• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.193-206
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• 2016

In this paper, we study boundary value problems for fractional integrodifferential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence solutions are established by virtue of fractional calculus and fixed point method under some mild conditions.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.237-249
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• 2004

This paper deals with existence of positive solutions of nonlinear elliptic singular boundary value problems in a ball. It is shown that results of Grandall et al. [1] and [2] follow as special cases of our results proved in this article.

• Journal of the Korea Society of Computer and Information
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• v.26 no.1
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• pp.69-76
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• 2021

Recentlly neural network approach for solving a singular perturbed integro-differential boundary value problem have been researched. Especially the model of the feed-forward neural network to be trained by the back propagation algorithm with various learning algorithms were theoretically substantiated, and neural network models such as deep learning, transfer learning, federated learning are very rapidly evolving. The purpose of this paper is to study the approaching method for developing a neural network model with high accuracy and speed for solving singular perturbed problem along with asymptotic methods. In this paper, we propose a method that the simulation for the difference between result value of singular perturbed problem and unperturbed problem by using neural network approach equation. Also, we showed the efficiency of the neural network approach. As a result, the contribution of this paper is to show the possibility of simple neural network approach for singular perturbed problem solution efficiently.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.1
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• pp.1-7
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• 2000

This paper studies the delay-characteristics using the singular values and vectors of Hankel operators for input delay systems. First, the computational method of Hankel singular values and their corresponding singular vectors are introduced, and then it is analytically provea that all the Hankel singular vlues have a monotone increasing properties as the length of delay time increases. Furthermore, through a simple numerical example, it is shown that the Hankel singular values are dependent only on the ratio of the time constant of a lumped parameter system to the length of delay , and in case that the time constant is relatively larger than the delay time, the lumped parameter characteristic has a great influence on the input delay systems.

• Smart Structures and Systems
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• v.22 no.5
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• pp.621-630
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• 2018

Boundary effect and the noise robustness are the two crucial aspects which affect the effectiveness of the damage localization based on the mode shape measurements. To overcome the boundary effect problem and enhance the noise robustness in damage detection, a simple damage localization method is proposed based on the Singular Value Decomposition (SVD) for the mode shape of composite plates. In the proposed method, the boundary effect problem is addressed by the decomposition and reconstruction of mode shape, and the noise robustness in enhanced by the noise filtering during the decomposition and reconstruction process. Numerical validations are performed on plate-like structures for various damage and boundary scenarios. Validations show that the proposed method is accurate and effective in the damage detection for the two-dimensional structures.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.21 no.2
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• pp.232-240
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• 2012

This study proposed efficient method of singular value for inverse problem, linear approximation of contact position and loading in single and double meshing of transmission contact element, using 2-dimension model considered near the tooth by root stress. Determination of root stress is carried out for the gear tooth by finite element method and boundary element method. Boundary element discretization near contact point is carefully performed to keep high computational accuracy. The predicted results of boundary element method are good accordance with that of finite element method.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2000.04a
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• pp.317-322
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• 2000

인터넷의 발달로 사용자들은 인터넷에서 필요한 정보를 습득할 수 있을 뿐만 아니라, 생활에 필요한 여러 가지 활동들을 할 수 있게 되었다. 특히 주목받는 부분은 구매 활동이다. 따라서 수많은 기업들이 사람들의 구매 활동에 관련된 전자상거래에 투자하고 있고, 현재 Amazon.com 등과 같은 세계적인 사이트들이 서비스를 실시하고 있다. 또한, 전자상거래 사이트들은 사용자들의 구매 활동을 도와주기 위해 추천 시스템의 도입을 추진하고 있다. 추천 시스템은 사용자들로부터 얻어진 정보를 학습하여 이용 가능한 상품 중에서 고객이 좋아할 만한 것은 추천해 주는 시스템이다. 본 논문에서는 추천 시스템에서 사용되는 주요한 방법인 협력적 여과방법에서 초기 rating 행렬의 희소성 문제를 해결하기 위하여 Singular Value decompositon의 적용 방법을 제안하고 있다.

• Proceedings of the KIEE Conference
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• 1989.11a
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• pp.467-469
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• 1989

A new singular value approach is presented and analized in order to determine the number of multi pie sinsoidal frequencies from the finite noisy data. Simulations are conducted for Akaike's information criterion(AIC), Rissanen's shortest data description(MDL) and a new singular value approach, in covariance matrix based methods. And then performances are compared.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.4
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• pp.413-419
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• 1998

A novel order-reduction technique for model predictive control(MPC) is proposed based on the singular value decomposition(SVD) of a pulse response circulant matrix(PRCM) of a concerned system. It is first investigated that the PRCM (in the limit) contains a complete information of the frequency response of a system and its SVD decomposes the information into the respective principal directions at each frequency. This enables us to isolate the significant modes of the system and to devise the proposed order-reduction technique. Though the primary purpose of the proposed technique is to diminish the required computation in MPC, the clear frequency decomposition of the SVD of the PRCM also enables us to improve the robustness through selective excitation of frequency modes. Performance of the proposed technique is illustrated through two numerical examples.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.697-710
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• 2010

In this paper, we prove existence of infinitely many positive and concave solutions, by means of a simple approach, to $3^{th}$ order three-point singular boundary value problem {$x^{\prime\prime\prime}(t)=\alpha(t)f(t,x(t))$, 0 < t < 1, $x(0)=x'(\eta)=x^{\prime\prime}(1)=0$, (1/2 < $\eta$ < 1). Moreover with respect to multiplicity of solutions, we don't assume any monotonicity on the nonlinearity. We rely on a combination of the analysis of the corresponding vector field on the phase-space along with Knesser's type properties of the solutions funnel and the well-known Krasnosel'ski$\breve{i}$'s fixed point theorem. The later is applied on a new very simple cone K, just on the plane $R^2$. These extensions justify the efficiency of our new approach compared to the commonly used one, where the cone $K\;{\subset}\;C$ ([0, 1], $\mathbb{R}$) and the existence of a positive Green's function is a necessity.