• Journal of Digital Contents Society
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• v.5 no.4
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• pp.289-294
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• 2004

For the purpose of image analysis, we usually take the application method relying on the various mathematical theories. On the respect of image as two variable function one may uses the gradient vector or several type of energy functions induced by the conventional (partial) derivative. We also have used the tangent plane or curvature vector from the concept of differential geometry {**]. However, these mathematical tools my assume that the given function should be sufficiently smoothing enough to depict every local variation continuously. But the real application of these mathematical methods to the natural images or phenomena may occur the ill-posed problem. In this paper, we have defined the weak derivative as a loose form of the derivative so that it my applied to the irregular case with less ill-posed problem.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.865-875
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• 2020

We provide detailed proofs for local gradient estimates for weak solutions to elliptic equations in divergence form with partial Dini mean oscillation coefficients subject to conormal derivative boundary conditions.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.575-584
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• 2011

We provide a semilocal convergence analysis for a Newtonlike method under weak conditions in a Banach space setting. In particular, we only assume that the Gateaux derivative of the operator involved is hemicontinuous. An application is also provided.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1273-1299
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• 2012

We prove the global regularity of weak solutions to a conormal derivative boundary value problem for quasilinear elliptic equations in divergence form on Lipschitz domains under the controlled growth conditions on the low order terms. The leading coefficients are in the class of BMO functions with small mean oscillations.

• YAKHAK HOEJI
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• v.43 no.1
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• pp.28-32
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• 1999

Four derivatives of kojic acid were synthesized and their inhibitory activities against tyrosinase were evaluated. The C-2 hydroxymethyl and C-7 hydroxyl of kojic acid were replaced by carboxylate and amine, respectively. These derivatives were coupled to L-phenylalanine, producing two amide compounds. The carboxylate derivative (3), its amide compound (5), and the amine derivative (7) were weak inhibitors. The amide compound (9) where amine derivative (7) coupled to L-phenylalanine showed strong inhibitory activity ($IC_{50}=24.6{\;}{\mu}M$) comparable to kojic acid.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.345-360
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• 2001

Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods. The first uses conditions on the first Frechet-derivative whereas the second theorem employs hypotheses on the mth(m≥2 an integer). Radius of convergence as well as rate of convergence results are derived. Results involving superlinear convergence and known to be true for inexact Newton methods are extended here. Moreover, we show that under hypotheses on the mth Frechet-derivative our radius of convergence can sometimes be larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also provided to show that our radius of convergence is larger than the one in [10].

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.393-406
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• 1999

Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods. The first uses conditions on the first Frechet-derivative whereas the second theorem employs hypotheses on the second. Radius of con-vergence as well as rate of convergence results are derived. Results involving superlinear convergence and known to be true for inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivation our radius of convergence results are derived. Results involving superlinear convergence and known to be true or inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivative our radius of conver-gence is larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also pro-vided to show that our radius of convergence is larger then the one in [10].

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.513-523
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• 2015

We present a local convergence analysis of some Newton-like methods of R-order at least three in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second $Fr{\acute{e}}chet$-derivative of the operator involved. These conditions are weaker that the corresponding ones given by Hernandez, Romero [10] and others [1], [4]-[9] requiring hypotheses up to the third $Fr{\acute{e}}chet$ derivative. Numerical examples are also provided in this study.

• Proceedings of the Korea Concrete Institute Conference
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• 2005.05b
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• pp.45-48
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• 2005

Self compacting concrete has the strong point in capability of concrete to be uniformly filled and compacted in every corners of formwork by its self-weight without vibration during placing. However, powder type self compacting concrete has the weak point in the heat of hydration, the drying shrinkage and the elastic property of concrete etc. Recently viscosity agent has been developed in order to overcome these weaknesses. In this study, self compacting concrete is made with viscosity agent based on polysaccharide derivative in order to develope the normal strength self compacting concrete. Slump flow, loss of slump flow and setting time are measured for comparison with normal concrete. Compressive strength, freezing and thawing test and carbonation test are conducted on normal and self compacting concrete using viscosity agent. In the experiment, we acquired good results in fresh and hardened self compacting concrete using viscosity agent based on polysaccharide derivative.

• The Korean Journal of Financial Management
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• v.26 no.4
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• pp.63-81
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• 2009

This paper empirically examines the relation between stock volatility and volatilities of macroeconomic variables and financial derivative trading. Previous studies have shown that stock volatility has been much greater than volatilities of macroeconomic variables, and their explanatory powers are too weak to confirm hypothesized theoretical relation between stock volatility and macroeconomic volatilities. The test for the relation using Korean data since 1980 verified such a finding. It is argued that this may have been the result from omitting the influence of financial activities on stock volatility. In particular, this paper demonstrates that, by including the volatility of financial derivative trading, stock volatility-macroeconomic volatility relation can not only be explained better, but also the hypothesized significance of macroeconomic volatilities can be restored.