• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.8
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• pp.22-29
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• 1996

This study describes a method to find the torso surface potential based on the boundary element method. In order to find the torso surface potential, the governing equation was developed based on the green's second theorem. The boundary element method (BEM) which has a good computing capability in case of homogeneous and isotropic medium was applied to solve the equation. to validate the BEM, we considered a homogeneous sphere model which has an electrric dopole source inside. The results showed the good agreement between the analytic solution and the computed solution. In normal heart, the simulated torso surface isopotential maps are good agreement with that obtained form the ventricular excitation.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.11a
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• pp.179-182
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• 2004

This paper deals with a new mathematical formulation of nonlinear wave profile based on Banach fixed point theorem. As application of the formulation and its solution procedure, some numerical solutions was presented in this paper and nonlinear equation was derived. Also we introduce a new operator for iteration and getting solution. A numerical study was accomplished with Stokes' first-order solution and iteration scheme, and then we can know the nonlinear characteristic of Stokes' high-order solution. That is, using only Stokes' first-oder(linear) velocity potential and an initial guess of wave profile, it is possible to realize the corresponding high-oder Stokian wave profile with tile new numerical scheme which is the method of iteration. We proved the mathematical convergence of tile proposed scheme. The nonlinear strategy of iterations has very fast convergence rate, that is, only about 6-10 iterations arc required to obtain a numerically converged solution.

• Structural Engineering and Mechanics
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• v.38 no.3
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• pp.261-281
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• 2011

A new method of formulation of a class of elements that are immune to mesh distortion effects is proposed here. The simple three-noded bar element with an offset of the internal node from the element center is employed here to demonstrate the method and the principles on which it is founded upon. Using the function space approach, the modified formulation is shown here to be superior to the conventional isoparametric version of the element since it satisfies the completeness requirement as the metric formulation, and yet it is in agreement with the best-fit paradigm in both the metric and the parametric domains. Furthermore, the element error is limited to only those that are permissible by the classical projection theorem of strains and stresses. Unlike its conventional counterpart, the modified element is thus not prone to any errors from mesh distortion. The element formulation is symmetric and thus satisfies the requirement of the conservative nature of problems associated with all self-adjoint differential operators. The present paper indicates that a proper mapping set for distortion immune elements constitutes geometric and displacement interpolations through parametric and metric shape functions respectively, with the metric components in the displacement/strain replaced by the equivalent geometric interpolation in parametric co-ordinates.

• 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 Chungcheong Mathematical Society
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• v.25 no.1
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• pp.65-72
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• 2012

Let T > 0 be given. Let $(C[0,T],m_{\varphi})$ be the analogue of Wiener measure space, associated with the Borel proba-bility measure ${\varphi}$ on ${\mathbb{R}}$, let $(L_{2}[0,T],\tilde{\omega})$ be the centered Gaussian measure space with the correlation operator $(-\frac{d^{2}}{dx^{2}})^{-1}$ and ${\el}_2,\;\tilde{m}$ be the abstract Wiener measure space. Let U be the space of all sequence $<c_{n}>$ in ${\el}_{2}$ such that the limit $lim_{{m}{\rightarrow}\infty}\;\frac{1}{m+1}\;\sum{^{m}}{_{n=0}}\;\sum_{k=0}^{n}\;c_{k}\;cos\;\frac{k{\pi}t}{T}$ converges uniformly on [0,T] and give a set function m such that for any Borel subset G of $\el_2$, $m(\mathcal{U}\cap\;P_{0}^{-1}\;o\;P_{0}(G))\;=\tilde{m}(P_{0}^{-1}\;o\;P_{0}(G))$. The goal of this note is to study the relationship among the measures $m_{\varphi},\;\tilde{\omega},\;\tilde{m}$ and $m$.

