• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.183-194
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• 2004

In this paper, we consider a Levenberg-Marquardt method for the solution of constrained nonlinear equation problems. The global convergence is established even without requiring the existence of an accumulation point. Some numerical tests are also presented.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.811-814
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• 1997

In this paper, the torque optimization of a kinematically redundant manipulator for minimizing the torque demands is discussed. The minimum torque solution based on a local optimization has been known to encounter the instability problem and then the global torque optimization was suggested as one of the alternatives. Herein, by adopting the infinity-norm rather than the 2-norm for the magnitude of torques, we are to propose a new cost function more advantageous to the avoidance of torque limits. By the way, a solution to the global torque optimization formulated with the new cost function can not be obtained by the previous methods due to their difficulties such as inability to treat discontinuous cost functions and various constraints on the joint variables. Thus, to overcome those deficiencies, we are developing a new approach using the dynamic programming. The effectiveness of the proposed method is shown through simulation examples for a 3-link planar redundant manipulator.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1269-1297
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• 2020

In this paper, we consider a two-species parabolic-parabolic-elliptic chemotaxis system with weak competition and a fractional diffusion of order s ∈ (0, 2). It is proved that for s > 2p₀, where p₀ is a nonnegative constant depending on the system's parameters, there admits a global classical solution. Apart from this, under the circumstance of small chemotactic strengths, we arrive at the global asymptotic stability of the coexistence steady state.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.531-551
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• 2018

In this paper we consider a class of nonlocal parabolic equations in bounded domains with Dirichlet boundary conditions and a new class of nonlinearities. We first prove the existence and uniqueness of weak solutions by using the compactness method. Then we study the existence and fractal dimension estimates of the global attractor for the continuous semigroup generated by the problem. We also prove the existence of stationary solutions and give a sufficient condition for the uniqueness and global exponential stability of the stationary solution. The main novelty of the obtained results is that no restriction is imposed on the upper growth of the nonlinearities.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.315-324
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• 2012

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a long periodic domain. We show by a simple argument that a strong solution exists globally in time when the initial velocity in $H^1$ and the forcing function in $L^p$([0; T);$L^2$), T > 0, $2{\leq}p{\leq}+\infty$ satisfy a certain condition. This condition common appears for the global existence in thin non-periodic domains. Larger and larger initial data and forcing functions satisfy this condition as the thickness of the domain $\epsilon$ tends to zero.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.10 s.241
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• pp.1369-1376
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• 2005

In structural design, the design variables are frequently selected from certain discrete values. Various optimization algorithms have been developed fDr discrete design. It is well known that many function evaluations are needed in such optimization. Recently, sequential algorithm with orthogonal arrays (SOA), which is a search algorithm for a local minimum in a discrete space, has been developed. It considerably reduces the number of function evaluations. However, it only finds a local minimum and the final solution depends on the initial values of the design variables. A new algorithm is proposed to adopt a genetic algorithm (GA) in SOA. The GA can find a solution in a global sense. The solution from the GA is used as the initial design of SOA. A sequential usage of the GA and SOA is carried out in an iterative manner until the convergence criteria are satisfied. The performance of the algorithm is evaluated by various examples.

• Journal of computational fluids engineering
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• v.17 no.4
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• pp.32-40
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• 2012

Efficient Global Optimization (EGO) method is a global optimization technique which can select the next sample point automatically by infill sampling criteria (ISC) and search for the global minimum with less samples than what the conventional global optimization method needs. ISC function consists of the predictor and mean square error (MSE) provided from the kriging model which is a stochastic metamodel. Also the constrained EGO method can minimize the objective function dealing with the constraints under EGO concept. In this study the constrained EGO method applied to the RAE2822 airfoil shape design formulated with the constraint. But the noisy CFD data caused the kriging model to fail to depict the true function. The distorted kriging model would make the EGO deviate from the correct search. This distortion of kriging model can be handled with the interpolation(p=free) kriging model. With the interpolation(p=free) kriging model, however, the search of EGO solution was stalled in the narrow feasible region without the chance to update the objective and constraint functions. Then the accuracy of EGO solution was not good enough. So the three-step search method was proposed to obtain the accurate global minimum as well as prevent from the distortion of kriging model for the noisy constrained CFD problem.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.161-172
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• 2015

In this paper, we consider the chemotaxis-haptotaxis model of tumor invasion with the proliferation and tissue re-establishment term in dimensions one and two. We show the global in time existence of a unique classical solution for the the model in two dimensional spatial domain without any restrictions on the coefficients.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.473-493
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• 2014

This paper concerns with a class of delayed Nicholson's blowflies model with a nonlinear density-dependent mortality term. Under appropriate conditions, we establish some criteria to ensure that the solutions of this model converge globally exponentially to a positive almost periodic solution. Moreover, we give some examples and numerical simulations to illustrate our main results.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.1039-1048
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• 2018

In this paper we study the dynamics of a general ${\omega}-periodic$ model. Necessary and sufficient conditions for the global stability of zero steady state of the model are given. The conditions under which there exists a unique periodic solutions to the model are determined. We also show that the unique periodic solution is the global attractor of all other positive solutions. Some applications to mathematical models for cancer and tumor growth are given.