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On Boundary Value Problems for Liénard Type Equation 论李纳式方程的边值问题
Q3 Mathematics Pub Date : 2023-12-06 DOI: 10.37394/23203.2023.18.47
A. Kirichuka, F. Sadyrbaev
The generalized Liénard type differential equation is studied together with the two-point linear boundary conditions of the Sturm-Liouville type. The existence and multiplicity of solutions are considered. The existence under suitable conditions is shown to follow from the lower and upper functions theory. For multiplicity, the polar coordinates approach is used. The multiplicity results are based on the comparison between behavior of solutions near the trivial one, and solutions near the special one, which is preassumed to be non-oscillatory. The existence of the latter is required. It is shown also, that these conditions are fulfilled for a relatively broad class of equations. Some examples are constructed, which are supplied by comments and illustrations.
研究了广义lisamadard型微分方程和Sturm-Liouville型的两点线性边界条件。考虑了解的存在性和多重性。从上下函数理论出发,证明了在适当条件下的存在性。对于多重性,采用极坐标方法。多重性的结果是基于在平凡解附近的解和在假定为非振荡的特殊解附近的解的行为的比较。后者的存在是必需的。我们还证明,这些条件对于一类比较广泛的方程是满足的。本文构造了一些例子,这些例子由注释和插图提供。
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引用次数: 0
Simulation of the Performance of the Financial Market of Ukraine in the Conditions of Overcoming Threats to Economic Security 乌克兰金融市场在克服经济安全威胁条件下的表现模拟
Q3 Mathematics Pub Date : 2023-12-06 DOI: 10.37394/23203.2023.18.48
I. Irtyshcheva, M. Stehnei, I. Kramarenko, O. Liashenko, H. Mykhalchynets, Nataliia Mykhalchynets, Viktor Neimet
The purpose of the article is the process of modeling the effectiveness of the financial market of Ukraine in the conditions of overcoming threats to economic security. Forecasting possible behavioral reactions to the integrated performance of the financial market of Ukraine is necessary for connection with the academic environment, the variability of risks formed by the content of influencing factors, by setting the volumes of critical operations to respond to the effect of influencing factors. This is because the volumes of critical financial market operations, according to its combinatorial structure, are also aimed at obtaining a result. Therefore, we suggest predicting possible behavioral reactions to the integrated performance of the financial market of Ukraine. The forecast is focused on obtaining reaction values regarding critical financial market operations for the next resolution/achievement of good target values. The received forecast of changes creates an opportunity with sufficient accuracy to reveal the conditions for the formation of results, notably that characteristic of critical operations of the financial market, using studies of its internal reactivity, which is guided by the action of influencing factors. According to the results of the performance evaluation, it is evident that the expected integral performance of the financial market of Ukraine will demonstrate a much lower expected increase in benefits due to the likely narrowing of the market capacity and reduction of investment options. The results of such analysis and forecasting will make it possible to reasonably approach the development of sets of priority actions within the framework of strategic maps, the fixation of outlined priorities, and predictive analysis of changes in their effectiveness over time (which provides visualization of the movement towards absorption or complete absorption of destabilizing processes in the financial market).
本文的目的是对乌克兰金融市场在克服经济安全威胁的情况下的有效性进行建模。预测对乌克兰金融市场综合表现可能产生的行为反应,需要与学术环境、影响因素内容所形成的风险变异性、通过设定关键业务量来响应影响因素的影响相联系。这是因为根据其组合结构,关键金融市场操作的数量也旨在获得结果。因此,我们建议预测对乌克兰金融市场综合表现可能做出的行为反应。预测的重点是获得关于关键金融市场操作的反应值,以便下一次解决/实现良好的目标值。收到的变化预测创造了一个足够准确的机会,可以利用对其内部反应性的研究,揭示结果形成的条件,特别是金融市场关键操作的特征,这种反应性是由影响因素的作用所指导的。根据业绩评价的结果,很明显,由于市场容量可能缩小和投资选择减少,乌克兰金融市场的预期整体业绩将显示出低得多的预期收益增长。这种分析和预测的结果将使我们能够在战略地图的框架内合理地制定一系列优先行动,确定概述的优先事项,并对其效力随时间的变化进行预测性分析(这提供了对吸收或完全吸收金融市场不稳定过程的运动的可视化)。
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引用次数: 0
Automatic System for Roadway Safety – ASRS 01 道路安全自动系统 - ASRS 01
Q3 Mathematics Pub Date : 2023-12-05 DOI: 10.37394/23203.2023.18.45
C. Ciufudean, C. Buzduga
One of the objectives of the European Union (EU) as well as of other state authorities is to create safe roads for vehicles all over the EU space. Considering the rapid development of road traffic and, regrettably, an increase in the number of accidents, the system presented in this paper has the role of informing road traffic participants about infrastructure and environmental conditions. Hardware support, software support as well and further development of the ASRS 01 system are presented.
