Inequality Criterion Research Articles

Ketimpangan Sosial Pada Sumberdaya Pertanian di Desa Sawangan Kecamatan Tombulu Kabupaten Minahasa

This study aims to analyze social inequality in agricultural resources in Sawangan Village, Tombulu District, Minahasa Regency. This study was conducted from April 2024 to June 2024. The research method used is a descriptive method to analyze the existing data. The data used are primary data and secondary data. Primary data was obtained directly from respondents by conducting direct interviews using a prepared questionnaire, while secondary data was obtained from other information data related to this study. The results of the study showed the results of a total score of 2631 which was obtained from the total score of inequality in land, inequality in capital and inequality in technology and information so that social inequality in agricultural resources in Sawangan Village, Tombulu District was in the high inequality criteria.

Iterative Dissipativity of Partial Difference Equation Dynamics in Open-Loop Iterative Learning Control Mode

Complex physical processes, which could evolve in both spatial and temporal dimensions and be represented by partial difference equations, could also operate in a repetitive mode with iterative learning methods as suitable control laws. For these three-dimensional systems (of the spatial, temporal, and iterative dimensions), the stability in the iterative direction is critical for many applications, which can be analyzed and synthesized under the proposed concept of iterative dissipativity. The definition of iterative dissipativity, which is first introduced in this paper, encapsulates the dominant information in both the spatial and temporal dimensions, while also placing a particular emphasis on the iteration improvement. This property allows for the derivation of sufficient conditions for asymptotic stability in the iteration direction, which are represented by linear matrix inequality criteria that can be readily solved. Performance in both the spatial and temporal dimensions can also be satisfied under this iterative dissipativity concept, even in absence of real-time feedback. Moreover, the optimization solutions of the control parameters can be determined. Finally, a thermal process and a numeric example are presented to illustrate the effectiveness of the proposed iteratively dissipative learning control approach.

Fractional impulsive controller design of fractional-order fuzzy systems with average dwell-time strategy and its application to wind energy systems

In this study, the issue of adaptive impulsive control of a permanent magnet synchronous generator (PMSG)-based wind energy system (WES) with an average dwell-time strategy is investigated using a Takagi–Sugeno (T-S) fuzzy model described by fractional-order differential equations. A T-S fuzzy model is employed to describe the nonlinear fractional-order PMSG (FOPMSG) model, an average dwell time, an average impulsive condition, a Lyapunov function, and a less conservative algebraic inequality criterion that guarantees stabilization for the considered nonlinear system. First, the mathematical model of the FOPMSG in the n−m reference frame is transformed into a dimensionless chaotic system through affine transformation and time scale transformation. Then, the stabilization problem of the nonlinear chaotic FOPMSG model is considered to validate the proposed sufficient conditions, leading to the derivation of a new stability criterion for the FOPMSG model, instead of addressing the general problem to validate the proposed result. Subsequently, the desired control gains can be obtained to ensure the stabilization of the addressed closed-loop system. By combining adaptive and impulsive control, the model under consideration can be stabilized for any target dynamics. Finally, we demonstrate the efficiency and feasibility of the suggested approach through numerical simulations and comparative results.

Necessary and Sufficient Criteria for a Four-Weight Weak-Type Maximal Inequality in the Orlicz Class

Let Φi(i=1,2) be two N-functions, f be a μ-measurable function, and ωi(i=1,2,3,4) be four weight functions. This study presents necessary and sufficient conditions for weight functions (ω1,ω2,ω3,ω4) such that the inequality ∫{x:Mf(x)>λ}Φ1(λω1(x))ω2(x)dμ(x)≤c1∫XΦ2(c1|f(x)|ω3(x))ω4(x)dμ(x) holds, which extends several established results.

Prescribed-Time Network-Based Deployment of Nonlinear Multiagent Systems: A Discrete-Space PDE Method.

