• Journal for History of Mathematics
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• v.31 no.1
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• pp.19-35
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• 2018

Taylor's Theorem is an important theorem which is applied to several disciplines. It is usually taught in a college-level calculus course for the first time. Many students have a hard time to understand or to make applications. In this paper, we look into the history of the development of Taylor's theorem and consider a teaching strategy of the theorem.

• Journal of the Korean Institute of Telematics and Electronics
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• v.20 no.5
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• pp.1-7
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• 1983

Generally, multiple-valued logic algebra is based on the number system of modulo-M. In this paper, characters a, b, c‥… each of them represents the independent state, are regarded as the elements of the symbolic multiple-valued logic. By using the set theory, the symbolic multiple - valued logic and their functions are defined. And Varation for the symbolic logic function due to the variation of a variable and their properties are suggested and analized. With these variations, the MacLaurin's and Taylor's Series expansions of the symbolic logic functions are proposed and proved.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.180-185
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• 2004

This paper investigates asimply supported orthotropic rectangular laminate with viscous interfaces subjected to bending. Additional mathematical difficulty is involved due to the presence of viscous interfaces because the behavior of the laminate depends on time. A step-by-step state-space approach is suggested, which is directly based on the threedimensional theory of elasticity. In particular, Taylor's expansion theorem is employed to model the variations of field variables with time. The proposed method is suitable for analyzing laminated plate of arbitrary thickness. Numerical calculations are performed and it is shown that the viscous interfaces have a significant fluence on the response.

• Journal for History of Mathematics
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• v.27 no.2
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• pp.127-138
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• 2014

In this paper we investigate how Newton discovered the generalized binomial theorem. Newton's binomial theorem, or binomial series can be found in Calculus text books as a special case of Taylor series. It can also be understood as a formal power series which was first conceived by Euler if convergence does not matter much. Discovered before Taylor or Euler, Newton's binomial theorem must have a good explanation of its birth and validity. Newton learned the interpolation method from Wallis' famous book ${\ll}$Arithmetica Infinitorum${\gg}$ and employed it to get the theorem. The interpolation method, which Wallis devised to find the areas under a family of curves, was by nature arithmetrical but not geometrical. Newton himself used the method as a way of finding areas under curves. He noticed certain patterns hidden in the integer binomial sequence appeared in relation with curves and then applied them to rationals, finally obtained the generalized binomial sequence and the generalized binomial theorem.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.4
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• pp.187-200
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• 1992

A general scheme is developed to determine the Langrangian motions of water particles by the Eulerian velocity at their mean positions by using Taylor's theorem. Utilizing the Stokes finite-amplitude wave theory, the orbital motions and the mass transport velocity including the effects of higher-order wave components are determined. The fifth-order approximation of orbital motion gives very good predictions of actual water particle motion in Stokes fifth-order wave theory except near the free-surface. The fifth-order theory predicts the mass transport velocity less than that given by the existing second-order theory over the whole water depth.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.2
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• pp.43-53
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• 1993

There exist two difficulties in the nonlinear wave-body problems. First is the abrupt behavior near the intersection point between the body and the free surface, and second is the far field treatment. In this paper, the far field treatment is considered. The main idea is the Taylor series expansion of free-surface geometry and the application of F.F.T. algorithm. The numerical step is as follows. The velocity potential is expressed by the Green's theorem. and the solution is obtained by iteration method. In the iteration stage, the expressions by the Green's theorem are transformed to the convolution forts with the expansion of free surface by the wave slope. Here F.F.T. is applied, so the computing time can be of O(Nlog N) where N is the number of unknowns. The numerical analysis is carried out and the results are compared with other results in linear floating body problem and nonlinear moving pressure patch problem, and good agreements are obtained. Finally nonlinear floating body radiation problem is carried out with computing time of O(Nlog N).

