Notion Of Convergence Research Articles

Some New Observations on Wijsman ℐ 2 -Lacunary Statistical Convergence of Double Set Sequences in Intuitionistic Fuzzy Metric Spaces

In this study, we investigate the notions of the Wijsman ℐ 2 -statistical convergence, Wijsman ℐ 2 -lacunary statistical convergence, Wijsman strongly ℐ 2 -lacunary convergence, and Wijsman strongly ℐ 2 -Cesàro convergence of double sequence of sets in the intuitionistic fuzzy metric spaces (briefly, IFMS). Also, we give the notions of Wijsman strongly ℐ 2 ∗ -lacunary convergence, Wijsman strongly ℐ 2 -lacunary Cauchy, and Wijsman strongly ℐ 2 ∗ -lacunary Cauchy set sequence in IFMS and establish noteworthy results.

On a fuzzy metric space and fuzzy convergence

In this paper we introduce a new type of fuzzy metric space and obtain several properties of it. Also some topological properties and boundedness are investigated. The notion of convergence of fuzzy sequences together with the notion of fuzzy cauchy sequences in a fuzzy metric space are discussed and some basic results related to these notions are investigated.

Price convergence: Representation and testing

This paper provides a new, unified, and flexible framework to measure and characterize a convergence process in time series. We formally define a general notion of price convergence, which encompasses convergence as steady-state and catching-up, and propose a model to represent a wide range of transition paths. Our framework enables the measurement of such transitional behaviors and the development of testing procedures. In particular, we use existing unit root tests (with and without breaks) to determine whether asymptotic convergence exists and, if so, its starting point and type: as steady-state or catching-up and in its weak or strong version. We illustrate the power and flexibility of the methodology with two different datasets with potential convergence processes: (1) the aggregated price level of the Eurozone's largest economies (Germany, France and Italy) after the introduction of the common currency and, (2) the transatlantic 19th Century wheat prices.

We’d Go Well Together: A Critical Race Analysis of Marijuana Legalization and Expungement in the United States

In the U.S., many state and local governments have either legalized or decriminalized small quantities of marijuana for recreational or medicinal use. Reforming these laws has had significant public support, with reformers arguing that dissolving prohibitions on use as a policy remedy, or recompense, for the economic and human cost born by African American communities in the so-called “War on Drugs.” However, we do not yet know what explains the shift in support for allowance, or, more specifically, what has widened the policy window for legislative reform across the country. Using the analytic framework of Critical Race Theory (CRT), specifically, Bell’s (1980) notion of issue convergence, this paper highlights how this specific policy change continues to reproduce inequality in the maintenance of racialized interests in terms of who benefits and is burdened by reform. It concludes by recommending additional legislative action, such as automatic expungements for certain marijuana-related crimes, a legal remedy that can limit the collateral consequences experienced by those with criminal records.

ROUGH STATISTICAL CONVERGENCE IN 2-NORMED SPACES

In this study, we introduced the notions of rough statistical convergence and defined the set of rough statistical limit points of a sequence and obtained statistical convergence criteria associated with this set in 2-normed space. Then, we proved that this set is closed and convex in 2-normed space. Also, we examined the relations between the set of statistical cluster points and the set of rough statistical limit points of a sequence in 2-normed space.

Lacunary Convergence of Double Sequences of Complex Uncertain Variables

In this paper, we introduce the notion of lacunary convergence for double sequences of complex uncertain variables. We have established the relation between lacunary convergence and strong Cesàro convergence. Also, we have established the relation between different concepts of lacunary convergence of double sequences of complex uncertain variables.

On rough convergence in amenable semigroups and some properties

The authors of the present paper, firstly, investigated relations between the notions of rough convergence and classical convergence, and studied on some properties of the rough convergence notion which the set of rough limit points and rough cluster points of a sequence of functions defined on amenable semigroups. Then, they examined the dependence of r-limit LIMrf of a fixed function f ∈ G on varying parameter r.

Is bioeconomic potential shared? An assessment of policy expectations at the regional level in Colombia

ABSTRACT As other technological promises, bioeconomy has raised expectations as a burgeoning field for the economy. Policy work in Colombia claims that such current focus on ‘bio’ should be profited by the country given its regional mega-diverse potential. Yet, the question remains to what extent such arrangements are shared regionally, in a country exhibiting variegated multi-cultural drivers and differentiated bio-potential. This paper tackles this question, assessing national policy documents and regional oil and mining royalties investment in the period 2012–2019. Conceptually, we build on the notions of integration and convergence to read regional funding and niche development as evidence of multi-level expectations. We combine content analysis, descriptive analysis and social network analysis to assess expectations at the macro, meso and micro levels. Results show that there is not a consistent regional translation of the discourse on bioeconomy, showing dispersed views about how to render bioeconomy real. Higher education institutions and regional governments play a central role in keeping the network together; however, the lead has been taken by regional governments.

