Average Convergence Research Articles

Improvement of BDS-3 inter-frequency clock bias estimation and its application in multi-frequency precise point positioning

BDS-3 broadcasts five civilian signals, establishing a fundamental basis for multi-frequency real-time precise point positioning (RT PPP). Nevertheless, the existence of inter-frequency clock bias (IFCB) renders the current satellite clock error product unsuitable for multi-frequency PPP processing. Consequently, there is a critical need to conduct a thorough analysis of BDS-3 IFCBs and propose real-time service methods for RT PPP users. In this study, 8-day BDS-3 multi-frequency data obtained from 130 International GNSS Service (IGS) stations are employed to scrutinize the characteristics of BDS-3 IFCBs and validate the proposed real-time service method. The results disclose a noticeable disparity between the constant part of IFCBs computed using the differential code bias (DCB) product and those estimated from observations. The time-varying parts of different IFCBs, estimated using various combinations, are examined using the Fast Fourier Transform (FFT). The outcomes indicate that these IFCBs exhibit identical periods of 12, 6, and 4 h, although their fourth-period terms differ. To model the sequences of IFCBs, a polynomial with a fourth-order harmonic model is utilized, and the coefficients of the fitted model are subsequently transmitted for RT PPP processing. Experimental results show that the predicted accuracies of IFCBs for most satellites exceed 90 %, albeit with a noticeable decline as the prediction time increases. When applied in RT PPP for 20 IGS stations, the method significantly shortens the convergence time in dual-frequency and triple-frequency RT PPP when predicted IFCBs are provided. In the B1C/B2a, B1C/B3I, and B1I/B2a dual-frequency combinations, the average convergence times for RT PPP are reduced by 58 %, 46 %, and 59 %, respectively. In the B1I/B2a/B3I triple-frequency combinations, it is reduced by 48 %.

BDS-3 full-frequency precise point positioning: models and performance comparison

With the BDS-3 six-frequency integration, there are more choices to implement the precise point positioning (PPP) technology. To take full advantage of the multi-frequency combination, six typical BDS-3 six-frequency PPP models using uncombined observation (UC), five dual-frequency ionospheric-free (IF) combinations (IF2), four triple-frequency IF combinations (IF3), three four-frequency IF combinations (IF4), two five-frequency IF combinations (IF5), and a single six-frequency IF combination (IF6) were constructed and compared. The results indicate that the positioning accuracies of the six models are similar. The static positioning accuracies reach 4, 3–5, and 12–14 mm in the east, north, and up directions, respectively, while the kinematic positioning accuracies are 24–26, 16–17, and 42–43 mm, respectively. Regarding the convergence times, the UC model is slightly worse than the five IF combined models, except for some cases in the up direction. In the static mode, benefiting from the smallest noise amplification factor, the average convergence times of the IF6 model are the shortest, reaching 12.1, 5.5, and 13.4 min in the three directions, respectively, and are 7%, 15%, and 6% shorter than those of the UC model. In the kinematic mode, with the combination of more signals into a single IF combination, the noise level of the IF combined observables gradually decreases, but the convergence times gradually increase. The kinematic average convergence times of the IF2 model are 15.3, 3.6, and 18.0 min in the three directions, which are 6%, 22%, and 10% and 1%, 16%, and 20% shorter than those of the UC and IF6 models, respectively. In addition, the observation residuals, and the estimates of inter-frequency bias, tropospheric zenith wet delay, and receiver clock offsets from different models were compared and analyzed. The specific selection of the model should be based on actual situations.

Norm and relative uniform convergence

In this paper, we show that if H is a Dedekind complete normed Riesz space with the local Egoroff property, then H is lattice isomorphic to an ideal of an AM-space if and only if for any order bounded norm null sequence in H. Based on this, several characterizations of discrete Banach lattices with order continuous norms are provided. As an application, we find the special regulator for every relative uniform convergent sequence in discrete Banach lattices with order continuous norms.