• Journal of the Korea Academia-Industrial cooperation Society
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• v.10 no.10
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• pp.2794-2802
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• 2009

Soil nailing method is widely used in reinforcing slopes and excavating earth. The analysis of nail-reinforced slopes, generally require complicated computer programs. The purpose of this paper is suggest, Soil stability Chart for nailed slopes which are very useful for pre-design, rapidly design, and final check. Three slope types, three nail lengths and three nail angles are selected for the stability analysis by using limit equilibrium method form Bishop and French. From the above results, this study propose the reinforced design charts for examine the necessity of reinforcement can be examined. The suggested stability chart and Taylor's Slope Stability Chart, showed similar safety factors. This Soil Nailing design charts can provide the solutions for necessity of reinforcement, economical of nail's length ratio and installation angle as well.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.358-358
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• 2012

최근 기후변화의 영향에 따라 강수량과 증발산량이 변하는 경향을 보이고 있으며, 그에 따라 유출량도 변하고 있다. 따라서 기후변화가 수자원에 미치는 영향도 커지고 있으며, 댐 유역의 유출량 산정은 홍수나 용수의 확보측면에서 중요시 되고 있다. 탱크모형은 일본의 Sugawara가 1961년 처음 개발한 모형으로 유역을 오리피스 유출공을 가진 저류형 수조의 조합으로 가정하여 유량을 산정하는 유출모형으로 매개변수가 많고, 이들을 시행착오로 결정해야 하기 때문에 숙련된 경험이 요구되는 단점이 있으나 계산법이 명확하고 수문현상을 잘 재현한다는 장점이 있다. 탱크에는 강수량, 유출량, 그리고 증발량과 같은 입력 자료가 필요하며, 정확한 실제 증발산량 값을 알기는 어렵기 때문에 물수지를 이용해 증발산량을 계산하여 사용하고 있지만 유출량 미계측 지역에서는 사용이 어렵다. 그러므로 태양복사에너지, 온도, 바람, 기압, 습도와 같은 기상학적 인자에 따라서 잠재증발량을 산정하여 탱크 모형의 입력 자료로 사용한다면, 유출량자료가 없는 유역에서도 탱크모형을 사용하여 유출량을 산정할 수 있을 것으로 사료된다. 본 연구에서는 섬진강댐유역과 합천댐유역의 유출량 산정을 위해 잠재 증발산량 산정식(Penman, FAO P-M, Makkink, Preistley-Taylor, Hargreaves)을 적용하여 Tank 모형 매개변수들의 민감도분석을 수행하였다. 섬진강댐은 전북 임실군 강진면 옥정리와 정읍시 산내면 종성리 사이에 있으며, 유역면적은 $763km^2$, 댐 높이는 64m, 제방길이 344.2m 댐으로 매개변수 민감도 분석 적용기간은 1975년~1992년이다. 합천댐은 경상남도 합천군 대병면 회양리에 있는 댐으로 높이 96m, 길이 472m, 유역면적 $925km^2$의 다목적 댐이며, 매개변수 민감도 분석 적용기간은 1989년~1999년이다.

• Journal of Korean Tunnelling and Underground Space Association
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• v.18 no.3
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• pp.291-303
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• 2016

Recently, various forms of diverging sections in tunnels have been designed as the demand for underground passageway in urban areas increases. Therefore, the complexity of the ventilation system in tunnels with diverging sections requires a ventilation analysis method different from the conventional method for the straight tunnels. None of the domestic and foreign tunnel ventilation design standards specifies the method for the ventilation network analysis, and the numerical analysis methods have been most widely used. This paper aims at reviewing the ventilation network analytical method applicable as the design standard. The proposed method is based on the characteristic equations rather than the numerical analysis. Thanks to the advantages of easy application, the Hardy-Cross method has been widely applied in the fields of mine ventilation and tunnel ventilation. However, limitations with the cutting errors in the Taylor series expansion and the convergence problem mainly caused by the mesh selection algorithm have been reported. Therefore, this paper examines the applicability of the ventilation analysis method for network-type tunnels with the gradient method that can analyze flow rate and pressure simultaneously without the configuration of mesh. A simple ventilation analysis method for network-type tunnels is proposed.