Different Types Of Convergence Research Articles

A novel links between the various modes of convergence

The article introduces several notions of convergence of a series from all possible angles (also called modes of convergence). There are several relations among the various modes of convergence ( Pointwise convergence, converges absolutely, uniformly and normally), which are discussed in the present paper and are summarized by a diagrams, we analyzes the genesis of new links between convergence at the present stage. Our idea is based on the classical convergences, during which a new algebraic properties are called. According Theorem 2.1 and the truth table we will find a new links between the various modes of convergence, Pointwise convergence, converges absolutely, uniformly and normally. These are all different kinds of convergence. A series might converge in one sense but not another. Some of these convergence types are ''stronger'' than others and some are ''weaker.'' Here, we would like to provide definitions of different types of convergence and discuss how they are related.

CHARTING THE GREEN PATH: EMPIRICAL INSIGHTS INTO EU-UKRAINE ENVIRONMENTAL CONVERGENCE

The aim of the study is to conduct an empirical analysis of environmental convergence between the EU and Ukraine. This involves evaluating a set of indicators, identifying clusters of EU and Ukrainian countries to obtain adequate empirical estimates, and directly assessing not only the convergence process but also other patterns of environmental and economic development. Methodology. In addition to the classical models of beta, sigma, gamma and delta convergence, the study of environmental convergence should apply methods that focus on the growth process and the increase in the level of economic development of less developed countries, rather than simply on the reduction of development disparities. Such methods should emphasise the importance of efforts and policies aimed at bringing countries closer together and creating favourable conditions for their growth towards higher levels of development. The authors use the concept of upward convergence (divergence). The empirical analysis of environmental convergence between the EU and Ukraine was conducted for the period 2000-2021, divided into two sub-periods: 2000-2013 and 2014-2021, in order to identify trends in the Russian military invasion in 2014 and its impact on environmental and economic convergence during the war. Results. Studies of different types of convergence between Ukraine and the EU show different results: some indicators indicate convergence, while others show divergence. In fact, the interaction between Ukraine and the EU is a complex process that manifests itself differently depending on the specific indicators. Some aspects of cooperation are already leading to convergence and similarity between the countries, while others are leading to divergence. This demonstrates the need to implement effective strategies and policies of cooperation between Ukraine and the EU to achieve sustainable development. Practical implications. The results obtained can be used to develop environmental policies, commitments, forms of manifestation and main consequences for the ecological and economic system of Ukraine in the context of the Association Agreement and the European Green Deal. The fulfilment of obligations under these initiatives should become the basis for developing effective means of ensuring sustainable development through the implementation of the relevant state environmental and economic policy. Value/originality. The advantage of the proposed approach is that it takes into account negative growth, including environmental pollution. The results of the upward convergence assessment serve as a basis for the development of appropriate strategies, mechanisms, policies, effective governance, investment in human capital and infrastructure, and the creation of favourable conditions for entrepreneurship and innovation.

Does Industrial Agglomeration Promote Regional Innovation Convergence in China? Evidence From High-Tech Industries

The literature examining the importance of industrial agglomeration in innovation performance has expanded greatly in recent years, but the impact of industrial agglomeration, especially high-tech industrial agglomeration on regional innovation convergence, has been neglected. Using quantitative data from 30 provinces in China pertaining to the period 2005–2016, in this article, we analyze regional innovation convergence by focusing on three different types of convergence: σ-convergence, absolute σ-convergence, and conditional β-convergence. On the basis of the spatial effects, this article empirically investigates the impact of high-tech industrial agglomeration on regional innovation convergence in China by using spatial econometric models. The empirical results show that there is significant spatial autocorrelation in regional innovation. Thus, in the assessment of regional innovation convergence, the spatial effects should not be neglected. Moreover, our results demonstrate that regional innovation exists three different types of convergence (i.e., σ-convergence, absolute β-convergence, and conditional β-convergence). In addition, high-tech industrial agglomeration can promote regional innovation convergence. Finally, the grouping of high-tech industries into five subindustries shows that industrial agglomeration has different effects on regional innovation convergence. Overall, our findings provide convincing empirical evidence of the relationship between the high-tech industrial agglomeration and regional innovation convergence and valuable insights into how to realize regional innovation convergence.

