As Convergence Research Articles

Remarkable 2023 North Atlantic Ocean Warming

AbstractIn 2023 the NOAA Daily Optimum Interpolation Sea Surface Temperature in the Atlantic set new records, peaking above 24. 3°C for the full basin 30°S–60°N and above 25. 3°C for the North Atlantic 0–60°N, both for the first time during the satellite era. Proposed mechanisms include anomalous radiative and thermodynamic surface fluxes, horizontal transport, changing mixed layer thickness and basal entrainment rates. To test these ideas the heat budget of the ocean mixed layer was examined in a numerical simulation. The results show that the anomalous SSTs in the North Atlantic during the summer of 2023 were caused by increased shortwave warming and reduced thermodynamic cooling. In contrast, ocean mean and eddy heat transport convergence and heat exchanges along the mixed layer base dominate only regionally. A second contributor to the record SSTs was the preconditioning of mixed layer temperature following a series of anomalously warm years.

Convergence of summability means of higher dimensional Fourier series and Lebesgue points

Convergence of summability means of higher dimensional Fourier series and Lebesgue points

Stochastic Two-Scale Convergence in the Mean in Orlicz-Sobolev’s Spaces and Applications to the Homogenization of an Integral Functional

In this article, we study the stochastic homogenization for a family of integral functionals with convex and nonstandard growth integrands defined on Orlicz-Sobolev’s spaces. One fundamental in this topic is to extend the classical compactness results of the two-scale convergence in the mean method to this type of spaces. Moreover, it is shown by the two-scale convergence in the mean method that the sequence of minimizers of a class of highly oscillatory minimizations problems involving convex functionals converges to the minimizers of a homogenized problem with a suitable convex function. 1

Evaluation of Accommodation Amplitude and Convergence Insufficiency in Patients with Multiple Sclerosis

ABSTRACT Purpose To evaluate the near reflex components, including accommodation, convergence, and binocular fusional vergences in patients with multiple sclerosis (MS). Material-Method MS patients under 35 years of age without visual evoked potential (VEP) abnormalities (MS Group) and age-matched healthy individuals of (Control Group) were included in the study. Fusional vergence amplitudes, the amplitude of accommodation (AA), stereopsis measurements, near-object fixation and near point of convergence (NPC) measurements, Convergence Insufficiency Symptoms Survey (CISS) results, and the presence of nystagmus were recorded retrospectively from the files of the cases. Statistical comparison was made between the groups. Results The mean age was 28.04 ± 3.7 years in the MS group (20 females, 4 males) and 27.16 ± 3.1 years in the control group (20 females, 5 males) (p = .763). There was no statistically significant difference between groups in stereopsis (p = .395), mean convergence (p = .666), and divergence amplitudes (p = .773) at a distance, and mean convergence and (p = .836) divergence amplitudes (p = .877) at near, and NPC measurements (p = .908). The mean AA was 5.31 ± 0.7 D in the MS group and 6.1 ± 0.8 D in the control group (p < .001). CISS results were lower in the control group (p < .001). In addition, gaze-evoked nystagmus was statistically significantly higher in the MS group (p < .001). Conclusion Compared to the healthy control group, MS patients under 35 who did not have optic neuritis had lower accommodation amplitude and more signs in favor of convergence insufficiency symptoms. In addition, gaze evoked nystagmus was observed at a higher rate in the MS group. These findings may guide us in understanding the asthenopia findings of MS patients without optic neuritis.

Analysis and assessment of multi-GNSS inter-system bias (ISB) and its benefit on real-time precise point positioning

Abstract To meet the high demand for convergence speed in real-time precise point positioning (RTPPP), this paper comprehensively considers both satellite clock offset services and the PPP user perspective, deriving the inter-system bias (ISB) in detail. Using the precise satellite clock offset products from Wuhan University along with self-computed products, we analyze the datum issues related to satellite clock offsets/ISB, taking into account the effects of daily boundary changes, and propose a reliable ISB product workflow. We examine the statistical characteristics of ISB for different receiver types, highlighting their potential to enhance RTPPP performance as prior constraints. Experimental results indicate that after datum unification, the discontinuity of ISB caused by daily boundary issues can be avoided; the ISB values for the same type of receivers are closely aligned, and the statistical characteristics of ISB remain stable. When utilizing ISB products as prior constraints in the Global Positioning System + BeiDou Navigation Satellite System dual-system RTPPP, the root mean square and convergence time in the East-Up-North direction improve by 18%, 10%, 2%, 8%, 3%, and 1% compared to the original PPP, respectively. For the Global Positioning System + Galileo navigation satellite system, the corresponding improvements are 28%, 26%, 17%, 39%, 31%, and 17%.

