• Korean Journal of Mathematics
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• v.18 no.4
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• pp.465-472
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• 2010

In this paper, we investigate the extent of the set on which the modulus of a meromorphic function is lower bounded by a term related to some Nevanlinna Theory functionals. A. I. Shcherba estimate the size of the set on which the modulus of an entire function is lower bounded by 1. Our theorem in this paper shows that the same result holds in the case that the lower bound is replaced by$lT(r,f)$, $0{\leq}l$ < 1, which improves Shcherba's result. We also give a similar estimation for meromorphic functions.

• Proceedings of the SCSK Conference
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• 2003.09a
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• pp.570-577
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• 2003

The importance of cornified envelope (CE)-bound lipids to epidermal barrier function is increasingly being recognized. In the present study, we intentionally damaged the cornified layer of hairless mice by ultraviolet irradiation and sodium dodecyl sulfate (SDS) treatment, and assessed the changes in epidermal barrier function by measuring Trans Epidermal Water Loss (TEWL). We also measured changes in the amount of CE-bound lipids using thin layer chromatography (TLC). The results showed that both treatments increased TEWL and decreased CE-bound lipids (omega-hydroxy cerami de and omega-hydroxy acid). In addition, investigation of the chronological changes in TEWL revealed an inverse relationship between TEWL and CE-bound lipids, and a correlation between CE-bound lipids and epidermal barrier function. We then measured the amount of CE-bound lipids in the cheek and the medial side of the upper arm in humans. The results showed that because the cheek receives external stimulation on a daily basis, the amount of CE-bound lipids was significantly lower, while the level of TEWL was higher. These observations, together with those from the animal study, indicate that CE-bound lipids are related to epidermal barrier function.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.10
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• pp.3624-3637
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• 2014

At SAC 2004, Junod and Vaudenay designed the FOX family based on the Lai-Massey scheme. They noted that it was impossible to find any useful differential characteristic or linear trail after 8 rounds of FOX64 or FOX128. In this paper, we provide the lower bound of differentially active S-boxes in consecutive rounds of the Lai-Massey scheme that has SPS as its F-function, and we propose the necessary conditions for the reachability of the lower bound. We demonstrate that similar results can be obtained with respect to the lower bound of linearly active S-boxes by proving the duality in the Lai-Massey scheme. Finally, we apply these results to FOX64 and FOX128 and prove that it is impossible to find any useful differential characteristics or linear trail after 6 rounds of FOX64. We provide a more precise security bound for FOX128.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.229-238
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• 1993

Let M be an n-dimensional compact Riemannian manifold with boundary .part.M. We consider the Neumann eigenvalue problem on M of the equation (Fig.) where .upsilon. is the unit outward normal vector to the boundary .part.M. due to the importance of Poincare inequality for analysis on manifolds, one wishes to obtain the lower bound of the first non-zero eigenvalue .eta.$_{1}$ of (1.1). For the purpose of applications, it is important to relax the dependency of the lower bound on the geometric quantities. For general compact manifolds with convex boundary, Li-Yau [3] obtained the lower bound of .eta.$_{1}$. Recently, Roger Chen [1] investigated the lower bound of the first Neumann eigenvalue .eta.$_{1}$ on compact manifold M with nonconvex boundary. We investigate the lower bound .eta.$_{1}$ with the same conditions as those of Roger chen. But, using the different auxiliary function, we have the following theorem.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.771-778
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• 1999

In this paper, we obtain some geometric inequalities for mixed volumes of a convex body and its polar dual. We also develop a lower bound of the product of quermassintegral of a convex body and its polar dual and give a lower bound for the product of the dual quermassintegral of any index of centrally symmetric convex body and that of its polar dual.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.2
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• pp.3-13
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• 1993

In this study, we develop a B & B type algorithm for the concave minimization problem with 0-1 knapsack constraint. Our algorithm reformulates the original problem into the singly linearly constrained concave minimization problem by relaxing 0-1 integer constraint in order to get a lower bound. But this relaxed problem is the concave minimization problem known as NP-hard. Thus the linear function that underestimates the concave objective function over the given domain set is introduced. The introduction of this function bears the following important meanings. Firstly, we can efficiently calculate the lower bound of the optimal object value using the conventional convex optimization methods. Secondly, the above linear function like the concave objective function generates the vertices of the relaxed solution set of the subproblem, which is used to update the upper bound. The fact that the linear underestimating function is uniquely determined over a given simplex enables us to fix underestimating function by considering the simplex containing the relaxed solution set. The initial containing simplex that is the intersection of the linear constraint and the nonnegative orthant is sequentially partitioned into the subsimplices which are related to subproblems.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1382-1390
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• 1990

Accurate load-carrying capacities and moment distributions of thin circular plates are obtained for clamped or simply-supported boundary condition under various concentrated circular loadings. The material is regarded as perfectly-plastic based on an arbitrary yield function such as the Tresca yield function, the Johansen yield function, and the farmily of .betha.-norms which possesses the von Mises yield function and the Frobenius norm. To obtain the lower bound solutions, a maximization formulation is derived and implemented for efficient numerical calculation with a finite difference method and the modified Newton's method. The numerical results demonstrate plastic collapse behavior of circular plates and provide their design criteria.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.389-400
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• 2023

In this paper, some estimations will be given for the analytic functions belonging to the class 𝓡(α). In these estimations, an upper bound and a lower bound will be determined for the first coefficient of the expansion of the analytic function h(z) and the modulus of the angular derivative of the function ${\frac{zh^{\prime}(z)}{h(z)}}$, respectively. Also, the relationship between the coefficients of the analytical function h(z) and the derivative mentioned above will be shown.

• Journal of the Korean Statistical Society
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• v.22 no.1
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• pp.1-12
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• 1993

An approach to make the information bound sharper in median-unbiased estimation, based on an analogue of the Cramer-Rao inequality developed by Sung et al. (1990), is introduced for continuous densities with a nuisance parameter by considering information quantities contained both in the parametric function of interest and in the nuisance parameter in a linear fashion. This approach is comparable to that of improving the information bound in mean-unbiased estimation for the case of two unknown parameters. Computation of an optimal weight corresponding to the nuisance parameter is also considered.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.235-240
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• 2007

In this paper the authors study the properties of the so-called exponent-quasiadditive functions and an application to the generalized $Gr\ddot{o}tzsch$ ring function of quasiconformal theory is specified.