• East Asian mathematical journal
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• v.29 no.3
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• pp.293-302
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• 2013

We research properties of ternary numbers and hyperholomorphic functions with values in $\mathbb{C}$(2). We represent reduced quaternion numbers and obtain some propertries in dual reduced quaternion systems in view of Clifford analysis. Moreover, we obtain Cauchy theorems with respect to dual reduced quaternions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.196-220
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• 2021

This study formulates a new geometric parameterization scheme to effectively address numerical analysis subject to the variation of the fiber radius of a square unit cell. In particular, the proposed mesh-morphing approach may lead to a parameterized weak form whose bilinear and linear forms are affine in the geometric parameter of interest, i.e. the fiber radius. As a result, we may certify the reduced basis analysis of a square unit cell model for any parameters in a predetermined parameter domain with a rigorous a posteriori error bound. To demonstrate the utility of the proposed geometric parameterization, we consider a two-dimensional, steady-state heat conduction analysis dependent on two parameters: a fiber radius and a thermal conductivity. For rapid yet rigorous a posteriori error evaluation, we estimate a lower bound of a coercivity constant via the min-θ method as well as the successive constraint method. Compared to the corresponding finite element analysis, the constructed reduced basis analysis may yield nearly the same solution at a computational speed about 29 times faster on average. In conclusion, the proposed geometric parameterization scheme is conducive for accurate yet efficient reduced basis analysis.

• Earthquakes and Structures
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• v.8 no.3
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• pp.639-663
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• 2015

Time history dynamic structural analysis is a time consuming procedure when used for large-scale structures or iterative analysis in structural optimization. This article proposes a new methodology for approximate prediction of extremum point of the response history via wavelets. The method changes original record into a reduced record, decreasing the computational time of the analysis. This reduced record can be utilized in iterative structural dynamic analysis of optimization and hence significantly reduces the overall computational effort. Design examples are included to demonstrate the capability and efficiency of the Reduced Record Method (RRM) when utilized in optimal design of frame structures using meta-heuristic algorithms.

• Steel and Composite Structures
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• v.5 no.1
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• pp.1-15
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• 2005

Important characteristics of the previously proposed reduced stiffness method and a summery of its design curves for the buckling of the axially loaded sandwich cylindrical shells is presented. Comparison of the lower bound obtained with FEM analysis with that from the reduced stiffness analysis shows that the proposed reduced stiffness method can provide safe lower bounds for the buckling of geometrically imperfect, axially loaded sandwich cylindrical shells. One of the attractive features of the reduced stiffness elastic lower bound analysis is that it provides safe estimates of buckling loads that do not depend on the specification of the precise magnitude of the imperfection spectra. As a result, designers can readily apply this method without being worried about possible geometrical imperfections that might be generated during fabrication and construction of sandwich cylindrical shells.

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.458-464
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• 2011

A new method identifies coupled fluid-structure system with a reduced set of state variables is presented. Assuming that the structural model is known a priori either from an analysis or a test and using linear transformations between structural and aeroelastic states, it is possible to deduce aerodynamic information from sampled time histories of the aeroelastic system. More specifically given a finite set of structural modes the method extracts generalized aerodynamic force matrix corresponding to these mode shapes. Once the aerodynamic forces are known, an aeroelastic reduced-order model can be constructed in discrete-time, state-space format by coupling the structural model and the aerodynamic system. The resulting reduced-order model is suitable for constant Mach, varying density analysis.

