• Journal of the Korean Society for Precision Engineering
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• v.22 no.5 s.170
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• pp.55-62
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• 2005

This paper presents mainly a procedure to get the mathematical form of the manufactured aspherical lens. Generally Schulz formula describes the aspherical lens profile. Therefore, the base curvature, conic constant. and high-order polynomial coefficient should be set to get the approximated design equation. To find the best-approximated aspherical form, lens profile is measured by a commercial stylus profiler, which has a sub-micrometer measurement resolution. The optimization tool is based on the minimization of the root mean square of error sum to get the estimated aspherical surface equation from the scanned aspherical profile. Error minimization step uses the Nelder-Mead simplex (direct search) method. The result of the lens refractive power measurement shows the experimental consistency with the curvature distribution of the best-approximated aspherical surface equation

• Journal of the Korean Society for Precision Engineering
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• v.15 no.7
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• pp.167-174
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• 1998

This paper presents an unoccluded cylindrical object pose measurement using a slit beam laser in which a robot recognizes all of the unoccluded objects from the top of jumbled objects, and picks them up one by one. The elliptical equation parameters of a projected curve edge on a slice are calculated using LSM. The coefficients of standard elliptical equation are compared with these parameters to estimate the object pose. The hamming distances between the estimated coordinates and the calculated ones are extracted as measures to evaluate a local constraint and a smoothing surface curvature. The edges between slices are linked using error function based on the edge types and the hamming distances. The linked edges on slices are compared with the model object's length to recognize the unoccluded object. This proposed method may provide a solution to the automation of part handling in manufacturing environments such as punch press operation or part assembly.

• Korean Journal of Veterinary Research
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• v.50 no.1
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• pp.11-17
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• 2010

Linear and non-linear regressions were used to derive the calibration function for the measurement of roxithromycin plasma concentration. Their results were compared with weighted least squares regression by usual weight factors. In this paper the performance of a non-linear calibration equation with the capacity to account empirically for the curvature, y = ax$^{b}$ + c (b $\neq$ 1) is compared with the commonly used linear equation, y = ax + b, as well as the quadratic equation, y = ax$^{2}$+ bx + c. In the calibration curve (range of 0.01 to 10 ${\mu}g/mL$) of roxithromycin, both heteroscedasticity and nonlinearity were present therefore linear least squares regression methods could result in large errors in the determination of roxithromycin concentration. By the non-linear and weighted least squares regression, the accuracy of the analytical method was improved at the lower end of the calibration curve. This study suggests that the non-linear calibration equation should be considered when a curve is required to be fitted to low dose calibration data which exhibit slight curvature.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.3
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• pp.702-707
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• 2004

This article is concerned with container pose estimation using CCD a camera and a range sensor. In particular, the issues of characteristic point extraction and image noise reduction are described. The Euler-Lagrange equation for gaussian and random noise reduction is introduced. The alternating direction implicit(ADI) method for solving Euler-Lagrange equation based on partial differential equation(PDE) is applied. The vertex points as characteristic points of a container and a spreader are founded using k order curvature calculation algorithm since the golden and the bisection section algorithm can't solve the local minimum and maximum problems. The proposed algorithm in image preprocess is effective in image denoise. Furthermore, this proposed system using a camera and a range sensor is very low price since the previous system can be used without reconstruction.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.75-85
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• 2005

In this paper, the visco-Da-Rios equation; (0.1) ($$\frac{{\partial}{\gamma}}{{\partial}t}=\frac{{\partial}{\gamma}}{{\partial}s}{\bigwedge}\frac{D}{ds}\frac{{\partial}{\gamma}}{{\partial}s}+{\nu}\frac{{\partial}{\gamma}}{{\partial}s}$$) is investigated on 3-dimensional complete orientable Riemannian manifolds. The global existence of solution is discussed by trans-forming (0.1) into a cubic nonlinear Schrodinger equation for complete orient able Riemannian 3-manifolds of constant curvature.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1285-1303
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• 2018

