• Journal of Information Processing Systems
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• 제15권6호
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• pp.1422-1437
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• 2019

With the rapid development of the Internet and the Mobile Internet, social communication based on the network has become a life style for many people. WeChat is an online social platform, for about one billion users, therefore, it is meaningful to study the spreading and evolution mechanism of the rumor on the WeChat social circle. The Rumor was injected into the WeChat social circle by certain individuals, and the communication and the evolution occur among the nodes within the circle; after the refuting-rumor-information injected into the circle, subsequently,the density of four types of nodes, including the Susceptible, the Latent, the Infective, and the Recovery changes, which results in evolving the WeChat social circle system. In the study, the evolution characteristics of the four node types are analyzed, through construction of the evolution equation. The evolution process of the rumor injection and the refuting-rumor-information injection is simulated through the structure of the virtual social network, and the evolution laws of the four states are depicted by figures. The significant results from this study suggest that the spreading and evolving of the rumors are closely related to the nodes degree on the WeChat social circle.

• 한국항해항만학회지
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• 제38권2호
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• pp.89-96
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• 2014

This paper presents an improvement for calculating method of astronomical ship position based on circle of equal altitude equation. In addition, to enhance the accuracy of ship position achieved from solving equation system, the authors used singular value decomposition (SVD) in least square method instead of normal decomposition. In maths, the SVD was proved more numerically stable than normal decomposition. Therefore, the solution of equation system will be more efficient and the result would be more accurate than previous methods. By proposal algorithm, a computer program have been developed to help the navigators in calculating directly ship position when the modern equipment has failure. Finally, some of experiments are carried out to verify effectiveness of proposed algorithm, the results show that the accuracy of ship position based on new method is better than the intercept method.

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 2013년도 추계학술대회
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• pp.130-132
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• 2013

This paper presents an improvement for calculating method of astronomical vessel position with circle of equal altitude equation based on using a virtual object in sun and two stars observation. In addition, to enhance the accuracy of ship position achieved from solving linear matrix system, and surmount the disadvantages on rank deficient matrices situation, the authors used singular value decomposition (SVD) in least square method instead of normal equation and QR decomposition, so, the solution of matrix system will be available in all situation. As proposal algorithm, astronomical ship position will give more accuracy than previous methods.

• 전기의세계
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• 제27권5호
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• pp.69-75
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• 1978

3 phase induction motor applied in the method of connecting it directly across the line needs large current when it starts. At that time, leakage magnetic pathes of interior of the motor are severely saturated and leakage reactances are decreased because of saturation. Consequently, increased current and raised powerfactor yield increase of starting torque. The author, noticing those phenomena, derived experimentally the raion of decreasing leakage reactance from the fact that when voltage applied to motor is increased under locked condition the magnitude of current and phase angle are varied, and determined tha equations of starting current and starting torque, considering the decrease of leakage reactance by the large starting current. The author calculated the characteristics of Current-Time and Speed-Time with the determined equation at specific load conditions, and compared the values obtained from above calculations with those from circle diagram's method and the practically recorded values at same load conditions. Therefore, the authos got a confidience that the results of the derived theory coincide with the practically measured values more well than circle diagram's results and circle diagram's equation should be modified in order to analize the starting status of a induction motor.

• 한국수학교육학회지시리즈A:수학교육
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• 제53권4호
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• pp.509-524
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• 2014

This study was to investigate the types of errors and the frequency of errors to understand students' solving process on the descriptive items with the students of an excellent high school which located in a non-leveling local school district of Gyunggi Province. All 11 items were developed in the equation of a circle and 120 students who attended this high school participated in solving them. The result showed a tendency as follows: Logically invalid inference(Type A, 38.83%) of errors, Omission error of the problem solving process(Type B, 25%), Technical error(Type C, 15.67%), Wrong conclusion(Type D, 11.94%), Use of wrong theorem(Type E, 5.97%), and Use of wrong picture(Type F, 2.61%). The logically invalid inference the students showed with a largest tendency was made because of the lack of reflection. This meant that this error could be corrected in a little treatment of carefulness.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.473-485
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• 2010

We consider the differential equation $$(x^2\;-\;1)u_{xx}\;+\;2xyu_{xy}\;+\;(y^2\;-\;1)u_{yy}\;+\;gxu_x\;+\;gyu_y\;=\;\lambda_nu,\;(*)$$ where $\lambda_n\;=\;n(n\;+\;9\;-\;1)$. We show that the differential equation (*) has a polynomial set as solutions if $g\;{\neq}\;-1$, -3, -5, $\cdots$. Also, we construct an orthogonalizing distributional weight for g < 1 and $g\;{\neq}\;1$, 0, -1, $\cdots$ by regularizing a one-dimensional integral with a singularity on the endpoint of the interval.

• 한국음향학회지
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• 제26권8호
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• pp.415-425
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• 2007

본 논문에서는 간섭 패턴 정합을 이용한 수중 광대역 음원의 위치 추정법을 제안한다. 두 개의 센서 스펙트로그램에 나타나는 간섭 패턴의 정합을 통해 음원과 두 센서간의 상대적인 거리비를 추정하고 이를 아폴로니오스 원의 방정식에 적용하였다. 아폴로니오스의 원은 두 정점에 이르는 거리비가 일정한 값으로 운동하는 점의 자취로 정의되며, 음원의 위치로 추정 가능한 궤적을 나타낼 수 있다. 그러나 아폴로니오스의 원 하나만으로는 정확한 음원의 위치추정이 어렵다. 그러므로 또 하나의 위치 궤적을 추정 할 수 있는 방정식이 필요하다. 따라서 음원과 두 센서간의 신호도달 시간차이를 이용한 쌍곡선의 방정식을 도입하여 최종적인 음원의 위치는 두 방정식의 교점의 좌표로 추정하였다. 제안된 방법의 성능 평가를 위하여 모의실험을 통해 위치 추정 오차율을 분석하고, 해상실험을 통하여 실제 적용 가능성을 분석하였다. 모의실험 및 해상실험 결과 본 논문에서 제안된 위치 추정 알고리즘이 오차율 10% 이내의 성능을 나타내었다.

• 대한수학회보
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• 제52권4호
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• pp.1241-1252
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• 2015

In this paper, we study the dynamical bifurcation of the modified Swift-Hohenberg equation on a periodic interval as the system control parameter crosses through a critical number. This critical number depends on the period. We show that there happens the pitchfork bifurcation under the spatially even periodic condition. We also prove that in the general periodic condition the equation bifurcates to an attractor which is homeomorphic to a circle and consists of steady states solutions.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.637-645
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• 2016

In this paper, we study dynamical Bifurcation of the Burgers-Fisher equation. We show that the equation bifurcates an invariant set ${\mathcal{A}}_n({\beta})$ as the control parameter ${\beta}$ crosses over $n^2$ with $n{\in}{\mathbb{N}}$. It turns out that ${\mathcal{A}}_n({\beta})$ is homeomorphic to $S^1$, the unit circle.

• 대한수학회논문집
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• 제12권3호
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• pp.645-653
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• 1997

We study centrally symmetric orthogonal polynomials satisfying an admissible partial differential equation of the form $$ Au_{xx} + 2Bu_{xy} + Cu_{yy} + Du_x + Eu_y = \lambda_n y, $$ where $A, B, \cdots, E$ are polynomials independent of n and $\lambda_n$ is the eignevalue parameter depending on n. We show that they are either the product of Hermite polymials or the circle polynomials up to a complex linear change of variables. Also we give some properties of them.