• Structural Engineering and Mechanics
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• 제17권6호
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• pp.767-788
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• 2004

The classical 8-node isoparametric serendipity element uses parametric shape functions for both test and trial functions. Although this element performs well in general, it yields poor results under severe mesh distortions. The distortion sensitivity is caused by the lack of continuity and/or completeness of shape functions used for test and trial functions. A recent element using parametric and metric shape functions for constructing the test and trial functions exhibits distortion immunity. This paper discusses the choice of parametric or metric shape functions as the basis for test and/or trial functions, satisfaction of continuity and completeness requirements, and their connection to distortion sensitivity. Also, the performances of four types of elements, viz., parametric, metric, parametric-metric, and metric-parametric, are compared for distorted meshes, and their merits and demerits are discussed.

• 대한수학회논문집
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• 제33권3호
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• pp.943-960
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• 2018

Our aim is to introduce the notion of a parametric $N_b-metric$ and study some basic properties of parametric $N_b-metric$ spaces. We give some fixed-point results on a complete parametric $N_b-metric$ space. Some illustrative examples are given to show that our results are valid as the generalizations of some known fixed-point results. As an application of this new theory, we prove a fixed-circle theorem on a parametric $N_b-metric$ space.

• Structural Engineering and Mechanics
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• 제38권3호
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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.

• 한국CDE학회논문집
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• 제3권2호
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• pp.140-144
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• 1998

We propose the area between a pair of non-self-intersecting 2-D parametric curves with same endpoints as an alternative distance metric between the curves. This metric is used when d curve is approximated with another in a simpler form to evaluate how good the approximation is. The traditional set-theoretic Hausdorff distance can he defined for any pair of curves but requires expensive calculations. Our proposed metric is not only intuitively appealing but also very easy to numerically compute. We present the numerical schemes and test it on some examples to show that our proposed metric converges in a few steps within a high accuracy.

• Structural Engineering and Mechanics
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• 제29권3호
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• pp.289-300
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• 2008

The use of metric trial functions to represent the real stress field in what is called the unsymmetric finite element formulation is an effective way to improve predictions from distorted finite elements. This approach works surprisingly well because the use of parametric functions for the test functions satisfies the continuity conditions while the use of metric (Cartesian) shape functions for the trial functions attempts to ensure that the stress representation during finite element computation can retrieve in a best-fit manner, the actual variation of stress in the metric space. However, the issue of how to handle situations where there is locking along with mesh distortion has never been addressed. In this paper, we show that the use of a consistent definition of the constrained strain field in the metric space can ensure a lock-free solution even when there is mesh distortion. The three-noded Timoshenko beam element is used to illustrate the principles. Some significant conclusions are drawn regarding the optimal strategy for finite element modelling where distortion effects and field-consistency requirements have to be reconciled simultaneously.

• Structural Engineering and Mechanics
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• 제26권1호
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• pp.31-42
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• 2007

The unsymmetric finite element formulation has been proposed recently to improve predictions from distorted finite elements. Studies have also shown that this special formulation using parametric functions for the test functions and metric functions for the trial functions works surprisingly well because the former satisfy the continuity conditions while the latter ensure that the stress representation during finite element computation can retrieve in a best-fit manner, the actual variation of stress in the metric space. However, a question that remained was whether the unsymmetric formulation was variationally correct. Here we determine that it is not, using the simplest possible element to amplify the principles.

• East Asian mathematical journal
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• 제25권1호
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• pp.45-53
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• 2009

In this paper, by using the technique of the resolvent operators, we study the behaviour and sensitivity analysis of the solutions set for a class of parametric completely generalized nonlinear variational inclusions with set-valued mappings.

• 한국CDE학회논문집
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• 제3권2호
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• pp.87-102
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• 1998

Given a sequence of cross-sectional curves, the skinning method generates a freeform surface that interpolates the given curves in that sequence. This thesis presents a construction method of a B-spline skinning surface that is fair and satisfies volume constraints. The fairness metric is based on the parametric energy functional of a surface. The degrees of freedom in surface control are closely related lo control points in the skinning direction. The algorithm fur finding a skinning surface consists of two step. In the first step, an initial fair surface is generated without volume constraints and one coordinate of each control point is fixed. In the second step, a final surface that meets all constraints is constucted by rearranging the other coordinates of each control point that defines the initial surface A variational Lagrange optimization method produces a system of nonlinear equations, which can be solved numerically. Moreover, the reparametrization of given sectional curves is important for the construction of a reasonable skinning surface. This thesis also presents an intuitive metric for reparametrization and gives some examples that are optimized with respect to that metric.