This article attempts to design the prescribed-time time-varying deployment schemes for first-order and second-order nonlinear multiagent systems (MASs). We assume that all agents can obtain the information of their current and final relative positions with their neighbors, and the final absolute velocities (as well as their current and final relative velocities, the final absolute accelerations for the second-order MASs) through a communication network, whereas two boundary agents are able to obtain their current and final absolute positions (as well as their current and final absolute velocities for the second-order MASs). The neighbor relationship of all agents is described by a spatial variable and two static-feedback controllers are introduced, which can be expressed as a second-order space difference of the spatial variable. Then, the deployment of MASs can be transformed into the stabilization of discrete-space partial differential equation (PDE) systems. Three virtual agents are introduced to constitute the Dirchlet and Neumann boundary conditions. Several algebraic inequality criteria are derived to guarantee that the prescribed-time time-varying deployment can be achieved within a prescribed time under the Dirchlet and mixed boundary conditions. Unlike the published results, our results are derived based on the discrete-space PDE systems instead of continuous-space PDE systems, which is consistent with the discrete spatial distribution of agents. Finally, two numerical examples are given to illustrate the effectiveness of our results.

A novel heap-based optimizer for allocation of shunt capacitors in radial distribution network

Due to power losses, a sizeable portion of the electrical power produced is lost, which causes voltage deviation and instability as a result of rising load demand at the radial distribution network (RDN). Shunt capacitor penetration will enhance the RDN’s efficiency by reducing power losses, improving the voltage profile and stability. For the best sizing and allocation of shunt capacitors (SCs) in RDN, a novel human-based metaheuristic heap-based optimizer (HBO) influenced by the ideas of corporate rank hierarchy (CRH) of standard organization is presented. The real power loss, voltage variation, and voltage stability index are all minimized while equality and inequality criteria are met by the HBO optimal allocation of SCs. One, two, and three numbers of SCs were investigated when installing the reactive compensating devices. Using typical IEEE 33-bus and 69-bus RDNs, covering a range of scenarios in the form of single- and multi-objective functions, the effectiveness of the HBO technique was examined. The real power loss for the conventional IEEE 33-bus and 69-bus RDN was reduced by 34.46% and 35.50%, respectively compared to their respective base cases. By contrasting the outcomes of the power loss with well-established and new optimization approaches, the efficacy and superiority of the suggested HBO were demonstrated.

Synchronization of fractional-order quaternion-valued neural networks with image encryption via event-triggered impulsive control

The finite-time synchronization and impulsive synchronization of fractional-order quaternion-valued neural networks (FOQVNNs) with delay are investigated in this research. To begin, instead of employing a decomposition method, a Lyapunov direct approach is proposed to achieve the finite-time synchronization of FOQVNNs using event-triggered control based on state errors. The settling time is then estimated using a unique fractional differential inequality. The event-triggered impulsive controller, which updates only during triggering instants, is proposed to be more inexpensive and efficient. Then, utilizing fractional Lyapunov theory and the comparison principle, several novel quaternion-valued linear matrix inequalities criteria are defined to assure the impulsive synchronization of the delayed FOQVNNs. Furthermore, the positive lower bound of the inter-event time is obtained to exclude the Zeno behavior. As proof of the feasibility and validity of these theoretical findings obtained, numerical examples are provided. At last, the use of the event-triggered control technique for FOQVNNs in image encryption and decryption is demonstrated and validated.

Dissipativity of Stochastic Competitive Neural Networks with Multiple Time Delays

The (Q,R,S)-γ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Q,R,S)-\\gamma -$$\\end{document}dissipative of stochastic competitive neural networks (SCNNs) with leakage delays and discrete delay is studied. Firstly, Lyapunov–Krasovskii functional is constructed, which studies the relationship between various types of time delays. Secondly, by using integral inequality technique, the linear matrix inequality (LMI) criterion of (Q,R,S)-γ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Q,R,S)-\\gamma -$$\\end{document}dissipative in the mean square sense of SCNNs is obtained. Furthermore, the obtained LMI criterion is extended to the passivity in the mean square sense, stability in the mean square sense, (Q,R,S)-γ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Q,R,S)-\\gamma -$$\\end{document}dissipative and passivity. Finally, the effectiveness of the obtained results are verified by numerical simulation.

