Convergence Of Sequence Research Articles

A Framework for I*-Statistical Convergence of Fuzzy Numbers

In this study, we investigate the concept of I*-statistical convergence for sequences of fuzzy numbers. We establish several theorems that provide a comprehensive understanding of this notion, including the uniqueness of limits, the relationship between I*-statistical convergence and classical convergence, and the algebraic properties of I*-statistically convergent sequences. We also introduce the concept of I*-statistical pre-Cauchy and I*-statistical Cauchy sequences and explore its connection to I*-statistical convergence. Our results show that every I*-statistically convergent sequence is I*-statistically pre-Cauchy, but the converse is not necessarily true. Furthermore, we provide a sufficient condition for an I*-statistically pre-Cauchy sequence to be I*-statistically convergent, which involves the concept of I*−liminf.

Wijsman and Wijsman Randomly Triple Ideal Convergence Sequences of Sets in Probabilistic Metric Spaces

Many authors have extended the concept of convergence from number sequences to sequences of sets. In this paper, we focus on two notable adaptations: Wijsman convergence and randomly ideal convergence. We introduce and analyze several new types of convergence for sequences of sets: IψW3-convergence, I∗,ψW3-convergence, IψW3-Cauchy, I∗,ψW3-Cauchy, (IψW3, IψW)-convergence, and (I∗,ψW3, I∗,ψ)-convergence. These new concepts expand the framework of convergence and provide a deeper understanding of the behavior of set sequences under various conditions. Through rigorous analysis, we demonstrate the relationships between these new forms of convergence and their classical counterparts, highlighting their theoretical significance and potential applications in mathematical analysis and related fields. Our findings offer a comprehensive exploration of these advanced convergence concepts, paving the way for further research and development in this area.

Methods of Multi-Criteria Optimization of Technological Processes in a Fuzzy Environment Based on the Simplex Method and the Theory of Fuzzy Sets

Many modern technological objects in practice are characterized by the uncertainty of the initial information necessary for their management. Recently, one of the pressing scientific and practical problems is the development of new optimization methods for controlling the operating modes of such objects in a fuzzy environment. In this regard, the objective of this study is to develop methods of multi-criteria optimization in a fuzzy environment by modifying the simplex method and various optimality principles based on fuzzy mathematics methods. The methodology of the proposed study is based on a hybrid approach, which consists of the integrated use and modification of simplex methods and optimization methods with various optimality principles for working in a fuzzy environment. The main results are as follows: a simplex method of multi-criteria optimization of immeasurable criteria (here, we are talking about the impossibility of physical measurements of criteria, the values of which are estimated by decision maker); a theorem on the convergence of the solution sequence obtained using the proposed method to the minimum value of the criteria; a heuristic method based on a modification for fuzziness and a combination of the maximin and Pareto optimality principles, which allows effectively solving multi-criteria optimization problems in a fuzzy environment. The heuristic method proposed will be used to solve a real production problem—optimization of the technological process of benzene production.

On the nature of Bregman functions

Let C⊂Rn be convex, compact, with nonempty interior and h be Legendre with domain C, continuous on C. We prove that h is Bregman if and only if it is strictly convex on C and C is a polytope. This provides insights on sequential convergence of many Bregman divergence based algorithm: abstract compatibility conditions between Bregman and Euclidean topology may equivalently be replaced by explicit conditions on h and C. This also emphasizes that a general convergence theory for these methods (beyond polyhedral domains) would require more refinements than Bregman's conditions.

Some Results on f-Statistical Convergence of Double Sequences

Some Results on f-Statistical Convergence of Double Sequences

Characterization and analysis of generalized grey incomplete gamma noise

The grey incomplete gamma distributions was established by one of the authors in a previous publication. In this article we use the Kondratiev characterization theorem to identify those via a suitable Laplace transform with holomorphic functions with suitable properties. We establish theorems for the integration and convergence of sequences of these distributions. As direct applications of these analytic tools we give the examples of Donsker's delta function, identify the time-derivative of the process as a suitable distribution and define the Gamma grey Ornstein–Uhlenbeck process.

