Concept Of Convergence Research Articles

Statistical Analysis of Atmospheric Delay Gradient and Rainfall Prediction in a Tropical Region

In recent years, precipitable water vapor has emerged as a key atmospheric parameter in weather prediction research. However, relying on only one parameter does not always accurately predict rainfall, as other atmospheric parameters also contribute to initiating rain events. In our previous study, we explored a methodology for rainfall forecasting based on the atmospheric delay gradient at an individual station in the tropical region. Commonly referred to as the atmospheric gradient, it accounts for the delay in GNSS signals due to changes in horizontal refractivity while propagating through the troposphere to the ground station. This paper discusses the spatial and temporal correlation of the gradient with precipitation occurring over a region. We have investigated different features, such as gradient magnitude, gradient convergence, and the flux of the atmospheric gradient, to propose potential nowcasting criteria for precipitation in the tropical climatic zone. The atmospheric gradient in the surrounding region orients toward the area of precipitation as the rain event approaches. This gradient gradually alters its orientation and converges toward the region of rainfall at the time of precipitation, introducing the concept of gradient convergence. This phenomenon results in an inward gradient flux at the time of the downpour, which presents a potential parameter for rainfall prediction over an area. We also proposed investigating area sizes of 4° × 4° or 8° × 8°, depending on the gradient feature, to establish a forecasting methodology for rainfall. The weather front in the tropical region begins to initiate 12 h before the actual time of occurrence and advances toward the area where it will have an impact from a more distant location. This article presents a detailed investigation of various features of the atmospheric gradient and its potential to nowcast rainfall for a region, as well as proposes the lead time for long-term weather predictions. Furthermore, a deep neural network has been employed to predict rainfall events for the next 6 h over an area in the tropical region.

ON I-DEFERRED STATISTICAL CONVERGENCE OF ORDER Α FOR COMPLEX UNCERTAIN SEQUENCES

In this paper, we introduce the concepts of I-deferred statistical convergence almost surely of order α, I-deferred statistical convergence in measure of order α, I-deferred statistical convergence in mean of order α, I-deferred statistical convergence in distribution of order α, I-deferred statistical convergence in uniformly almost surely of order α and some relationships among them are discussed.

On the Generalized Weighted Statistical Convergence

Statistical convergence and summability represent a significant generalization of traditional convergence for sequences of real or complex values, allowing for a broader interpretation of convergence phenomena. This concept has been extensively examined by numerous researchers using various mathematical tools and applied to different mathematical structures over time, revealing its relevance across multiple disciplines. In the present study, a generalized definition of the concepts of statistical convergence and summability, termed (△_v^m )_u-generalized weighted statistical convergence and (△_v^m )_u-generalized weighted by [¯N_t ]-summability for real sequences, is introduced using the weighted density and generalized difference operator. Based on this definition, several fundamental properties and inclusion results, obtained by differentiating the components used in the definitions, are provided.

Analisis Kemampuan Mahasiswa Matematika FMIPA Unimed dalam Menyelesaikan Permasalahan Konvergensi dan Divergensi Barisan Bilangan Real dengan Berbantuan Software MATLAB

This research aims to analyze the ability of FMIPA Mathematics students at Medan State University (Unimed) in solving problems of convergence and divergence of real number sequences, as well as evaluating the effectiveness of using MATLAB software in supporting understanding of these concepts. This research is based on the aim of overcoming students' difficulties in understanding the concepts of convergence and divergence. The research method used was qualitative, with a sample of 20 students selected using purposive sampling. Data was collected through written tests and observations of the use of MATLAB which were distributed via Google Form in solving questions. The results show that 55% of students are in the "very understanding" category, with MATLAB proving to be very effective in making problem solving easier and deepening understanding.

Sifat Kekonvergenan Lemah pada Ruang Bernorma beserta Operator pada Ruang Barisan Konvergen Lemah

The concept of weak convergence is generated by “weakening” the existing convergence properties in normed spaces. The outcome of this article is to prove the basic properties of weak convergence, the space of weakly convergent sequence is a Banach space and the operators from the space of weakly convergent sequence to other sequence spaces (l1(X),lp(X), linfty(X),S(X) ) and vice versa are linear and bounded .