Unified finite‐time fault estimation and fault‐tolerant control for Takagi–Sugeno fuzzy singular systems

SummaryWith the aid of a proportional integral framework, the presented article focuses on the problems of finite‐time boundedness and fault estimation for Takagi–Sugeno fuzzy singular systems subject to time delays, faults and external disturbances. To commence, we conjure up a fuzzy‐dependent intermediate variable and from thereon, a proportional integral‐based fuzzy intermediate estimator is constructed. Moreover, the constructed estimator precisely facilitates for estimating the fault signals and system states in simultaneously. Besides this, the integral term in the proportional integral estimator offers greater design flexibility and higher resilience. Secondly, an intermediate estimator‐based fault‐tolerant control is devised by availing the information from the proportional integral‐based fuzzy intermediate estimator, which aids in effectively compensating the faults arising in the system. Subsequently, by setting up an appropriate Lyapunov–Krasovskii functional, the set of adequate requirements asserting the finite‐time boundedness with the endorsed mixed and passivity performance index is established in terms of linear matrix inequalities. After that, an explicit framework for the requisite gain matrices can be found forth basing on the formed linear matrix inequality criteria. Ultimately, simulation findings are supplied to evaluate the utility and applicability of the theoretical insights.

Цифровое неравенство в системе местного самоуправления: понятие, критерии, пути преодоления

Introduction. Since the end of the 20th and beginning of the 21st centuries, all areas of social management, including public management, have been seriously influenced by modern digital technologies, which, on the one hand, create new opportunities to increase the efficiency of management activities; on the other hand, they pose certain risks, potentially provoking digital inequality. The article presents an analysis of the prerequisites and causes of digital inequality in municipalities. The criteria for such inequality are identified and generalized. An attempt was made to find out the attitude of local governments and citizens, living under digital lockdown, towards the digital transformation of public administration and local economy. Proposals have been made to level the digital divide in municipalities. Theoretical analysis. The problem of digital inequality has been the focus of attention of researchers for over 20 years. However, the scientific discourse on digital inequality is still fragmented: there is no universal interpretation of this phenomenon in the theoretical aspect; there are no uniform parameters for measuring it, and no algorithm for overcoming it has been developed. It is noted that approaches to understanding digital inequality and its consequences have undergone major changes: from unhindered access to the Internet to a person’s request to use digital resources, including those in the field of local government. Empirical analysis. The analysis of the legal regulation of digital transformation was carried out. As a result, it was concluded that flexible or “soft” legal regulation of the digitalization of public administration currently prevails. It is indicated that a special federal law regulating the process of digital transformation in the public administration system and in the local government system, respectively, has not been adopted in the Russian Federation. The criteria for assessing the digital inequality of Russian subjects, the possibility and feasibility of scaling them to the level of local government were analyzed. Results. Based on the results of the study, it is shown that at the local government level, digital inequality is an urgent problem that has a complex technological, socio-economic, socio-cultural and legal nature. It has been proven that there has been a transformation in the essence and understanding of digital inequality: from the problem of access to digital technologies to ensuring equal conditions for citizens to exercise their constitutional rights through such technologies, including the right to local self-government. A proposal for a special program approach has been made to overcome the digital divide in municipalities.

Mittag-Leffler projective synchronization of uncertain fractional-order fuzzy complex valued neural networks with distributed and time-varying delays

<p>To study the Mittag-Leffler projective synchronization (MLPS) problem of fractional-order fuzzy neural networks (FOFNNs), in this work we introduced the FOFNNs model. On this basis, we discussed the MLPS of uncertain fractional-order fuzzy complex valued neural networks (FOFCVNNs) with distributed and time-varying delays. Utilizing Banach contraction mapping principle, we proved the existence and uniqueness of the model solution. Moreover, employing the construction of a new hybrid controller, an adaptive hybrid controller, and the fractional-order Razumikhin theorem, algebraic criteria was obtained for implementing MLPS. The algebraic inequality criterion obtained in this article improves and extends the previously published results on MLPS, making it easy to prove and greatly reducing the computational complexity. Finally, different Caputo derivatives of different orders were given, and four numerical examples were provided to fully verify the accuracy of the modified criterion.</p>

Exponential Stability of Impulsive Timescale-Type Nonautonomous Neural Networks With Discrete Time-Varying and Infinite Distributed Delays.