Arithmetic statistically convergent on neutrosophic normed spaces

This work is concerned with several important different types of convergence that will be described on neutrosophic normed spaces. In the study, arithmetic convergence was combined with different types of statistical convergence and then integrated into the structure of neutrophic spaces established through the membership function. For this purpose, in the neutrophic normed space, firstly, some important definitions that can be established with lacunary sequence, ideal structures and arithmetic convergent, arithmetic statistical convergence concepts are given, and then some relationships between convergent sequences in this sense are examined. Then, new convergence definitions were established by evaluating lambda sequences together with arithmetic convergence and statistical convergence with the help of Neutrophic normed space structure properties. Finally, with the help of the definitions of degree of convergence, the inclusion relationship between the two set is given.

Trajectory Tracking in Unicycle Mobile Robots: A Homogeneity–based Control Approach

This paper contributes to the design of a family of homogeneous controllers to deal with the trajectory tracking problem in unicycle mobile robots (UMRs). The control strategy is based on a cascade control paradigm, which includes the position and orientation tracking error subsystems. The proposed homogeneous controllers provide different types of convergence to zero for the tracking error dynamics, i.e., asymptotic, exponential, and finite-time convergence. Simulation results illustrate the performance of the proposed family of homogeneous controllers.

Stability of Woven Frames

This article studies the stability of woven frames by introducing some special limits. We show that there exist certain relations among the different types of convergence of frames and obtain some new and more general stability results. As an application of these results, we provide a method for constructing woven frames.

Subsequences of Real Valued Sequences and Convergence

Convergence of real valued sequences is a classical subject of study for many mathematicians and it continues to be studied in recent years. Different types of convergence including ordinary, statistical, almost and ideal convergence, and related properties have been researched. In some studies, the relationship of a sequence and its subsequences regarding some type of convergence is investigated, using Lebesgue measure and Baire category. In this paper we revisit ordinary convergence and study the properties of subsequences of a real valued sequence using measure and category. We state and prove some simple theorems offering fresh insights into a classical subject.

Several Different Types of Convergence for ND Random Variables under Sublinear Expectations

The goal of this paper is to build average convergence and almost sure convergence for ND (negatively dependent) sequences of random variables under sublinear expectation space. By using the basic definition of sublinear expectation space, Markov inequality, and C r inequality, we extend average convergence and almost sure convergence theorems for ND sequences of random variables under sublinear expectation space, and we provide a way to learn this subject.

Vrste i načini merenja dohodovne konvergencije

Income convergence is one of the key research domains in the field of economic growth and development. The theoretical discussion of income convergence among countries began with the introduction of Robert Solow's neoclassical growth model. The first empirical research appeared in the 1980s, and to this day the results are ambiguous. There are several approaches of convergence, however, the most commonly used approach is income convergence between countries and regions. When it comes to income convergence, there are two concepts, namely s-convergence and b-convergence, where b-convergence can be absolute and relative. The paper presents different types of convergence, as well as methods of measuring income convergence.

