Conditions For Convergence Research Articles

On the Kantorovich Theory for Nonsingular and Singular Equations

We develop a new Kantorovich-like convergence analysis of Newton-type methods to solve nonsingular and singular nonlinear equations in Banach spaces. The outer or generalized inverses are exchanged by a finite sum of linear operators making the implementation of these methods easier than in earlier studies. The analysis uses relaxed generalized continuity of the derivatives of operators involved required to control the derivative and on real majorizing sequences. The same approach can also be implemented on other iterative methods with inverses. The examples complement the theory by verifying the convergence conditions and demonstrating the performance of the methods.

Distribution Characteristics of the Short-term Heavy Rainfall of an MCC in Shandong Province

This study employs a comprehensive approach, utilizing conventional meteorological observation data, Fengyun satellite cloud imagery, and ERA5 reanalysis data to examine a short-term heavy rainfall event and its underlying causes in Shandong Province from August 14 to 16, 2020. The findings reveal that: (1) This event represents a typical Mesoscale Convective Complex (MCC)-induced rainfall process, with the primary precipitation zone in central and southern Shandong. The most intense hourly rainfall is observed along the side of the MCC with the steepest Tropical Brightness Temperature Blackbody (TBB) gradient. The heaviest hourly rainfall happens right around the time of the lowest TBB interval. (2) The rainfall event is marked by a vertical atmospheric structure with a high-altitude westerly jet and a low-level southwest jet, which makes it easy for water vapour to move and shear lines to form. Favourable conditions for water vapour convergence and high specific humidity are noted. During episodes of heavy precipitation, there is a marked upward motion in the lower troposphere, aligning with the vertical pattern of low-level convergence and high-level divergence.

The how, when, and why of an abandoned bedrock meander of the Colorado River, Utah (U.S.)

AbstractRiver meanders entrenched into bedrock are found worldwide, and they are famously well represented in the Colorado Plateau of the southwestern U.S. Meandering of bedrock streams can eventually lead to cutting off canyon loops, and these abandoned “rincons” are locations with high preservation of fluvial deposits and landforms. We document and luminescence date the fluvial terraces in and around the Jackson Hole rincon along the Colorado River downstream of Moab, Utah. Results indicate cutoff and abandonment of the rincon at ~200 ka and also record the rapid and unsteady incision in this region over the past 300 ky. A convergence of conditions contributed to the cutoff of the rincon, including alluvial‐channel conditions at the onset of MIS 6 glacial‐climate, which provided channel‐bed cover and enhanced lateral erosion of weak strata. Also, a contemporaneous rock‐avalanche partially obstructed the paleochannel just downstream of the breach, potentially creating a backwater that further enabled a flood to avulse across the neck. Although other studies show that bedrock‐channel meandering and cutoff can generate unpaired strath terraces and short‐term increases in incision rates, these are not evident in the record at the Jackson Hole rincon. This novel case study leverages the high preservation potential within abandoned bedrock meanders to illuminate the processes and controls of rincon formation during landscape evolution.

Convergence of aquatic products consumption: A disaggregated analysis in European countries

Several benefits of consuming fishery and aquaculture products have been documented by the extant literature. However, the literature has been largely silent on few dimensions of aquaculture products, including the convergence of aquatic products consumption. An importance of investigating the convergence of aquatic products is that it provides hindsight on which countries should be the focus of exporters of the products. Convergence analysis of aquatic products consumption provides information that is relevant to the need to boost local production of aquatic products, and to conserve foreign exchange earnings. The aim of this study is to investigate the convergence of total aquatic products consumption per capita in 27 European Union countries plus United Kingdom, during 1993–2019. We have further considered the convergence of the components of total aquatic products consumption, which include aquatic animals, cephalopods, crustaceans, demersal fish, freshwater fish, marine fish, molluscs, and pelagic fish. Additionally, we have examined conditional convergence by evaluating the determinants of convergence of total aquatic products consumption. Using recently introduced unit root tests that provide for both smooth and sharp breaks, the results provide support for stochastic convergence of total aquatic products consumption per capita. Using a new conditional convergence approach, the analysis demonstrates that population growth rate, real gross domestic product, and prices of aquatic products are factors that enable the convergence of total aquatic products. The results are not materially different across the components of total aquatic products consumption. The implications of the results are discussed in the paper.

