• The Pure and Applied Mathematics
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• v.24 no.3
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• pp.129-145
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• 2017

In this paper, we establish lower estimates for the modulus of the non-tangential derivative of the holomorphic functionf(z) at the boundary of the unit disc. Also, we shall give an estimate below |f''(b)| according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and $z_0{\neq}0$.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.3.2-3
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• 2003

We propose a method of surface extension method using several functions. Interpolation theory is well developed in curve and surface. But extrapolation theory is not well developed because it is not unique outside the useful domain. It requires continuous, first derivative, second derivative continuous extension for matching in NC(Numerical Control) machine. In the past, we generate data outside the useful area and refit those data using least squares method. this has some problems which have some errors within the useful area. We keep the useful area and extend the unuseful area by a function

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.12
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• pp.2092-2100
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• 2003

Sensitivity information has been used for linearization of nonlinear functions in optimization. Basically, sensitivity is a derivative of a function with respect to a design variable. Design sensitivity is repeatedly calculated in optimization. Since sensitivity calculation is extremely expensive, there are studies to directly use the sensitivity in the design process. When a small design change is required, an engineer makes design changes by considering the sensitivity information. Generally, the current process is performed one-by-one for design variables. Methods to exploit the sensitivity information are developed. When a designer wants to change multiple variables with some relationship, the directional derivative can be utilized. In this case, the first derivative can be calculated. Only small design changes can be made from the first derivatives. Orthogonal arrays can be used for moderate changes of multiple variables. Analysis of Variance is carried out to find out the regional influence of variables. A flow is developed for efficient use of the methods. A software system with the flow has been developed. The system can be easily interfaced with existing commercial systems through a file wrapping technique. The sensitivity information is calculated by finite difference method. Various examples are solved to evaluate the proposed algorithm and the software system.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.685-696
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• 1999

We present local and semilocal convergence results for New-ton's method in a Banach space setting. In particular using Lipschitz-type assumptions on the second Frechet-derivative we find results con-cerning the radius of convergence of Newton's method. Such results are useful in the context of predictor-corrector continuation procedures. Finally we provide numerical examples to show that our results can ap-ply where earlier ones using Lipschitz assumption on the first Frechet-derivative fail.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.29-40
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• 2000

We provide semilocal convergence theorems for Newton-like methods in Banach space using outer and generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Frechet-derivative. This way our Newton-Kantorovich hypotheses differ from earlier ones. Our results can be used to solve undetermined systems, nonlinear least square problems and ill-posed nonlinear operator equations.

• Bulletin of the Korean Chemical Society
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• v.33 no.8
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• pp.2647-2650
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• 2012

The total synthesis of biologically interesting ${\beta}$-hydroxypyranochalcones, purpurenone (1), its derivative 2, praecansone B (3), and pongapinone A (4) has been accomplished starting from commercially available 2,4-dihydroxyacetophenone or 6-methoxy-2,4-dihydroxyacetophenone in 3 steps by a convergent strategy through benzopyran formations, O-methylations, and coupling reactions.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.271-283
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• 2018

In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.

• Journal of the Korea Society of Computer and Information
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• v.21 no.3
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• pp.33-38
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• 2016

Research on the development of key technologies of social work protection and content mashup tools has been carried out as an R&D project granted by the Korea Copyright Commission from 2013. The research aims to provide efficiency of the production environment of the secondary work of the digital contents as well as a systematic solution to the regulation-related problems. The essential features of the distribution management system for cooperative works developed though this study are the decision of the selling prices reflecting various license fee factors and the transparent distribution of the license fees. This paper represents a model which can automatically calculate the amount of the license fee in each derivative stage, independently of the license fee policies on each of the subsidiary contents when N-th works are producted on the basis of a previously approved first work.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2001.11a
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• pp.130-134
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• 2001

In the re-entry control system, errors apt to induce because the time derivative of drag acceleration is analytically estimated. Still more, the difficulty of estimation of the exact drag coefficient in hypersonic velocity and the nun-reality of the scale height cause a steady-state drag error. This paper proposes the additional method of the disturbance observer. This reduces the steady-state drag error according to the following series. First, this method estimates a error in drag acceleration time derivative by the analytic calculation and then creates the new drag acceleration time derivative using the estimated error. The performance of the re-entry control system is verified about 32 reference trajectories.