• East Asian mathematical journal
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• 제31권5호
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• pp.727-735
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• 2015

We introduce the fundamental theorem of upper and lower solutions for a class of singular ($p_1,\;p_2$)-Laplacian systems and give the proof by using the Schauder fixed point theorem. It will play an important role to study the existence of solutions.

• 한국경영과학회지
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• 제17권3호
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• pp.171-180
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• 1992

This paper proposes a solution approach to linear problems with many constraints of variable upper bound (VUB) type. This type of constraints are commonly found in various scheduling type problems for which tighter bounds are essential to achieve an efficiency in enumeration. An analytical framework based on factorization is adopted to devise a solution approach to the problem and extend it for more generalized VUB problem (GVUB). This research shows why the VUB type constraints are amenable to the factorization and gives a unified approach to generalized upper bound(GUB) problems, VUB problems and GVUB problems. Implementation issues are also included.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권4호
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• pp.89-99
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• 2007

In this paper, we define the upper and lower solutions for a p-Laplacian system with singular nonlinearity at the boundaries. And we prove the theorem for the upper and power solutions method.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.425-427
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• 1993

Some upper bounds for the solution of the continuous algebraic Riccati equation are presented. These consist of bounds for summations of eigenvalues, products of eigenvalues, individual eigenvalues and the minimum eigenvalue of the solution matrix. Among these bounds, the first three are the first results for the upper bound of each case, while bounds for the minimum eigenvalue supplement the existing ones and require no side conditions for their validities.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.1011-1020
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• 2021

In this paper, first order nonlinear Liouville-Caputo fractional differential equations is studied. The existence and uniqueness of a solution are investigated by using Krasnoselskii and Banach fixed point theorems and the method of lower and upper solutions. Finally, an example is given to illustrate our results.

• Nuclear Engineering and Technology
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• 제45권2호
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• pp.191-202
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• 2013

A numerical analysis of thermal stratification in the upper plenum of the MONJU fast breeder reactor was performed. Calculations were performed for a 1/6 simplified model of the MONJU reactor using the commercial code, CFX-13. To better resolve the geometrically complex upper core structure of the MONJU reactor, the porous media approach was adopted for the simulation. First, a steady state solution was obtained and the transient solutions were then obtained for the turbine trip test conducted in December 1995. The time dependent inlet conditions for the mass flow rate and temperature were provided by JAEA. Good agreement with the experimental data was observed for steady state solution. The numerical solution of the transient analysis shows the formation of thermal stratification within the upper plenum of the reactor vessel during the turbine trip test. The temporal variations of temperature were predicted accurately by the present method in the initial rapid coastdown period (~300 seconds). However, transient numerical solutions show a faster thermal mixing than that observed in the experiment after the initial coastdown period. A nearly homogenization of the temperature field in the upper plenum is predicted after about 900 seconds, which is a much shorter-term thermal stratification than the experimental data indicates. This discrepancy may be due to the shortcoming of the turbulence models available in the CFX-13 code for a natural convection flow with thermal stratification.

• Structural Engineering and Mechanics
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• 제24권6호
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• pp.727-740
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• 2006

A simple plane-strain solution is derived in this paper for the functionally graded multilayered isotropic elastic cylinder under static deformation. The solution is obtained using method of separation of variables and is expressed in terms of the summation of the Fourier series in the circumferential direction. While the solution for order n = 0 corresponds to the axisymmetric deformation, that for n = 2 includes the special deformation frequently utilized in the upper and lower bounds analysis. Numerical results for a three-phase cylinder with a middle functionally graded layer are presented for both axisymmetric (n = 0) and general (n = 2) deformations, under either the traction or displacement boundary conditions on the surface of the layered cylinder. The solution to the general deformation case (n = 2) is further utilized for the first time to find the upper and lower bounds of the effective shear modulus of the layered cylinder with a functionally graded middle layer. These results could be useful in the future study of cylindrical composites where FGMs and/or multilayers are involved.

• International Journal of Industrial Entomology and Biomaterials
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• 제33권2호
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• pp.144-148
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• 2016

Recently, silk sericin has been studied extensively for biomedical and cosmetic applications because of its unique properties, including UV resistance and wound healing ability. For use in applications, sericin is fabricated in various forms including films and gels. However, the mechanical properties of sericin are too weak. In this basic study on improving the mechanical properties of sericin, a silk sericin aqueous solution was separated into two layers by centrifugation. The solution viscosity, molecular conformation, and mechanical properties of each separation layer of the sericin were examined. Sericin from the lower layer had a higher solution viscosity and film mechanical properties (strength and strain) than that from the upper layer, implying that sericin from the lower layer had a higher molecular weight than that from the upper layer. The molecular conformation of the sericin films varied depending on the casting solvent. In aqueous solution, the sericin film from the lower layer showed a ${\beta}$-sheet conformation, whereas that from the upper layer displayed a random coil conformation. All the sericin films showed a highly ${\beta}$-sheet-crystallized state when cast in formic acid, regardless of the separation layer.

• 대한조선학회논문집
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• 제56권5호
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• pp.418-426
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• 2019

To derive a simplified analytic solution which can be utilized as a fundamental solution for the wave maker design, a segment of the wave board has been idealized as a submerged line segment in a two dimensional domain of a wave flume. The lower end of the line segment could be located at arbitrary depth of the wave flume and the upper end of the board could be also submerged to any depth from the free surface. The freely oscillating motion of the wave board is assumed to be defined by determining the condition of horizontal oscillation on both ends differently. The submerged wave board oscillating in horizontal direction could be specified by selecting the amplitude, frequency and the phase lag differently on lower and upper ends of the board. The simplified two dimensional wave generated by the wave board segment has been obtained by the first order perturbation method. It is found that the general solution of the freely oscillating wave board in two dimensional domain could be decomposed into the solution of flap motion with lower end hinge and swing motion with upper end hinge. The case study of the analytic solutions has been carried out to evaluate the effect on the wave height due to the difference of oscillation frequency, phase difference and variation of stroke between for the motion of both ends. It is found that the solution of the freely oscillating wave board could be utilized for the development of high performance wavemaker especially for irregular waves.

• 한국경영과학회지
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• 제20권1호
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• pp.1-10
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• 1995

The purpose of this paper is to develop a method of the sensitivity analysis that can be applied to a non-tree solution of the minimum cost flow problem. First, we introduce two types of sensitivity analysis. A sensitivity analysis of Type 1a is the well known method applicable to a tree solution. However this method can not be applied to a non-tree solution. So we propose a sensitivity analysis of Type 2 that keeps solutions of upper bounds at upper bounds, those of lower bounds at lower bounds, and those of intermediate values at intermediate values. For the cost coefficient we present a method that the sensitivity analysis of Type 2 is solved by finding the shortest path. Besides we also show that the results of Type 2 and Type 1 are the same in a spanning tree solution. For the right-hand side constant or the capacity, the sensitivity analysis of Type 2 is solved by a simple calculation using arcs with intermediate values.