• 대한수학회보
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• 제52권6호
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• pp.2071-2093
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• 2015

In this paper, we investigate the similarity transformations in the Minkowski n-space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null curve according to a similarity motion of ${\mathbb{E}}_1^n$. We determine the parametrizations of non-null self-similar curves in ${\mathbb{E}}_1^n$.

• 대한수학회지
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• 제52권5호
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• pp.991-1001
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• 2015

In this work we obtain conditions for nonspecial line bundles on general ${\kappa}$-gonal curves failing to be normally generated. Let L be a nonspecial very ample line bundle on a general ${\kappa}$-gonal curve X with ${\kappa}{\geq}4$ and $deg\mathcal{L}{\geq}{\frac{3}{2}}g+{\frac{g-2}{{\kappa}}}+1$. If L fails to be normally generated, then L is isomorphic to $\mathcal{K}_X-(ng^1_{\kappa}+B)+R$ for some $n{\geq}1$, B and R satisfying (1) $h^0(R)=h^0(B)=1$, (2) $n+3{\leq}degR{\leq}2n+2$, (3) $deg(R{\cap}F){\leq}1$ for any $F{\in}g^1_k $. Its converse also holds under some additional restrictions. As a corollary, a very ample line bundle $\mathcal{L}{\simeq}\mathcal{K}_X-g^0_d+{\xi}^0_e$ is normally generated if $g^0_d{\in}X^{(d)}$ and ${\xi}^0_e{\in}X^{(e)}$ satisfy $d{\leq}{\frac{g}{2}}-{\frac{g-2}{\kappa}}-3$, supp$(g^0_d{\cap}{\xi}^0_e)={\phi}$ and deg$(g^0_d{\cap}F){\leq}{\kappa}-2$ for any $F{\in}g^1_k$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권2호
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• pp.25-30
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• 2002

Let $E/{\mathbb{Q}$ be an elliptic curve defined over rationals, P is a non-torsion rational point of E and $$S=\{[n]P{\mid}n{\in}{\mathbb{Z}}\}$$. then S is dense in the component of $E({\mathbb{R}})$ which contains the infinity in the usual Euclidean topology or in the topology defined by the invariant Haar measure and it is uniformly distributed.

• 한국해양공학회지
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• 제35권2호
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• pp.161-171
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• 2021

For the fatigue design of offshore structures, it is essential to understand and use the S-N curves specified in various industry standards and codes. This study compared the characteristics of the S-N curves for five major codes. The codes reviewed in this paper were DNV Classification Rules (DNV GL, 2016), ABS Classification Rules (ABS, 2003), British Standards (BSI, 2015), International Welding Association Standards (IIW, 2008), and European Standards (BSI, 2005). Types of stress, such as nominal stress, hot-spot stress, and effective notch stress, were analyzed according to the code. The basic shape of the S-N curve for each code was analyzed. A review of the survival probability of the basic design S-N curve for each code was performed. Finally, the impact on the conservatism of the design was analyzed by comparing the S-N curves of three grades D, E, and F by the five codes. The results presented in this paper are considered to be a good guideline for the fatigue design of offshore structures because the S-N curves of the five most-used codes were analyzed in depth.

• The Korean Journal of Ecology
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• 제27권1호
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• pp.27-33
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• 2004

Cryptomeria japonica plantation was monitored every year during 15 years from 1983 to 1997 for stem diameter and volume. The reciprocal equation, 1/Y = A + B/N, was applied to the relationship between cumulative volume Y and cumulative number N from the largest tree in the stand each year. The parameters A and B, which means respectively the reciprocal of an asymptotic value of total stand stem volume and the reciprocal of the maximum stem volume, are related by a power function. The power functional relationship between A and B derived a linear relationship of B-points ( $N_{B}$, $V_{B}$; $N_{B}$ = B/A, $Y_{B}$ = 1/2A) of each Y-N curve on log-log coordinates. The gradient of B-point line was so steep that the Y-N curve moved parallel upward year by year. The time trajectory of mean stem volume (W) and density ($\rho$) provided evidence in favor of the 3/2 power law of self-thinning, because the gradient of W - $\rho$ trajectory on log-log coordinates approximated to -3/2 at the final stage of stand development. On the basis of the results of Y-N curves and W - $\rho$ trajectory, the time trajectory of maximum stem volume $W_{max obs}$ and $\rho$ was derived theoretically. The gradient of $W_{max obs}$ - $\rho$ trajectory on log-log coordinates is calculated to be -0.6105 at the final stage. The gradient of $W_{max obs}$ - $\rho$ trajectory was steeper than that of W - $\rho$ trajectory at the early stage, while the former is gentler than the latter at the later stage.stage.e.age.e.