The Yearning to Be Everything to Everyone: Examining the Homogenization of Social Media Platforms in the Context of Convergence

Social media platforms are continually adding new features and enhancing existing ones to attract users and extend their screen time. These platforms constantly innovate to capture users' attention and gain an edge in the competitive landscape of social media. This study focuses on identifying the similarities between features of popular social media platforms and examines whether these similarities lead to homogenization. Specifically, presenting the chronological development of these features over time is crucial for understanding the historical development and evolution of social media. The framework of this research is based on the concept of convergence. The convergence concept is used to assess whether there are commonalities in the tools, interfaces, and interaction modes offered by the platforms to their users. In this context, the study investigates how the features provided by social media platforms become similar over time and how user experiences become homogenized. The 'walkthrough method' was employed to analyze the interfaces of the selected platforms. This method involves a step-by-step examination of user experiences on the platforms to understand how features are presented and how they are utilized by users. Data were collected through notes and recordings made by researchers while using the platforms. The results indicate a significant similarity and convergence in the features offered by popular social media platforms. For instance, features such as story sharing, live streaming, filter usage, and the explore tab have become widespread across different platforms. Platforms that consider users' habits and preferences offer familiar and easily accessible experiences through these similar features. Consequently, it can be said that social media platforms create a form of homogenization in user experiences by providing similar features over time. This phenomenon offers important insights into the evolution and future development of social media. Additionally, the study suggests that the concept of convergence not only encompasses the merging of features from different technologies but also indicates a tendency for similar platforms to converge internally.

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.

GRP – A direct Godunov extension

The classical paper [40] by S. K. Godunov had a revolutionary effect on the field of numerical simulations of compressible fluid flows. Yet, for some twenty years after its publication, it was mostly used by the mathematical community in the Soviet Union. The seminal paper of van Leer [85] has inaugurated the period of universal interest in high-resolution extensions of Godunov's scheme. The first step to take was to modify the (locally) self-similar solution to the Riemann Problem (at discontinuities) by allowing piecewise-polynomial (rather than piecewise-constant) initial data. The GRP (Generalized Riemann Problem) analysis [6] provided analytical solutions (for piecewise-linear data) that could be readily implemented in a high-resolution robust code. This review paper focuses on the evolution of some mathematical aspects of this method. It addresses the three concepts of consistency, stability and convergence in the context of compact finite difference (or finite volume) schemes for systems of nonlinear hyperbolic conservation laws. The treatment utilizes the framework of “balance laws”, a common viewpoint in relevant physical conservation laws. The first significant observation is that under very mild conditions a weak solution is indeed a solution to the balance law (obtained by a formal application of the Gauss-Green formula). Since high-resolution schemes require the computation of several quantities per mesh cell (e.g., slopes), the notion of “consistency” must be extended to this framework. A combination of consistency hypothesis with stability of the scheme leads to a suitable convergence theorem, generalizing the classical convergence theorem of Lax and Wendroff [52]. Finally, the limit functions are shown to be entropy solutions by using a notion of “Godunov compatibility”, which serves as a substitute to the entropy condition.

On a nonlinear general eigenvalue problem in Musielak–Orlicz spaces

Abstract In this paper, we concern the existence result of the following general eigenvalue problem: { 𝒜 ⁢ ( u ) = λ ⁢ ℬ ⁢ ( u ) in ⁢ Ω , D α ⁢ ( u ) = 0 on ⁢ ∂ ⁡ Ω , \left\{\begin{aligned} \displaystyle{}\mathcal{A}(u)&\displaystyle={\lambda}% \mathcal{B}(u)&&\displaystyle\phantom{}\text{in }{\Omega},\\ \displaystyle D^{\alpha}(u)&\displaystyle=0&&\displaystyle\phantom{}\text{on }% {\partial\Omega},\end{aligned}\right. in an arbitrary Musielak–Orlicz spaces, where 𝒜 {\mathcal{A}} and ℬ {\mathcal{B}} are quasilinear operators in divergence form of order 2 ⁢ n {2n} and 2 ⁢ ( n - 1 ) {2(n-1)} , respectively. The main assumptions in this case are that 𝒜 {\mathcal{A}} and ℬ {\mathcal{B}} are potential operators with 𝒜 {\mathcal{A}} being elliptic and monotone. In this study, we intentionally avoid imposing constraints on the growth of a generalized N-function, including the Δ 2 {\Delta_{2}} -condition for both the generalized N-function and its conjugate. Consequently, this necessitates the formulation of the approximation theorem and the extensive utilization of modular convergence concepts.

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.