Frequency domain stability and relaxed convergence conditions for filtered error adaptive feedforward

SummaryThe convergence of filtered error and filtered reference adaptive feedforward is limited by three effects: model mismatch, unintended input‐disturbance interaction and too fast parameter adaptation. In this article, the first two effects are considered for MIMO systems under the slow parameter adaptation assumption. The convergence with model mismatch is conventionally guaranteed using a strictly positive‐real condition. This condition can be easily verified in the frequency domain, but due the high‐frequency parasitic dynamics of real systems, it is hardly ever satisfied. Nevertheless, filtered error and filtered reference adaptive feedforward have successfully been implemented in numerous applications without satisfying the strictly positive‐real condition. It is shown in this article that the strictly positive‐real condition can be relaxed to a power‐weighted integral condition, that is less conservative and provides a practical check for the convergence of filtered error adaptive feedforward for real systems in the frequency domain. The effects of input‐disturbance interaction are analysed and conditions for the stability are given in the frequency domain. Both conditions give clear indicators for frequency domain filter tuning, and are verified on an experimental active vibration isolation system.

The Discrete, Fractional Order Model of a Two-Dimensional Temperature Field using Grünwald-Letnikov Definition

In the paper a new, fractional order, discrete model of a two-dimensional temperature field is addressed. The proposed model uses Grünwald-Letnikov definition of the fractional operator. Such a model has not been proposed yet. Elementary properties of the model: practical stability, accuracy and convergence are analysed. Analytical conditions of stability and convergence are proposed and they allow to estimate the orders of the model. Theoretical considerations are validated using exprimental data obtained with the use of a thermal imaging camera. Results of analysis supported by experiments point that the proposed model assures good accuracy and convergence for low order and relatively short memory length.

Design, Construction, and Performance Testing of a Collapsible Parabolic Dish Solar Cooker for Temperature Control

This paper proposes solar energy as a viable alternative to biomass fuels for cooking, introducing a collapsible parabolic solar cooker designed to regulate heat production. The collector is divided into three sectors, with a specific condition for effective convergence of reflected radiation. The total concentration ratio is 89.4, with the primary sector covering 42%, while sectors 2 and 3 occupy 29% each. In the analysis ASAE protocol was employed. The results obtained from the ASAE S580.1 test revealed a range of cooking power values, with a minimum of 215.5 W and a maximum of 280.9 W. The single measure of performance of the cooker was gauged at 234.17 W. Regarding the Standard Stagnation Temperature, it was observed that a reduction of the collector area by 0.343݉ଶ resulted in a temperature decrease of 59.5℃. The highest recorded SST for the entire solar cooker (when all three sectors were expanded) reached 279℃.

Ricci Solitons on Spacelike Hypersurfaces of Generalized Robertson–Walker Spacetimes

Ricci Solitons on Spacelike Hypersurfaces of Generalized Robertson–Walker Spacetimes

Social Mobility and Youth Aspirations: An Analysis of the Conditional Convergence of Aspirations in India

This article examines the complex interplay between social mobility and the aspirations of Indian youth within the context of India's modest ranking on the Global Social Mobility Index. Utilizing a multidisciplinary approach, the study synthesizes empirical data and theoretical insights to explore how socio-economic backgrounds, government policies, societal attitudes, and individual actions shape aspirations. Central to this analysis is the concept of "conditionally convergent aspirations," which describes how socio-economic and cultural barriers lead to a narrowing of aspirations within homogeneous groups, thereby limiting the potential for upward social mobility. The findings suggest that effective policy interventions must address these foundational disparities through comprehensive educational reforms, robust social equity measures, and economic empowerment initiatives. By offering a detailed review of the literature and proposing targeted policy recommendations, the study aims to contribute to the discourse on social justice and economic development, advocating for a strategic approach to foster a more equitable society where the aspirations of all Indian youth can be realised.