On power series statistical convergence and new uniform integrability of double sequences

On power series statistical convergence and new uniform integrability of double sequences

Convex combinations of some convergent sequences

We consider the convex combinations , of a pair of sequences of real numbers and such that , converging to , and study the location of the limit inside the intervals , for every or for sufficiently large . We also investigate the same problem for the case of two corresponding sequences converging to . Among other results, we prove some, a bit, unexpected ones. Namely, for each , we determine the exact index at which the sequence changes the monotonicity, and we also determine the type of the monotonicity. A number of interesting remarks are also presented.

Neutrosophic Fuzzy Tribonacci ℐ-Lacunary Statistical Convergent Sequence Spaces

Abstract The aim of this paper is to introduce and investigate some neutrosophic fuzzy tribonacci ℐ-lacunary statistical convergent sequence spaces by utilizing the domain of regular tribonacci matrix A = (ajk ). Morever, we also put forward various algebraic and topological features of these convergent sequence spaces and establish several interesting inclusion relations.

Rapid synthesis and screening of natively paired antibodies against influenza hemagglutinin stem via oPool+ display.

Antibody discovery is crucial for developing therapeutics and vaccines as well as understanding adaptive immunity. However, the lack of approaches to synthesize antibodies with defined sequences in a high-throughput manner represents a major bottleneck in antibody discovery. Here, we presented oPool+ display, which combines oligo pool synthesis and mRNA display to construct and characterize many natively paired antibodies in parallel. As a proof-of-concept, we applied oPool+ display to rapidly screen the binding activity of >300 natively paired influenza hemagglutinin (HA) antibodies against the conserved HA stem domain. Structural analysis of 16.ND.92, one of the identified HA stem antibodies, revealed a unique binding mode distinct from other known broadly neutralizing HA stem antibodies with convergent sequence features. Yet, despite such differences, 16.ND.92 remained broadly reactive and conferred in vivo protection. Overall, this study not only established an experimental platform that can be applied in both research and therapeutics to accelerate antibody discovery, but also provides molecular insights into antibody responses to the influenza HA stem, which is a major target for universal influenza vaccine development.

Diverse Origins of Near-Identical Antifreeze Proteins in Unrelated Fish Lineages Provide Insights Into Evolutionary Mechanisms of New Gene Birth and Protein Sequence Convergence.

Determining the origins of novel genes and the mechanisms driving the emergence of new functions is challenging yet crucial for understanding evolutionary innovations. Recently evolved fish antifreeze proteins (AFPs) offer a unique opportunity to explore these processes, particularly the near-identical type I AFP (AFPI) found in four phylogenetically divergent fish taxa. This study tested the hypothesis of protein sequence convergence beyond functional convergence in three unrelated AFPI-bearing fish lineages. Through comprehensive comparative analyses of newly sequenced genomes of winter flounder and grubby sculpin, along with available high-quality genomes of cunner and 14 other related species, the study revealed that near-identical AFPI proteins originated from distinct genetic precursors in each lineage. Each lineage independently evolved a de novo coding region for the novel ice-binding protein while repurposing fragments from their respective ancestors into potential regulatory regions, representing partial de novo origination-a process that bridges de novo gene formation and the neofunctionalization of duplicated genes. The study supports existing models of new gene origination and introduces new ones: the innovation-amplification-divergence model, where novel changes precede gene duplication; the newly proposed duplication-degeneration-divergence model, which describes new functions arising from degenerated pseudogenes; and the duplication-degeneration-divergence gene fission model, where each new sibling gene differentially degenerates and renovates distinct functional domains from their parental gene. These findings highlight the diverse evolutionary pathways through which a novel functional gene with convergent sequences at the protein level can evolve across divergent species, advancing our understanding of the mechanistic intricacies in new gene formation.