On paranormed Ideal convergent sequence spaces defined by Jordan totient function

The study of sequence spaces and summability theory has been an important aspect in defining new notions of convergence for the sequences that do not converge in the usual sense. Paving the way into the applications of law of large numbers and theory of functions, it has proved to be an essential tool. In this paper we generalise the classical Maddox sequence spaces c_{0}(p), c(p), ell (p) and ell _{infty }(p) and define new ideal paranormed sequence spaces c^{I}_{0}(Upsilon ^{r}, p), c^{I}(Upsilon ^{r}, p), ell ^{I}_{ infty }(Upsilon ^{r}, p) and ell _{infty }(Upsilon ^{r}, p) defined with the aid of Jordan’s totient function and a bounded sequence of positive real numbers. We develop isomorphism between certain maps and also find their α-, β- and γ-duals. We examine algebraic and topological properties of these corresponding spaces. Further we study some standard inclusion relations and prove the decomposition theorem.

A new approach to Korovkin-type approximation via deferred Cesàro statistical measurable convergence

The work of this paper aims to introduce the notions of statistical mean convergence, statistical measurable convergence, and statistical Lebesgue measurable convergence by means of deferred Cesàro summability and apply them in Korovkin-type new approximations. We first established some fundamental results to understand the connections among them. Then we established new versions of Korovkin-type theorems with three algebraic test functions via deferred Cesàro statistical Lebesgue measurable convergence for sequences of measurable functions. Also, several examples have been given in the sequel to support our new ideas and findings.

Local weak limits of Laplace eigenfunctions

In this paper, we introduce a new notion of convergence for the Laplace eigenfunctions in the semiclassical limit, the local weak convergence. This allows us to give a rigorous statement of Berry's random wave conjecture. Using recent results of Bourgain, Buckley and Wigman, we will prove that some deterministic families of eigenfunctions on $\mathbb{T}^2$ satisfy the conclusions of the random wave conjecture. We also show that on an arbitrary domain, a sequence of Laplace eigenfunctions always admits local weak limits. We explain why these local weak limits can be a powerful tool to study the asymptotic number of nodal domains.

Catching-up Convergence and its Speed: Representation and Testing

This paper provides a new, unified, and flexible framework to measure and characterize a convergence process. Specifically, we formally define a general notion of asymptotic price convergence, which encompasses convergence as steady-state and catching-up, and propose a model to represent a wide range of transition paths. Our framework enables the econometric measurement of such transitional behaviors and the development of testing procedures. In particular, we use unit root tests (with and without breaks) to determine whether asymptotic convergence exists and, if so, its starting point and its type: as steady-state or catching-up and in its weak or strong version. We apply this methodology to illustrate the convergence process in two very different cases: (1) the aggregated price level of the Eurozone’s largest economies (Germany, France and Italy) and, (2) the transatlantic 19th Century wheat prices.

What fosters interorganizational frame convergence: Examining a semantic network during the opioid crisis

Public relations and strategic communication scholars have advocated for a social network perspective for a more relational and nuanced understanding of crisis communication. Drawing upon literature from crisis communication, framing, and network theories, we explicate the notion of interorganizational frame convergence (IFC), the extent to which different organizations share interpretations (i.e., frames) on a particular issue. This study examined an IFC network in which cross-sectoral organizations were connected by semantic ties based on the extent to which they shared similar frames in a crisis. We carried out a content analysis of organizational press releases during the US opioid crisis from 2017 to 2019 (N = 420) and the profiles of these organizations (N = 34). Results from network analyses revealed patterns, processes, and antecedents of IFC during the opioid crisis. We argue that understanding the antecedents and processes of IFC allows more relational and systemic theory construction as well as more effective relationship building.

Convergence in OPEC carbon dioxide emissions: Evidence from new panel stationarity tests with factors and breaks

Convergence in per capita emissions occurs when countries with higher initial levels of per capita emissions experience lower emission growth than countries with lower initial levels of per capita emissions. The recent literature adopts the notion of stochastic convergence, which implies that per capita emissions tend to converge to a stationary level over time. The empirical literature on emissions convergence has yielded mixed results. We present new panel stationarity tests that account for cross-correlations and structural breaks. These new tests are more general than previous tests for stochastic convergence. Using annual data for 13 OPEC countries and 18 non-OPEC oil-producing countries from 1960 to 2016, we find less evidence of stochastic convergence than previous studies. The absence of convergence in per capita emissions across countries could hinder the acceptance of climate agreements based on the allocation of per capita emissions obligations. Policy actions to address emissions growth are also discussed.

