• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.53-69
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• 2022

In this paper, we are concerned with a class of mixed Hessian curvature equations with non-degeneration. By using the maximum principle and constructing an auxiliary function, we obtain the interior gradient estimate of (k - 1)-admissible solutions.

• Journal of the military operations research society of Korea
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• v.24 no.1
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• pp.146-156
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• 1998

Cholesky factorization is known to be inefficient to problems with dense column and network problems in interior point methods. We use the conjugate gradient method and preconditioners to improve the convergence rate of the conjugate gradient method. Several preconditioners were applied to LPABO 5.1 and the results were compared with those of CPLEX 3.0. The conjugate gradient method shows to be more efficient than Cholesky factorization to problems with dense columns and network problems. The incomplete Cholesky factorization preconditioner shows to be the most efficient among the preconditioners.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.173-190
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• 2011

In this paper, we construct a new approach of affine scaling interior algorithm using the affine scaling conjugate gradient and Lanczos methods for bound constrained nonlinear optimization. We get the iterative direction by solving quadratic model via affine scaling conjugate gradient and Lanczos methods. By using the line search backtracking technique, we will find an acceptable trial step length along this direction which makes the iterate point strictly feasible and the objective function nonmonotonically decreasing. Global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, we present some numerical results to illustrate the effectiveness of the proposed algorithm.

• Journal of the Semiconductor & Display Technology
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• v.20 no.4
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• pp.134-140
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• 2021

This study investigates the flow efficiency and temperature based on flow path shape. Five models are designed to the no flow path, one flow path, two flow path, three flow path, add inlet flow path and add interior space gradient. Results show that two flow model(add inlet flow path and add interior space gradient), It was confirmed that model(add inlet flow path) is the optimal shape for coolant heat transfer, and model(add interior space gradient) is the optimal shape for coolant flow, demonstrates optimal design among the five models. The results of this study can be utilized to efficiently control the coolant flow through various types of flow paths.

• Geomechanics and Engineering
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• v.18 no.5
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• pp.481-492
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• 2019

Due to the underground openings, the tangentially concentrated stress of the tunnel remains larger at excavation boundary and decreases toward the interior of the surrounding rock with a certain gradient. In order to study the effect of different gradient stress on rockburst, the true-triaxial gradient and hydraulic-pneumatic combined test apparatus were carried out to simulate the rockburst processes. Under the different gradient stress conditions, the rock-like specimen (gypsum) was tested independently through three principal stress directions loading--fast unloading of single surface--top gradient and hydraulic-pneumatic combined loading, which systematically analyzed the macro-mesoscopic damage phenomena, force characteristics and acoustic emission (AE) signals of the specimen during rockburst. The experimental results indicated that the rockburst test under the gradient and hydraulic-pneumatic combined loading conditions could perfectly reflect the rockburst processes and their stress characteristics; Relatively high stress loading could cause specimen failure, but could not determine its mode. The rockburst under the action of gradient stress suggested that the failure mode of specimen mainly depended on the stress gradient. When the stress gradient was lower, progressive and static spalling failure occured and the rockburst grades were relatively slight. On the other hand, shear fractures occurred in rockbursts accounted for increasingly large proportion as the stress gradient increased and the rockburst occurred more intensely and suddenly, the progressive failure process became unconspicuous, and the rockburst grades were moderate or even stronger.

• Journal of computational fluids engineering
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• v.3 no.2
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• pp.27-38
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• 1998

Rotating flow of a stratified fluid contained in a circular cylinder with unstable temperature gradient imposed on the side wall of it has been numerically studied. The temperatures at the endwall disks are constant. The top disk of the container is coider than that of the bottob disk, as much as the temperature difference n${\Delta}$T, (0${\leq}$n${\leq}$3). Flows in the vessel are driven by an impulsive rotation of the hot bottom disk with respect to the central axis of the cylinder. Flow details have been acquired. For this flow, the principal balance in the interior core is characterized by a relationship between the radial temperature gradient and the vertical shear in the azimuthal velocity. As the buoyancy effect becomes appreciable, larger portions of the meridional fluid transport are long-circuit from the bottom disk to the interior region via the side wall.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.397-409
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• 2017

In this paper, we investigated the extinction, positivity, and decay estimates of the solutions to the initial-boundary value problem of the semilinear parabolic equation with nonlinear gradient source and interior absorption terms by using the integral norm estimate method. We found that the decay estimates depend on the choices of initial data, coefficients and domain, and the first eigenvalue of the Laplacean operator with homogeneous Dirichlet boundary condition plays an important role in the proofs of main results.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.355-379
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• 2024

In this paper, we establish the curvature estimates for a class of curvature equations with general right hand sides depending on the gradient. We show an existence result by using the continuity method based on a priori estimates. We also derive interior curvature bounds for solutions of a class of curvature equations subject to affine Dirichlet data.

• Korean Management Science Review
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• v.21 no.1
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• pp.77-86
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• 2004

In this paper, we present a methodology for solving the multicommodity network flow problems using interior point methods. In our method, the minimum cost network flow problem extracted from the given multicommodity network flow problem is solved by primal-dual barrier method in which normal equations are solved partially using preconditioned conjugate gradient method. Based on the solution of the minimum cost network flow problem, a warm-start point is obtained from which Castro's specialized interior point method for multicommodity network flow problem starts. In the computational experiments, the effectiveness of our methodology is shown.

• Journal of KIBIM
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• v.12 no.1
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• pp.55-61
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• 2022

Recently, demand for designing own space is increasing as the rapid growth of home furnishing market. However, there is a limitation that it is not easy to compare the style between before construction view and after view. This study aims to translate real image into another style with GAN model learned with interior images. To implement this, first we established style criteria and collected modern, natural, and classic style images, and experimented with ResNet, UNet, Gradient penalty concept to CycleGAN algorithm. As a result of training, model recognize common indoor image elements, such as floor, wall, and furniture, and suitable color, material was converted according to interior style. On the other hand, the form of furniture, ornaments, and detailed pattern expressions are difficult to be recognized by CycleGAN model, and the accuracy lacked. Although UNet converted images more radically than ResNet, it was more stained. The GAN algorithm allowed us to represent results within 2 seconds. Through this, it is possible to quickly and easily visualize and compare the front and after the interior space style to be constructed. Furthermore, this GAN will be available to use in the design rendering include interior.