• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.3
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• pp.239-245
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• 2008

A level set based topological shape optimization using extended B-spline basis functions is developed for steady-state heat conduction problems. The only inside of complicated domain identified by the level set functions is taken into account in computation, so we can remove the effects of domain outside parts in heat conduction problem. The solution of Hamilton-Jacobi equation leads to an optimal shape according to the normal velocity field determined from the sensitivity analysis, minimizing a thermal compliance while satisfying a volume constraint. To obtain exact shape sensitivity, the precise normal and curvature of geometry need to be determined using the level set and B-spline basis functions. Using topological derivative concept, the nucleation of holes for topological changes can be made whenever and wherever necessary during the optimization.

• Steel and Composite Structures
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• v.47 no.5
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• pp.569-585
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• 2023

This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.

• Korean Journal of Microbiology
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• v.53 no.4
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• pp.286-291
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• 2017

In eukaryotic cells, histone modification is an important mechanism to regulate the chromatin structure. The methylation of the fourth lysine on histone H3 (H3K4) by Set1 complex is one of the various well-known histone modifications. Set1 complex has seven subunits including Swd2, which is known to be important for H2B ubiquitination dependent on H3K4 methylation. Swd2 was reported to regulate Set1's methyltransferase activity by binding to near RNA recognition motif (RRM) domain of Set1 and to act as a component of CPF (Cleavage and Polyadenylation Factors) complex involved in RNA 3' end processing. According to the recent reports, two functions of Swd2 work independently of each other and the lethality of Swd2 knockout strain was known to be caused by its function as a component of CPF complex. In this study, we found that Swd2 could influence the Set1's stability as well as histone methyltransferase activity through the association with RRM domain of Set1. Also, we found that ${\Delta}swd2$ mutant bearing truncated-Set1, which cannot interact with Swd2, lost its lethality and grew normally. These results suggest that the dual functions of Swd2 in H3K4 methylation and RNA 3' end processing are not independent in Saccharomyces cerevisiae.

• East Asian mathematical journal
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• v.24 no.4
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• pp.317-328
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• 2008

In this paper we introduce ${\pi}G{\alpha}$-LC sets, ${\pi}G{\alpha}-LC^*$ sets and ${\pi}G{\alpha}-LC^{**}$ sets and different notions of generalizations of continuous functions in topological space and discuss some of their properties. Further we prove pasting lemma for ${\pi}G{\alpha}-LC^{**}$ continuous functions and ${\pi}G{\alpha}-LC^{**}$ irresolute functions.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.3
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• pp.356-361
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• 2010

M. Demirci[Vague groups, J. math. Anal. Appl. vol.230, pp. 142-156, 1999] studied the vague group operation on a crisp set as a fuzzy function and estabished the vague group structure on a crisp set. In this paper we consider bi-groups which are studied by A.A.A. Agboola and L.S. Akinola. And we also will define vague bi-groups and fuzzy bi-functions and we investigate some basic operations on the vague bi-group and fuzzy bi-functions.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.423-443
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• 2020

Generalizations of essential arity of partial functions, based on essential sets of arguments, are introduced, and their interplay with the minor relation of functions is investigated.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.119-130
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• 2006

A new class of functions is introduced in this paper. This class is called almost ${\delta}$-precontinuity. This type of functions is seen to be strictly weaker than almost precontinuity. By using ${\delta}$-preopen sets, many characterizations and properties of the said type of functions are investigated.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.10a
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• pp.412-417
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• 1998

This paper provides accurate flexural vibration solutions for thick (Mindlin) sectorial plates. A Ritz method is employed which incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of Mindlin “corner functions". These corner functions model the singular vibratory moments and shear forces, which simultaneously exist at the vertex of corner angle exceeding 180$^{\circ}$. The first set guarantees convergence to the exact frequencies as sufficient terms are taken. The second set represents the corner singularities, and accelerates convergence substantially. Numerical results are obtained for completely free sectorial plates. Accurate frequencies are presented for a wide spectrum of vertex angles (90$^{\circ}$, 180$^{\circ}$, 270$^{\circ}$, 300$^{\circ}$, 330$^{\circ}$, 350$^{\circ}$, 35 5$^{\circ}$,and 359$^{\circ}$)and thickness ratios.tios.

• East Asian mathematical journal
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• v.23 no.1
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• pp.83-101
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• 2007

In this paper the concept of somewhat pairwise fuzzy continuous functions and somewhat pairwise fuzzy open functions are introduced. Some interesting properties of these functions are investigated besides giving some characterizations of these functions.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.507-517
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• 2018

In this article, we introduce a new integral operator involving normalized Bessel functions of the first kind and we obtain a set of sufficient conditions for univalence. Our results contain some interesting corollaries as special cases. Further, as particular cases, we improve some of the univalence conditions proved in [2].