• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.1-1
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• 2003

In this talk, a reduced-order modeling methodology based on centroidal Voronoi tessellations (CVT's)is introduced. CVT's are special Voronoi tessellations for which the generators of the Voronoi diagram are also the centers of mass (means) of the corresponding Voronoi cells. The discrete data sets, CVT's are closely related to the h-means clustering techniques. Even with the use of good mesh generators, discretization schemes, and solution algorithms, the computational simulation of complex, turbulent, or chaotic systems still remains a formidable endeavor. For example, typical finite element codes may require many thousands of degrees of freedom for the accurate simulation of fluid flows. The situation is even worse for optimization problems for which multiple solutions of the complex state system are usually required or in feedback control problems for which real-time solutions of the complex state system are needed. There hava been many studies devoted to the development, testing, and use of reduced-order models for complex systems such as unsteady fluid flows. The types of reduced-ordered models that we study are those attempt to determine accurate approximate solutions of a complex system using very few degrees of freedom. To do so, such models have to use basis functions that are in some way intimately connected to the problem being approximated. Once a very low-dimensional reduced basis has been determined, one can employ it to solve the complex system by applying, e.g., a Galerkin method. In general, reduced bases are globally supported so that the discrete systems are dense; however, if the reduced basis is of very low dimension, one does not care about the lack of sparsity in the discrete system. A discussion of reduced-ordering modeling for complex systems such as fluid flows is given to provide a context for the application of reduced-order bases. Then, detailed descriptions of CVT-based reduced-order bases and how they can be constructed of complex systems are given. Subsequently, some concrete incompressible flow examples are used to illustrate the construction and use of CVT-based reduced-order bases. The CVT-based reduced-order modeling methodology is shown to be effective for these examples and is also shown to be inexpensive to apply compared to other reduced-order methods.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.765-770
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• 2018

In this paper, we investigate the majorization properties for certain subclasses of analytic functions of complex order. Moreover, some interesting consequences of our main theorem are pointed out.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.461-470
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• 2019

In this note, we consider the growth of solutions to second order and higher order linear complex differential equations on annuli instead of the complex plane. We establish several theorems that are analogues of the results in the complex plane.

• Structural Engineering and Mechanics
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• v.78 no.3
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• pp.369-378
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• 2021

This paper reviewed a few output-only system identification algorithms and identified the shortcomings of those popular blind source separation methods. To address the issues such as less sensors than the targeted modal modes (under-determinate problem), repeated natural frequencies as well as systems with complex mode shapes, this paper proposed a complex wavelet modified second order blind identification method (CWMSOBI) by transforming the time domain problem into time-frequency domain. The wavelet coefficients with different dominant frequencies can be used to address the under-determinate problem, while complex mode shapes are addressed by introducing the complex wavelet transformation. Numerical simulations with both high and low signal-to-noise ratios validate that CWMSOBI can overcome the above-mentioned issues while obtaining more accurate identified results than other blind identification methods.

• Journal of the Korean Society for Library and Information Science
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• v.50 no.2
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• pp.101-118
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• 2016

For the effective classification of complex subjects, a library classification scheme should adopt multiple division principles (or facets). Each of the multiple principles adopted for the division of complex subjects is sequentially applied at each stage of division. The order of application of these multiple principles during the process of division of complex subjects is called citation order. In order for a classification scheme to be consistent and logical, the citation order of division principles applied to classify complex subjects should be concrete and consistent. Especially, in case of enumerative classification system, decisions on citation order to represent complex subjects significantly affect the structure and organization of the classification system. There are basic principles and theoretical canons of the classification theory on the citation order and its application, but they cannot be applied solidly in the process of classification system development for practical reasons. Therefore, this paper first reviews previous works on classification theories regarding citation order, then explores the conditions and circumstances for the application of citation order.

• Proceedings of the Membrane Society of Korea Conference
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• 1994.04a
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• pp.61-62
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• 1994

In order to prepare polyion complex membranes useful for the separation of water-alcohol by pervaporation, k-carrageenan containing artionic sulfate groups in the backbone and good hydrophilicity was selected for the polyanion membrane material and poly{1,3-bis[4-butyl pyridinium] propane. bromide}, one of the polycations synthesized in our lab and containing cationic pyridinium groups., was used. The polyion complex membranes were prepared by the ion complex formation between kcarrageenan films and poly{1,3-bis[4-butyl pyridinium] propane. bromide}. On the formation process of polyion complex membranes, the way of potyion complex formation was carefully studied. In order to study the effect of the morphology on the permeation properties of the polyion complex membranes, which is one of the important factors affecting on the permeation properties of membranes but rarely studied, the microstructure behaviors of the polyion complex mem6ranes in methanol-water mixtures with different compositions Were also studied with x-ray diffractometry and polarizing microscopy.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1625-1647
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• 2014

By making use of the familiar concept of neighborhoods of analytic functions, we prove several inclusion relationships associated with the (n, ${\delta}$)-neighborhoods of certain subclasses of p-valent analytic functions of complex order with missing coefficients, which are introduced here by means of the Saitoh operator. Special cases of some of the results obtained here are shown to yield known results.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.367-372
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• 2009

In this paper, univalence of a certain integral operator and some interesting properties involving the integral operators on the classes of complex order are obtained. Relevant connections of the results, which are presented in this paper, with various other known results are also pointed out.

• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.711-714
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• 2002

This paper presents a method to determine the propagation properties in the junctions between straight and bent waveguides using cylindrical functions of complex order. The proposed method was succeeded by developing the method of numerical calculation of cylindrical functions of complex order. As a result, we numerically calculate the reflection and transmission coefficients in the junctions in various situations, and we compare these results with the results by the perturbation method.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1495-1506
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• 2021

The growth of solutions of second order complex differential equations f" + A(z)f' + B(z)f = 0 with transcendental entire coefficients is considered. Assuming that A(z) has a finite deficient value and that B(z) has either Fabry gaps or a multiply connected Fatou component, it follows that all solutions are of infinite order of growth.