A New Notion of Convergence Defined by The Fibonacci Sequence: A Novel Framework and Its Tauberian Conditions

The Fibonacci sequence has broad applications in mathematics, where its inherent patterns and properties are utilized to solve various problems. The sequence often emerges in areas involving growth patterns, series, and recursive relationships. It is known for its connection to the golden ratio, which appears in numerous natural phenomena and mathematical constructs. In this research paper, we introduce new concepts of convergence and summability for sequences of real and complex numbers by using Fibonacci sequences, called Δ-Fibonacci statistical convergence, strong Δ-Fibonacci summability, and Δ-Fibonacci statistical summability. And, these new concepts are supported by several significant theorems, properties, and relations in the study. Furthermore, for this type of convergence, we introduce one-sided Tauberian conditions for sequences of real numbers and two-sided Tauberian conditions for sequences of complex numbers.

The matroid of a graphing

Graphings serve as limit objects for bounded-degree graphs. We define the “cycle matroid” of a graphing as a submodular setfunction, with values in [0,1], which generalizes (up to normalization) the cycle matroid of finite graphs. We prove that for a Benjamini–Schramm convergent sequence of graphs, the total rank, normalized by the number of nodes, converges to the total rank of the limit graphing.

Certain topological properties for almost convergent Catalan-Motzkin sequence space

The purpose of this paper is to introduce a new almost convergent sequence space by means of a matrix involving Catalan and Motzkin numbers. It is demonstrated that this novel sequence space and the space of all almost convergent sequences are linearly isomorphic and the $\beta$-dual of this new space is deduced. In addition, by defining Catalan-Motzkin core of a complex-valued sequence, certain inclusion relations are derived for it.

Mackey convergence and separation in $(L, M)$-fuzzy bornological vector spaces

This paper aims to introduce the concepts of Mackey convergence degree for sequences and separation degree for spaces in $(L, M)$-fuzzy bornological vector spaces. Additionally, the paper presents the concept of bornological closure degree for fuzzy sets. Moreover, the paper discusses various characteristics of these concepts. Furthermore, the paper examines the degree relationships among a Mackey convergence sequence, a separated space, and a bornologically closed fuzzy set. Finally, the paper analyzes the properties of functors $\omega$ and $\iota$ between $M$-fuzzifying bornological vector spaces and $(L, M)$-fuzzy bornological vector spaces in terms of Mackey convergence degree and separation degree.

Novel generalized policy iteration for efficient evolving control of nonlinear systems

In this article, we construct a novel generalized policy iteration framework to address optimal regulation problems for discrete-time nonlinear systems in a more efficient way. Relevant properties are investigated for the framework, including monotonicity and convergence of the iterative value function sequence as well as the admissibility of the iterative control policy. Additionally, an innovative approach is developed to seek an initial admissible control policy for the framework with an adjustable searching speed. Based on these, an evolving control algorithm is presented with stability guarantee. This algorithm employs iterative control policies for system control during the computation of the optimal control policy, as opposed to waiting for the generation of the optimal control policy before implementing control. Eventually, two simulation experiments are conducted with real-world physical backgrounds, in order to illustrate the performance of the proposed strategy.

The Berry–Esseen bound in de Jong’s CLT

We prove a Berry–Esseen bound in de Jong’s classical CLT for normalized, completely degenerate U-statistics, which says that the convergence of the fourth moment sequence to three and a Lindeberg–Feller type negligibility condition are sufficient for asymptotic normality. Our bound is of the same optimal order as the bound on the Wasserstein distance to normality that has recently been proved by Döbler and Peccati (2017).

Matrix transforms of the set of α-absolutely convergent sequences with speed

Matrix transforms of the set of α-absolutely convergent sequences with speed

ROUGH IDEAL CONVERGENCE OF DOUBLE SEQUENCES IN INTUITIONISTIC FUZZY NORMED SPACES

The idea of rough statistical convergence for double sequences was studied by Ozcan and Or [34] in a intuitionistic fuzzy normed space. Recently the same has been generalized in the ideal context by Hossain and Banerjee [17] for sequences. Here in this paper we have discussed the idea of rough ideal convergence of double sequences in intuitionistic fuzzy normed spaces generalizing the idea of rough statistical convergence of double sequences. Also we have defined rough I2-cluster points for a double sequence and also investigated some of the basic properties associated with rough I2-limit set of a double sequence in a intuitionistic fuzzy normed space.

New types of convergence of double sequences in neutrosophic fuzzy G -metric spaces

New types of convergence of double sequences in neutrosophic fuzzy G -metric spaces