Capital deepening and land average grain yield convergence: Evidence from China

The shift of agricultural labor force to non-agricultural sectors has paralleled China's economic development, leading to a substantial rise in labor costs relative to capital. Consequently, the agricultural production has witnessed a shift towards capital-intensive practices. The capital deepening coincides with the significant increase in China's grain output while the main cause of capital deepening in China's grain production is poorly understood. This study examines the effect of increasing in various capital investments on the grain yield growth and growth convergence in China's main production areas, based on the data collected from the data set of the Compilation of Cost-Benefit Data of Agricultural Products (CCBDAP). Results show that the increases of chemical fertilizer, pesticide and machinery input have played key roles in the increase of grain yield. For early indica rice, japonica rice, wheat and maize, the average land output bears a β convergence. These findings suggest that more capital investments are supposed to accelerate the growth of grain yield per unit of land, take the opportunity of practicing the cross-provincial balance system of occupation and compensation of cultivated land. Moreover, strategic adjustments to the spatial distribution of grain cultivation are recommended to maximize the utilization of limited arable land resources while upholding national food security objectives.

On the Rate of Convergence of Ergodic Averages for Functions of Gordin Space

For an automorphisms with non-zero Kolmogorov-Sinai entropy, a new class of $L_2$-functions called the Gordin space is considered. This space is the linear span of Gordin classes constructed by some automorphism-invariant filtration of $\sigma$-algebras~$\mathfrak{F}_n$. A function from the Gordin class is an orthogonal projection with respect to the operator $I-E(\cdot|\mathfrak{F}_n)$ of some $\mathfrak{F}_m$-measurable function. After Gordin's work on the use of the martingale method to prove the central limit theorem, this construction was developed in the works of Voln\'{y}. In this review article we consider this construction in ergodic theory. It is shown that the rate of convergence of ergodic averages in the $L_2$ norm for functions from the Gordin space is simply calculated and is $\mathcal{O}(\frac{1}{\sqrt{n}}).$ It is also shown that the Gordin space is a dense set of the first Baire category in ${L_2(\Omega,\mathfrak{F},\mu)\ominus L_2(\Omega,\Pi(T,\mathfrak{F}),\mu)},$ where $\Pi(T,\mathfrak{F})$ is the Pinsker $\sigma$-algebra.

A biological circuit to anticipate trend

Abstract Organisms gain by anticipating future changes in the environment. Those environmental changes often follow stochastic trends. The steeper the slope of the trend, the more likely the trend’s momentum carries the future trend in the same direction. This article presents a simple biological circuit that measures the momentum, providing a prediction about future trend. The circuit calculates the momentum by the difference between a short-term and a long-term exponential moving average. The time lengths of the two moving averages can be adjusted by changing the decay rates of state variables. Different time lengths for those averages trade off between errors caused by noise and errors caused by lags in predicting a change in the direction of the trend. Prior studies have emphasized circuits that make similar calculations about trends. However, those prior studies embedded their analyses in the details of particular applications, obscuring the simple generality and wide applicability of the approach. The model here contributes to the topic by clarifying the great simplicity and generality of anticipation for stochastic trends. This article also notes that, in financial analysis, the difference between moving averages is widely used to predict future trends in asset prices. The financial measure is called the moving average convergence–divergence indicator. Connecting the biological problem to financial analysis opens the way for future studies in biology to exploit the variety of highly developed trend models in finance.

Air volume reconstruction and sensor optimization distribution in building intelligent ventilation network

Ensuring the accuracy and reliability of ventilation parameter monitoring is pivotal for the development of intelligent ventilation systems. To attain a visual representation of airflow, solving the challenge of airflow reconstruction necessitates the strategic use of a limited number of sensors. In addressing these concerns, this article introduces an optimization approach for ventilation airflow leveraging the Breadth-First Search (BFS) algorithm. Additionally, it proposes an optimization distribution method for mine ventilation sensors, grounded in the Independent Cut Set algorithm. Research has found that compared to the traditional PSO algorithm, the BFS algorithm produces a higher optimal air volume solution when optimizing the air volume; Comparatively, the proposed algorithm exhibits significantly shorter average running times than the Particle Swarm Optimization (PSO) algorithm. It boasts the highest average convergence rate, ensuring superior accuracy, and possesses a notable capability to escape local minima, facilitating the acquisition of optimal solutions. Leveraging the independent cut set algorithm optimizes the calculation process through matrix operations. Exploiting the properties of matrices allows for a more rapid and intuitive resolution of sensor localization problems.

