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| viXra.org > Functions and Analysis > 2410 |
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[10] viXra:2410.0189 [pdf] submitted on 2024-10-31 20:00:47
Authors: Subrat Kumar Verma
Comments: 7 Pages. CC-BY
This article discusses the notion of uniform continuity, its relation with the derivative of differentiable functions and Lipschitzcontinuity or even more weakly Hölder continuity related in some way to how wildly the function oscillates. It also discusses its connectionwith compactness for the very large general class of functions - continuous functions. Further, a few properties of uniform continuous function especially with regards to unique continuous extension of functions are discussed.
Category: Functions and Analysis
[9] viXra:2410.0140 [pdf] submitted on 2024-10-22 22:11:22
Authors: Kang Kum Phyong, Ji Ryong Hwan, Kang Hyok Chol
Comments: 9 Pages.
In control system synthesis, it is interesting to use orthogonal basis functions such as various polynomials and series.However, there are still no examples of applying spectral methods to closed-loop control systems and poor applications to nonlinear plants.In this paper, we proposed a control method of allowing the state of the plant to pass through the desired points that the user suggests subjectively in case a model of the control plant is given and the boundary values at a given time point are given.In other words, to generate the optimal response curve of the Volza problem, we used the standard Chebyshev pseudo-spectral (PS) method, which deals with the state and control of the plant with Chebyshev polynomial approximation, based on which the optimization problem is considered to be a nonlinear programming problem. At that time we obtained the desired control quantity u with the polynomial coefficients and thus implemented the control.In this paper, we demonstrated the practical applicability of this method by showing not only examples of linear plants but also applications of nonlinear plants.
Category: Functions and Analysis
[8] viXra:2410.0139 [pdf] submitted on 2024-10-22 22:10:30
Authors: Ri Kum Ju, Kang Yu Song, Kang Hyok Chol
Comments: 18 Pages.
In this paper, we propose a response optimization method for time-varying or nonlinear systems using lattice matrix operators.In order to compare the effectiveness and accuracy of this method against previous nonlinear optimal control methods, simulation results for nonlinear plants with time-varying and gap nonlinearity are presented in this paper.This method overcomes the drawbacks of previous controller design methods that have been complicated by the characteristics of the plant and allows easy and general development of controllers by matrix algebraic equations for objects with time-varying or nonlinear or uncertain parameters, which have strong robustness to variations in disturbances, environmental noise and parameters.
Category: Functions and Analysis
[7] viXra:2410.0138 [pdf] submitted on 2024-10-22 22:09:38
Authors: Kang Hun Won, Chol Sik Ryang, Un Jong Hong, Kang Song Ham, Yu Gang Song
Comments: 11 Pages.
In this paper, new algorithm is proposed to estimate the state of lithium ion battery capacity using Chaos optimization-least squares support vector machine. Here ,at first we had set parameters of the least squares support vector machine using Chaos optimization algorithms. Next we had made the regression model of least squares support vector machine using Gaussian kernel function. Also it had estimated the state of lithium ion battery capacity using Chaos optimization-least squares support vector machine.And the exactness on the estimation model of Chaos optimization-least squares support vector machine had verified through the simulation analysis.
Category: Functions and Analysis
[6] viXra:2410.0137 [pdf] submitted on 2024-10-22 22:08:43
Authors: Chol-Sik Ryang, Kyong-Min Yun, Tae-Song Kwan, Il Song Rim, Hyon Ho Han
Comments: 19 Pages.
This paper makes an accurate fractional model of the existing non-linear systems using fractional order theory and various intelligent optimization methods and proposes a novel method to identify time-varying parameters of the fractional non-linear system offline and online. More accurate mathematical model of the proposed system was made by applying approximated fractional derivative into the state space model of the classical non-linear system. The initial parameter values of the proposed non-linear fractional system were identified offline by using hybrid particle swarm optimization-genetic algorithm method that is a combination of particle swarm optimization(PSO) and genetic algorithm(GA) that are typical intelligent optimization methods. The time-varying parameters of the non-linear fractional order systems were identified online in real-time by using the output error technique and the recursive least square method. In order to verify the efficiency of the proposed identification technique, we made a simulation experiment for offline and online identification of the time-varying parameters in the existing nonlinear fractional Lorentz system and nonlinear fractional lithium-ion battery system. Simulation results show that the proposed novel identification method can be effectively used for offline and online parameter identification of many complicated non-linear fractional order systems in practice.
