• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.191-207
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• 2007

Based on a mixed Galerkin approximation, we construct the fully discrete approximations of $U_y$ as well as U to a single-phase quasilinear Stefan problem with a forcing term in non-divergence form. We prove the optimal convergence of approximation to the solution {U, S} and the superconvergence of approximation to $U_y$.

• Structural Engineering and Mechanics
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• 제16권2호
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• pp.195-217
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• 2003

This paper, which is an extension of a previous work by Viola et al. (2002), deals with the dynamic stability of beams under a triangularly distributed sub-tangential forces when the effect of an elastically restrained end is taken into account. The sub-tangential forces can be realised by a combination of axial and tangential follower forces, that are conservative and non-conservative forces, respectively. The studied beams become unstable in the form of either flutter or divergence, depending on the degree of non-conservativeness of the distributed sub-tangential forces and the stiffness of the elastically restrained end. A non-conservative parameter ${\alpha}$ is introduced to provide all possible combinations of these forces. Problems of this kind are usually, at least in the first approximation, reduced to the analysis of beams according to the Bernoulli-Euler theory if shear deformability and rotational inertia are negligible. The equation governing the system may be derived from the extended form of Hamilton's principle. The stability maps will be obtained from the eigenvalue analysis in order to define the divergence and flutter domain. The passage from divergence to flutter is associated with a noticeable lowering of the critical load. A number of particular cases can be immediately recovered.

• 대한수학회지
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• 제51권6호
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• pp.1209-1220
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• 2014

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder$\acute{o}$n-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권2호
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• pp.59-71
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• 2018

We consider the boundary value problem with a Dirichlet condition for a second order linear uniformly elliptic operator in a non-divergence form. We study some properties of a barrier at infinity which was introduced by Meyers and Serrin to investigate a solution in an exterior domains. Also, we construct a modified barrier for more general domain than an exterior domain.

• 대한수학회지
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• 제56권1호
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• pp.239-263
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• 2019

The $Calder{\acute{o}}n$-Zygmund type estimate is proved for elliptic obstacle problems in bounded non-smooth domains. The problems are related to divergence form nonlinear elliptic equation with measurable nonlinearities. Precisely, nonlinearity $a({\xi},x_1,x^{\prime})$ is assumed to be only measurable in one spatial variable $x_1$ and has locally small BMO semi-norm in the other spatial variables x', uniformly in ${\xi}$ variable. Regarding non-smooth domains, we assume that the boundaries are locally flat in the sense of Reifenberg. We also investigate global regularity in the settings of weighted Orlicz spaces for the weak solutions to the problems considered here.

• Nuclear Engineering and Technology
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• 제55권3호
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• pp.827-838
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• 2023

Centrifugal pump is a key part of nuclear power plant systems, and its health status is critical to the safety and reliability of nuclear power plants. Therefore, fault diagnosis is required for centrifugal pump. Traditional fault diagnosis methods have difficulty extracting fault features from nonlinear and non-stationary signals, resulting in low diagnostic accuracy. In this paper, a new fault diagnosis method is proposed based on the improved particle swarm optimization (IPSO) algorithm-based variational modal decomposition (VMD) and relevance vector machine (RVM). Firstly, a simulation test bench for rotor faults is built, in which vibration displacement signals of the rotor are also collected by eddy current sensors. Then, the improved particle swarm algorithm is used to optimize the VMD to achieve adaptive decomposition of vibration displacement signals. Meanwhile, a screening criterion based on the minimum Kullback-Leibler (K-L) divergence value is established to extract the primary intrinsic modal function (IMF) component. Eventually, the factors are obtained from the primary IMF component to form a fault feature vector, and fault patterns are recognized using the RVM model. The results show that the extraction of the fault information and fault diagnosis classification have been improved, and the average accuracy could reach 97.87%.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권1호
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• pp.13-19
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• 2016