Stochastic convergence behaviour in carbon dioxide emissions: Fourier panel unit root approach

ABSTRACT This study examines the convergence of per capita carbon dioxide emissions using two Fourier-based panel unit root tests allowing for smooth transitions. Additional panel unit root tests without structural breaks and with sharp shifts were conducted for comparison. The analysis spans 68 countries from 1965 to 2019. Results reveal non-stationarity in emissions for low- and middle-income countries, while emissions in high-income countries were stationary under constant and trend components. Evidence indicates limited convergence, with constrained forms observed only in high-income nations. These findings align partially with the Environmental Kuznets Curve hypothesis. This study offers nuanced insights into global carbon dioxide emission dynamics and enriches the empirical discourse on environmental sustainability.

State-level energy intensity convergence in the US: fresh empirical evidence

ABSTRACT Energy intensity refers to energy consumption per unit of GDP. Therefore, a decline in energy intensity implies that either more output is produced with the same amount of energy use or less energy is used to produce the same output level. Considering that fossil energy dominates the energy mix in the US and that fossil energy use causes many environmental problems, it is crucial to determine the levels of energy intensities of the states in the US and whether they tend to converge over time. This study aims to analyze the possible convergence patterns in energy intensity for the states in the US over the period 2000-2021. Accordingly, the paper first examines β-convergence and then investigates stochastic convergence. This study diverges from prior research in two respects. First, the study gives state-specific findings. Second, one of the unit root tests employed in this work considers structural breaks, whilst the other is based on machine learning methodologies. The findings indicate that the convergence hypothesis is validated solely for Alaska, Oklahoma, Texas, and Vermont, suggesting there is minimal evidence supporting energy intensity convergence among the states. This study contends that to decrease energy intensity in the US, it is crucial to provide greater support for environmental innovations, particularly in states with high energy intensities.

Stochastic and club convergence analysis of environmental tax revenues across EU countries.

The European Union (EU) has taken several initiatives over the past two decades to harmonize environmental taxation policies across member countries. The directive on energy taxation (Directive 2003/96/EC) provides the framework for the taxation of energy products within the EU. These harmonization efforts are part of a broader strategy to ensure environmental sustainability and combat climate change. This paper examines whether these efforts have had any impact on the convergence of environmental taxation across EU countries during the period 1995-2021. This paper uses a new panel unit root test that accounts for cross-correlations and structural breaks within the panel since regulations on taxation increase the possibility that EU countries may have commonalities on these issues. The club convergence test is also used to test for the existence of multiple equilibria within groups of countries. The results of the traditional convergence test show that environmental tax revenues are converging across EU countries. Furthermore, the results of the stochastic convergence test indicate that there is a convergence of relative environmental tax revenues. As for the break dates, the results from the tax revenue series show that the first and second break are concentrated in the periods 2002-2007 and 2012-2017, respectively. Finally, the results of the club convergence test reject the full panel convergence and reveal the existence of different convergence clubs. The empirical results of this paper have some implications for environmental taxation in the EU.

Innovative Approaches to Beam Forming Antenna Array Systems with Adaptive Partial Update NLMS Algorithms

Innovative Approaches to Beam Forming Antenna Array Systems with Adaptive Partial Update NLMS Algorithms

Stochastic convergence of renewable energy intensity across US States: evidence from a panel unit root test with asymmetries and common factors

ABSTRACT This study examines the stochastic convergence of renewable energy intensity (REI) across US states. We test for the stationarity of relative REI (stochastic convergence) using a recently developed quantile panel unit root test that accommodates both cross-sectional dependence and asymmetric behaviour. Our overall finding is that most states exhibit convergence, which implies that economic growth is sustainable with a higher share of renewable energy in the energy mix. This result provides support for those advocating that state governments should increase investment in renewable energy in advancing the clean energy transition. However, over half of the states display asymmetric stochastic convergence, which implies that how effective policies will be in promoting renewable energy efficiency will depend on the size and type of shocks impacting REI. Our results imply that in states that encounter relatively large positive shocks to REI, it may be necessary to invest more in the diffusion of renewable energy technologies and set long-term targets. Asymmetric convergence behavior also makes it difficult to coordinate policy responses across states, providing support for a decentralized approach in which each state invests in renewable energy technologies specific to their unique economic circumstances, rather than adopting a mandated overall national policy approach.

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.

