• Communications of the Korean Mathematical Society
• /
• v.13 no.1
• /
• pp.85-94
• /
• 1998

The purpose of this paper is to give sample characterizations of n-dimensional CR-submanifolds of (n-1) CR-semifolds of (n-1) CR-dimension immersed in a complex projective space $CP^{(n+p)/2}$ with Fubini-Study metric and we study an n-dimensional compact, orientable, minimal CR-submanifold of (n-1) CR-dimension in $CP^{(n+p)/2}$.

• Communications of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.59-69
• /
• 2024

Let R be a commutative ring. An R-module E is said to be regular injective provided that Ext¹_R(R/I, E) = 0 for any regular ideal I of R. We first show that the class of regular injective modules have the hereditary property, and then introduce and study the regular injective dimension of modules and regular global dimension of rings. Finally, we give some homological characterizations of total rings of quotients and Dedekind rings.

• Journal of Korea Water Resources Association
• /
• v.32 no.3
• /
• pp.291-300
• /
• 1999

The Snyder's synthetic unit hydrograph method is selected to apply the concept of the fractal dimension by stream order for the practicable rainfall-runoff generation, and fourth types of the Snyder's relation are derived from topographic and observed unit hydrograph data of twenty-nine basins. As a result of the analysis of twenty-nine basins and the verification of two basins, the Snyder's relation which considers the fractal dimension of the stream length and uses calculated unit hydrograph data shows the best result. The concept of the fractal dimension by stream order is applied to the Snyder's synthetic unit hydrograph method. The topographic factors, used in the Snyder's synthetic unit hydrograph method, which have a property of the stream length like $L_{ma}$ (mainstream length) and $L_{ca}$ (length along the mainstream to a point nearest the watershed centroid) were considered. In order to simplify the fractal property of stream length, it is supposed that $L_{ma}$ has not the fractal dimension and the stream length between $L_{ma}$ and ($L_{ma}\;-\;L_{ca}$) has the fractal dimension of 1.027. From the utilization of this supposition, a new Snyder's relation which consider the fractal dimension of the stream length occurred by the map scale used was finally suggested.

• Korean Journal of Ichthyology
• /
• v.18 no.3
• /
• pp.209-215
• /
• 2006

A closely associated set of characteristics was analyzed using both classical and truss dimensions to discriminate the morphometric traits of three species of torrent catfish (Amblycipitidae) in Korea. After arcsine square root transformation, 18 measurements relative to the standard length and three measurements relative to the head length of each species of torrent catfish were compared statistically. Classical and truss dimensions of each of four morphometric traits showed higher values in the bullhead torrent catfish, Liobagrus obesus, than the Korean and south torrent catfish (L. andersoni and L. mediadiposalisa, respectively; P<0.05). Truss dimensions of three morphometric traits were higher in the bullhead and Korean torrent catfish than in the south torrent catfish (P<0.05). There were no significant differences in six morphometric traits among these Amblycipitidae. The dimensions used in this study may be useful as taxonomic indicators to discriminate species of Liobagrus in Korea.

• Korean Journal of Mathematics
• /
• v.32 no.1
• /
• pp.43-57
• /
• 2024

Given a domain X and a collection H of functions h : X → {0, 1}, the Vapnik-Chervonenkis (VC) dimension of H measures its complexity in an appropriate sense. In particular, the fundamental theorem of statistical learning says that a hypothesis class with finite VC-dimension is PAC learnable. Recent work by Fitzpatrick, Wyman, the fourth and seventh named authors studied the VC-dimension of a natural family of functions ℋ'²_t(E) : 𝔽²_q → {0, 1}, corresponding to indicator functions of circles centered at points in a subset E ⊆ 𝔽²_q. They showed that when |E| is large enough, the VC-dimension of ℋ'²_t(E) is the same as in the case that E = 𝔽²_q. We study a related hypothesis class, ℋ^d_t(E), corresponding to intersections of spheres in 𝔽^d_q, and ask how large E ⊆ 𝔽^d_q needs to be to ensure the maximum possible VC-dimension. We resolve this problem in all dimensions, proving that whenever |E| ≥ C_dq^d-1/(d-1) for d ≥ 3, the VC-dimension of ℋ^d_t(E) is as large as possible. We get a slightly stronger result if d = 3: this result holds as long as |E| ≥ C_3q^7/3. Furthermore, when d = 2 the result holds when |E| ≥ C_2q^7/4.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.23 no.57
• /
• pp.51-62
• /
• 2000

