• Journal for History of Mathematics
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• v.28 no.2
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• pp.103-115
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• 2015

Contemporary differential geometry owes much to the theory of connections on the bundles over manifolds. In this paper, following the work of Gauss on surfaces in 3 dimensional space and the work of Riemann on the curvature tensors on general n dimensional Riemannian manifolds, we will investigate how differential geometry had been developed from mid 19th century to early 20th century through lives and mathematical works of Christoffel, Ricci-Curbastro and Levi-Civita. Christoffel coined the Christoffel symbol and Ricci used the Christoffel symbol to define the notion of covariant derivative. Levi-Civita completed the theory of absolute differential calculus with Ricci and discovered geometric meaning of covariant derivative as parallel transport.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.149-160
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• 2010

Let $W(x)={\prod}_{k=1}^m{\mid}x-x_k{\mid}^{{\gamma}_k}{\cdot}{\exp}(-{\mid}x{\mid}^{\alpha})$. Associated with the weight W, upper and lower bounds of the generalized Christoffel functions for generalized nonnegative polynomials are obtained.

• Bulletin of the Society of Naval Architects of Korea
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• v.18 no.4
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• pp.13-20
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• 1981

The hydrodynamic added mass of two dimensional cylinders oscillating vertically at high frequencies in the free surface is of interest to ship vibration problems. Conformal transformation is one of the methods commonly in use for computing the inertia coefficient. Especially, Schwarz-Christoffel transformation has been employed to evaluate the inertia coefficient for the cylinders of straight frames and chines. In this paper, the inertia coefficient for the cylinders with round corners in vertical oscillation at high frequencies are evaluated by employing the Schwarz-Christoffel transformation for the concave corner. The results of calculation by employing the Schwarz-Christoffel transformation are found to be well within the expected range of values compared to Lewis form and the results obtained by source distribution method.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.121-134
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• 1999

Generalized nonnegative polynomials are defined as the products of nonnegative polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We extend some results on Infinite-Finite range inequalities, Christoffel functions, and Nikolski type inequalities corresponding to weights W\ulcorner(x)=exp(-｜x｜\ulcorner), $\alpha$>0, to those for generalized nonnegative polynomials.

• Journal of Electrical Engineering and Technology
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• v.12 no.5
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• pp.1963-1969
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• 2017

In order to overcome the manufacturing difficulty of the transverse-flux permanent magnet linear motor (TFPMLM) and enhance its performance much better, a novel TFPMLM with E-core and 3 dimension (3D) magnetic structures is proposed in this paper. Firstly, its basic structure and operating principle are presented. Then the equivalent 2D configuration of the TFPMLM is transformed, so that the Schwarz-Christoffel (SC) mapping method can be used to analyze the motor. Furthermore, the air gap flux density distribution is solved by SC mapping method, based on which, the EMF waveform, no-load cogging force waveform and load force waveform are obtained. Finally, the prototyped TLPMLM is manufactured and the results are obtained from the experiment and 3D FEM, respectively, which are used to compare with those from SC mapping method.

• Bulletin of the Society of Naval Architects of Korea
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• v.5 no.2
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• pp.1-26
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• 1968

This work is a general treatment of added mass calculation of two-dimensional cylinders with straight-framed sections and chines oscillating in the free surface of an ideal fluid with high frequencies. Two and three parameter families in vertical oscillations are treated by employing Schwarz-Christoffel transformation. The results are presented with regards to geometrical parameters such as chine engles, sectional area coefficient and beam draft ratio.

• Journal of Ocean Engineering and Technology
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• v.2 no.2
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• pp.46-50
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• 1988

$90^{\circ}$-모서리 주위의 유동에 관한 수치해석결과를 바탕으로 그 유동구조를 점근적으로 해석하였다. 전체유동구조는 고전적 자유유선 이론에 의한 모델과 일치하였으며 경계층 박리점 주위의 유동구조는 최근의 트리플뎨 이론에 근거하였으며 그 결과가 수치해석의 결과와 아주 잘 맞는데 따른 결과이다.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.731-738
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• 2012

Let L(M) be the bundle of all linear frames over $M,\;u$ an arbitrarily given point of L(M), and ${\nabla}\;:\;\mathfrak{X}(M)\;{\times}\;\mathfrak{X}(M)\;\rightarrow\;\mathfrak{X}(M)$ a linear connection on L(M). Then the following results are well known: the horizontal subspace and the connection form at the point $u$ may be written in terms of local coordinates of $u\;{\epsilon}\;L(M)$ and Christoffel's symbols defined by $\nabla$. These results are very fundamental on the study of the theory of connections. In this paper we show that the local expressions of those at the point $u$ do not depend on the choice of a local coordinate system around the point $u\;{\epsilon}\;L(M)$, which is rarely seen. Moreover we give full explanations for the following fact: the covariant derivative on M which is defined by the parallelism on L(M), determined from the connection form above, coincides with $\nabla$.

• Magazine of the Korean Society of Agricultural Engineers
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• v.18 no.1
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• pp.4071-4078
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• 1976

The authors analyzed the seepage by means of the following mathmatical solutions of the Laplace Equations on the given boundary conditions. The boundaries of the flow region are of two types i) impervious boundaries (${\Phi}$=constant), and ii) reservoir boundaries (${\Phi}$=constant). The corresponding w plane, bounding the flow region, is the rectangle in Fig. 8-a. As the z plane and w plane are both polygons, by means of the Schwarz-Christoffel transformation the flow region in each of these planes can be mapped con for mally onto the same half of an auxiliary t plane, there by yielding, say, the functions z=f1(t) and w=f2(t). Then, either by eliminating the variable t or by using t as a parameter, the function w=f(z) can be established.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.867-879
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• 2012

For ${\beta}$ > 1, let $T_{\beta}$ : [0, 1] ${\rightarrow}$ [0, 1) be the ${\beta}$-transformation. We consider an invariant $T_{\beta}$-orbit closure contained in a closed interval with diameter 1/${\beta}$, then define a function ${\Xi}({\alpha},{\beta})$ by the supremum such $T_{\beta}$-orbit with frequency ${\alpha}$ in base ${\beta}$, i.e., the maximum value in $T_{\beta}$-orbit closure. This paper effectively determines the maximal domain of ${\Xi}$, and explicitly specifies all possible minimal intervals containing $T_{\beta}$-orbits.