THE MAIN DIRECTIONS OF COMMUNICATIVE DYNAMISM IN THE SPACE OF RELIGIOUS COMMUNICATION

e features of the modern situation in Ukraine demonstrate a growth of the interest in the phenomenon of the linguistic programming of personality, which is correlated to the media, political and religious influences simultaneously. The article is devoted to the categories of communicative ethics and responsibility in the religious discourse. The main directions of renovation of religious communication in Ukraine have been stated. The effects of communicative dynamism are corresponded to the political, marketing, social functions and are represented by the religious advertisement, religious branding, religious tourism, religious naming, media activity of the Orthodox and proselyte religious groups, the different types of convergence with political values. The objects of the research are the hidden aspects of verbal religious communication. The subject of the article is renovating communicative status of religious texts. The tasks are the following: to analyze the innovative forms of communicative interactions in the modern Ukrainian religious discourse. The methodology of the research is based on the current approaches to scientific studying of linguistic suggestion. I use discourse analysis (critical) for the science qualification of interactional aspects, sociopsychological and sociocognitive characteristics, frameworks and contexts.In religious discourse, text representation has some characteristics of the independent semantic field, but in a communicative process a religious text can acquire the forms of power and control, which are used by the religious leaders and institutions. Therefore, the use of mass media channels for retranslation of religious ideas, in which the media literacy is ignored, promotes the growth of all types of verbal manipulation. In Ukraine the present-day informational situation is determined by the needs of popularisation of knowledge about existing manipulative technologies and linguistic manipulative techniques, in particular.

Asymptotic error distribution for the Euler scheme with locally Lipschitz coefficients

In traditional works on numerical schemes for solving stochastic differential equations (SDEs), the globally Lipschitz assumption is often assumed to ensure different types of convergence. In practice, this is often too strong a condition. Brownian motion driven SDEs used in applications sometimes have coefficients which are only Lipschitz on compact sets, but the paths of the SDE solutions can be arbitrarily large. In this paper, we prove convergence in probability and a weak convergence result under a less restrictive assumption, that is, locally Lipschitz and with no finite time explosion. We prove if a numerical scheme converges in probability uniformly on any compact time set (UCP) with a certain rate under a global Lipschitz condition, then the UCP with the same rate holds when a globally Lipschitz condition is replaced with a locally Lipschitz plus no finite explosion condition. For the Euler scheme, weak convergence of the error process is also established. The main contribution of this paper is the proof of n weak convergence of the normalized error process and the limit process is also provided. We further study the boundedness of the second moments of the weak limit process and its running supremum under both global Lipschitz and locally Lipschitz conditions.

The convergence characteristics of China's carbon intensity: Evidence from a dynamic spatial panel approach

In recent years, China's CO2 emissions have surged as the country's economy has expanded rapidly. Faced with mounting international and domestic pressures, China has made great efforts to curb CO2 emissions. To formulate targeted regional reduction plans, the features and characters of provincial carbon intensity should be carefully evaluated. In this study, the existence of convergence in China's carbon intensity and possible technological factors that may influence the convergence, are carefully investigated by building a united framework and employing dynamic spatial panel approach. The estimation results verify that there is significant spatial correlation in China's provincial carbon intensity. There is also evidence that the three different types of convergence (i.e., stochastic convergence, σ-convergence and β-convergence) exist during the sample period of 2000–2016. Moreover, among the technological factors of conditional β-convergence, indigenous innovation activity is most critical. Not all foreign innovations stem from the inflow of foreign direct investment and trade exert a positive effect on carbon intensity reduction. Besides, it is estimated that the spatial spillovers effects from neighboring provinces are important to carbon intensity.

FURTHER RESULTS OF CONVERGENCE OF UNCERTAIN RANDOM SEQUENCES

Convergence is an issue being widely concerned about. Thus, in this paper, we mainly put forward two types of concepts of convergence in mean and convergence in distribution for the sequence of uncertain random variables. Then some of theorems are proved to show the relations among the three convergence concepts that are convergence in mean, convergence in measure and convergence in distribution. Furthermore, several examples are given to illustrate how we use the theorems to make sure the uncertain random sequence being convergent. Finally, several counterexamples are taken to explain the relations between these different types of convergence.

Measuring and Evaluating Convergence Processes Across a Series of Group Discussions

As groups develop, members’ knowledge and expectations regarding the task and the group tend to converge. Such convergence allows members to anticipate and coordinate their own and others’ actions, facilitating productive group work. Using zero-history laboratory groups, this study analyzes the presence and trajectory of cognitive convergence as groups worked on a series of three similar tasks. We focus on two types of convergence: anticipatory expectations for future work, and reflective assessments regarding previous group discussions. Results indicate immediate convergence for reflective cognitions but delayed convergence for anticipatory cognitions. Associations among the different types of convergence also vary at the group- and individual-levels of analysis. The discussion addresses measurement implications of both types of convergence in regard to emergence of group-like cognitive structures.

