• Journal of applied mathematics & informatics
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• v.27 no.5_6
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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 $g_0(y(a),y'(a),{\cdots},y^{2n-3}(a))=0,g_1(y^{(2n-2)}(a),y^{(2n-1)}(a))=0$, $h_o(y(c),y'(c))=0,h_i(y^{(i)}(c),y^{(i+1)}(c))=0(i=2,3,{\cdots},2n-2)$.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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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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• v.24 no.1_2
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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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• v.56 no.1
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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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• v.28 no.1
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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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.12
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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.

• KIPS Transactions on Computer and Communication Systems
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• v.5 no.6
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• pp.135-142
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• 2016

We proposed the new method to estimate the blood pressure with the differential value of the digital arterial pulse waveform and BP relation equation. To get the digital arterial pulse waveform, we use the arterial pulse waveform measurement system that has digital air-pressure sensor device and smart phone. The acquired digital arterial pulse waveforms are classified as hypertension group, normal group, and hypotension group, and we can derive the average differential value between the highest point and lowest point of a single waveform of individuals along with the group. In this study, we found the functional correlation between the blood pressure and differential value as a form of BP relation equation through the regression process on the average of differential value and blood pressure value from a tonometer. The Experimental results show the BP relation equation can give easy blood pressure estimation method with a high accuracy. Although this estimation method has over 66 % error rate and does not give the high level of the accuracy for the diastolic compares to the commercial tonometer, the estimation results for the systolic show the high accuracy that has less than 10 % error rate.

• The KSFM Journal of Fluid Machinery
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• v.8 no.1 s.28
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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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• v.23 no.1
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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.

• Journal of the Institute of Convergence Signal Processing
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• v.8 no.3
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• pp.192-198
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• 2007

In this paper, a new method to reduce the size of ROM in the direct digital frequency synthesizer(DDFS) is proposed. The new ROM compression method can reduce the ROM size by using the two ROM. The quantized value of sine is stored by the quantized-ROM(Q-ROM) and the differential ROM(D-ROM). To reduce the ROM size, we use the differential quantization technique with this two ROM. First, we quantize the quarter sine wave with the $2^L$ address and store the quantized value at the Q-ROM. Second, after the $2^L$ address are equally divided into $2^M$ sampling intervals, the sampling value is quantized. And the D-ROM store only the difference between this quantized value and the Q-ROM. So the total size of the ROM in the proposed DDFS is significantly reduced compared to the original ROM. The ROM compression ratio of 67.5% is achieved by this method. Also, the power consumption is affected mostly by this ROM reduction.