Category: Functions and Analysis
[5] viXra:2410.0136 [pdf] submitted on 2024-10-22 22:07:49
Authors: Jo Sok Chol, Ryang Chol Sik, Choe Yu Song, Kim Hyok Jin, U Hyok Chol
Comments: 5 Pages.
This paper proposes a novel denoising and edge detection algorithms for image using least squares support vector machine (LS-SVM) with Gaussian radial basis functions (RBF) kernel. The new filter, called least squares support vector machine filter (LS-SVMF) for image denoising, is based on the general concept of binary filters and machine learning theory. Using the LS-SVM, a set of the new gradient operators and the corresponding second derivative operators are obtained. Computer experiments are carried out for denoising and extracting edge information from real images. The results obtained for the applications show that the proposed algorithms outperform many other existing methods in the image denoising task and the traditional edge detectors. The proposed algorithms can be successfully applied for the processing of images corrupted with impulsive noise while maintaining the visual quality and a low reconstruction error.
Category: Functions and Analysis
[4] viXra:2410.0131 [pdf] submitted on 2024-10-22 21:57:53
Authors: Tae Hyok Kim, Yun Hak Ri, Yong Ho Kim
Comments: 17 Pages.
This paper proposes a method to improve the disturbance rejection performance and guarantee the high-precision tracking performance in the active disturbance rejection control(ADRC) system using the m-th order extended state observer(ESO) with frequency e.
Category: Functions and Analysis
[3] viXra:2410.0084 [pdf] submitted on 2024-10-15 23:41:09
Authors: Parker Emmerson
Comments: 8 Pages.
This paper presents a mathematical framework for integrating tensor fields with angular components, combining linear and angular integrands to form a comprehensive expression. We focus on the integration over spatial variable ( x_i ) and angular variable ( theta ), deriving a combined integrand that reflects the interplay between these dimensions. The methods are implemented computationally, and the resulting combined integrand is visualized to provide insights into its behavior.
Category: Functions and Analysis
[2] viXra:2410.0044 [pdf] submitted on 2024-10-08 18:53:37
Authors: Shumpei Sakuragi
Comments: 25 Pages.
Algorithms by stochastic methods to partial differential equations of the fourth order involving biharmonic operators are stated. The author considered a construction of the solution of a partial differential equation using a certain probability space and stochastic process. There are two algorithms for the fourth-order partial differential equations by stochastic methods. The first one is the method using signed measures. This is a methodwhich constructs a signed measure by a solution using the Fourier transform and obtains a coordinate mapping process. The second method uses iterated Brownian motion. The latter is treated in this paper. The definition ofiterated Brownian motion was modified to investigate the properties of its distribution. The author also defined an iterated random walk corresponding to discretization of that, and showed that it converges to an iteratedBrownian motion in law to the iterated Brownian motion, and obtained its order. In the conventional method, the partial differential equation of the fourth order corresponding to iterated Brownian motion, the Laplacian ofthe boundary condition arises in the remainder term. In other words, if the boundary condition is harmonic, the representation of the partial differential equation involving the biharmonic operator is possible.By focusing on the distribution of the iterated Brownian motion, the representation of the partial differential equation including the biharmonic operator is possible when the boundary condition is biharmonic.
Category: Functions and Analysis
[1] viXra:2410.0017 [pdf] submitted on 2024-10-03 20:33:51
Authors: CholBok Ri, Kwang Ri, CholJun Choe
Comments: 10 Pages.
In this paper, we provide some useful lemmas for construction continued fraction based on a given power series. Then we establish a new continued fraction approximation and bounds for the psi function. Especially, we analytically determine all parameters of the continued fraction by Bernoulli numbers.
Category: Functions and Analysis
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