In this paper, we study some characterizations of unbounded domains. Among these, so-called G-domain is introduced by Cabre for the Aleksandrov-Bakelman-Pucci maximum principle of second order linear elliptic operator in a non-divergence form. This domain is generalized to wG-domain by Vitolo for the maximum principle of an unbounded domain, which contains G-domain. We study the properties of these domains and compare some other characterizations. We prove that sA-domain is wG-domain, but using the Cantor set, we are able to construct a example which is wG-domain but not sA-domain.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2004년도 제22회 춘계학술대회논문집
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• pp.528-531
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• 2004

For a simple one-dimensional ignition problem a mathematical model is described to investigate the difficulties in numerical simulations. Some computation results are obtained and comparison is made with analytical solution. Discussions are made on topics such as 1) coordinate transformation, 2) gas-phase and solid-phase analysis; (divergence form of the governing system, a finite-volume discretization, implicit time integration, upwind split flux, spatial accuracy improvement are described. Mass, reagent mass, and energy conservations are solved.), and 3) method to determine quantities on the burning surface (matching). Results obtained for small values of the non-dimensional pressure show a steady-combustion and good agreement with the analytical solution. Numerical instability appeared for larger values of the pressure, discussion on the cause of the problem is made. This effort is a part of a study of flame spread phenomena on solid propellant surface.

• 한국소음진동공학회논문집
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• 제24권8호
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• pp.583-591
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• 2014

The mathematical modeling on the free vibration and stability of a multi-stepped shaft of turbo compressor is performed in this study. The multi-stepped shaft is modeled as a non-uniform Timoshenko beam supported by anisotropic bearings. It is assumed that the shaft is spinning with constant speed about its longitudinal axis and subjected to a conservative axial force induced by front and rear impellers attached to the shaft. The structural model incorporates non-classical features such as transverse shear and rotary inertia. A structural coupling between vertical and lateral motions is induced by Coriolis acceleration terms. The governing equations are derived via Hamilton's variational principle and the equations are transformed to the standard form of an eigenvalue problem. The implications of combined gyroscopic effect, conservative axial force, bearing stiffness and damping are revealed and a number of pertinent conclusions are outlined. In this study analytical results are compared with those from ANSYS finite element analysis and experimental modal testing.

• 대한원격탐사학회지
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• 제20권2호
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• pp.91-102
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• 2004

본 연구는 지형학적 순간단위유량도 작성을 위한 EOC 영상의 적용가능성에 대한 연구이다. EOC 영상으로부터 생성된 소유역에 대한 수치표고모형을 생성하여 유역밀도와 도수분포를 해석한 후 지형학적 순간단위유량도에 미치는 영향을 분석하여 EOC 영상의 지형수문학적 적용가능성을 검토하였다. 원격탐사기법을 이용한 유역특성 분석은 다른 방식에 비해 연구과정이 상당히 복잡하고 많은 시간이 걸리기 때문에 지형학적 수문해석의 기본 자료인 EOC 스테레오 영상으로 수치표고모형을 생성시켰다. 그리고 영상자료와 수치지도로부터 소하천 유역의 격자간격을 10m에서 100m까지 10m 간격으로 나눈 뒤 격자별로 하천에 대한 기본적인 분석을 실시한 후, 도수함수를 이용한 유역 면적와 하천길이의 통계분석을 실시하였다. 통계분석 후 지형학적 분기율, 면적비, 길이비에 대한 격자별 비교 분석 후 지형학적 순간단위유량도에 의한 첨두유량, 첨두도달시간을 비교 검토 하였다. 지형학적 순간단위도의 첨두유량과 도달시간은 유역인자 뿐만 아니라 격자 크기에 따라 비선형적으로 변화하는데 격자크기는 첨두도달시간과 유량의 중요한 지형수문학적 인자 중의 하나임을 알 수가 있으며, 유출해석을 위한 EOC영상의 활용이 가능할 것이다.