work, the authors studied various geodetic and dominating extensions with respect to the Indu-Bala product of graphs. The Aα matrix associated with a graph is a convex linear combination of its adjacency matrix and degree diagonal matrix, offering deeper insights into the properties of both matrices. In this article the authors discuss the Aα spectrum of Indu-Bala product of graphs.
In this paper we prove some curvature properties of anti-invariant submanifold of Lorentzian para-Kenmotsu manifold (briefly, LP-Kenmotsu manifolds) with respect to Zamkovoy connection (∇∗). Next, we study Einstein soliton on anti-invariant submanifold of LP-Kenmotsu manifold with respect to Zamkovoy connection. Further, we study η-Einstein soliton on this submanifold with respect to Zamkovoy connection under different curvature conditions. Finally, we give an example of anti-invariant submanifold of 5-dimensional LP-Kenmotsu manifold admitting η-Einstein soliton with respect to ∇∗ and verify a relation on it.
The class of generalized Berwald metrics contains the class of Berwald metrics as a special case. Let F= αΦ(s), s=β/α, be a generalized Berwald (α, β)-metric on manifold M. We show that F has vanishing S-curvature S=0 and is of relatively isotropic Landsberg curvature L+ cFC=0 if and only if B=0, where c=c(x) is a scalar function on M.
In this paper, we investigate a Finsler space characterized by a cubic changed infinite series metric given by F(γ, β)=β2/(β-γ_. We derive the fundamental tensors necessary to describe the geometric properties of this Finsler space. Additionally, we determine the conditions under which this Finsler space with the cubic modified infinite series metric can be simplified into special types of Finsler spaces, including quasi-C-reducible, semi-C-reducible, C-reducible, and C2-like Finsler spaces, based on its various forms of the Cartan tensor.
The aim of this research paper to use the concept of Intimate mappings to demonstrate the existence and uniqueness of common fixed point theorems for self-mappings in intuitionistic fuzzy metric space. The goal of this research work is to prove the existence and uniqueness of common fixed point theorems for selfmappings in intuitionistic fuzzy metric space using the notion of intimate mappings
For Krasner hyperrings, we study d-prime hyperideals where d is a homo-derivation. Furthermore, we show that every maximal d-hyperideal and d-prime hyperideal is a prime hyperideal of a commutative hyperring. Finally, we prove that if W is a d-prime hyperideal of a hyperring R and d(qn) ∈ W for some q∈R, then d2(q)∈ W.
This article aims to compare the efficiency of different imputation methods with missing data. In this way we use mean, median, Expected-Maximization (EM), regression imputation(RI) and multiple imputations (MI) to replace missing data.In fact, we employ three proposed combination methods, namely EM imputation with MI imputation (EMMI), EM imputation with regression imputation (EMR), and regression imputation with MIimputation (MI). In this paper, we compare these methods using an example study of Waterborne Container Trade by the US Customs Port (2000-2017) where the methods with different missing percent-ages. Several criteria, are used to compare estimations efficiency, such as mean, Standard Deviation (SD), and Mean Squared Error (MSE). The results show that the efficiency of composite imputation methods in almost all situations, in terms of MSE, RMI imputation method outperforms other methods. Nevertheless, when the missing percentage is small, the EMR imputation method performs better. In terms of the SD criterion, we find that the MI method is better than the other methods, where the RMI method is good when the missing percentage is large. When the missing percentage is in the range (40-50%), the EMR and RMI imputation methods give a better MSE.
This study investigates the efficacy of a novel PDα-type fractional-order iterative learning control (FOILC) approach for a class of fractional-order linear continuous-time delaying switched systems. The approach is evaluated in terms of Lp norm performance, aiming to mitigate the challenges associated with time delays in repetitive regulation of fractional-order linear systems. The generalised Young inequality of the convolution integral is used to leverage the resilience of the PDα-type approach in the iteration domain when the systems are perturbed by constrained external disturbances. We next analyse the convergence of the techniques for noise-free systems. The results demonstrate that it is feasible to guarantee both convergence and robustness over the duration of the experiment in certain situations. We study the convergence of error for the proposed class of fractional-order linear continuous-time delaying switched systems.
Carbon nanosheets are nanomaterials consisting of two-dimensional circular arrangements of carbon atoms with diameters. A C4C8 nanosheet is a lattice obtained from a trivalent arrangement of carbon atoms into alternating squares C4 and octagons C8. T1UC4C8[p, q] and T2UC4C8[p, q] are two types of nanosheets made by C4C8 decorations. In nanotechnology, topological indices are used to quantify the structural properties of nanoparticles. In this paper, we investigate the application of topological indices, specifically weighted Mostar indices, to characterize the structures of nanosheets. We employ a variant of the cut method to determine explicit expressions for the additively weighted Mostar index and multiplicatively weighted Mostar index for T1UC4C8[p, q] and T2UC4C8[p, q] nanosheets.
As an extension of intuitionistic fuzzy sets, we introduce the notion of -fuzzy set ( denoted by SSR) of QS -ideals on a OS -algebra and investigate its properties. Furthermore we study the homomorphic image and inverse image of SSR -fuzzy QS -ideals of a QS -algebra under homomorphism of QS -algebras. Moreover, the Cartesian product of SSR -fuzzy QS -ideals in Cartesian product QS-algebras is given. Finally, novel correlation coefficient between two SSR- fuzzy sets are also studied.
