• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.4
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• pp.207-231
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• 2023

This paper aims to improve the alternative formulation of the fifth- and sixth-order accurate weighted essentially non-oscillatory (AWENO) finite difference schemes. The first is to derive the AWENO scheme with sixth-order accuracy in the smooth region of the solution. Second, a new weighted polynomial functions combining the perturbed forms with conserved variable to the AWENO is constructed; the new form of tunable functions are invented to maintain non-oscillatory property. Detailed numerical experiments are presented to illustrate the behavior of the new perturbational AWENO schemes. The performance of the present scheme is evaluated in terms of accuracy and resolution of discontinuities using a variety of one and two-dimensional test cases. We show that the resulted perturbational AWENO schemes can achieve fifth- and sixth-order accuracy in smooth regions while reducing numerical dissipation significantly near singularities.

• Steel and Composite Structures
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• v.48 no.1
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• pp.73-88
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• 2023

This paper presents a novel implicit level set method for topology optimization of functionally graded (FG) structures with pre-existing discontinuities (pre-cracks) using radial basis functions (RBF). The mathematical formulation of the optimization problem is developed by incorporating RBF-based nodal densities as design variables and minimizing compliance as the objective function. To accurately capture crack-tip behavior, crack-tip enrichment functions are introduced, and an eXtended Finite Element Method (X-FEM) is employed for analyzing the mechanical response of FG structures with strong discontinuities. The enforcement of boundary conditions is achieved using the Hamilton-Jacobi method. The study provides detailed mathematical expressions for topology optimization of systems with defects using FG materials. Numerical examples are presented to demonstrate the efficiency and reliability of the proposed methodology.

• Animal Systematics, Evolution and Diversity
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• v.40 no.1
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• pp.102-107
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• 2024

Two colonial ascidians, Eudistoma glaucum and Eudistoma purpureum, are reported for the first time in Korean waters through taxonomic study on ascidians collected from a subtidal zone of Jejudo Island. Eudistoma glaucum is distinguished by opaque green color of colony in living, massive colony with large corona, smooth surface of corona, sparse sand only at the peduncle, zooids in circle, about 8-10 stigmata of 3 stigmata rows and test process. Eudistoma purpureum is distinguished by brilliant, opaque, purple color of colony in living, less lobed colony form, smooth shiny surface, sparse sand only at the basal test, absence of symbionts, zooids in circle, no distinct bulging sphincter in siphon, long atrial siphon and about 20 stigmata of 3 stigmata rows. As a result of this study, four species of the genus Eudistoma are now recorded in Korean fauna.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.57-66
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• 2024

In this paper, we study how the Hilbert polynomial, associated with a reduced closed subscheme X of codimension 2 in ℙ^N, reveals geometric information about X. Although it is known that the Hilbert polynomial can tell us about the scheme's degree and arithmetic genus, we find additional geometric information it can provide for smooth varieties of codimension 2. To do this, we introduce the concept of Gotzmann coefficients, which helps to extract more information from the Hilbert polynomial. These coefficients are based on the binomial expansion of values of the Hilbert function. Our method involves combining techniques from initial ideals and partial elimination ideals in a novel way. We show how these coefficients can determine the degree of certain geometric features, such as the singular locus appearing in a generic projection, for smooth varieties of codimension 2.

• Anatomy and Cell Biology
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• v.55 no.2
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• pp.255-258
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• 2022

Anatomical variation is defined as normal flexibility in the topography and morphology of body structures. Such variations are not uncommon in muscles, particularly in the upper limb. Subclavius muscle (SM) has a proximal attachment to the first costochondral junction and the muscle fibers are then directed upwards and laterally to get attached distally to the subclavian groove of the clavicle. Having similar attachments as the subclavius, the costocoracoid ligament (CCL) is the thickening of the proximal part of clavipectoral fascia extending up to the coracoid process. Both SM and CCL help in the maintenance of smooth movements of the pectoral girdle and both may not always be present. Absent SM may be due to anomalous development from the muscle matrix that also forms the inferior belly of the omohyoid apart from the SMs. This anatomical variation may be associated with thickened CCLs and can be correlated to the smooth functioning of the pectoral girdle.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.519-529
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• 1995

Let M be a compact smooth manifold of dimension n and let E be a flat (complet) vector bundle over M of rank r.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.911-925
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• 1997

We derive quadrature formulas for approximating wavelet coefficients for smooth functions from equally spaced point values with arbitrarily high degree of accuracy. Wa also estimate the error of quadrature formulas.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.09a
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• pp.40-41
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• 2005

• Proceedings of the Korea Society for Energy Engineering kosee Conference
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• 2003.11a
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• pp.241-246
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• 2003

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.181-188
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• 2009

In this article we consider nontrivial solutions of an elliptic system in the bounded smooth domain with homogeneous Dirichlet data. We apply the linking theorem for showing the existence results that is obtained by Massa.