In this study, the psycho-physiological response of drivers was investigated in terms of EEG(Electroencephalogram), especially with the fractal dimensions computed by Chaotic algorithm. The Chaotic algorithm Is well Known to sensitively analyze the non-linear information such as brain waves. An automobile with a fully equipped data acquisition system was used to collect the data. Ten healthy subjects participated in the experiment. EEG data were collected while subjects were driving the car between Won-ju and Shin-gal J.C. on Young-Dong highway The results were presented in terms of 3-Dimensional attractor to confirm the chaotic nature of the EEG data. The correlation dimension and fractal dimension were calculated to evaluate the complexity of the brain activity as the driving duration changes. In particular, the fractal dimension indicated a difference between the driving condition and non-driving condition while other spectral variables showed inconsistent results. Based upon the fractal dimension, drivers processed the most information at the beginning of the highway driving and the amount of brain activity gradually decreased and stabilized. No particular decrease of brain activity was observed even after 100 km driving. Considering the sensitivity and consistency of the analysis by Chaotic algorithm, the fractal dimension can be a useful parameter to evaluate the psycho-physiological responses of human brain at various driving conditions.

• Wind and Structures
• /
• v.31 no.4
• /
• pp.363-371
• /
• 2020

Proper understanding of offshore wind speed variability is of essential importance in practice, which provides useful information to a wide range of coastal and marine activities. In this paper, long-term wind speed data recorded at various offshore stations are analyzed in the framework of fractal dimension analysis. Fractal analysis is a well-established data analysis tool, which is particularly suitable to determine the complexity in time series from a quantitative point of view. The fractal dimension is estimated using the conventional box-counting method. The results suggest that the wind speed data are generally fractals, which are likely to exhibit a persistent nature. The mean fractal dimension varies from 1.31 at an offshore weather station to 1.43 at an urban station, which is mainly associated with surface roughness condition. Monthly variability of fractal dimension at offshore stations is well-defined, which often possess larger values during hotter months and lower values during winter. This is partly attributed to the effect of thermal instability. In addition, with an increase in measurement interval, the mean and minimum fractal dimension decrease, whereas the maximum and coefficient of variation increase in parallel.

• Structural Engineering and Mechanics
• /
• v.41 no.5
• /
• pp.663-673
• /
• 2012

A number of mode shape-based structure damage identification methods have been verified by numerical simulations or experiments for on-line structure health monitoring (SHM). However, many of them need a baseline mode shape generated by the healthy structure serving as a reference to identify damages. Otherwise these methods can hardly perform well when multiple cracks conditions occur. So it is important to solve the problems above. By aid of the fractal dimension method (FD), Qiao and Wang proposed a generalized fractal dimension (GFD) to detect the delamination damage. As a modification of GFD, Qiao and Cao proposed the approximate waveform capacity dimension (AWCD) technique to simplify the calculation of fractal and overcome the false peak appearing in the high mode shapes. Based on their valued work, this paper combined and applied the AWCD method and curvature mode shape data to detect multiple damages in beam. In the end, the identification properties of the AWCD for multiple damages have been verified by groups of Monte Carlo simulations and experiments.

• Tribology and Lubricants
• /
• v.27 no.4
• /
• pp.209-212
• /
• 2011

The capacitive application(prove) can be used to measure the complex permittivity of dielectric material of various thickness and cross section. This paper presents that we designed the analysis system of engine oil permittivity to know the relation between the engine oil deterioration and the prove dimension. Each of the dimension of capacitive prove is changed and then electric capacity is measured by LCR {Inductance(L), Capacitance (C), and Resistance (R)} meter. The engine oil permittivity has extracted in the prove measurement. As the additional research, this paper suggest the best of the prove dimension for the permittivity measurement.

• Journal of Agricultural Extension & Community Development
• /
• v.9 no.2
• /
• pp.215-231
• /
• 2002

The objectives of this study were (1) to measure the level of satisfaction on rural for local public service. (2) and analyse variables related to the public service. Reviewing the literature and related studies for theoretical framework, Six criteria characterize public service : (1) responsiveness. (2) convenience, (3) speed, (4) correctness, (5) pleasantness, (6) equality, which are reflected in the instrument of this study. By the results of analysis, two dimensions (convenience, responsiveness) and total satisfaction are related to their residential lengths of the same rural area. For the total public service satisfaction gender, age, educational level, income level, occupation, and residential years explained in 13.3% For the convenience dimension their variables accounted for 22.4%. For responsiveness dimension their variables interpreted in 23.2%. For speed and correctness dimension their variables explained in 21.6%. For pleasantness dimension their variables accounted for local public services in 15.3%. For equality dimension their variables explained in 16.2%.