Patient-Driven Solutions: Integrating Vildagliptin and Dapagliflozin in Diabetes Management

Type 2 diabetes mellitus (T2DM), an ongoing, chronic and multifactorial condition frequently necessitates multiple anti-hyperglycemic medications for optimal glycemic control. Diabetes rarely occurs in isolation, commonly coexisting with obesity, cardiovascular disease (CVD), and kidney dysfunction. Shared risk factors, such as sedentary lifestyles and poor dietary choices, contribute to the convergence of these health conditions. The interplay between obesity and insulin resistance (IR), a precursor to diabetes, amplifies cardiovascular risks through shared pathological pathways. Addressing this complex interrelation necessitates a holistic approach involving early detection, lifestyle modifications, and comprehensive management to navigate the intricate web of interrelated ailments. Clinical guidelines advocate early adoption of combination therapy. Combining two different therapeutic classes is a promising theoretical strategy for achieving safe and optimum glycemic regulation. Recent research trials combining dipeptidyl peptidase-4 inhibitor (DPP-4i) and sodium-glucose cotransporter-2 inhibitor (SGLT2i) confirm their safety and clinical efficacy and consequently, this combination emerges as an appealing therapy for T2DM patients, offering a favorable safety profile and positive clinical effects in terms of weight management and cardiorenal protection. This review highlights the utilization of Vildagliptin and Dapagliflozin in diabetes management, underscoring their necessity, pleiotropic advantages, and the importance of an individualized, patient-centric approach for optimal outcomes.

A class of maximum-based iteration methods for the generalized absolute value equation

In this paper, by using |x|=2max{0,x}−x, a class of maximum-based iteration methods is established to solve the generalized absolute value equation Ax−B|x|=b. Some convergence conditions for the proposed method are presented. By some numerical experiments, the effectiveness and feasibility of the proposed method are confirmed.

Neural critic learning with accelerated value iteration for nonlinear model predictive control

In practical industrial processes, the receding optimization solution of nonlinear model predictive control (NMPC) is always a very knotty problem. Based on adaptive dynamic programming, the accelerated value iteration predictive control (AVI-PC) algorithm is developed in this paper. Integrating iteration learning with the receding horizon mechanism of NMPC, a novel receding optimization solution pattern is exploited to resolve the optimal control law in each prediction horizon. Besides, the basic architecture and the specific form of the AVI-PC algorithm are demonstrated, including the relationship among the iterative learning process, the prediction process, and the control process. On this basis, the convergence and admissibility conditions are established, and the relevant properties are comprehensively analyzed when the accelerated factor satisfies the established conditions. Furthermore, the accelerated value iterative function is approximated through the single critic network constructed by utilizing the multiple linear regression method. Finally, the plentiful simulation experiments are conducted from various perspectives to verify the effectiveness and progressiveness of the AVI-PC algorithm.

Special aspects of patch antennas synthesis using genetic algorithm

Microstrip-fed patch antenna synthesis can be performed using one of the numerous optimization algorithms, such as a genetic algorithm (GA). VBA or IronPython script engines implemented in modern CAD systems make it possible to implement GA. However, the capabilities of these languages for processing matrix data are limited. The use of a MATLAB environment script could combine the capabilities of MATLAB and CAD for electromagnetic modelling. It would make it possible to generate chromosomes of individuals of a given length, build antenna models in CAD that reflect the genetic code of individuals, process modelling results in MATLAB, carry out crossing over and mutations with a given probability for obtaining patch antennas that provide a user-specified value of the goal function. The primary purpose of this work is to propose a script in the MATLAB environment that allows complete automation of microstrip antennas' structural synthesis in MATLAB - CAD using GA, as well as to study GA selection methods and their influence on the results of this algorithm. As a result, a MATLAB script has been developed, combining the capabilities of electromagnetic modelling CAD and the MATLAB environment for processing matrix data for fully automated synthesis of the microstrip-fed patch antenna. It is shown that the proposed script randomly generates an initial population, creates a CAD model corresponding to each individual, determines the value of the goal function for each individual, performs crossing over and mutations, and then iteratively repeats the above actions until the GA convergence condition is satisfied. This paper highlights that the GA convergence speed depends on the selection method chosen before crossing over. Recommendations for choosing a selection method are formulated. The results of synthesizing a microstrip antenna with a frequency band 5.2 times greater than the frequency band of the reference antenna are presented. The presented script combines the capabilities of electromagnetic modelling CAD and MATLAB to fully automate the process of structural synthesis of microstrip antennas with a given frequency response and the main lobe direction of the radiation pattern.

