• 대한수학회지
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• 제44권2호
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• pp.373-391
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• 2007

We study an (n+3)($n\;{\geq}\;7-dimensional$ real submanifold of a (4m+3)-unit sphere $S^{4m+3}$ with Sasakian 3-structure induced from the canonical quaternionic $K\"{a}hler$ structure of quaternionic (m+1)-number space $Q^{m+1}$, and especially determine contact three CR-submanifolds with (p-1) contact three CR-dimension under the equality conditions given in (4.1), where p = 4m - n denotes the codimension of the submanifold. Also we provide necessary conditions concerning sectional curvature in order that a compact contact three CR-submanifold of (p-1) contact three CR-dimension in $S^{4m+3}$ is the model space $S^{4n_1+3}(r_1){\times}S^{4n_2+3}(r_2)$ for some portion $(n_1,\;n_2)$ of (n-3)/4 and some $r_1,\;r_2$ with $r^{2}_{1}+r^{2}_{2}=1$.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2009년도 추계학술대회 논문집
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• pp.103-103
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• 2009

In this study, in order to develop high power piezoelectric transformer, we compared the piezoelectric transformers dimension. The basic composition of piezoelectric ceramics is ternary $0.01Pb(Ni_{1/3}Nb_{2/3})O_3-0.08Pb(Mn_{1/3}Nb_{2/3})O_3-0.91Pb(Zr_{0.505}Ti_{0.495})O_3$. The voltage step up ratio of piezoelectric transformer showed the maximum value at the near of 81 kHz and increased according to the increase of load resistance.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집D
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• pp.600-604
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• 2001

The relation between the aerodynamic diameter and some morphological parameters was studied for flame-generated aggregates. $SiO_{2}$ aggregates were generated from $SiCl_{4}$ in premixed methane/air flames. These aggregates were sampled and classified according to their aerodynamic diameter by a cascade impactor; moreover, computer program was developed and tested to find the equivalent area diameter and the fractal dimension of the aggregates. We calculated the parameters from the digitized images of the aggregate TEM micrographs. The aerodynamic diameters of the sampled aggregates were larger than $0.4{\mu}m$ in this experiment. In most cases, fractal dimension of their projection image was very close to 2.0 for these large aggregates. It was found that the equivalent area diameter of these aggregates was approximately three times larger than the Stokes' diameter of them.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2001년도 봄 학술발표회 논문집
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• pp.333-338
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• 2001

Fractal geometry is a non-Euclidean geometry which has been developed to quantitative analysis irregular or fractional shapes. Fractal dimension of irregular surface has fractal values ranging from 2 to 3 and of irregular line profile has fractal values ranging from 1 to 2. In this paper, quantitative analysis of crack growth patterns during the fracture processing of fiber-reinforced cement composites based on fractal geometry. The fracture behaviors of fiber reinforced mortar beams subjected to three-point loading in flexure. The beams all had a single notch depth, but varing volume fractions of polypropylene, cellulose fibers. The crack growth behaviors, as observed through the image processing system, and the box counting method was used to determine the fractal dimension, Df. The results showed that the linear correlation exists between fractal dimension and fracture energy of the fiber reinforced cement mortar.

• Journal of Welding and Joining
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• 제16권6호
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• pp.86-96
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• 1998

This study proposes the analysis method of time series ultrasonic signal using the chaotic feature extraction for degradation extent evaluation. Features extracted from time series data using the chaotic time series signal analyze quantitatively degradation extent. For this purpose, analysis objective in this study is fractal dimension, lyapunov exponent, strange attractor on hyperspace. The lyapunov exponent is a measure of the rate at which nearby trajectories in phase space diverge. Chaotic trajectories have at least one positive lyapunov exponent. The fractal dimension appears as a metric space such as the phase space trajectory of a dynamical system. In experiment, fractal correlation) dimensions, lyapunov exponents, energy variation showed values of 2.217∼2.411, 0.097∼ 0.146, 1.601∼1.476 voltage according to degardation extent. The proposed chaotic feature extraction in this study can enhances precision ate of degradation extent evaluation from degradation extent results of the degraded materials (SA508 CL.3)