欧盟(EU)以及其他国家当局的目标之一是在欧盟范围内为车辆创造安全的道路。考虑到道路交通的快速发展,令人遗憾的是,事故数量的增加,本文提出的系统具有告知道路交通参与者有关基础设施和环境状况的作用。介绍了asrs01系统的硬件支持、软件支持和进一步发展。
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引用次数: 0
Parameter Estimation of Electrical Vehicle Motor 电动汽车电机参数估算
Q3 Mathematics Pub Date : 2023-12-05 DOI: 10.37394/23203.2023.18.46
H. Oubouaddi, Fatima Ezzahra El Mansouri, Ali Bouklata, Ramzi Larhouti, A. Ouannou, Adil Brouri
Presently, the problem of parameter estimation of motors used in electrical vehicles is discussed. To make the control more efficient, a model of the electrical motor is developed. Then, a parameter estimation method is established to determine the parameters of the used electrical motor. The proposed method is easy and can be easily implemented. Furthermore, a mathematical model of an electrical vehicle’s motor using linear and nonlinear blocks is obtained. The given model will allow us to perform several experiments without any extra fees.
目前,对电动汽车用电机的参数估计问题进行了研究。为了使控制更有效,建立了电动机的模型。然后,建立了一种参数估计方法来确定用电机的参数。该方法简单易行,易于实现。在此基础上,建立了基于线性和非线性模块的电动汽车电机数学模型。给定的模型将允许我们在不收取任何额外费用的情况下进行几个实验。
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引用次数: 0
Cuckoo Search Approach for Optimal SVC Design in A Multimachine Power System 多机电力系统中 SVC 优化设计的布谷鸟搜索法
Q3 Mathematics Pub Date : 2023-11-27 DOI: 10.37394/23203.2023.18.44
E. Ali, S. M. A. Elazim
In this paper, a new metaheuristic method, the Cuckoo Search (CS) approach, based on the life of a bird family is proposed for the optimal design of a Static Var Compensator (SVC) in a multimachine environment. The SVC parameter tuning problem is converted to an optimization problem which is solved by the CS approach. The performance of the proposed CS-based SVC (CSSVC) has been compared with Particle Swarm Optimization (PSO) based SVC (PSOSVC) under various operating conditions. The superiority of the suggested technique in damping oscillations and enhancing voltage profile over a wide range of operating conditions and system configurations is confirmed through eigenvalue, performance indices, and time domain simulation results over the PSO.
本文提出了一种新的元启发式方法--布谷鸟搜索(CS)方法,该方法以鸟类家族的生活为基础,用于多机器环境下静态可变补偿器(SVC)的优化设计。SVC 参数调整问题被转换为优化问题,由 CS 方法解决。在各种运行条件下,对所提出的基于 CS 的 SVC (CSSVC) 和基于粒子群优化 (PSO) 的 SVC (PSOSVC) 的性能进行了比较。通过特征值、性能指标和时域仿真结果,证实了所建议的技术在各种运行条件和系统配置下抑制振荡和改善电压曲线方面优于 PSO。
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引用次数: 0
Formal Verification of Dynamical Control Systems (Addressing Integral Windup Phenomena Using Model-Checking) 动态控制系统的形式化验证(利用模型检查解决积分上升现象)
Q3 Mathematics Pub Date : 2023-11-15 DOI: 10.37394/23203.2023.18.41
Mohammed Tloul, M. Schwarz, J. Börcsök
This paper investigates the utilization of model-checking as a potent method for verifying system designs, emphasizing its early error detection capabilities, reducing failures, increasing safety, and saving costs. The study explores the application of the UPPAAL tool and model-checking techniques within control systems. A case study in the paper concentrates on formally verifying Proportional Integral Derivative (PID) controllers, emphasizing integral windup issues. A model is constructed in UPPAAL for a control system that includes the system dynamics and the actuator limitations. The model’s accuracy is validated against the MATLAB/Simulink® model. Formal requirements addressing integral windup are formulated, and a practical model-checking example using UPPAAL illustrates its utility in control system verification.