Quantitative convergence of the nonlocal Allen–Cahn equation to volume-preserving mean curvature flow

We prove a quantitative convergence result of the nonlocal Allen–Cahn equation to volume-preserving mean curvature flow. The proof uses gradient flow calibrations and the relative entropy method, which has been used in the recent literature to prove weak–strong uniqueness results for mean curvature flow and convergence of the Allen–Cahn equation. A crucial difference in this work is a new notion of gradient flow calibrations. We add a tangential component to the velocity field in order to prove the Gronwall estimate for the relative energy. This allows us to derive the optimal convergence rate without having to show the closeness of the Lagrange-multipliers.

Stochastic homogenization for wave equation with random potential and non-periodic coefficients

This paper is concerned with stochastic homogenization for wave equation with random potential and non-periodic coefficients. First, we show the stochastic homogenization for deterministic wave equation with random potential and non-periodic coefficients by the stochastic two-scale convergence approach. Then, we present the stochastic homogenization for stochastic wave equation with random potential and non-periodic coefficients by the similar approach.

An augmented complex-valued gradient-descent total least-squares algorithm for noncircular signals

An augmented complex-valued gradient-descent total least-squares algorithm for noncircular signals

Statement of Retraction: Convergence in quadratic mean of averaged stochastic gradient algorithms without strong convexity nor bounded gradient

Statement of Retraction: Convergence in quadratic mean of averaged stochastic gradient algorithms without strong convexity nor bounded gradient

Analytical model of an active noise control system for performance analysis of adaptive algorithms in HVAC system

In real-world acoustic scenarios related to the problem with the low-frequency noise such as HVAC systems, the signal is a stochastic, non-stationary and time-varying process where the performance of the active noise control technique mainly depends on the characteristics of the adaptive filtering techniques. In this paper, a method for analytical modeling of active noise control of signals in MATLAB/Simulink is presented, in which the acquisition of audio signals is provided by using a National Instruments control and acquisition module. For the realization of the active noise control, an adaptive filtering system model for signal analysis has been developed, using three adaptive algorithms (LMS,RLS and NLMS). The analysis of the characteristics of each of the three investigated adaptive algorithms is performed according to four parameters: Mean Square Error (MSE), convergence speed, stability and robustness. The conclusions are presented through a comparative analysis of the results obtained from the implemented methodology. The individual characteristics and parameters that are observed for correct adaptation and optimal results of each of the adaptive filters are explained in detail.

Pointwise Convergence of Noncommutative Fourier Series

This paper is devoted to the study of pointwise convergence of Fourier series for group von Neumann algebras and quantum groups. It is well-known that a number of approximation properties of groups can be interpreted as summation methods and mean convergence of the associated noncommutative Fourier series. Based on this framework, this paper studies the refined counterpart of pointwise convergence of these Fourier series. As a key ingredient, we develop a noncommutative bootstrap method and establish a general criterion of maximal inequalities for approximate identities of noncommutative Fourier multipliers. Based on this criterion, we prove that for any countable discrete amenable group, there exists a sequence of finitely supported positive definite functions tending to 1 1 pointwise, so that the associated Fourier multipliers on noncommutative L p L_p -spaces satisfy the pointwise convergence for all p &gt; 1 p&gt;1 . In a similar fashion, we also obtain results for a large subclass of groups (as well as quantum groups) with the Haagerup property and the weak amenability. We also consider the analogues of Fejér and Bochner-Riesz means in the noncommutative setting. Our approach heavily relies on the noncommutative ergodic theory in conjunction with abstract constructions of Markov semigroups, inspired by quantum probability and geometric group theory. Finally, we also obtain as a byproduct the dimension free bounds of the noncommutative Hardy-Littlewood maximal inequalities associated with convex bodies.

Secure distributed estimation via an average diffusion LMS and average likelihood ratio test

Secure distributed estimation via an average diffusion LMS and average likelihood ratio test

Is military spending converging across middle eastern countries and Turkiye? A comprehensive unit root test analysis

AbstractThe Middle East is a region of chronic insecurity due to internal and external tensions. These tensions and insecurity have made the Middle East one of the world's leading regions in military armaments. This study investigates the stochastic convergence of military burden in 10 selected Middle Eastern countries using comprehensive unit root analysis. Stochastic convergence for each country from 1977 to 2020 is examined using conventional, structural break, nonlinear, and Fourier‐based unit root tests. Empirical results provide strong evidence of convergence with regional averages in Bahrain, Saudi Arabia, and Oman. There is also some evidence of convergence in the case of Israel, Egypt, Kuwait, Lebanon, and Turkiye. However, evidence for the existence of convergence in Iran and Jordan is weak.

Mean Convergence Theorems for the Maximum Normed Partial Sums of Random Vectors in Hilbert Spaces under a General Condition of Weighted Integrability

Mean Convergence Theorems for the Maximum Normed Partial Sums of Random Vectors in Hilbert Spaces under a General Condition of Weighted Integrability