UPDs estimation and ambiguity resolution performance evaluation of LEO navigation system

Low-Earth orbit (LEO) satellites have fast motion and thus provide rapid geometric change relation to the ground stations in a short period of time, which are expected to improve the positioning performance. In this study, a LEO constellation of 160 LEO satellites was simulated and simulated LEO observation data at global, European, and American stations were used to estimate the uncalibrated phase delays (UPDs) and achieve static and kinematic precise point positioning (PPP) ambiguity resolution (AR). The quality of the estimated UPD products were evaluated. More than 89 % and 96 % of the wide- and narrow-lane UPDs had a posteriori residual of less than 0.15 and 0.25 cycles, respectively. In static PPP, all ambiguity fixing rates were larger than 63 %. Compared with float solutions, the average convergence time of the fix solutions at the global, European and American stations was accelerated by 8 %, 6 % and 7 %, respectively; the average root-mean-square errors (RMSEs) in the east, north, and up components at the global, European and American stations were decreased by (22 %, 20 %, 15 %), (36 %, 34 %, 28 %) and (44 %, 31 %, 29 %), respectively. In kinematic PPP, all ambiguity fixing rates were larger than 40 %. Compared with float solutions, the average convergence time of the fix solutions at the global, European and American stations was accelerated by 4 %, 19 % and 14 %, respectively; the average RMSEs in the east, north, and up components at the global, European and American stations were decreased by (10 %, 10 %, 7 %), (27 %, 22 %, 11 %) and (32 %, 20 %, 10 %), respectively. In both static and kinematic PPP, AR accelerated the convergence time and improved the positioning accuracy.

Multi-Cell Cooperative Resource Allocation and Performance Evaluation for Roadside-Assisted Automated Driving

The proliferation of wireless technologies, particularly the advent of 5G networks, has ushered in transformative possibilities for enhancing vehicular communication systems, particularly in the context of autonomous driving. Leveraging sensory data and mapping information downloaded from base stations using I2V links, autonomous vehicles in these networks present the promise of enabling distant perceptual abilities essential to completing various tasks in a dynamic environment. However, the efficient down-link transmission of vehicular network data via base stations, often relying on spectrum sharing, presents a multifaceted challenge. This paper addresses the intricacies of spectrum allocation in vehicular networks, aiming to resolve the thorny issues of cross-station interference and coupling while adapting to the dynamic and evolving characteristics of the vehicular environment. A novel approach is suggested involving the utilization of a multi-agent option-critic reinforcement learning algorithm. This algorithm serves a dual purpose: firstly, it learns the most efficient way to allocate spectrum resources optimally. Secondly, it adapts to the ever-changing dynamics of the environment by learning various policy options tailored to different situations. Moreover, it identifies the conditions under which a switch between these policy options is warranted as the situation evolves. The proposed algorithm is structured in two layers, with the upper layer consisting of policy options that are shared across all agents, and the lower layer comprising intra-option policies executed in a distributed manner. Through experimentation, we showcase the superior spectrum efficiency and communication quality achieved by our approach. Specifically, our approach outperforms the baseline methods in terms of training average reward convergence stability and the transmission success rate. Control-variable experiments also reflect the better adaptability of the proposed method as the environmental conditions change, underscoring the significant potential of the proposed method in aiding successful down-link transmissions in vehicular networks.

