• Structural Engineering and Mechanics
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• v.17 no.6
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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.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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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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• 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.

• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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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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• v.29 no.3
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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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• v.26 no.1
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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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• v.25 no.1
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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.

• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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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.

• Journal of KIISE:Software and Applications
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• v.37 no.1
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• pp.1-8
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• 2010

Recently lots of attention has been paid to gene set analysis for identifying differentially expressed gene-sets between two sample groups. Unlike earlier approaches, the gene set analysis enables us to find significant gene-sets along with their functional characteristics. For this reason, various novel approaches have been suggested lately for gene set analysis. As one of such, PAGE is a parametric approach that employs average difference (AD) as an expression metric to quantify expression differences between two sample groups and assumes that the distribution of gene scores is normal. This approach is preferred to non-parametric approach because of more effective performance. However, the metric AD does not reflect either gene expression intensities or variances over samples in calculating gene scores. Thus, in this paper, we investigate the usefulness of several other expression metrics for parametric gene-set analysis, which consider actual expression intensities of genes or their expression variances over samples. For this purpose, we examined three expression metrics, WAD (weighted average difference), FC (Fisher's criterion), and Abs_SNR (Absolute value of signal-to-noise ratio) for parametric gene set analysis and evaluated their experimental results.

• Korean Journal of Ecology and Environment
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• v.54 no.3
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• pp.199-208
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• 2021

Environmental DNA (eDNA) metabarcoding is effective method with high detection sensitivity for evaluating fish biodiversity and detecting endangered fish from natural water samples. We compared the richness of operational taxonomic units(OTUs) and composition of freshwater fishes according to filters(cellulose nitrate filter vs. glass fiber filter), extraction kits(DNeasy2^® Blood & Tissue Kit vs. DNeasy2^® PowerWater Kit), primer sets (12S rDNA vs. 16S rDNA), and PCR methods (conventional PCR vs. touchdown PCR) to determine the optimal conditions for metabarcoding analysis of Korean freshwater fish. The glass fiber filter and DNeasy2^® Blood & Tissue Kit combination showed the highest number of freshwater fish OTUs in both 12S and 16S rDNA. Among the four types, the primer sets only showed statistically significant difference in the average number of OTUs in class Actinopterygii (non-parametric Wilcoxon signed ranks test, p=0.005). However, there was no difference in the average number of OTUs in freshwater fish. The species composition also showed significant difference according to primer sets (PERMANOVA, Pseudo-F=6.9489, p=0.006), but no differences were observed in the other three types. The non-metric multidimensional scaling (NMDS) results revealed that species composition clustered together according to primer sets based on similarity of 65%; 16S rDNA primer set was mainly attributed to endangered species such as Microphysogobio koreensis and Pseudogobio brevicorpus. In contrast, the 12S rDNA primer set was mainly attributed to common species such as Zacco platypus and Coreoperca herzi. This study provides essential information on species diversity analysis using metabarcoding for environmental water samples obtained from rivers in Korea.