Global exponential stability (GES) for impulsive timescale-type nonautonomous neural networks (ITNNNs) with mixed delays is investigated in this article. Discrete time-varying and infinite distributed delays (DTVIDDs) are taken into consideration. First, an improved timescale-type Halanay inequality is proven by timescale theory. Second, several algebraic inequality criteria are demonstrated by constructing impulse-dependent functions and utilizing timescale analytical techniques. Different from the published works, the theoretical results can be applied to GES for ITNNNs and impulsive stabilization design of timescale-type nonautonomous neural networks (TNNNs) with mixed delays. The improved timescale-type Halanay inequality considers time-varying coefficients and DTVIDDs, which improves and extends some existing ones. GES criteria for ITNNNs cover the stability conditions of discrete-time nonautonomous neural networks (NNs) and continuous-time ones, and these theoretical results hold for NNs with discrete-continuous dynamics. The effectiveness of our new theoretical results is verified by two numerical examples in the end.

Convergence-Rate-Based Event-Triggered Mechanisms for Quasi-Synchronization of Delayed Nonlinear Systems on Time Scales.

Most of the existing event-triggered mechanisms (ETMs) were designed according to the difference between the quadratic form of measurement errors and the quadratic form of sampling states (or real-time states). In order to reduce the amount of data transmission and develop ETMs for continuous-time and discrete-time delayed nonlinear systems (NSs) simultaneously, this article investigates quasi-synchronization (QS) of NSs on time scales based on a novel ETM, which is designed according to the convergence rate instead of measurement errors of the addressed systems. First, a novel ETM is designed under known nonlinear dynamics, and it is demonstrated that QS with given convergence rate and error level can be achieved under matrix inequality criteria. Second, if the nonlinear functions are unknown, we adapt our ETM to handle this special case. Not only QS but also complete synchronization with given convergence rate can be achieved under the ETMs. If the constructed Lyapunov functions passes through 0, the designed ETM will keep it at the origin. In this case, finite-time synchronization is achieved. Third, under the designed ETMs, it is proved that Zeno behavior can be excluded. At last, four numerical simulations are presented to demonstrate the feasibility and the advantage of the designed ETMs in this article.

Adaptive Drive-Response Synchronization of Timescale-Type Neural Networks With Unbounded Time-Varying Delays.

In recent years, adaptive drive-response synchronization (DRS) of two continuous-time delayed neural networks (NNs) has been investigated extensively. For two timescale-type NNs (TNNs), how to develop adaptive synchronization control schemes and demonstrate rigorously is still an open problem. This article concentrates on adaptive control design for synchronization of TNNs with unbounded time-varying delays. First, timescale-type Barbalat lemma and novel timescale-type inequality techniques are first proposed, which provides us practical methods to investigate timescale-type nonlinear systems. Second, using timescale-type calculus, novel timescale-type inequality, and timescale-type Barbalat lemma, we demonstrate that global asymptotic synchronization can be achieved via adaptive control under algebraic and matrix inequality criteria even if the time-varying delays are unbounded and nondifferentiable. Adaptive DRS is discussed for TNNs, which implies our control schemes are suitable for continuous-time NNs, their discrete-time counterparts, and any combination of them. Finally, numerical examples on TNNs and timescale-type chaotic Ikeda-like oscillator with unbounded time-varying delays are carried out to verify the adaptive control schemes.

Generalized Nonlinear Sector Approaches for Takagi-Sugeno Models

The Nonlinear Sector Approach (NLSA) is a way to construct Takagi-Sugeno (T-S) models which exactly represent nonlinear systems with bounded nonlinearities. Generally, the nonlinearities are bounded by a box-shaped set, however, this paper generalizes the NLSA for polytopic and smooth convex bounding sets, providing new ways of reducing the intrinsic conservatism of T-S representations with interdependent scheduling parameters. Some Linear Matrix Inequalities (LMI) criteria for stability analysis of these models are provided throughout the paper.