Is plate tectonics a post-Archean phenomenon? A petrological perspective

The petrogenesis of contemporary igneous and metamorphic rocks is commonly explained by plate tectonics, but how far back in time does this relationship hold? Here we investigate whether the distinctive petrological features of recent ocean crust, subduction-related magmatism and regional metamorphism can be unambiguously identified in the Archean geological record. From an igneous perspective based on geological relationships and Th–Nb systematics, it is difficult to claim that any Archean ‘ophiolite’ was part of a global plate system rather than deriving from a plume ascending through attenuating lithosphere. Furthermore, the rarity of subduction-related rocks, particularly their plutonic equivalents, which have good preservation potential, is consistent with the concept of local convergence and short-lived subduction. From a metamorphic perspective, the appearance of orogenic eclogites in the Paleoproterozoic, the widespread occurrence of blueschists and ultrahigh-pressure metamorphic rocks since the late Neoproterozoic, and a change from a unimodal to a bimodal distribution of metamorphic T / P during the Proterozoic, are responses to secular cooling and the evolution of global tectonics since the Archean. Our petrological perspective is that plate tectonics analogous to that on Earth today is probably a post-Archean phenomenon.

Examining an Evolving Biologically Inspired Design Professional Learning Environment through Conjecture Mapping and Design-Based Research.

Biologically inspired design (BID) in engineering is a convergent, systematic approach that uses analogies from biological organisms to develop solutions for human engineering and design problems. Based on outcomes from prior studies of integrating BID in higher education, incorporating BID into pre-college education is a logical evolution. For effective BID instruction of these convergent concepts in pre-college education, teachers need to be well-equipped with biological, engineering, and pedagogical knowledge, both in general and those unique to the convergent, still evolving discipline. In this paper, we investigate the Professional Learning (professional learning) environment designed to foster engineering teachers' understanding of BID integration in engineering and to determine to what extent the evolving professional learning environment fostered engineering teachers' conceptual knowledge of BID across the three-year project. This design study applies conjecture mapping with design-based research (DBR) to examine a professional learning environment that changed over three summers and its impact on teachers' conceptual understanding of BID integration in engineering. The analysis indicates that a combination of experiential and informal learning experiences along with engagement in a formal design challenge promoted teacher enthusiasm and a conceptual understanding of BID across the three years. Professional learning fostered teachers' understanding of BID integration in engineering and enabled them to integrate BID into their engineering teaching practice.

Networked learning in a postdigital-biodigital age

Networked Learning has developed predominantly in university / research settings and communities, yet much of the research across decades can be shown to have implicit links with current popular and much broader global concepts, such as bioinformation, biodigitalism, postdigitalism, and viral modernity. In this paper we explore these implicit connections as an important and perhaps less unrecognized part of Networked Learning. We therefore seek to surface some postdigital-biodigital challenges in Networked Learning by revisiting relevant histories, concepts, and definitions and also noticing where there are parallels and connections, particularly when Networked Learning and Postdigital Science and Education have developed in the same Zeitgeist. Despite radically different histories, these areas of research seem to have resulted in different, yet often overlapping theories, research approaches, and ethos. After taking time to look into a number of these cross-cutting areas of interest, we ask the question of why a focus towards postdigital-biodigital challenges in Networked Learning is worthwhile, and indeed, why now? Based on our explorations we perceive Networked Learning to implicitly hold a long history of deep and successful engagement with postdigital-biodigital challenges in theory and through the concept of convergence. The role of convergence is an important and sustained concept in Networked Learning that can help in breaking down perceived barriers to developing cross-cutting research in any of the areas discussed throughout this paper. It is therefore timely to bring to light explicitly such connections, to help us to focus our research efforts on Networked Learning in a postdigital-biodigital age.

A Generalized Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-Convergence Concept for a Class of Equilibrium Problems

A novel generalization of Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-convergence applicable to a class of equilibrium problems is studied. After the introduction of the latter, a variety of its applications is discussed. The existence of equilibria with emphasis on Nash equilibrium problems is investigated. Subsequently, our Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-convergence notion for equilibrium problems is introduced and discussed as well as applied to a class of penalized generalized Nash equilibrium problems and quasi-variational inequalities. The work ends with a comparison of our results to previous generalizations in the literature.

The Solo Broadcast Journalism Practices from an Industry Perspective

Social networking is a rapidly growing source of news in broadcast journalism. Broadcast journalism is facing a continuing decline in electronic media circulation and social media changes. The concept of online convergence in broadcast journalism has become a news trend on social media. Solo broadcast journalism and social media are becoming practices in news organisations today. Therefore, this article aims to identify the practices of solo broadcast journalism from an industry practitioner’s perspective. A qualitative methodological approach was used in this study. Face-to-face interviews were conducted with eight informants who practised solo broadcast journalism. The data were analysed thematically. The results showed that production tasks, location reviews, good time management, relationships with the community, preparation tasks, and comfortable places are among the concepts of practising solo broadcast journalism in news organisations. The findings of this study show that journalists practice solo broadcast journalism to get news in line with the development of digital media today. The findings of this study are expected to benefit the National ICT Agenda on National Broadband Policy from the perspective of newspaper organisations in expanding the use of technology in the distribution and publication of stories for news. The findings of this study will help make appropriate adjustments to develop human capital by integrating broadcast journalism practices with technology-assisted work in solo broadcast journalism. In addition, this study is also significant to the National Education Policy. The study will impact the educational curriculum of broadcast journalism by introducing changes in line with the development of solo broadcast journalism. Keywords: Practice, solo broadcast journalism, industry practitioner, Industrial Revolution 4.0, social media.