• Structural Engineering and Mechanics
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• 제69권4호
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• pp.361-369
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• 2019

The determination of Paris' law parameters based on crack growth experiments is an important procedure of fatigue life assessment. However, it is a challenging task because it involves various sources of uncertainty. This paper proposes a novel probabilistic method, termed the S-N Paris law (SNPL) method, to quantify the uncertainties underlying the Paris' law parameters, by finding the best estimates of their statistical parameters from the S-N curve data using a Bayesian approach. Through a series of steps, the SNPL method determines the statistical parameters (e.g., mean and standard deviation) of the Paris' law parameters that will maximize the likelihood of observing the given S-N data. Because the SNPL method is based on a Bayesian approach, the prior statistical parameters can be updated when additional S-N test data are available. Thus, information on the Paris' law parameters can be obtained with greater reliability. The proposed method is tested by applying it to S-N curves of 40H steel and 20G steel, and the corresponding analysis results are in good agreement with the experimental observations.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.451-457
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• 2011

The function f(z) = $e^{p(z)}$ where p(z) is a polynomial of degree n has 2n Julia lines. Julia lines of $e^{p(z)}$ divide the complex plane into 2n equal sectors with the same vertex at the origin. In each sector, $e^{p(z)}$ has radial limits of 0 or innity. Main results of the paper are concerned with maximum curves of $e^{p(z)}$. We deal with some properties of maximum curves of $e^{p(z)}$ and we give some examples of the maximum curves of functions of the form $e^{p(z)}$.

• 생물정신의학
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• 제27권2호
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• pp.94-100
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• 2020

Objectives Amyloid β positron emission tomography (Aβ PET) is widely used as a diagnostic tool in patients who have symptoms of cognitive impairment, however, this diagnostic examination is too expensive. Thus, predicting the positivity of Aβ PET before patients undergo the examination is essential. We aimed to analyze clinical predictors of patients who underwent Aβ PET retrospectively, and to develop a predicting model of Aβ PET positivity. Methods 468 patients who underwent Aβ PET with cognitive impairment were recruited and their clinical indicators were analyzed retrospectively. We specified the primary outcome as Aβ PET positivity, and included variables such as age, sex, body mass index, diastolic blood pressure, systolic blood pressure, education, dementia family history, Mini Mental Status Examination (MMSE), Clinical Dementia Rating (CDR), Clinical Dementia Rating-Sum of Box (CDR-SB), hypertension (HTN), diabetes mellitus (DM) and presence of apolipoprotein E (ApoE) E4 as potential predictors. We developed three final models of amyloid positivity prediction for total subjects, mild cognitive impairment (MCI) and Alzheimer's disease (AD) dementia using a multivariate stepwise logistic regression analysis. Receiver operating characteristic (ROC) curve analysis was performed and the area under curve (AUC) value was calculated for the ROC curve. Results Aβ PET negative patients were 49.6% (n = 232), and Aβ PET positive patients were 50.4% (n = 236). In the final model of all subjects, older age, female sex, presence of ApoE E4 and lower MMSE are associated with Aβ PET positivity. The AUC value was 0.296. In the final model of MCI subjects (n = 244), older age and presence of ApoE E4 are associated with Aβ PET positivity. The AUC value was 0.725. In the final model of AD subjects (n = 173), lower MMSE scores, the presence of ApoE E4 and history of HTN are associated with Aβ PET positivity. The AUC value was 0.681. Conclusions The cerebral amyloid positivity model, which was based on commonly available clinical indicators, can be useful for prediction of amyloid PET positivity in MCI or AD patients.

• 한국농공학회지
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• 제44권6호
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• pp.106-114
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• 2002

In this study, the results of a series of consolidation test for undisturbed Ariake clay in Japan were analyzed by three methods, e-log p (e: void ratio, p: consolidation pressure), log e-log p and n-log p (n: porosity). Moreover, the characteristics of each analysis method were studied. For undisturbed Ariake clay, the log o-Log p and the n-log p relationships can be found as two groups of straight lines of different gradients, but both the elastic consolidation and plastic consolidation regions of e-log p relationship are expressed as a curve. In this paper, the porosity of consolidation yield n$\_$y/, consolidation yield stress p$\_$y/, and the gradient of the plastic consolidation region C$\_$p/ were represented by the log e-log p method, and n$\_$c/, P$\_$cn/ and C$\_$cn/ were represented by the n-log p method. The meaning and the relationships of each value were studied, and the interrelationships among compression indices i.e. C$\_$cn/, C$\_$p/ and C$\_$c/ are obtained from each analysis method as a function of initial porosity n$\_$0/.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 1997년도 추계학술대회 논문집
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• pp.44-47
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• 1997

In spite of the addtion of Zn, a high quality of Zn-doped GaN film were prepared. The growth rates of Zn-doped GaN films were varied from 0.14${\mu}{\textrm}{m}$/min to 0.05${\mu}{\textrm}{m}$/min according to the amount of Zn incorporated, The smallest value of the FWHM of x-ray rocking curve was 407 arcsec. The Zn-related Photoluminescence emission peaks which occurred at 2.927 and 2.824 eV shifted toward the low energy region by increasing Zn partial pressures. It was compared between the intensities of D-A pair (3.259eV) and that of the exciton bound to acceptor band(E$_{x-A}$=3.449eV).).