• Journal of Korean Institute of Industrial Engineers
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• v.25 no.3
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• pp.290-297
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• 1999

In interior point methods for linear programming, we must solve a linear system with a symmetric positive definite matrix at every iteration, and Cholesky factorization is generally used to solve it. Therefore, if Cholesky factorization is not done successfully, many iterations are needed to find the optimal solution or we can not find it. We studied methods for improving the numerical stability of Cholesky factorization and the accuracy of the solution of the linear system.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.37-49
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• 2011

We investigate the asymptotic equivalence for linear differential systems by means of the notions of $t_{\infty}$-similarity and strong stability.

• Proceedings of the KIEE Conference
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• 1999.07b
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• pp.589-591
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• 1999

In this paper, we consider the robust pole assignment for linear system with time-varying uncertainty. The considered uncertainty is an unstructured uncertainty. Based on Lyapunov stability and linear matrix inequality technique, we present a condition that guarantees the robust pole assignment inside a circular disk and the robust stability of uncertain linear systems. Finally, we show the usefulness of our results by an example.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.261-269
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• 2009

We adopt the idea of $C\check{a}dariu$ and Radu to prove the stability of Jordan triple linear derivations and we take account of the Jacobson radical range problem for linear derivations.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.10
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• pp.1508-1512
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• 2012

This paper presents a relaxed stability condition for continuous-time affine fuzzy system using fuzzy Lyapunov function. In the previous studies, stability conditions for the affine fuzzy system based on quadratic Lyapunov function have a conservativeness. The stability condition is considered by using the fuzzy Lyapunov function, which has membership functions in the traditional Lyapunov function. Based on Lyapunov-stability theory, the stability condition for affine fuzzy system is derived and represented to linear matrix inequalities(LMIs). And slack matrix is added to stability condition for the relaxed stability condition. Finally, simulation example is given to illustrate the merits of the proposed method.

• Publications of The Korean Astronomical Society
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• v.30 no.2
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• pp.297-299
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• 2015

In this paper we have examined the linear stability of triangular equilibrium points in the photogravitational restricted three body problem when both primaries are triaxial rigid bodies, the bigger one an oblate spheroid and source of radiation. The orbits about the Lagrangian equilibrium points are important for scientific investigation. A number of space missions have been completed and some are being proposed by various space agencies. We analyze the periodic motion in the neighbourhood of the Lagrangian equilibrium points as a function of the value of the mass parameter. Periodic orbits of an infinitesimal mass in the vicinity of the equilibrium points are studied analytically and numerically. The linear stability of triangular equilibrium points in the photogravitational restricted three body problem with Poynting-Robertson drag when both primaries are oblate spheroids has been examined by A. Kumar (2007). We have found the equations of motion and triangular equilibrium points for our problem. With the help of the characteristic equation we have discussed stability conditions. Finally, triangular equilibrium points are stable in the linear sense. It is further seen that the triangular points have long or short periodic elliptical orbits in the same range of ${\mu}$.

• Journal of the Semiconductor & Display Technology
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• v.15 no.1
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• pp.6-11
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• 2016

For high volume manufacturing using extreme ultraviolet (EUV) lithography, mask protection from contamination during lithography process must be solved, and EUV pellicle is the strongest solution. Based on the technical requirements of EUV pellicle, EUV pellicle should have large membrane area ($110{\times}140mm^2$) with film transmittance over 90% and mechanical stability. Even though pellicle that satisfies size standard with high transmittance has been reported, its mechanical stability has not been confirmed, nor is there a standard to evaluate the mechanical stability. In this study, we suggest a rather simple method evaluating mechanical stability of pellicle membrane using spin-coater which can emulate the linear accelerated motion. The test conditions were designed by simulating the acceleration distribution inside pellicle membrane through correlating the linear acceleration and centripetal acceleration, which occurs during linear movement and rotation movement, respectively. By these simulation results, we confirmed the possibility of using spin-coater to evaluate the mechanical stability of EUV pellicle.

• Computers and Concrete
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• v.19 no.1
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• pp.1-6
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• 2017

Prestressed concrete I-girders are subject to different load types at their construction stages. At the time of strand release, i.e., detensioning, prestressed concrete girders are under the effect of dead and prestressing loads. At this stage, the camber, total net upward deflection, of prestressed girder is summation of the upward deflection due to the prestressing force and the downward deflection due to dead loads. For the calculation of the upward deflection, it is generally considered that prestressed concrete I-girder behaves linear-elastic. However, the field measurements on total net upward deflection of prestressed I-girder after detensioning show contradictory results. In this paper, camber calculations with the linear-elastic beam and elastic-stability theories are presented. One of a typical precast I-girder with 120 cm height and 31.5 m effective span length is selected as a case study. 3D finite element model (FEM) of the girder is developed by SAP2000 software, and the deflections of girder are obtained from linear and nonlinear-static analyses. Only geometric nonlinearity is taken into account. The material test and field measurement of this study are performed at prestressing girder plant. The results of the linear-elastic beam and elastic-stability theories are compared with FEM results and field measurements. It is seen that the camber predicted by elastic-stability theory gives acceptable results than the linear-elastic beam theory while strand releasing.

• Korea-Australia Rheology Journal
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• v.17 no.2
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• pp.63-69
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• 2005

The stability of low-speed spinning process exhibiting spinline flow-induced crystallization (FIC) with no neck-like spinline deformation has been investigated using the method of linear stability analysis. Effects of various process conditions such as fluid viscoelasticity and the spinline cooling on the spinning stability have been found closely related to the development of the spinline crystallinity. It also has been found that the FIC makes the system less stable or more unstable than no FIC cases when the spinline crystallinity reaches its maximum possible value, whereas the FIC generally stabilizes the system if the crystallinity doesn't reach its maximum value on the spinline. It is believed that the destabilizing effect of the FIC on low-speed spinning when the crystallinity is fully developed on the spinline is due to the reduction of the real spinning length available for deformation on the spinline. On the other hand, the increased spinline tension caused by the FIC when the maximum crystallinity is not reached on the spinline and thus no reduction in the spinning length occurs, makes the sensitivity of spinline variables to external disturbances smaller and hence stabilizes the system. These linear stability results are consistent with the findings by nonlinear transient simulation, as first reported by Lee et al. (2005b).

• Journal of the Korean Society of Propulsion Engineers
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• v.17 no.5
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• pp.27-36
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• 2013

Linear stability analysis for combustion instability within a cylindrical port of solid rocket motor has been conducted. The analysis of acoustic energy has been performed by a commercial COMSOL code to obtain the mode function associated to each acoustic mode prior to the calculation of stability alpha. An instability diagnosis based on the linear stability analysis of Culick is performed where special interests have been focused on 5 stability factors(alpha) such as pressure coupling, nozzle damping, particle damping and additionally, flow turning effect and viscous damping to take into account the flow and viscosity effect near the fuel surface. The instability decay characteristics depending on the particle size is also analyzed.