• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.8
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• pp.726-730
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• 2001

In this paper, we consider the observability conditions for the following nonlinear fuzzy neutral functional differential equations in E$^{2}$$_{N}$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.1
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• pp.19-30
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• 2011

In [21], we compared the Newton-Krylov method and some high-order methods to solve nonlinear systems. In this paper, we propose high-order Newton-Krylov methods combining the Newton-Krylov method with some high-order iterative methods to solve systems of nonlinear equations. We provide some numerical experiments including comparisons of CPU time and iteration numbers of the proposed high-order Newton-Krylov methods for several nonlinear systems.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.37-50
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• 2014

Using variational methods, we prove some results on the nonexistence and multiplicity of weak solutions for a class of semilinear elliptic systems of two equations involving Grushin type operators with sign-changing nonlinearities. We also shows that the similar results can be obtained for systems of m equations, where m is arbitrary.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.63-65
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• 2003

General classes of boundary-pressure-driven flows of incompressible Newtonian fluids in three­dimensional (3D) channels and in 3D pipes with known steady laminar realizations are investigated respectively. The characteristic physical and geometrical quantities of the flows are subsumed in the kinetic Reynolds number Re and a parameter $\psi$, which involves the energetic ratio and the directions of the boundary-driven part and the pressure-driven part of the laminar flow. The solution of non-stationary dimension-free Navier-Stokes equations is sought in the form $\underline{u}=u_{L}+U,\;where\;u_{L}$ is the scaled laminar velocity and periodical conditions are prescribed for U in the unbounded directions. The objects of our numerical investigations are autonomous systems (S) of ordinary differential equations for the time-dependent coefficients of the spatial Stokes eigenfunction, where these systems (S) were received by application of the Galerkin-method to the dimension-free Navier-Stokes equations for u.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.2
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• pp.145-153
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• 2014

With reasonable control selections on the space of functions, various application models can take the shape of a well-defined control system on mathematics. In the credibility space, controlability management of fuzzy differential equation is as much important issue as stability. This paper addresses exact controllability for fuzzy differential equations in the credibility space in the perspective of Liu process. This is an extension of the controllability results of Park et al. (Controllability for the semilinear fuzzy integro-differential equations with nonlocal conditions) to fuzzy differential equations driven by Liu process.

• Transactions of the Korean Society of Automotive Engineers
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• v.4 no.6
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• pp.247-259
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• 1996

Kinematic design sensitivity analysis for vehicle in suspension systems design is performed. Suspension systems are modeled using composite joins to reduce the number of the constraint equations. This allows a semi-analytical approach that is computerized symbolic manipulation before numerical computations and that may compensate for their drawbacks. All the constraint equations including design variables are derived in symbolic equations for sensitivity analysis. By directly differentiating the equations with respect to design variables, sensitivity equations are obtained. Since the proposed method only requires the hard point data, sensitivity analysis is possible in suspension design stage.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.29-36
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• 1999

It is shown that a new Krylov subspace method for solving symmetric indefinite systems of linear equations can be obtained. We call the method as the projection method in this paper. The residual vector of the projection method is maintained at each iteration, which may be useful in some applications.

• Journal of Korea Society of Industrial Information Systems
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• v.9 no.4
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• pp.68-74
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• 2004

We investigate various $\phi(t)-stability$ of comparison differential equations and We obtain necessary and/or sufficient conditions for the asymptotic and uniform asymptotic stability of the differential equations x'=f( t, x)

• Nuclear Engineering and Technology
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• v.55 no.3
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• pp.861-869
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• 2023

This article proposes a novel approach to measure the performance of Safety-Critical Systems (SCS). Such systems contain multiple processing nodes that communicate with each other is modeled by a Petri nets (PN). The paper uses the PN for the performance evaluation of SCS. A set of ordinary differential equations (ODEs) is derived from the Petri net model that represent the state of the system, and the solutions can be used to measure the system's performance. The proposed method can avoid the state space explosion problem and also introduces new metrics of performance, along with their measurement: deadlock, liveness, stability, boundedness, and steady state. The proposed technique is applied to Shutdown System (SDS) of Nuclear Power Plant (NPP). We obtained 99.887% accuracy of performance measurement, which proves the effectiveness of our approach.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.939-952
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• 2011

This paper is concerned with the solution of ill-conditioned Systems of Linear Equations (SLE's) via the solution of equivalent SLE's which are well-conditioned. A matrix is rst constructed from that of the given ill-conditioned system. Then, an adequate right-hand side is computed to make up the instance of an equivalent system. Formulae and algorithms for computing an instance of this equivalent SLE and solving it will be given and illustrated.