• The Korean Journal of Applied Statistics
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• v.34 no.6
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• pp.905-922
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• 2021

Cluster analysis is one of unsupervised learning techniques used for discovering clusters when there is no prior knowledge of group membership. K-means, one of the commonly used cluster analysis techniques, may fail when the number of variables becomes large. In such high-dimensional cases, it is common to perform tandem analysis, K-means cluster analysis after reducing the number of variables using dimension reduction methods. However, there is no guarantee that the reduced dimension reveals the cluster structure properly. Principal component analysis may mask the structure of clusters, especially when there are large variances for variables that are not related to cluster structure. To overcome this, techniques that perform dimension reduction and cluster analysis simultaneously have been suggested. This study proposes probabilistic reduced K-means, the transition of reduced K-means (De Soete and Caroll, 1994) into a probabilistic framework. Simulation shows that the proposed method performs better than tandem clustering or clustering without any dimension reduction. When the number of the variables is larger than the number of samples in each cluster, probabilistic reduced K-means show better formation of clusters than non-probabilistic reduced K-means. In the application to a real data set, it revealed similar or better cluster structure compared to other methods.

• Journal of the Korea Concrete Institute
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• v.26 no.5
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• pp.599-606
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• 2014

Since progressive collapse of tall buildings can cause enormous damage, it should be considered during the design phase of tall buildings. The progressive collapse analysis of tall buildings using finite element methods is almost impossible due to the vast amount of computing time. In this paper, applied element method was evaluated as an alternative to the finite element method. Reduced DOFs modeling technique was proposed to enable the progressive collapse analysis of tall buildings. The reduced DOFs model include only the part which is subjected to direct damage from blast load and the structural properties such as mass, transferred load and stiffness of excluded parts are accumulated into the top story of the reduced DOFs model. The proposed modeling technique was applied to the progressive collapse analysis of 20-story RC building using three collapse scenarios. The reduced DOFs model showed similar collapse behavior to the whole model while the computing time was reduced by 30%. The proposed modeling technique can be utilized in the progressive collapse analysis of tall buildings due to abnormal loads.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.5
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• pp.439-450
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• 2008

In this study, the reduced system for the dynamic analysis is proposed and the selection criterion of the primary degrees of freedom is presented considering the relation between natural frequency and external loading frequency. A well-constructed reduced system can assure the accurate representation of the dynamic behavior under arbitrary dynamic loads. For selecting the primary degrees of freedom of the reduced system, we employ the robust two-level condensation scheme of which the reliability has been proven through previous study. In the numerical examples, the reliability of the dynamic analysis based on the reduced system is demonstrated through comparing with those of global system.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.9 s.252
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• pp.1070-1077
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• 2006

In the present study, sizing and shape optimizations are performed based on the reduced system of large-scaled problem. In the analysis part to achieve efficiency and reliability of computation, two-level condensation scheme is applied. In the construction of reduced system of large scaled problems, it is much more efficient to use sub-domain method. Thus, in the present paper, two-level reduction method combined with sub-domain method is employed. Once the reduced system is constructed, it is straightforward to obtain design sensitivities from the analysis results of the reduced system We use semi-analytic method to obtain design sensitivities. Performance of the efficiency and reliability of the present reduction method in the structural optimization problem is demonstrated through the numerical examples. The present framework of reduction method should serve as a fast and reliable design tool in analysis and design of large-scaled dynamic problems.

• Korean Journal of Breeding Science
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• v.42 no.1
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• pp.23-27
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• 2010

The objective of this study was to map the gene for reduced embryo size in rice using DNA markers. The reduced embryo size mutant was induced from N-methyl-N-nitrosourea (MNU) treated Taichung 65. Genetic analysis revealed that the phenotype of the reduced embryo was controlled by a single recessive gene, designated as re-1. For mapping the gene controlling embryo size, an $F_2$ population was developed from a cross between the Korean Tongil-type, Milyang 23 (Oryza sativa ssp. indica) and the mutant. The ratio of $F_2$ seeds nearly fitted to 3:1 ratio, indicating that this phenotype was controlled by a single recessive gene. Bulked sergeant analysis was performed with SSR markers. The gene for the reduced embryo size was detected on chromosome 1. The gene was further mapped between two SSR markers, RM315 and RM265 on chromosome 1 (approximately 1.5 Mb interval). The linked markers will facilitate selection of this grain character in a breeding program and provide the foundation for positional cloning of this gene.