• Tribology and Lubricants
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• v.38 no.3
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• pp.73-83
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• 2022

This paper is concerned with an analysis of a surface edge crack emanated from a sharp contact edge. For a geometrical model, a square wedge is in contact with a half plane whose materials are identical, and a surface perpendicular crack initiated from the contact edge exists in the half plane. To analyze this crack problem, it is necessary to evaluate the stress field on the crack line which are induced by the contact tractions and pseudo-dislocations that simulate the crack, using the Bueckner principle. In this Part I, the stress filed in the half plane due to the contact is re-summarized using an asymptotic analysis method, which has been published before by the author. Further focus is given to the stress field in the half plane due to a pseudo-edge dislocation, which will provide a stress solution due to a crack (i.e. a continuous distribution of edge dislocations) later, using the Burgers vector. Essential result of the present work is the corrective functions which modify the stress field of an infinite domain to apply for the present one which has free surfaces, and thus the infiniteness is no longer preserved. Numerical methods and coordinate normalization are used, which was developed for an edge crack problem, using the Gauss-Jacobi integration formula. The convergence of the corrective functions are investigated here. Features of the corrective functions and their application to a crack problem will be given in Part II.

• Journal of Korean Society of Forest Science
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• v.90 no.5
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• pp.650-662
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• 2001

The growth and yield models for five different kinds of natural forest types were systemically developed in the natural Broadleaved-Korean pine Forests in Northeast China. The data were collected from 359 temporary plots and 58 permanent plots with area ranged from 0.06 ha to 1.0 ha, ranging in stand age from 43 to 364 years. The Site Class Index (SCI) was introduced to evaluate site quality and the Crown Competition Factor (CCF) was selected as a measure of stand density for the mixed natural forest. The Chapman-Richards function was adopted to develop SCI equation and height-diameter curve. The Schumacher growth function was selected as base model to develop the DBH, basal area, and stand volume growth models by using re-parameterized method. In modeling mean DBH and basal area growth, it was found that the asymptotic parameter A of Schumacher function was exponentially related to site quality (SCI) and stand density (CCF). The rate parameter k was related to stand density and it was independent of SCI. Several validation measures for predicted stand variables were evaluated in the growth and yield models using independent data sets. The results indicated that relative mean errors (RME) in predicted stand attributes were less than ${\pm}5%$ and the estimated precision values of the stand variables were all greater than 95%.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.4
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• pp.183-190
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• 2018

This paper presents optimization of the main spar of Human-Powered Aircraft (HPA) wing. Mass minimization was attempted, while considering large torsional deformation of the beam. Sequential Quadratic Programming (SQP) method was adopted as a relevant tool to conduct structural optimization algorithm. An inner diameter and ply thicknesses of the main spar were selected as the design variables. The objective function includes factors such as mass minimization, constant tip bending displacement, and constant tip twist of the beam. For estimation of bending and torsional deformation, the geometrically exact beam model, which is appropriate for large deflection, was adopted. Properties of the cross sectional area which the geometrically exact beam model requires were obtained by Variational Asymptotic Beam Sectional Analysis (VABS), which is a cross sectional analysis program. As a result, maintaining tip bending displacement and tip twist within 1.45%, optimal design that accomplished 7.88% of the mass reduction was acquired. By the stress and strain recovery, structural integrity of the optimal design and validity of the present optimization procedure were authenticated.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.583-611
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• 1998

We consider a general class of real-valued Levy processes {X(t), $t\geq0$}, and obtain suitable large deviation results for the empiricals L(t, A) defined by $t^{-1}{\int^t}_01_A$(X(s)ds for t > 0 and a Borel subset A of R. These results are used to obtain the asymptotic behavior of P{Z(t) < a}, where Z(t) = $sup_{u\leqt}\midx(u)\mid$ as $t\longrightarrow\infty$, in terms of the rate function in the large deviation principle. A subclass of these processes is the Feller class: there exist nonrandom functions b(t) and a(t) > 0 such that {(X(t) - b(t))/a(t) : t > 0} is stochastically compact, i.e., each sequence has a weakly convergent subsequence with a nondegenerate limit. The stable processes are in this class, but it is much larger. We consider processes in this class for which b(t) may be taken to be zero. For any t > 0, we consider the renormalized process ${X(u\psi(t))/a(\psi(t)),u\geq0}$, where $\psi$(t) = $t(log log t)^{-1}$, and obtain large deviation probability estimates for $L_{t}(A)$ := $(log log t)^{-1}$${\int_{0}}^{loglogt}1_A$$(X(u\psi(t))/a(\psi(t)))dv$. It turns out that the upper and lower bounds are sharp and depend on the entire compact set of limit laws of {X(t)/a(t)}. The results extend to random walks in the Feller class as well. Earlier results of this nature were obtained by Donsker and Varadhan for symmetric stable processes and by Jain for random walks in the domain of attraction of a stable law.