本文研究了利用模型检查作为验证系统设计的有效方法,强调其早期错误检测能力、减少故障、提高安全性和节约成本。研究探讨了 UPPAAL 工具和模型检查技术在控制系统中的应用。论文中的一个案例研究集中于正式验证比例积分微分(PID)控制器,强调了积分上升问题。在 UPPAAL 中为控制系统构建了一个模型,其中包括系统动力学和执行器限制。根据 MATLAB/Simulink® 模型验证了模型的准确性。制定了解决积分上升问题的正式要求,并通过使用 UPPAAL 的实际模型检查示例说明了其在控制系统验证中的实用性。
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引用次数: 0
Admissible Directions in Optimal Control Under Uniqueness Assumptions 唯一性假设下最优控制的可允许方向
Q3 Mathematics Pub Date : 2023-11-15 DOI: 10.37394/23203.2023.18.40
J. F. Rosenblueth
It is well-known that, for a mathematical programming problem involving equality and inequality constraints, the uniqueness of a Lagrange multiplier associated with a local solution implies, under certain smoothness assumptions, second order necessary optimality conditions. Those conditions hold on a set of critical directions defined by those points satisfying the constraints and for which the minimizing function and the standard Lagrangian coincide. No similar links between uniqueness of multipliers and second order conditions seem to have been established for optimal control problems. In this paper, we provide some results in this direction. In particular, we study and completely solve a natural conjecture which provides, under uniqueness assumptions, nonnegative second variations on a classical cone of admissible directions.
众所周知,对于涉及相等和不相等约束条件的数学程序设计问题,与局部解相关的拉格朗日乘数的唯一性意味着,在某些平稳性假设下,二阶必要最优条件。这些条件在一组临界方向上成立,这些临界方向由满足约束条件的点定义,最小化函数和标准拉格朗日重合。对于最优控制问题,乘数唯一性和二阶条件之间似乎还没有建立起类似的联系。本文提供了这方面的一些结果。特别是,我们研究并完全解决了一个自然猜想,在唯一性假设下,该猜想提供了可容许方向的经典锥体上的非负二阶变化。
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引用次数: 0
Fuzzy PID Controller Design for a Coupled Tank Liquid Level Control System 耦合储罐液位控制系统的模糊 PID 控制器设计
Q3 Mathematics Pub Date : 2023-11-15 DOI: 10.37394/23203.2023.18.42
M. Saad, Muad Alshara, Khaled Mustafa
In industrial processes, the most important loop is the liquid-level control loop. The coupled tank system CT-100 becomes an essential apparatus for process control researchers. This paper introduces two controller techniques to control the water level in the second tank as a single input single output system. The PID controller is designed to control the linearized model, where the controller parameters are tuned using the Ziegler- Nichols tuning method. In addition, Fuzzy PID is designed based on adequate knowledge and experience. The proposed control approaches are simulated using MATLAB Simulink. Then, the obtained results using these controllers are compared in terms of time response specifications and the ITAE criterion. It is also, tested for step-change tracking signal and disturbance rejection. Finally, the simulation results showed that the Fuzzy PID controller has a robust performance.
