• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.87-99
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• 2017

To indicate the statistical complexity of dynamical systems, we introduce the notions of higher order irregular set and higher order maximal Birkhoff average oscillation in this paper. We prove that, in the setting of topologically mixing Markov chain, the set consisting of those points having maximal k-order Birkhoff average oscillation for all positive integers k is as large as the whole space from the topological point of view. As applications, we discuss the corresponding results on a repeller.

• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.337-352
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• 2022

We consider the set of points with historic behavior (which is also called the irregular set) for continuous flows and suspension flows. In this paper under the hypothesis that (X_t)_t is a continuous flow on a d-dimensional Riemaniann closed manifold M (d ≥ 2) with gluing orbit property, we prove that the set of points with historic behavior in a compact and invariant subset ∆ of M is either empty or is a Baire residual subset on ∆. We also prove that the set of points with historic behavior of a suspension flows over a homeomorphism satisfyng the gluing orbit property is either empty or Baire residual and carries full topological entropy.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.591-601
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• 2005

The results of fuzzy linear regression are very sensitive to irregular data. When this points exist in a set of data, a fuzzy linear regression model can be incorrectly interpreted. The purpose of this paper is to detect irregular data and to propose robust fuzzy linear regression based on M-estimators with triangular fuzzy regression coefficients for crisp input-output data. Numerical example shows that irregular data can be detected by using the residuals based on M-estimators, and the proposed robust fuzzy linear regression is very resistant to this points.

• Korean Journal of Remote Sensing
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• v.19 no.6
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• pp.457-464
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• 2003

Triangulated irregular network is one of the most frequently used terrain modeling methods. It represents terrain precisely using only a small amount of data, and enables fast rendering of terrain. In this paper, ridges and valleys are extracted from the terrain, and used as a set of vertices for the construction of triangulated irregular network. An experiment shows the new method reduces the time for construction of the triangulated irregular network significantly with almost equal amount of induced error.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.8 no.2
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• pp.1-8
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• 1990

A regular grid or a triangulated irregular network is generally used as the data structure of digital terrain models. A Regular grid is simple and easy to manipulate, but it can't describe well terrain surface features and requires vast volumes of data. In the meantime, a triangulated irregular network has complex data structure, but it can describe well terrain surface features and can achieve the accuracy suitable to its application with relatively little data. This paper aims at the construction of efficient digital terrain models by the improvment of a triangulated irregular network based on Delaunay triangulation. Regular and irregular data set are sampled from existing contour maps, and the efficiency and the accuracy of the two data structures are compared.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.3
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• pp.260-265
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• 1994

A new set of elliptic wave equations describing the deformations of irregular waves on a large-scale current field in water of irregular depth is given, and using finite difference scheme an efficient numerical method is also presented. The elliptic equations are solved in a similar way to Initial value problem. This method is extensively used for the calculation of wave spectral transformation. and computation results agree very well with experimental data (Hiraishi, 1991). Finally numerical examples are presented concerning the interactions between waves and currents over a mildly sloping beach and also over a mound.

• Earthquakes and Structures
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• v.6 no.4
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• pp.351-373
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• 2014

This paper investigates the seismic response of lightweight acceleration-sensitive non-structural components (NSCs) mounted on irregular reinforced concrete (RC) primary structures (P-structures) using non-linear dynamic finite element (FE) analysis. The aim of this paper is to study the influence of NSC to P-structure vibration period ratio, peak ground acceleration, NSC to P-structure height ratio, and P-structure torsional behaviour on the seismic response of the NSCs. Representative constitutive models were used to simulate the behaviour of the RC P-structures. The NSCs were modelled as vertical cantilevers fixed at their bases with masses on the free ends and varying lengths so as to match the frequencies of the P-structures. Full dynamic interaction is considered between the NSCs and P-structures. A set of 21 natural and artificial earthquake records were used to evaluate the seismic response of the NSCs. The numerical results indicate that the behaviour of the NSCs is significantly influenced by the investigated parameters. Comparison between the FE results and Eurocode (EC8) predictions suggests that EC8 underestimates the response of NSCs mounted on the flexible sides of irregular RC P-structures when the fundamental periods and heights of the NSCs match those of the P-structures. The perceived cause of this discrepancy is that EC8 does not take into account the amplification in the dynamic response of NSCs induced by the torsional behaviour of RC P-structures.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.12 no.2
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• pp.209-218
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• 1994

This study aims to generate triangulated irregular network in a form of digital terrain model which is being increasingly used. In general, grid digital elevation model and triangulated irregular network are reasonable units for solving terrain problems. But, triangulated irregular network is an efficient alternative to grid digital elevation model because of their efficiency in storing data and their convenient data structure for accommodating irregularly spaced elevation data. Various methods represented for extracting triangulated irregular networks from grid digital elevation model, and then algorithm that get accurate results for triangulation with their data set was introduced. The new approach for triangulation in this study uses the Elevation and Changeable Distance criterion, and adding interpolation points and restricted constraint lines can generate triangulated irregular network which is more close to real surface. This made database efficient construction and could be used for many applications of geo-spatial information system.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.673-683
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• 2000

We define the centered-net covering and the centered-net parking measure and then show that the regular sets induced by the two centered measures are equal for $C{\frac}{\delta}{R}$ almost everywhere.

• Journal of computational fluids engineering
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• v.9 no.3
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• pp.73-80
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• 2004

A LS(Level Set) formulation is developed for computing two-phase flows on non- orthogonal meshes. Compared with the VOF(Volume-of-Fluid) method based on a non-smooth volume-fraction function, the LS method can calculate an interfacial curvature more accurately by using a smooth distance function. Also, it is quite straightforward to implement for 3-D irregular meshes compared with the VOF method requiring much more complicated geometric calculations. The LS formulation is implemented into a general purpose program for 3-D flows and verified through several test problems.