Real-time time-varying economic nonlinear model predictive control for wind turbines

Economic nonlinear model predictive control is a great choice to tackle the control issues appearing in the current wind energy industry. In this paper, instead of generator power, aerodynamic power is employed in the economic cost function to establish the required conditions of stability and convergence of the economic performance, such as turnpike and problem convexity. However, since aerodynamic power depends on time-varying wind speed, conventional time-invariant economic nonlinear model predictive controllers cannot guarantee the stability and convergence of economic performance. This paper proposes a new time-varying economic nonlinear model predictive controller for wind turbine control that considers an economic trajectory, instead of a steady-state, in its optimization problem. The proposed time-varying economic cost function directly considers aerodynamic power, the activity of pitch angle and generator torque, and fatigue loads on the shaft and tower. Therefore, this controller can maximize power extraction and reduce fatigue load on the tower, drivetrain, and actuators. Furthermore, a fast-parallel Newton-type method is used to implement the proposed controller in actual wind turbines. An accurate aeroelastic model is used to validate the performance of the proposed control scheme. The proposed controller is also compared with two tracking nonlinear model predictive controllers, the baseline controller, and a newly developed method, under fatigue and extreme load scenarios in the presence and absence of uncertainty. The simulation results show the superior economic performance of the proposed approach. Moreover, the real-time results verify the computational speed that the proposed controller requires to deploy actual wind turbines.

Certain properties of [formula omitted]-analogue of M-function

The intent of this work is to create and study certain fundamental characteristics of new generalizations of the M-function using q-calculus. We establish its characteristics, like the convergence condition, recurrence relation, integral representations, q-derivative formulae, q-Laplace and q-Sumudu transformations, and image formulas for the Caputo fractional q-derivative and the Hilfer fractional q-derivative. Furthermore, we analyze some specific situations to demonstrate of our key findings.

Multiple-stage spatial–temporal cooperative guidance without time-to-go estimation

This paper investigates the spatial–temporal cooperative guidance problem for multiple flight vehicles without relying on time-to-go information. First, a two-stage cooperative guidance strategy, namely the cooperative guidance and the Proportional Navigation Guidance (PNG) stage strategy, is developed to realize the spatial–temporal constraints in two dimensions. At the former stage, two controllers are designed and superimposed to satisfy both impact time consensus and impact angle constraints. Once the convergent conditions are satisfied, the flight vehicles will switch to the PNG stage to ensure zero miss distance. To further extend the results to three dimensions, a planar pursuit guidance stage is additionally imposed at the beginning of guidance. Due to the independence of time-to-go estimation, the proposed guidance strategy possesses great performance in satisfying complex spatial–temporal constraints even under flight speed variation. Finally, several numerical simulations are implemented to verify the effectiveness and advantages of the proposed results under different scenarios.

Distant small spot presentation in midair haptics using polyhedral reflector.