• The Korean Journal of Ecology
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• v.27 no.1
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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.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.47 no.5
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• pp.390-394
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• 2002

Spikelet number per unit area(SPN) is a major determinant of rice yield. Nitrogen nutrition status and biomass during reproductive stage determine the SPN. To formulate a model for estimating SPN, the 93 field experiment data collected from widely different regions with different japonica varieties in Korea and Japan were analyzed for the upper boundary lines of SPN responses to nitrogen nutrition index(NNI), shoot dry weight and shoot nitrogen content at panicle initiation and heading stage. The boundary lines of SPN showed asymptotic responses to all the above parameters(X) and were well fitted to the exponential function of $f(X)=alphacdot{1-etacdotexp(gamma;cdot;X)}$. Excluding the constant, from the boundary line equation, the values of the equation range from 0 to 1 and represent the indices of parameters expressing the degree of influence on SPN. In addition to those indices, the index of shoot dry weight increase during reproductive stage was calculated by directly dividing the shoot dry weight increase by the maximum value ($800 extrm{g/m}^{-2}$) of dry weight increase as it showed linear relationship with SPN. Four indices selected by forward stepwise regression at the stay level of 0.05 were those for NNI ($I_{NNI}_P$) at panicle initiation, NNI($I_{NNI}_h$) and shoot dry weight($I_{DW}_h$) at heading stage, and dry weight increase($I_{DW}$) between those two stages. The following model was obtained: SPN=48683ㆍ $I_{DWH}$$^{0.482}$ㆍ $I_{NNIp}$$^{0.387}$ㆍ $I_{NNIH}$$^{0.318}$ㆍ $I_{DW}$ $^{0.35}$). This model accounted for about 89% of the variation of spikelet number. In conclusion this model could be used for estimating the spikelet number of japonica rice with some confidence in widely different regions and thus, integrated into a rice growth model as a component model for spikelet number estimation.n.n.

• The Korean Journal of Applied Statistics
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• v.8 no.1
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• pp.89-104
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• 1995

This paper is concerned with the method of estimating lifetime distributin from field data for products with multiple modes of failure. When product failures occur within warranty period, a manufacturer can obtain failure-record data; failure times, causes of failure, and covariates. Since these data are seriously incomplete for satisfactory inference, that is, only failures occured during warrantly period may be recorded, it is usually necessary to incoporate the failure-record data by taking a supplementary sample of items obtained following up a portion of products that survive warranty time. The log linear function is considered as a model for describing the relation between failure time of a product and covariates. General methods for obtaining pseudo maximum likelihood estimators(PMLEs) for the parameters are outlined and their asymptotic properties are studied, and specific formulas for exponential or Weibull distribution are obtained. Effects of follow-up percentage on the PMLEs are investigated. Extensions to calendar time warranty or calendar and obtaining time warranty are also considered.

• Asian-Australasian Journal of Animal Sciences
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• v.27 no.9
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• pp.1250-1253
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• 2014

The objective of this study was to estimate the parameters of Gompertz growth curves with the measurements of body conformation, real-time ultrasound longissimus dorsi muscle area (LMA) and backfat thickness (BFT) in Hanwoo cows. The Hanwoo cows (n = 3,373) were born in 97 Hanwoo commercial farms in the 17 cities or counties of Gyeongbuk province, Korea, between 2000 and 2007. A total of 5,504 ultrasound measurements were collected for the cows at the age of 13 to 165 months in 2007 and 2008. Wither height (HW), rump height (HR), the horizontal distance between the top of the hips (WH), and girth of chest (GC) were also measured. Analysis of variance was conducted to investigate variables affecting LMA and BFT. The effect of farm nested in location was included in the statistical model, as well as the effects of HW, HR, WH, and GC as covariates. All of the effects were significant in the analysis of variance for LMA and BFT (p<0.01), except for the HR effect for LMA. The two ultrasound measures and the four body conformation traits were fitted to a Gompertz growth curve function to estimate parameters. Upper asymptotic weights were estimated as $54.0cm^2$, 7.67 mm, 125.6 cm, 126.4 cm, 29.3 cm, and 184.1 cm, for LMA, BFT, HW, HR, WH, and GC, respectively. Results of ultrasound measurements showed that Hanwoo cows had smaller LMA and greater BFT than other western cattle breeds, suggesting that care must be taken to select for thick BFT rather than an increase of only beef yield. More ultrasound records per cow are needed to get accurate estimates of growth curve, which, thus, helps producers select animals with high accuracy.

• The Korean Journal of Applied Statistics
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• v.27 no.3
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• pp.397-406
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• 2014

The minimum density power divergence estimation has been a popular topic in the field of robust estimation for since Basu et al. (1988). The minimum density power divergence estimator has strong robustness properties with the little loss in asymptotic efficiency relative to the maximum likelihood estimator under model conditions. However, a limitation in applying this estimation method is the algebraic difficulty on an integral involved in an estimation function. This paper considers a minimum density power divergence estimation method with approximated divergence avoiding such difficulty. As an example, we consider the normal-exponential convolution model introduced by Bolstad (2004). The estimated divergence in this case is too complicated; consequently, a Laplace approximation is employed to obtain a manageable form. Simulations and an empirical study show that the minimum density power divergence estimators based on an approximated estimated divergence for the normal-exponential model perform adequately in terms of bias and efficiency.

• Convergence Security Journal
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• v.12 no.6
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• pp.85-92
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• 2012

There are many software reliability models that are based on the times of occurrences of errors in the debugging of software. It is shown that it is possible to do asymptotic likelihood inference for software reliability models based on infinite failure model and non-homogeneous Poisson Processes (NHPP). For someone making a decision about when to market software, the conditional failure rate is an important variables. The finite failure model are used in a wide variety of practical situations. Their use in characterization problems, detection of outliers, linear estimation, study of system reliability, life-testing, survival analysis, data compression and many other fields can be seen from the many study. Statistical Process Control (SPC) can monitor the forecasting of software failure and there by contribute significantly to the improvement of software reliability. Control charts are widely used for software process control in the software industry. In this paper, we proposed a control mechanism based on NHPP using mean value function of log Poission, log-linear and Parto distribution.