• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1465-1472
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• 2009

In This paper we shall study the existence of solutions of nonlinear two point boundary value problems for nonlinear 2nth-order differential equation $y^{(2n)}=f(t,y,y',{\cdots},y^{(2n-1)})$ with the boundary conditions $g_0(y(a),y'(a),{\cdots},y^{2n-3}(a))=0,g_1(y^{(2n-2)}(a),y^{(2n-1)}(a))=0$, $h_o(y(c),y'(c))=0,h_i(y^{(i)}(c),y^{(i+1)}(c))=0(i=2,3,{\cdots},2n-2)$.

• 대한수학회보
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• 제47권1호
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• pp.81-87
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• 2010

In this paper, we consider the existence of nontrivial solutions for the nonlinear fractional differential equation boundary-value problem(BVP) $-D_0^{\alpha}+u(t)=\lambda[f(t, u(t))+q(t)]$, 0 < t < 1 u(0) = u(1) = 0, where $\lambda$ > 0 is a parameter, 1 < $\alpha$ $\leq$ 2, $D_{0+}^{\alpha}$ is the standard Riemann-Liouville differentiation, f : [0, 1] ${\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is continuous, and q(t) : (0, 1) $\rightarrow$ [0, $+\infty$] is Lebesgue integrable. We obtain serval sufficient conditions of the existence and uniqueness of nontrivial solution of BVP when $\lambda$ in some interval. Our approach is based on Leray-Schauder nonlinear alternative. Particularly, we do not use the nonnegative assumption and monotonicity which was essential for the technique used in almost all existed literature on f.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.231-243
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• 2007

The existence of solutions of a class of two-point boundary value problems for higher order differential equations is studied. Sufficient conditions for the existence of at least one solution are established. It is of interest that the nonlinearity f in the equation depends on all lower derivatives, and the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don't apply the Green's functions of the corresponding problem and the method to obtain a priori bound of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.221-233
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• 2016

The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제28권1호
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• pp.33-58
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• 2024

This paper reviews basic concepts for Physics-Informed Neural Networks (PINN) applied to the initial value problems for ordinary differential equations. In particular, using only basic calculus, we derive the error estimates where the error functions (the differences between the true solution and the approximations expressed by neural networks) are dominated by training loss functions. Numerical experiments are conducted to validate our error estimates, visualizing the relationship between the error and the training loss for various first-order differential equations and a second-order linear equation.

• 전기학회논문지
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• 제61권12호
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• pp.1801-1806
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• 2012

This paper presents a simple and practical method which enables to prevent malfunction of protection relay due to differential current caused by one end CT saturation in case of external fault. This method uses difference of magnitude(instantaneous value) between the both end current just before the occurrence of differential current without a separate method to CT staturation detection. One end CT saturation is simulated by current transformer model using type-96 component and the presented method is verified by using EMTP MODELS with respect to internal and external fault with one end CT staturation. The presented method distinguished rightly bewteen external and internal fault with one end CT saturation. This information can be used to prevent malfunction of current differential protection relay in case of external fault. And this method is not affected by sampling rate and has no calculation burden, so it will be applicable to differential current protection relay with ease.

• 정보처리학회논문지:컴퓨터 및 통신 시스템
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• 제5권6호
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• pp.135-142
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• 2016

본 연구에서는 디지털 방식으로 측정된 맥파의 파형으로부터 최대 높이와 최소 높이의 차이, 즉 맥파의 차동값을 이용하여 혈압을 측정하는 측정 기법을 제시한다. 이를 위하여 본 연구에서는 적분 방식의 디지털 압력 센서와 블루투스, 스마트폰으로 구성되는 맥파 측정 시스템을 이용하여 맥파 데이터를 수집하였다. 수집된 맥파 데이터들은 고혈압, 정상, 저혈압의 군으로 분류되고, 각 맥파 파형의 최고 값과 최저 값의 개인별 차동값 평균을 도출한다. 맥파 측정시 동시에 혈압계로 측정한 최고혈압과 최저혈압의 값과 맥파 데이터로부터 도출된 차동값의 평균값들을 회귀 분석하면 맥파 차동값과 혈압과의 상관관계인 혈압상관관계식을 도출할 수 있다. 이 혈압상관관계식을 이용하여 임의의 실험자의 맥파 측정을 통한 혈압 추정 실험을 수행한 결과 실험자들의 혈압값들을 용이하게 추정할 수 있었다. 기존의 혈압계를 사용한 측정치에 대하여 제안된 기법은 최저혈압의 경우는 최대 66 %의 오차를 보이므로 그다지 높은 정확성을 보이지 못하지만, 최고혈압의 경우에는 10 % 이하의 오차로 혈압값을 추정할 수 있었다.

• 한국유체기계학회 논문집
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• 제8권1호
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• pp.16-22
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• 2005

This paper presents the method of ROL(Rate Of Loading) improvement for the Motor Operated Gate Valve operated in high differential pressure condition. ROL is one of the most important evaluation parameters for the valve ability. It is close to correlation in stem factor (SF) and appears different value by the differential pressure of fluid. ROL and SF are analyzed by the static test and dynamic test. The obtained result show that the modification of stem factor is very important factor for the ROL improvement. In order to obtain the same value of SF between static and dynamic test, stem and stem nut should be combined appropriately by the repetition test.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.205-230
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• 2015

A class of periodic type boundary value problems of coupled impulsive fractional differential equations are proposed. Sufficient conditions are given for the existence of solutions of these problems. We allow the nonlinearities p(t)f(t, x, y) and q(t)g(t, x, y) in fractional differential equations to be singular at t = 0, 1 and be involved a sup-multiplicative-like function. So both f and g may be super-linear and sub-linear. The analysis relies on a well known fixed point theorem. An example is given to illustrate the efficiency of the theorems.

• 융합신호처리학회논문지
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• 제8권3호
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• pp.192-198
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• 2007

본 논문에서는 ROM의 크기를 줄여 전력 소모를 줄일 수 있는 DDFS를 제안하였다. 새롭게 제안된 ROM 압축방식은 두 개의 ROM을 사용하여 원하는 주파수를 합성함으로써 전체적인 ROM들의 크기를 줄여준다. 표본화된 사인파의 양자화 값은 양자화 ROM(Quantized ROM : Q-ROM)과 차동 ROM(Differential ROM : D-ROM)에 저장된다. ROM 크기를 줄이기 위해 사인파를 양자화 할 때 일련의 차동 양자화 기술을 응용, 변형하여 두 개의 ROM을 사용한 QD-ROM 압축방식을 제안한다. 1/4주기의 사인파를 $2^L$개의 블록으로 나누어 양자화하고 이를 Q-ROM에 저장한다. D-ROM에는 Q-ROM의 표본화 간격을 $2^M$으로 나누어 표본화하고 양자화된 값은 그 블록의 표본화된 Q-ROM과의 차이만을 양자화하여 저장한다. 이렇게 함으로써 D-ROM에 저장되는 양자화 값의 최대 크기는 Q-ROM에 저장되는 양자화 값보다 작은 양이기 때문에 적은 데이터 길이로도 저장이 가능하다. 이를 사용함으로써 최대 67.5%의 ROM 크기를 감소시켜 전력소모를 줄일 수 있다.