Empirical spectral measures of quantum graphs in the Benjamini-Schramm limit

We introduce the notion of Benjamini-Schramm convergence for quantum graphs. This notion of convergence, intended to play the role of the already existing notion for discrete graphs, means that the restriction of the quantum graph to a randomly chosen ball has a limiting distribution. We prove that any sequence of quantum graphs with uniformly bounded data has a convergent subsequence in this sense. We then consider the empirical spectral measure of a convergent sequence (with general boundary conditions and edge potentials) and show that it converges to the expected spectral measure of the limiting random rooted quantum graph. These results are similar to the discrete case, but the proofs are significantly different.

Bootstrapping non-stationary stochastic volatility

In this paper we investigate to what extent the bootstrap can be applied to conditional mean models, such as regression or time series models, when the volatility of the innovations is random and possibly non-stationary. In fact, the volatility of many economic and financial time series displays persistent changes and possible non-stationarity. However, the theory of the bootstrap for such models has focused on deterministic changes of the unconditional variance and little is known about the performance and the validity of the bootstrap when the volatility is driven by a non-stationary stochastic process. This includes near-integrated exogenous volatility processes as well as near-integrated GARCH processes, where the conditional variance has a diffusion limit; a further important example is the case where volatility exhibits infrequent jumps. This paper fills this gap in the literature by developing conditions for bootstrap validity in time series and regression models with non-stationary, stochastic volatility. We show that in such cases the distribution of bootstrap statistics (conditional on the data) is random in the limit. Consequently, the conventional approaches to proofs of bootstrap consistency, based on the notion of weak convergence in probability of the bootstrap statistic, fail to deliver the required validity results. Instead, we use the concept of ‘weak convergence in distribution’ to develop and establish novel conditions for validity of the wild bootstrap, conditional on the volatility process. We apply our results to several testing problems in the presence of non-stationary stochastic volatility, including testing in a location model, testing for structural change using CUSUM-type functionals, and testing for a unit root in autoregressive models. Importantly, we work under sufficient conditions for bootstrap validity that include the absence of statistical leverage effects, i.e., correlation between the error process and its future conditional variance. The results of the paper are illustrated using Monte Carlo simulations, which indicate that a wild bootstrap approach leads to size control even in small samples.

On Tribonacci I -convergent sequence spaces

In this paper, we use the notion of ideal convergence (\(I\)-convergence) to introduce Tribonacci \(I\)-convergent sequence spaces, that is, \(c_{_{0}}^{I} (T), c_{_{}}^{I} (T) \) and \(l_{_{\infty}}^{I} (T)\) as a domain of regular Tribonacci matrix \(T=(t_{jn})\) (constructed by the Tribonacci sequence). We also present few inclusion relations and prove some topological and algebraic properties based results with respect to these spaces.

On statistical mathfrak{A}-Cauchy and statistical mathfrak{A}-summability via ideal

The notion of statistical convergence was extended to mathfrak{I}-convergence by (Kostyrko et al. in Real Anal. Exch. 26(2):669–686, 2000). In this paper we use such technique and introduce the notion of statistically mathfrak{A}^{mathfrak{I}}-Cauchy and statistically mathfrak{A}^{mathfrak{I}^{ast }}-Cauchy summability via the notion of ideal. We obtain some relations between them and prove that under certain conditions statistical mathfrak{A}^{mathfrak{I}}-Cauchy and statistical mathfrak{A}^{mathfrak{I}^{ast }}-Cauchy summability are equivalent. Moreover, we give some Tauberian theorems for statistical mathfrak{A}^{mathfrak{I}}-summability.

Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows

We introduce a notion of uniform convergence for local and nonlocal curvatures. Then, we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation. We apply such a general theory to characterize the limits of s-fractional mean curvature flows as and In analogy with the s-fractional mean curvature flows, we introduce the notion of s-Riesz curvature flows and characterize its limit as Eventually, we discuss the limit behavior as of the flow generated by a regularization of the r-Minkowski content.

Sequence selection properties in Cp (X) with the double ideals

Abstract Recently Bukovský, Das and Šupina [Ideal quasi-normal convergence and related notions, Colloq. Math. 146 (2017), 265–281] started the study of sequence selection properties (𝓘, 𝓙-α 1) and (𝓘, 𝓙-α 4) of Cp (X) using the double ideals, where 𝓘 and 𝓙 are the proper admissible ideals of ω, which are motivated by Arkhangeľskii local αi -properties [The frequency spectrum of a topological space and the classification of spaces, Dokl. Akad. Nauk SSSR 13 (1972), 1185–1189]. In this paper, we obtain some characterizations of (𝓘, 𝓙-α 1) and (𝓘, 𝓙-α 4) properties of Cp (X) in the terms of covering properties and selection principles. Under certain conditions on ideals 𝓘 and 𝓙, we identify the minimal cardinalities of a space X for which Cp (X) does not have (𝓘, 𝓙-α 1) and (𝓘, 𝓙-α 4) properties.