• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.63-78
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• 1999

Let $\mu$(x) be an increasing function on the real line with finite moments of all oeders. We show that for any linear operator T on the space of polynomials and any interger n $\geq$ 0, there is a constant $\gamma n(T)\geq0$, independent of p(x), such that $\parallel T_p\parallel\leq\gamma n(T)\parallel P\parallel$, for any polynomial p(x) of degree $\leq$ n, where We find a formular for the best possible value $\Gamma_n(T)\;of\;\gamma n(T)$ and estimations for $\Gamma_n(T)$. We also give several illustrating examples when T is a differentiation or a difference operator and $d\mu$(x) is an orthogonalizing measure for classical or discrete orthogonal polynomials.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.589-602
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• 2008

As a survey-type article, the paper reviews various digital topological utilities from digital covering theory. Digital covering theory has strongly contributed to the calculation of the digital k-fundamental group of both a digital space(a set with k-adjacency or digital k-graph) and a digital product. Furthermore, it has been used in classifying digital spaces, establishing almost Van Kampen theory which is the digital version of van Kampen theorem in algebrate topology, developing the generalized universal covering property, and so forth. Finally, we remark on the digital k-surface structure of a Cartesian product of two simple closed $k_i$-curves in ${\mathbf{Z}}^n$, $i{\in}{1,2}$.

• Advances in Computational Design
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• v.5 no.3
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• pp.277-289
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• 2020

This article describes the technology for constructing of a multiply-connected three-dimensional area's finite element representation. Representation of finite-element configuration of an area is described by a discrete set that consist of the number of nodes and elements of the finite-element grid, that are orderly set of nodes' coordinates and numbers of finite elements. Corresponding theorems are given, to prove the correctness of the solution method. The adequacy of multiply-connected area topology's finite element model is shown. The merging of subareas is based on the criterion of boundary nodes' coincidence by establishing a simple hierarchy of volumes, surfaces, lines and points. Renumbering nodes is carried out by the frontal method, where nodes located on the outer edges of the structure are used as the initial front.

• Journal of the Korean Society for Railway
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• v.9 no.4 s.35
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• pp.467-472
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• 2006

This paper deals with the applicability of long-gauge deformation fiber optic sensors (FOS) to prestressed concrete structures. A main motivation is the desire to monitor the deflection of the railway bridges without intervenes of the signal intensity fluctuations. A 25 m long, 1.8 m deep PSC girder was fabricated compositely with 22 cm thick reinforced concrete deck. Two pairs of 3 m long-gauge sensors are attached to the prestressed concrete girder with parallel topology. Using the relationship between curvature and vortical deflection and the quadratic regression of curvatures at the discrete point, it is possible to extrapolate the deflection curve of the girder. The estimated deflection based on the developed method is compared with the results using conventional strain gauges and LVDTS. It has been demonstrated that the proposed instrumentation technique is capable of estimating the vertical deflection and neutral axis position of the prestressed concrete girder up to weak nonlinear region.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.6
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• pp.1013-1018
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• 2016

In this paper, three kinds of the inverter topologies for the variable speed drive of 2-phase induction motor are compared and analyzed. The 2-phase inverters are classified into 2-leg, 3-leg, and 4-leg types depending on the number of power switching devices. And they use the output voltage vectors of the different forms according to the inverter topologies. Based on the comparative analyzed results, the effective values of output voltage have been defined by the linear modulation range. Therefore, the motor design guideline is proposed in order to decide a rated voltage of 2-phase induction motor according to the inverter topologies. Also, the computer simulations are carried out to verify the output voltage and current characteristics of each inverter topology.

• Structural Engineering and Mechanics
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• v.10 no.4
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• pp.313-336
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• 2000

The focus of this paper is on the development and implementation of a methodology for automated design of discrete structural systems. The research is aimed at utilizing Genetic Algorithms (GA) as an automated design tool. Several key enhancements are made to the simple GA in order to increase the efficiency, reliability and accuracy of the methodology for code-based design of structures. The AISC-ASD design code is used to illustrate the design methodology. Small as well as large-scale problems are solved. Simultaneous sizing, shape and topology optimal designs of structural framed systems subjected to static and dynamic loads are considered. Comparisons with results from prior publications and solution to new problems show that the enhancements made to the GA do indeed make the design system more efficient and robust.