Combining dynamic adaptive snake algorithm with perturbation and observation for MPPT in PV systems under shading conditions

Photovoltaic (PV) systems play an increasingly vital role in the global new energy landscape. However, when PV arrays are affected by partial shading, their power-voltage (P-U) characteristic curves exhibit dynamic multi-peak features, posing challenges to traditional Maximum Power Point Tracking (MPPT) techniques, including slow convergence speed, low tracking efficiency, and oscillations around the Maximum Power Point (MPP), leading to unnecessary power losses. Therefore, this study proposes a dual-layer control MPPT technology that integrates dynamic adaptive snake optimization algorithm with variable step perturbation and observation (ISO-IP&O) to address the MPP extraction problem of PV systems under complex weather conditions. This study compares and analyzes the proposed ISO-IP&O controller with current renowned MPPT techniques, including Grey Wolf Optimization combined with P&O (GWO-P&O), Improved Squirrel Search Algorithm (ISSA), Original Snake Optimization (SO), Horse Herd Optimization (HHO), and Adaptive Factor Selection Multi-Swarm Particle Swarm Optimization (FMSPSO), validating the effectiveness of the proposed ISO-IP&O controller. Simulation results demonstrate that the ISO-IP&O technology achieves an average tracking efficiency of 99.91 % under various shading conditions, with an average convergence speed of only 0.07 seconds. Compared with other existing methods, the ISO-IP&O technology exhibits superior performance in terms of GMPP tracking speed, maximum power tracking efficiency, and stability. Experimental validation on the HIL+RCP physical experimental platform shows that under eight partial shading conditions(PSC), the proposed method still achieves the highest average tracking efficiency of 99.68 %, with the fastest average tracking speed of 0.66 seconds. The ISO-IP&O controller achieves rapid, robust, and efficient GMPP tracking under various complex shading conditions, contributing to the enhancement of PV system performance.

Time two-grid fitted scheme for the nonlinear time fractional Schrödinger equation with nonsmooth solutions

In this paper, we delve into the regularity properties and the development of an efficient numerical strategy for addressing the nonlinear time-fractional Schrödinger equation. Initially, we embark on an examination of the solution’s regularity, followed by an investigation into regularity enhancement through the application of the Laplace and finite Fourier sine transforms. Subsequently, after the decomposition of u-u0, we introduce an innovative time two-grid fitted scheme designed for the equation’s resolution, which demonstrates unconditional stability and convergence in the L2 norm, achieving the global convergence order of O(τF2+τC4+h2). Here, τF and τC denote the temporal step sizes on the fine and coarse grids, respectively, while h represents the spatial step size. Notably, this is the inaugural application of such an approach for solving the nonlinear time fractional Schrödinger equation. Ultimately, our numerical experiments validate that this method not only retains computational efficiency but also significantly enhances convergence accuracy.

A Comprehensive Study on Trend Analysis of Selected Stocks by Using Selected Technical Indicators

In this research, we delve into an in-depth exploration of the Relative Strength Index (RSI), Moving Average Convergence Divergence (MACD), and pivot points indicators to gauge their efficacy in forecasting stock price trends. The study draws upon a rich dataset sourced from reputable financial platforms, covering the period from January 2023 to April 2024. To ensure a representative sample, we adopt a stratified sampling approach, meticulously selecting five major companies based on their market capitalization. These companies—Reliance Industries, Tata Consultancy Services, HDFC Bank, ICICI Bank, and Infosys—serve as focal points for our analysis, offering insights into various sectors of the economy. By offering a nuanced understanding of the interplay between technical indicators and market dynamics, our study endeavors to contribute meaningfully to the discourse on stock price forecasting and investment strategies. Key Words: Stock price prediction, Relative Strength Index (RSI), Moving Average Convergence Divergence (MACD), Data analysis, Statistical methods, Market capitalization,

Impact of Visual Disturbances on the Trend Changes of COP Displacement Courses Using Stock Exchange Indices