Mediation and Convergent Sociality: Toward a Theory of Social Dialogue

The article investigates the mechanisms shaping a new quality of social development in contemporary Russia amidst growing societal challenges. Four key mechanisms are explored: mediation, social dialogue, polysubjectivity, and convergence. These are analyzed for their role in fostering novel forms of social integration and development. The mechanisms serve as tools for studying and shaping the current interplay between tradition and innovation, cultural stasis and social dynamics across various sociocultural contexts and transitional processes. The paper draws upon works presented at the All-Russian Scientific Conference “Individualization and Collectivism in Contemporary Russian Society,” offering an original interpretation that synthesizes and structures these studies. Notable contributions include V.A. Lektorsky’s concept of “the supra-individual as social universality,” which advances our understanding of socio-individual meaning formation and transcends the individual-society dichotomy. A.A. Auzan’s analysis of the dual-core structure of Russian culture aptly captures the unique challenges of social development in Russia. O.V. Aksenova’s examination of the contradictory nature of social action subjects in an increasingly technologized society illuminates the complexities of balancing freedom with necessity, and uniformity with diversity in social action. V.M. Rozin’s approach is considered for its potential to facilitate mediational social dialogue in Russian society. The author argues that neither the individualistic nor the collectivist cores of Russian culture can independently drive effective modernization. Instead, the concept of convergence is proposed as a means to transcend the extremes of ego-individualism and totalitarian collectivism. Three primary directions for implementing convergent strategies are identified: synthesizing individual and social aspects in social action and dialogue, optimizing center-periphery interactions in governance, and developing public-private partnership models as a form of economic convergence. The study emphasizes the need for new forms of social integration and concludes that Russia’s sustainable social development requires an integrative socio-individual model, combining elements of individual freedom and collective solidarity.

Administrative Constitutionalism as a Concept of Positive Convergence of European Liberal Values and the Russian World Idea in the National State Law Reality

Administrative Constitutionalism as a Concept of Positive Convergence of European Liberal Values and the Russian World Idea in the National State Law Reality

Economic growth in the Sub-Saharan African world region: convergence theory

Purpose The processes of convergence are particularly challenging in the Sub-Saharan African frameworks, considering the diversity of contexts and endogenous particularities. Creating conditions to support these nations to improve their socioeconomic dynamics and performance requires additional contributions from international organisations, governments and the scientific community. In this scenario, this paper aims to analyse the convergence process in Sub-Saharan African countries over the past three decades. Design/methodology/approach To achieve these objectives, data from the World Bank were considered for the gross domestic product (GDP) per capita over the period 1990–2021. This statistical information was assessed through panel data approaches based on the models from the convergence theory. Specifically, the concepts of sigma and beta convergence were addressed, as well as the concept of catch-up rates. Findings The findings obtained highlight evidence of the existence of clubs of convergence among the Sub-Saharan African countries and the processes of catching up. These results may be relevant support for the policymakers and international funds and programmes. Originality/value This research provides a new perspective on the convergence of GDP per capita in Sub-Saharan African countries, based on an analysis focused on groups of countries identified on the basis of catch-up rates. This approach presents a way of dealing with the different specificities of these nations.

Credit Accessibility Across Indian States: Evidence From Club Convergence

Indian states are immensely heterogeneous in terms of their socioeconomic activities. The economic structure of India is consequently bifurcated too. This study examines, under given heterogeneities, whether credit accessibility among states converges over time, particularly in industrial and agricultural lending. We employ the concept of club convergence and find that substantial heterogeneities and multiple transition paths exist for industrial credit convergence across states, while agriculture credit is relatively less heterogeneous as compared with industry. Therefore, more attention is required to reduce access to banking credit for industries in poorer states.

REFLEXIVITY OF LINEAR n-NORMED SPACE WITH RESPECT TO b-LINEAR FUNCTIONAL

In this paper, we discuss various consequences of Hahn-Banach theorem for bounded b-linear functional in linear n-normed space and describe the notion of re exivity of linear n-normed space with respect to bounded b-linear functional. The concepts of strong convergence and weak convergence of a sequence of vectors with respect to bounded b-linear functionals in linear n-normed space have been introduced and some of their properties are being discussed.