This note is motivated by gradient estimates of Li-Yau, Hamilton, and Souplet-Zhang for heat equations. In this paper, our aim is to investigate Yamabe equations and a non linear heat equation arising from gradient Ricci soliton. We will apply Bochner technique and maximal principle to derive gradient estimates of the general non-linear heat equation on Riemannian manifolds. As their consequence, we give several applications to study heat equation and Yamabe equation such as Harnack type inequalities, gradient estimates, Liouville type results.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.177-183
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• 2020

The object of the present paper is to study the critical point equation (CPE) on 3-dimensional α-cosymplectic manifolds. We prove that if a 3-dimensional connected α-cosymplectic manifold satisfies the Miao-Tam critical point equation, then the manifold is of constant sectional curvature -α², provided Dλ ≠ (ξλ)ξ. We also give several interesting corollaries of the main result.

• The Journal of Engineering Geology
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• v.25 no.2
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• pp.273-280
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• 2015

Delays in horizontal well drilling when encountering heterogeneous sediments can have negative effects on the construction process at a riverbank filtration site. Grain size analysis, including calculation of the coefficient of uniformity and the coefficient of curvature, was conducted on soil samples collected at each drilling depth during the process of drilling horizontal wells. These results were then used to develop a linear equation for estimating drilling velocity using the coefficient of uniformity and the coefficient of curvature as inputs. Testing of the linear equation in other horizontal wells indicates that the equation is most appropriate for coarse-sand-sized and well-sorted sediment. Because this study was conducted in a region with small- to medium-sized streams, more data are needed from larger rivers to modify the general equation. Our results will provide better estimates of drilling velocity, in turn enabling more detailed design and more effective construction management at riverbank filtration sites.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1085-1100
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• 2023

For any given function f, we focus on the so-called prescribed mean curvature problem for the measure e^-f(|x|2)dx provided thate^-f(|x|2) ∈ L¹(ℝⁿ⁺¹). More precisely, we prove that there exists a smooth hypersurface M whose metric is ds² = dρ² + ρ²d𝜉² and whose mean curvature function is ${\frac{1}{n}}(\frac{u^p}{{\rho}^{\beta}})e^{f({\rho}^2)}{\psi}(\xi)$ for any given real constants p, β and functions f and ψ where u and ρ are the support function and radial function of M, respectively. Equivalently, we get the existence of a smooth solution to the following quasilinear equation on the unit sphere 𝕊ⁿ, $${\sum_{i,j}}({{\delta}_{ij}-{\frac{{\rho}_i{\rho}_j}{{\rho}^2+|{\nabla}{\rho}|^2}})(-{\rho}ji+{\frac{2}{{\rho}}}{\rho}j{\rho}i+{\rho}{\delta}_{ji})={\psi}{\frac{{\rho}^{2p+2-n-{\beta}}e^{f({\rho}^2)}}{({\rho}^2+|{\nabla}{\rho}|^2)^{\frac{p}{2}}}}$$ under some conditions. Our proof is based on the powerful method of continuity. In particular, if we take $f(t)={\frac{t}{2}}$, this may be prescribed mean curvature problem in Gauss measure space and it can be seen as an embedded result in Gauss measure space which will be needed in our forthcoming papers on the differential geometric analysis in Gauss measure space, such as Gauss-Bonnet-Chern theorem and its application on positive mass theorem and the Steiner-Weyl type formula, the Plateau problem and so on.

• Proceedings of the Korea Concrete Institute Conference
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• 2002.10a
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• pp.111-116
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• 2002

The flexural ductility capacity of reinforced concrete columns can be expressed either in terms of curvature ductility or displacement ductility. To evaluate ductility capacity of reinforced concrete columns, analytical models and a non-linear analysis program, NARCC have been developed, which is applicable to the RC columns subjected to seismic loading. The analytical results by using computer program NARCC are in good agreement with the test results. In order to develop relationships between the curvature ductility and the displacement ductility, the analysis for total 21,600 RC circular columns using the computer program NARCC have been carried out for parametric studies. Based on the results from the parametric studies, a correlation equation between the curvature ductility and the displacement ductility was developed.