The Relations between Several Kinds of Convergence of Random Variables

In this paper, we study the convergence of random variables. We outline the definition and fundamental properties of various kinds convergence and study their relations. We focus on proving several theorem, these theorems show the relations between the different types of convergence, and we give some counter example to show that some relations are not true. Convergence in the r − thmean is the simplest in form, its relationship with others is the weakest. Convergence almost surely is the strongest, but it doesn’t imply convergence in the r −thmean. Both convergence almost surely and convergence in the r − th mean imply convergence in probability, convergence in probability implies convergence in distribution. Cauchy convergence can judge the convergence of sequences of random variables by using certain characteristics of sequences.

Some types of convergence related to the reconstruction property in Banach spaces

Casazza and Christensen [Canad. Math. Bull., 51 (2008), 348--358] introduced and studied the reconstruction property in Banach spaces. In this paper, we discuss different types of convergence of series related to the reconstruction property in Banach space. First we discuss the uniform convergence of series associated with the reconstruction property in Banach spaces. Necessary and sufficient conditions for the uniform convergence of certain series related to the reconstruction property in Banach spaces are given. A sufficient condition for a Banach space to be finite dimensional in terms of the uniform convergence of a series related to the reconstruction property in Banach spaces is obtained. Motivated by a series of papers by Casazza, we discuss unconditional convergence of series associated with the reconstruction property in Banach spaces. A necessary condition in this direction is given. An absolute type reconstruction property in Banach spaces is also discussed which depends on the absolute convergence of series related to the reconstruction property in Banach spaces.

A survey of converging solutions for heterogeneous mobile networks

In 5G systems, the current machine-tomachine communications using Wi-Fi or Bluetooth provide a good opportunity to dramatically increase overall performance. Converged mobile networks can provide M2M communications with significant performance improvements by sharing unlicensed spectrum bands in cellular networks, such as Long Term Evolution-Advanced, by using cognitive radio technology. Thus, the converged mobile network will become one of the most popular future research topics because mobile multimedia content services have been generally accepted among mobile device users. In this article, we provide an overview of converged mobile networks, investigating different types of converged mobile networks, different types of convergence, and the current problems and solutions. This survey article also proposes potential research topics in converged mobile networks.

Statistical convergence of order [formula omitted] in probability

In this paper the ideas of different types of convergence of a sequence of random variables in probability, namely, statistical convergence of order α in probability, strong p-Cesàro summability of order α in probability, lacunary statistical convergence or Sθ-convergence of order α in probability, and Nθ-convergence of order α in probability have been introduced and their certain basic properties have been studied.

The Study of the Basically same Convergence Problem

There are many different types of convergence in real analysis.In this paper,the basic convergence problem of a variety of convergence was discussed.Ultimate ideology in analysis was applied flexibly,uniform convergence problem was detailed analysis in-depth from the conditions of the topics, and illustrate that corresponding results will produce with the changed of the conditions.Therefore, we can conclude that basically consistent with the convergence condition is the strongest in a variety of convergence.

Divergence in Firms: How Technology Convergence Relate to Organizational Boundaries

Research in industrial organization and organizational theory has long studied the dynamics of industry and organizational evolution. Yet, we do not know how organizational boundaries of competing firms co-evolve when previously distinct technologies converge, bringing standards, products/services, markets and industries together. Drawing on the Transaction Cost Theory and the larger framework of Market Failure (Williamson, 1975; 2010), we explain how various types of convergence attend differently to the rearrangement of organizational boundaries in firms with different positions in value-chains and in markets. Based on a new convergence taxonomy and a sequential hierarchy that accounts for related contingencies, we develop a theoretical model that explains where and how organizational boundaries change as convergence proceeds. We also argue that the direction of convergence, towards either higher or lower market failure potential, is also a significant variable in understanding boundary dynamics during convergence. In conclusion, we discuss how different types of convergence can be accounted for, while making boundary decisions in different organizations, together with theoretical implications and potential further research.