• 한국정보과학회논문지:소프트웨어및응용
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• 제37권1호
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• pp.1-8
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• 2010

최근 마이크로어레이 데이터를 기반으로 두 개의 샘플 그룹간에 유의한 발현 차이를 나타내는 생물학적 기능 그룹을 검출하기 위한 유전자 집합 분석(gene set analysis) 연구가 많은 주목을 받고 있다. 기존의 유의 유전자 검출 연구와는 달리, 유전자 집합 분석 연구는 유의한 유전자 집합과 이들의 기능적 특징을 함께 검출할 수 있다는 장점이 있다. 이러한 이유로 최근에는 PAGE, GSEA 등과 같은 다양한 통계적 방식의 유전자 집합 분석 방법들이 소개되고 있다. 특히, PAGE의 경우 두 샘플 그룹간의 유전자 발현 차이를 나타내는 스코어의 분포가 정규 분포임을 가정하는 모수적 접근 방식을 취하고 있다. 이러한 방법은 GSEA 등과 같은 비모수적 방식에 비해 계산량이 적고 성능이 비교적 우수한 장점이 있다. 하지만, PAGE에서 유전자 발현 차이를 정량화하기 위한 메트릭으로 사용하고 있는 AD(average difference)의 경우, 두 그룹간에 절대적 평균 발현 차이만을 고려하기 때문에 실제 유전자의 발현값 크기나 분산의 크기에 따른 상대적 중요성을 반영하지 못하는 문제가 있다. 본 논문에서는 이를 보완하기 위해 실제 유전자의 발현값 크기나 그룹 내 샘플들의 분산 정보 등을 스코어 계산에 함께 반영하는 WAD(weighted average difference), FC(Fisher's criterion), 그리고 Abs_SNR(Absolute value of signal-to-noise ratio)을 모수적 방식의 유전자 집합 분석에 적용하고 이에 따른 유의 유전자 집합 검출 결과를 실험을 통해 비교 분석하였다.

• 생태와환경
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• 제54권3호
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• pp.199-208
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• 2021

메타바코딩을 이용한 환경 DNA 분석은 검출 감도가 높아 어류의 생물다양성 평가 및 멸종위기종의 검출에 유용한 기술이다. 이번 연구는 메타바코딩을 이용해 우리나라 담수어류를 대상으로 높은 검출 효율을 보일 수 있는 적합한 분석방법을 확인하기 위해 4가지 분석조건별, 즉 필터(cellulose nitrate filter, glass fiber filter), 추출 키트(DNeasy^® Blood & Tissue Kit, DNeasy^® PowerWater Kit), 프라이머 조합(12S rDNA, 16S rDNA) 그리고 PCR 방법(conventional PCR, touchdown PCR)로 나타나는 Operational Taxonomic Units(OTUs) 수와 종 조성을 비교하였다. Glass fiber filter와 DNeasy^® Tissue & Blood Kit를 이용해 추출한 시료는 12S rDNA와 16S rDNA 프라이머 조합에서 담수어류 OTUs가 가장 많이 검출되었다. 모든 분석조건 중 프라이머 조합에서만 조기어강(Class Actinopterygii) 평균 OTUs 수에서 통계적으로 유의한 차이를 보였고(Non-parametric Wilcoxon Signed Ranks Test, p=0.005), 담수어류 평균 OTUs 수는 유의하지 않았다. 종 조성 비교 결과 역시 프라이머 조합에서 유의한 차이를 보였고(PERMANOVA, Pseudo-F=6.9489, p=0.006), 나머지 분석조건에서는 유의한 차이를 보이지 않았다. NMDS 분석 결과 종 조성은 유사도 65% 기준에서 프라이머 조합에 따라 묶였고, 16S rDNA 프라이머 세트는 주로 멸종위기종인 모래주사(Microphysogobio koreensis), 꼬치동자개(Pseudogobio brevicorpus)가 기여하였고, 12S rDNA 프라이머 세트는 주로 일반종인 피라미(Zacco platypus), 꺽지(Coreoperca herzi) 등이 기여한 것으로 나타났다. 본 연구는 국내 하천에서 채취한 시료에 대한 메타바코딩을 이용한 종 다양성 분석의 기초정보를 제공한다.