• Journal of Ocean Engineering and Technology
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• v.23 no.4
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• pp.91-99
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• 2009

Many longitudinally arranged pipes in ships are subject to considerable displacement loads caused by the hull girder bending of ships and/or thermal loads in some special pipes through which fluids with highly abnormal temperatures are conveyed. As these loads may cause failure in the pipes or their supporting structures, loops have been widely adopted as a measure to prevent such failure, with the idea that they can lower the stress level in a pipe by absorbing some portion of these loads. But since such loops have some negative effects, such as causing extra manufacturing cost and occupying extra space, the number and dimensions of the loops need to be minimized. This research developed design formulas for pipe loops, modeling them as a spring element, for which the axial stiffness is calculated based on the beam theory, incorporating the effects of the curvature of loop corners and the flexibility of the straight portion of the pipe. The accuracy of the proposed design formulas was verified by comparing two results respectively obtained by the proposed formulas and MSC/NASTRAN. The paper ends with a sample application of the proposed formulas showing their efficiency.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37A no.12
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• pp.1031-1037
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• 2012

We study an algorithm that can efficiently find square roots and cube roots by modifying Tonelli-Shanks algorithm, which has an application in Number Field Sieve (NFS). The Number Field Sieve, the fastest known factoring algorithm, is a powerful tool for factoring very large integer. NFS first chooses two polynomials having common root modulo N, and it consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root. The last step of NFS needs the process of square root computation in Number Field, which can be computed via square root algorithm over finite field.

• The Mathematical Education
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• v.21 no.3
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• pp.7-11
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• 1983

A measurable function f defined on a measurable subset A of the real line R is called pth power summable on A if │f│$^{p}$ is integrable on A and the set of all pth power summable functions on A is denoted by L$^{p}$ (A). For each member f in L$^{p}$ (A), we define ∥f∥$_{p}$ =(equation omitted) For real numbers p and q where (equation omitted) and (equation omitted), we discuss the Holder's inequality ∥fg∥$_1$<∥f∥$_{p}$ ∥g∥$_{q}$ , f$\in$L$^{p}$ (A), g$\in$L$^{q}$ (A) and the Minkowski inequality ∥＋g∥$_{p}$ <∥f∥$_{p}$ ＋∥g∥$_{p}$ , f,g$\in$L$^{p}$ (A). In this paper also discuss that L$_{p}$ (A) becomes a metric space with the metric $\rho$ : L$^{p}$ (A) $\times$L$^{p}$ (A) longrightarrow R where $\rho$(f,g)=∥f-g∥$_{p}$ , f,g$\in$L$^{p}$ (A). Then, in this paper prove the Riesz-Fischer theorem, i.e., the space L$^{p}$ (A) is complete and that the space L$^{p}$ (A) is separable.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.879-882
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• 2005

This paper shows a method for design of the nano-positioning planar scanner used in the scanning probe microscope. The planar scanner is composed of flexure guides, piezoelectric actuators and feedback sensors. In the design of flexure guides, the Castigliano's theorem was used to find the stiffness of the guide. The motion amplifying mechanism was used in the piezoelectric actuator to achieve a large travel range. We found theoretically the travel range of the total system and verified using the commercial FEM(Finite element method) program. The maximum travel range of the planar scanner is above than 140 $\mu$m. The 3 axis positioning capability was verified by the mode analysis using the FEM program. Moreover, we presented the actual AFM(Atomic Force Microscope) imaging results with up to 2Hz imaging scan rate. Experimental results show that the properties of the proposed planar scanner is well enough to be used in SPM applications like AFM.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1225-1236
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• 2016

Let R be a commutative ring with $1{\neq}0$ and n a positive integer. In this article, we introduce the n-Krull dimension of R, denoted $dim_n\;R$, which is the supremum of the lengths of chains of n-absorbing ideals of R. We study the n-Krull dimension in several classes of commutative rings. For example, the n-Krull dimension of an Artinian ring is finite for every positive integer n. In particular, if R is an Artinian ring with k maximal ideals and l(R) is the length of a composition series for R, then $dim_n\;R=l(R)-k$ for some positive integer n. It is proved that a Noetherian domain R is a Dedekind domain if and only if $dim_n\;R=n$ for every positive integer n if and only if $dim_2\;R=2$. It is shown that Krull's (Generalized) Principal Ideal Theorem does not hold in general when prime ideals are replaced by n-absorbing ideals for some n > 1.