This work aims to define a strategy for maintaining a vertical posture of the human body under conditions of conflicting sensory stimuli using a method of trend change analysis. The investigations involved 28 healthy individuals (13 females, 15 males, average age = 21, SD = 1.3 years). Measurements were conducted with eyes opened and closed and in the virtual environment with two sceneries oscillating at two frequencies. Values in the time domain were calculated—the mean center of pressure (COP) velocity and movement range in the AP direction—as well as values based on the moving average convergence divergence (MACD) computational algorithm—the trend change index (TCI), MACD_dT, MACD_dS, and MACD_dV. After dividing the analysis into distinct time periods, an increase in TCI values was identified in the oscillating scenery at 0.7 and 1.4 Hz during the 0.5–1 and 0.2–0.5 s time periods, respectively. Statistically significant differences were observed between measurements with an oscillation frequency of 0.7 Hz and those with an oscillation frequency of 1.4 Hz during the 0.2–0.5 s and 0.5–1 s periods. The use of stock exchange indices in the assessment of the ability to keep a stable body posture supplements and extends standard analyses in the time and frequency domains.

Applications of martingale Hardy Orlicz–Lorentz–Karamata theory in Fourier analysis

In this article, we discuss the applications of martingale Hardy Orlicz–Lorentz–Karamata spaces in Fourier analysis. More precisely, we show that the partial sums of the Walsh–Fourier series converge to the function in norm if f∈LΦ,q,b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\in L_{\\Phi ,q,b}$$\\end{document} with 1<p-≤p+<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1<p_-\\le p_+<\\infty $$\\end{document}. The equivalence of maximal operators on martingale Hardy Orlicz–Lorentz–Karamata spaces is presented. The Fejér summability method is also studied and it is proved that the maximal Fejér operator is bounded from martingale Hardy Orlicz–Lorentz–Karamata spaces to Orlicz–Lorentz–Karamata spaces. As a consequence, we obtain conclusions about almost everywhere and norm convergence of Fejér means.

Experimental and numerical study of unsteady flows in a compound open channel

Unsteady flows are investigated in a compound open-channel flume, consisting of a Main Channel (MC) and an adjacent Flood Plain (FP). Two types of inflow hydrographs are studied, i.e., a discharge hydrograph with, at any time: a slightly unbalanced inflow partition between MC and FP (Case I); and a noticeably unbalanced inflow partition (Case II). Ensemble averages of the time-varying discharges, water depths and velocities are estimated based on 100 successive runs. The main focus of the experimental study is on assessing (i) the time-varying lateral discharge and depth-averaged Reynolds stress at the MC/FP interface, and (ii) the influence of the inflow partition on the downstream flow parameters. The experimental flows are then simulated using a 1D (one-dimensional) code that was adapted to implement the 1D+ Independent Sub-sections Model (ISM) (Proust et al. in Water Resour Res 45:1–16, 2009). The numerical study aims at validating the ISM under unsteady flow conditions, using classical 1D simulations as benchmark. It is experimentally found that 90 successive runs are required to get convergence of the ensemble averages of sub-section discharges and flow depth, while interfacial velocity is not fully converged after 100 runs. The influence of the inflow partition on the downstream parameters is felt along the whole flume. The ISM simulations are closer to the measurements than the classical 1D simulations. The ISM can accurately predict the time-varying flow depths and interfacial lateral discharge, and can approximate the interfacial Reynolds stresses.

Norm convergence of subsequences of matrix transform means of Walsh–Fourier series

Norm convergence of subsequences of matrix transform means of Walsh–Fourier series

Association rules forecasting for the foreign exchange market

Several association rule mining algorithms exist, and among them, Apriori is one of the most commonly used methods for extracting frequent item sets from vast databases and generating association rules to gain insights. In this research, we have applied a data mining technique to implement association rules and explore frequent item sets. Our study introduced a model that employs association rules to uncover associations between the foreign exchange market, the gold commodity, and the National Association of Securities Dealers automated quotations (NASDAQ). We suggested a method that used data mining to identify the good points of buying and selling in the foreign exchange market by utilizing technical indicators such as moving average convergence divergence (MACD) and the stochastic indicator to create association rules. The experimental findings indicate that the proposed model successfully generates strong association rules.