In midair haptics, ultrasound phased arrays are mainly used due to their high spatiotemporal controllability. The constraint on the presentation distance of phased arrays to form a focus can be mitigated by utilizing concave reflectors. This paper numerically examines the convergence of a surface approximated by multiple planes serving as a reflector, substituted for an ideal concave surface. A mirrored phased array produced by the planar segments forms a focus and concurrently creates interference among imaginary sources. A single-point convergence condition is derived that constrains the accuracy of the approximated reflector and the phased array size. As long as it satisfies the convergence condition, the approximated reflector can form a single focal point. Numerical simulations were conducted to confirm the validity of the convergence equation and the 5% tolerance of the segment size for the reflector deformation. An experimental campaign was also conducted and confirmed that the polyhedral reflector was able to form a single small focus by controlling the phase shift of the sound source.

Analysis on characteristics of extreme precipitation indices and atmospheric circulation in Northern Shanxi

This article utilizes daily precipitation data from 28 national meteorological stations in northern Shanxi Province spanning from 1972 to 2020, and the US NCEP/NCAR monthly average reanalysis and ERA5 monthly average reanalysis data. The study employs techniques such as empirical orthogonal function (EOF) decomposition, Mann-Kendall mutation and other methods to investigate the spatiotemporal distribution of extreme precipitation index in northern Shanxi and their correlation with atmospheric circulation. The research results show that: the absolute index, relative index, intensity index and sustained dry period index (CDD) in the continuous index appear from southwest to northeast. The spatial distribution characteristics of the central region decrease, while the continuous wet period (CWD) decreases from the central to the east and west. The three indices Rx1day, Rx5day, and CWD mutated in 1978, 1975, and 1983 respectively, and other extreme precipitation indices all appeared in a sudden change from a low-value period to a high-value period occurred around 2010. In the high-value years of the summer extreme precipitation index, there is a significant negative anomaly in the height field in the mid-high latitude regions of Eurasia. Northern Shanxi is controlled by a broad low-pressure trough in the Lake Baikal area. Water vapor transported via the east, west, and south routes converges in the northern Shanxi region and encounters cold air from the north. There is a strong upward motion anomaly at 500 hPa in the troposphere, and the dynamic conditions of upper-level divergence and lower-level convergence lead to more summer extreme precipitation in the northern Shanxi region. Conversely, in the low-value years of the summer extreme precipitation index, northern Shanxi is affected by a strong high-pressure ridge north of Lake Baikal. There is a downward motion anomaly at 500 hPa, and the northern Shanxi region lacks water vapor. The cold and warm air cannot converge, and both the water vapor conditions and dynamic conditions are poor, which is not conducive to the production of extreme precipitation in northern Shanxi.

µ-Integrable Functions and Weak Convergence of Probability Measures in Complete Paranormed Spaces

This paper works with functions defined in metric spaces and takes values in complete paranormed vector spaces or in Banach spaces, and proves some necessary and sufficient conditions for weak convergence of probability measures. Our main result is as follows: Let X be a complete paranormed vector space and Ω an arbitrary metric space, then a sequence {μn} of probability measures is weakly convergent to a probability measure μ if and only if limn→∞∫Ωg(s)dμn=∫Ωg(s)dμ for every bounded continuous function g: Ω → X. A special case is as the following: if X is a Banach space, Ω an arbitrary metric space, then {μn} is weakly convergent to μ if and only if limn→∞∫Ωg(s)dμn=∫Ωg(s)dμ for every bounded continuous function g: Ω → X. Our theorems and corollaries in the article modified or generalized some recent results regarding the convergence of sequences of measures.

A modified gradient‐based iterative algorithm for solving the complex conjugate and transpose matrix equations

In this paper, we first develop the modified gradient‐based iterative (MGI) method for the complex conjugate and transpose matrix equations . By adopting the updated technique, we can make full use of the latest information to compute the next result, which leads to a faster convergence rate. In theory, we apply the real representation of a complex matrix and the vec‐operator to prove the convergence properties. Furthermore, we extend the MGI algorithm to solve the generalized complex conjugate and transpose matrix equations. Then, the necessary and sufficient conditions for convergence of the MGI algorithm are presented. Lastly, three numerical examples are introduced to testify the efficiency of our methods.