在工业过程中,最重要的回路是液位控制回路。耦合水箱系统 CT-100 成为过程控制研究人员必不可少的设备。本文介绍了两种控制器技术,以控制作为单输入单输出系统的第二个水箱中的水位。设计了 PID 控制器来控制线性化模型,控制器参数采用 Ziegler- Nichols 调节方法进行调节。此外,还根据充足的知识和经验设计了模糊 PID。使用 MATLAB Simulink 对所提出的控制方法进行了模拟。然后,从时间响应规格和 ITAE 标准的角度对使用这些控制器获得的结果进行比较。此外,还对阶跃变化跟踪信号和干扰抑制进行了测试。最后,仿真结果表明,模糊 PID 控制器具有稳健的性能。
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引用次数: 0
A Combined Transformed Variable for Population Mean Estimators When Missing Data Occur with an Application to COVID-19 Incidence 当出现缺失数据时,用于人口平均值估计的组合变换变量,并应用于 COVID-19 发病率
Q3 Mathematics Pub Date : 2023-11-15 DOI: 10.37394/23203.2023.18.43
Natthapat Thongsak, Nuanpan Lawson
COVID-19 has killed many people and continues to be a major problem in all countries around the world. Estimating COVID-19 data in advance is helpful for the World Health Organization and governments in countries all over the globe to prepare the necessary resources. However, some of this information may be missing and needs to be dealt with before processing to estimation. The transformation method of an auxiliary variable can assist by increasing the performance of estimating the population mean. A combined transformed variable is suggested for estimating population mean when a study variable contains some missing values with uniform nonresponse, and it is applied in an application to data on COVID-19 incidence. The bias and mean square error of the suggested estimator are investigated and the performance is compared with existing estimators via a simulation study and an application to COVID-19 data. The results show that the suggested combined transformed estimators overtake existing estimators in terms of higher efficiency which yields the estimated value of total deaths of COVID-19 equal to 29497 cases.
COVID-19 已造成许多人死亡,并将继续成为世界各国的一个主要问题。提前估算 COVID-19 数据有助于世界卫生组织和世界各国政府准备必要的资源。然而,有些信息可能会缺失,需要在处理后再进行估算。辅助变量的转换方法可以提高估计人口平均值的性能。当研究变量包含一些均匀无响应的缺失值时,建议使用组合转换变量来估计总体均值,并将其应用于 COVID-19 发病率数据的应用中。通过模拟研究和 COVID-19 数据的应用,研究了所建议的估计器的偏差和均方误差,并将其性能与现有的估计器进行了比较。结果表明,建议的组合转换估计器在效率方面超过了现有的估计器,得出的 COVID-19 死亡总人数估计值等于 29497 例。
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引用次数: 0
Approximating the ARL of Changes in the Mean of a Seasonal Time Series Model with Exponential White Noise Running on a CUSUM Control Chart 在 CUSUM 控制图上近似运行指数白噪声季节时间序列模型均值变化的 ARL
Q3 Mathematics Pub Date : 2023-11-15 DOI: 10.37394/23203.2023.18.39
W. Peerajit
Control charts comprise an excellent statistical process control tool for monitoring industrial processes. Especially, the CUSUM control chart is very sensitive to small-to-moderate process parameter changes. The proposed approach utilizes the numerical integral equation (NIE) method to approximate the average run length (ARL) of changes in the mean of a seasonal time series model with underlying exponential white noise running on a CUSUM control chart. This was achieved by solving a system of linear equations and integration through partitioning and summation using the area under the curve of a function obtained by applying the Gauss-Legendre quadrature. A numerical study was conducted to compare the capabilities of the ARL derivations obtained using the NIE method and explicit formulas to detect changes in the mean of a long-memory model with exponential white noise running on a CUSUM control chart. The results reveal that the performances of both were comparable in terms of the accuracy percentage, which was greater than 95%, meaning that the ARL values were highly consistent. Thus, the NIE method can be used to validate ARL results for this situation.
控制图是监控工业过程的绝佳统计过程控制工具。特别是,CUSUM 控制图对中小规模的过程参数变化非常敏感。所提出的方法利用数值积分方程 (NIE) 方法来近似计算在 CUSUM 控制图上运行的带有潜在指数白噪声的季节性时间序列模型平均值变化的平均运行长度 (ARL)。其方法是求解线性方程组,并利用通过应用高斯-回归正交获得的函数曲线下面积,通过分割和求和进行积分。通过数值研究,比较了使用 NIE 方法和显式公式获得的 ARL 推导在检测 CUSUM 控制图上运行的指数白噪声长记忆模型均值变化方面的能力。结果表明,二者在准确率方面表现相当,都大于 95%,这意味着 ARL 值高度一致。因此,NIE 方法可用于验证这种情况下的 ARL 结果。
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引用次数: 0
期刊
WSEAS Transactions on Systems and Control
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