LA-ViT: A Network With Transformers Constrained by Learned-Parameter-Free Attention for Interpretable Grading in a New Laryngeal Histopathology Image Dataset.

Grading laryngeal squamous cell carcinoma (LSCC) based on histopathological images is a clinically significant yet challenging task. However, more low-effect background semantic information appeared in the feature maps, feature channels, and class activation maps, which caused a serious impact on the accuracy and interpretability of LSCC grading. While the traditional transformer block makes extensive use of parameter attention, the model overlearns the low-effect background semantic information, resulting in ineffectively reducing the proportion of background semantics. Therefore, we propose an end-to-end network with transformers constrained by learned-parameter-free attention (LA-ViT), which improve the ability to learn high-effect target semantic information and reduce the proportion of background semantics. Firstly, according to generalized linear model and probabilistic, we demonstrate that learned-parameter-free attention (LA) has a stronger ability to learn highly effective target semantic information than parameter attention. Secondly, the first-type LA transformer block of LA-ViT utilizes the feature map position subspace to realize the query. Then, it uses the feature channel subspace to realize the key, and adopts the average convergence to obtain a value. And those construct the LA mechanism. Thus, it reduces the proportion of background semantics in the feature maps and feature channels. Thirdly, the second-type LA transformer block of LA-ViT uses the model probability matrix information and decision level weight information to realize key and query, respectively. And those realize the LA mechanism. So, it reduces the proportion of background semantics in class activation maps. Finally, we build a new complex semantic LSCC pathology image dataset to address the problem, which is less research on LSCC grading models because of lacking clinically meaningful datasets. After extensive experiments, the whole metrics of LA-ViT outperform those of other state-of-the-art methods, and the visualization maps match better with the regions of interest in the pathologists' decision-making. Moreover, the experimental results conducted on a public LSCC pathology image dataset show that LA-ViT has superior generalization performance to that of other state-of-the-art methods.

Analysis and simulation of the (2 + 1)-dimensional Fisher’s reaction-diffusion equation with higher order finite element method

In this article, a finite element analysis of Fisher’s reaction-diffusion equation is performed, by using quadratic shape elements. The higher-order elements in the finite element method (FEM) are known to yield better results in the approximation of solutions. However, such elements are less explored in the literature. Therefore, quadratic shape functions are taken into consideration for the finite element analysis of Fisher’s reaction-diffusion equation. A priori error estimates for the semi-discrete solution are derived by applying the Galerkin approximation. For the fully discrete solution, a priori error estimates are derived using the Crank-Nicolson method and the predictor-corrector scheme. Also, the stability of the time-discrete scheme is analyzed by the energy technique. Third-order convergence for space discretization in L 2 ( Ω ) norm and second-order convergence in H 1 ( Ω ) norm are observed. Furthermore, second-order convergence for time discretization is also found. Finally, we validate our theoretical results by considering a variety of numerical examples in one and two-dimensional spaces, which also illustrate the reliability of the developed finite element algorithm. Through comparison tables, 3D plots, and convergence plots, the results of the current study are compared with the results from the existing literature.

The Unregistered Child Marriage on Lumbang Society Norm Perspective Legal Pluralism

Unregistered child marriage has become a custom in the Lumbang community. Nevertheless, the Lumbang community registered their marriage with the State when they had children. The existence of this phenomenon shows that the Lumbang community adopts more than one norm regarding child marriage. This article will reflect on the legal practices in the Lumbang community regarding child marriage. This article is an empirical legal research with a legal anthropology approach. This article uses John Griffith's theory of legal pluralism as a means of uncovering the facts of legal practice in the Lumbang community. This research shows that legal pluralism occurs strongly in the practice of unregistered child marriage in Lumbang. The practice of strong legal pluralism occurs through the incorporation of religion-adult law, State-adult law, and the distinction of State-adult law. The community conducts unregistered child marriage as a convergence of customary-religious norms as well as divergence of norms due to restrictions on the minimum age of marriage by the State. Then, the State will register the marriage when they have children as a form of convergence of State-adult norms.