• 대한수학회보
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• 제52권2호
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• pp.531-540
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• 2015

Let (R, m) be a Noetherian local ring, I an ideal of R, and A an Artinian R-module. Let $k{\geq}0$ be an integer and $r=Width_{>k}(I,A)$ the supremum of length of A-cosequence in dimension > k in I defined by Nhan-Hoang [8]. It is shown that for all $t{\leq}r$ the sets $$(\bigcup_{i=0}^{t}Att_R(Tor_i^R(R/I^n,A)))_{{\geq}k}\;and\\(\bigcup_{i=0}^{t}Att_R(Tor_i^R(R/(a_1^{n_1},{\cdots},a_l^{n_l}),A)))_{{\geq}k}$$ are independent of the choice of $n,n_1,{\cdots},n_l$ for any system of generators ($a_1,{\cdots},a_l$) of I.

• 대한기계학회논문집A
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• 제33권9호
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• pp.870-877
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• 2009

This study provides how the Dimension Reduction (DR) method as an efficient technique for reliability analysis can acquire its increased efficiency when it is applied to highly nonlinear problems. In the highly nonlinear engineering systems, 4N+1 (N: number of random variables) sampling is generally recognized to be appropriate. However, there exists uncertainty concerning the standard for judgment of non-linearity of the system as well as possibility of diverse degrees of non-linearity according to each of the random variables. In this regard, this study judged the linearity individually on each random variable after 2N+1 sampling. If high non-linearity appeared, 2 additional sampling was administered on each random variable to apply the DR method. The applications of the proposed sampling to the examples produced the constant results with increased efficiency.

• Kyungpook Mathematical Journal
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• 제55권4호
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• pp.817-826
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• 2015

Let R be a commutative ring with total quotient ring K. Each monomorphic R-module endomorphism of a cyclic R-module is an isomorphism if and only if R has Krull dimension 0. Each monomorphic R-module endomorphism of R is an isomorphism if and only if R = K. We say that R has property (${\star}$) if for each nonzero element $a{\in}R$, each monomorphic R-module endomorphism of R/Ra is an isomorphism. If R has property (${\star}$), then each nonzero principal prime ideal of R is a maximal ideal, but the converse is false, even for integral domains of Krull dimension 2. An integral domain R has property (${\star}$) if and only if R has no R-sequence of length 2; the "if" assertion fails in general for non-domain rings R. Each treed domain has property (${\star}$), but the converse is false.

• Steel and Composite Structures
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• 제6권2호
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• pp.87-101
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• 2006

The deformation and dynamic behavior mechanism of submerged shell-like lattice structures with membranes are in principle of a non-conservative nature as circulatory system under hydrostatic pressure and disturbance forces of various types, existing in a marine environment. This paper deals with a characteristic analysis on quasi-periodic and chaotic behavior of a circular arch under follower forces with small disturbances. The stability region chart of the disturbed equilibrium in an excitation field was calculated numerically. Then, the periodic and chaotic behaviors of a circular arch were investigated by executing the time histories of motion, power spectrum, phase plane portraits and the Poincare section. According to the results of these studies, the state of a dynamic aspect scenario of a circular arch could be shifted from one of quasi-oscillatory motion to one of chaotic motion. Moreover, the correlation dimension of fractal dynamics was calculated corresponding to stochastic behaviors of a circular arch. This research indicates the possibility of making use of the correlation dimension as a stability index.

• Fisheries and Aquatic Sciences
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• 제3권2호
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• pp.163-171
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• 2000

A series of numerical experiments are performed to examine the generation of inter-annual variations by an inertial current in an idealized semi-enclosed basin with dimension comparable to that of the East Sea. Model results indicate that the inter-annual variations dominate the kinetic energy spectrum with a peak around the time scales of 2-3 years. These variations are mostly due to the westward propagating meanders and large eddies induced by the instability of current, indicating their dependency on the eddy-resolving capacity of the model. They are generated in the interior of the basin but their energy is largely confined near the western boundary such that the east-west dimension of the basin cannot be considered as a critical factor as long as the basin covers enough western boundary region. Overall, this study suggests that the inter-annual variation observed in the East Sea is due to the meandering and large eddies induced by the instability of the current.