Asymptotic stability and quantitative synchronization of fractional competitive neural networks with multiple restrictions

The fractional competitive neural networks (FCNNs) with multiple restrictions are considered in this article. Specially, the FCNNs with memristors and time-varying delays in complex field (FCMCNNs) are first introduced, as well as the asymptotic stability (AS) and quantitative synchronization (QTS) issues are investigated. Firstly, applying Filippov’s conclusion theory, a model of FCMCNNs is reduced to a simpler one containing the time-switching memristive coefficients. Secondly, in virtue of the Banach fixed-point theorem, the AS is sufficiently discussed. Thirdly, in the light of the quantized controller (QTC), some concise inequality criteria are drawn to attain the QTS of the master–slave systems. Lastly, by providing two simulation examples, the results obtained manifest the availability and practicality.

Quantum steering in two-forked tree-shaped networks

Abstract Network quantum steering (NQS) arises from network models required with classification of trusted and untrusted parties. The network local hidden state (NLHS) models have first been proposed to define the NQS in a linear network with end points being trusted. In the paper, we devote to establishing the NLHS model to define the NQS in a kind of more complex and applied-extensively networks, namely, the two-forked tree-shaped network. Here we assume that the parties at the last layer are trusted while the remaining parties are untrusted in this network. According to the NLHS model, we observe that network nonlocality implies network steerability. Furthermore, we pay more attentions to discovering the relationship between the network quantum unsteerability and separability/unsteerability of bipartite sources in this two-forked tree-shaped network. Moreover, we generalize two kinds of bipartite steering inequality criteria as the NQS criteria. They are built based on statistical quantities, which can be directly evaluated in experiments.

Stability analysis of fractional-order neural networks with time-varying delay utilizing free-matrix-based integral inequalities

The stability problem of fractional-order neural networks in consideration of time-varying delay is addressed by utilizing Lyapunov functional approach in this paper. Firstly, a class of novel Lyapunov-Krasovskii functions are designed to deal with the time-varying delay terms, which reduces the conservatism of the stability criteria. In addition, to estimate the fractional-order derivative of the Lyapunov-Krasovskii functions, a novel free-matrix-based fractional-order integral inequality is then established, which encompasses the Wirtinger one and leads to tractable linear matrix inequality criteria. Then, based on the designed adaptive control and the proposed Lyapunov-Krasovskii functions, some stability criteria depending on time-varying delay information and fractional-order α are deduced. Finally, numerical simulation shows that the presented approach can significantly reduce the conservatism of the existing results and has a broader application prospect.

Weak and strong type inequalities criteria for fractional maximal functions and fractional integrals associated with Gegenbauer differential operator

Abstract This paper deals with the introduction and study of a new, Orlicz type space associated with the Gegenbauer differential operator and briefly called here a G-Orlicz space. We prove that such spaces are Banach function spaces. The necessary and sufficient conditions are established which ensure the validity of weak and strong type inequalities for fractional maximal functions and fractional integrals of G-Orlicz spaces.

Impulsive control strategies of mRNA and protein dynamics on fractional-order genetic regulatory networks with actuator saturation and its oscillations in repressilator model

In genetic regulatory networks (GRNs), the control strategies of messenger RNA (mRNA) and protein play a key role in regulatory mechanisms of gene expression, especially in translation and transcription. However, the influence of impulsive control strategies on oscillatory gene expression is not well understood. In this article, by considering the impulsive control strategies of mRNA and protein, a novel fractional-order genetic regulatory networks with actuator saturation is proposed. By applying polytopic representation technique, the actuator saturation term is first considered into the design of impulsive controller, and less conservative linear matrix inequalities (LMIs) criteria that guarantee finite-time Mittag-Leffler stabilization problem for fractional-order genetic regulatory networks are given. The derived sufficient conditions can easily be verified by designing impulsive control gains and solving simple LMIs. Finally, to investigate the effectiveness and applicability of the control strategies, an interesting simulation example as a synthetic oscillatory network of transcriptional regulators in Escherichia coli is illustrated.