• The Bulletin of The Korean Astronomical Society
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• v.43 no.2
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• pp.36.3-37
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• 2018

By utilizing large-scale graph analytic tools in the modern Big Data platform, Apache Spark, we investigate the topological structures of five different multiverses produced by cosmological n-body simulations with various cosmological initial conditions: (1) one standard universe, (2) two different dark energy states, and (3) two different dark matter densities. For the Big Data calculations, we use a custom build of stand-alone Spark cluster at KIAS and Dataproc Compute Engine in Google Cloud Platform with the sample sizes ranging from 7 millions to 200 millions. Among many graph statistics, we find that three simple graph measurements, denoted by (1) $n_\k$, (2) $\tau_\Delta$, and (3) $n_{S\ge5}$, can efficiently discern different topology in discrete point distributions. We denote this set of three graph diagnostics by kT5+. These kT5+ statistics provide a quick look of various orders of n-points correlation functions in a computationally cheap way: (1) $n = 2$ by $n_k$, (2) $n = 3$ by $\tau_\Delta$, and (3) $n \ge 5$ by $n_{S\ge5}$.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.7
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• pp.607-615
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• 2020

The purpose of this study was to analyze the research status and trends related to the industrial mathematics based on text mining techniques with a sample of 4910 papers collected in the SIAM Journal on Applied Mathematics from 1970 to 2019. The R program was used to collect titles, abstracts, and key words from the papers and to analyze topic modeling techniques based on LDA algorithm. As a result of the coherence score on the collected papers, 20 topics were determined optimally using the Gibbs sampling methods. The main results were as follows. First, studies on industrial mathematics were conducted in a variety of mathematics fields, including computational mathematics, geometry, mathematical modeling, topology, discrete mathematics, probability and statistics, with a focus on analysis and algebra. Second, 5 hot topics (mathematical biology, nonlinear partial differential equation, discrete mathematics, statistics, topology) and 1 cold topic (probability theory) were found based on time series regression analysis. Third, among the fields that were not reflected in the 2015 revised mathematics curriculum, numeral system, matrix, vector in space, and complex numbers were extracted as the contents to be covered in the high school mathematical curriculum. Finally, this study suggested strategies to activate industrial mathematics in Korea, described the study limitations, and proposed directions for future research.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.4A
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• pp.353-359
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• 2010

Cementitious matrix based composites are vulnerable to the drying shrinkage crack during the curing process. In this study, the drying shrinkage induced fracture behavior of the fiber reinforced concrete is simulated and the effects of the fiber reinforcement conditions on the fracture characteristics are analysed. The numerical model is composed of conduit elements and rigid-body-spring elements on the identical irregular lattice topology, where the drying shrinkage is presented by the coupling of nonmechanical-mechanical behaviors handled by those respective element types. Semi-discrete fiber elements are applied within the rigid-body-spring network to model the fiber reinforcement. The shrinkage parameters are calibrated through the KS F 2424 free drying shrinkage test simulation and comparison of the time-shrinkage strain curves. Next, the KS F 2595 restrained drying shrinkage test is simulated for various fiber volume fractions and the numerical model is verified by comparison of the crack initiating time with the previous experimental results. In addition, the drying shrinkage cracking phenomenon is analysed with change in the length and the surface shape of the fibers, the measurement of the maximum crack width in the numerical experiment indicates the judgement of the crack controlling effect.

• Magazine of the Korea Concrete Institute
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• v.8 no.1
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• pp.145-153
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• 1996

The fracture process zone in concrete is a region ahead of a traction-free crack, in which two major mechanisms, microcracking and bridging, play important roles. The toughness due to bridging is dominant compared to toughness induced by microcracking, so that the bridging is dominani: mechanism governing the fracture process of concrete. Fracture mechanics does work for concrete provided that the fracture process zone is being considered, so that the development of model for the fracture process zone is most important to describe fracture phenomena in concrete. In this paper the bridging zone, which is a part of extended rnacrocrack with stresses transmitted by aggregates in concrete, is modelled by a Dugdale-Barenblatt type model with linear tension-softening curve. Two finite element techniques are shown for the analysis of progressive cracking in concrete based on the discrete crack approach: one with crack element, the other without crack element. The advantage of the technique with crack element is that it dees not need to update the mesh topology to follow the progressive cracking. Numerical results by the techniques are demonstrated.