• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.229-241
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• 1999

The fractal space is often associated with natural phenomena with many length scales and the functions defined on this space are usually not differentiable. First we define a $\sigma$-multifractal from $\sigma$-iterated function systems with probability. We introduce the measure derivative through the invariant measure of the $\sigma$-multifractal. We show that the non-differentiable function on the $\sigma$-multifractal can be differentiable with respect to this measure derivative. We apply this result to some examples of ordinary differential equations and diffusion processes on $\sigma$-multifractal spaces.

• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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• pp.63-68
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• 1990

In this paper, we give the Radon-Nikodym derivative of a measure taking values in a dual Banach space.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.199-213
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• 2006

We compute the holomorphic derivative of the harmonic measure associated to a $C^\infty$bounded domain in the plane and show that the exact Bergman kernel function associated to a $C^\infty$ bounded domain in the plane relates the derivatives of the Ahlfors map and the Szego kernel in an explicit way. We find several formulas for the exact Bergman kernel and the Szego kernel and the harmonic measure. Finally we survey some other properties of the holomorphic derivative of the harmonic measure.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.913-921
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• 2010

The derivative influence measure is adapted to the Cholesky decomposition of a covariance matrix. Formulas for the derivative influence of observations on the Cholesky root and the inverse Cholesky root of a sample covariance matrix are derived. It is easy to implement this influence diagnostic method for practical use. A numerical example is given for illustration.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1418-1421
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• 1993

The main purpose of this paper is to introduce and develop the notion of a fuzzy measure in separable Banach space. This definition of fuzzy measure is a natural generalization of the set-valued measure. Radon-Nikod m theorems for fuzzy measure are established.

• The Mathematical Education
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• v.29 no.2
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• pp.141-143
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• 1990

• Journal of Magnetics
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• v.22 no.1
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• pp.43-48
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• 2017

In order to detect the current flowing through concealed conductor, this paper proposes a new method based on derivative method. Firstly, this paper analyzes the main peak characteristic of the derivative function of magnetic field generated by a current-carrying conductor, and a relationship between the current flowing through the conductor and the main peak of the derivative function is obtained and applied to calculate the current. Then, the method is applied to detect the conductor current flowing through grounding grids of substations. Finally, the numerical experimental and field experiment verified the feasibility and accuracy of the method, and the computing results show that the method can effectively measure the conductor current of grounding grids with low error, and the error is within 5 %.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.833-842
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• 2011

We prove that Toeplitz operators with symbols in RW are bounded and we calculate some upper bounds of the norm of these Toeplitz operators. We also analyze n-th derivative of Toeplitz operators and get some local estimates.

• The Journal of the Korea Contents Association
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• v.12 no.3
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• pp.285-294
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• 2012

Under conditions of increasing environmental uncertainty, firms' risk management become important. This study examines the impact of foreign currency derivative usage on firm value using 3,004 Korean non-financial firms from 2002 to 2007. The results showed that there was no significant relationship between foreign currency derivative usage and firm value for the whole period and from 2002 to 2004 when exchange rate was relatively less volatile. But form 2005 to 2007 when exchange rate was volatile, foreign currency derivative usage gave significant negative impact on firm value, whereas when contract value was used, the relatinship was significantly positive. These results might be come from the characteristics of contract value and fair value of foreign currency derivatives. increased firm value when contract value was used as foreign currency derivative usage measure. But when fair value was used, there was no significance. For control variables, major shareholders ownership and foreign blockholders ownership was positively related with firm value.

• Transactions on Control, Automation and Systems Engineering
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• v.1 no.1
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• pp.8-15
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• 1999

One of the main reason advocating redundant manipulators' superiority in application is that they can afford to optimize a dexterity measure, for example the manipulability measure. However, to obtain the gradient of the manipulability is not an easy task in case of general manipulator with high degrees of redundancy. This article proposes a method to compute the gradient of the manipulability, based on recursive algorithm to compute the Jacobian and its derivative using Denavit-Hartenberg parameters only. To characterize the null motion of redundant manipulators, the null space matrix using square minors of the Jacobian is also proposed. With these capabilities, the inverse kinematics of a redundant manipulator system can be done automatically. The result is easily extended to dual manipulator system using the relative kinematics.