• International Journal of Reliability and Applications
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• v.16 no.1
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• pp.27-34
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• 2015

Based on increasing concave ordering a new class of life distribution is introduced. The new class of life distribution is named used better than aged in increasing concave ordering and is denoted by UBAC(2). The implication of our proposed class of life distribution with other classes is given. The properties of UBAC(2) under convolution, discrete mixture and formation of a coherent system are studied. Finally a characterization of the proposed class of life distributions by Laplace transform is discussed.

• Journal of Information Science Theory and Practice
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• v.1 no.3
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• pp.6-11
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• 2013

A new explanation, using exponential functions, is given for the S-shaped functional relation between the mean citation score and the proportion of top 10% (and other percentages) publications for the 500 Leiden Ranking universities. With this new model we again obtain an explanation for the concave or convex relation between the proportion of top $100{\theta}%$ publications, for different fractions of ${\theta}$.

• Kyungpook Mathematical Journal
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• v.18 no.1
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• pp.31-36
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• 1978

This paper studies some problems suggested by Stirling numbers, and defines generalized Stirling numbers s(n, k, r), S(n, k, r) and proves that generalized Stirling numbers and certain linear combination of generalized Stirling numbers are strong logarithmic concave functions of k for fixed n and r.

• Korean Journal of Heritage: History & Science
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• v.39
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• pp.281-314
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• 2006

Several explanations exist about the usage of disk-shaped bronze implements in the ancient society. Some argue that they were used as mirrors, others suggest percussion instruments, and still others bronze ornaments. Differences between disk-shaped bronze implements and mirrors with multiple knobs are that the former have no visible design, only one handle, and a sharp curvature unlike the latter with smooth curvature. The question is whether disk-shaped bronze implements excavated from Korean peninsula have any light reflecting function. To answer this question, I carefully studied the concave surfaces of disk-shaped bronze implements excavated from Goejeong-dong, Tongso-ri and Hapsong-ri sites. The main findings are as follows: (1) The concave sides of the disk-shaped bronze implements excavated from Goejeong-dong and Tongso-ri sites were highly polished, and they were as reflective as bronze mirrors. (2) The concave side of the disk-shaped bronze implement from Hapsong-ri site was unpolished, and it was different from bronze mirrors. (3) As for the convex sides of the disk-shaped bronze implements, they did not appear to have been polished with care. Considering the above findings, the disk-shaped bronze implements excavated from Goejeong-dong and Tongso-ri sites belong to the stage where they could act as both mirrors and instruments. On the contrary, the disk-shaped bronze implement from Hapsong-ri site can belong to the stage where it lost the function of being a mirror as the result of maintaining only its function as an instrument. Even though disk-shaped implements had two functions, it can be considered that the light reflecting function expanded the role of a mirror with multiple knobs and the sound function helped the engraved round bronze implement to be converted into an eight-armed bronze rattle. Since it has been reported that shamans used bronze mirrors as percussion instruments in their performances in Korean peninsula and Siberia, I propose a reconsideration of the usage of mirrors in the ancient East Asia. Although the essential function of a mirror is to reflect light, other possible usages involving important functions need to be further investigated.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.785-794
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• 2018

In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous Dirichlet boundary condition with one corner singularity at the origin, and compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. This approach uses the polar coordinate and the cut-off function to control the singularity and the boundary condition. In this paper we consider Poisson equations with multiple singular points, which involves different cut-off functions which might overlaps together and shows the way of cording in FreeFEM++ to control the singular functions and cut-off functions with numerical experiments.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.659-666
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• 2014

Let $\mathcal{A}$ be the class of analytic functions f in the open unit disk $\mathbb{U}$={z : ${\mid}z{\mid}$ < 1} with the normalization conditions $f(0)=f^{\prime}(0)-1=0$. If $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ and ${\delta}$ > 0 are given, then the $T_{\delta}$-neighborhood of the function f is defined as $$TN_{\delta}(f)\{g(z)=z+\sum_{n=2}^{\infty}b_nz^n{\in}\mathcal{A}:\sum_{n=2}^{\infty}T_n{\mid}a_n-b_n{\mid}{\leq}{\delta}\}$$, where $T=\{T_n\}_{n=2}^{\infty}$ is a sequence of positive numbers. In the present paper we investigate some problems concerning $T_{\delta}$-neighborhoods of function in various classes of analytic functions with $T=\{2^{-n}/n^2\}_{n=2}^{\infty}$. We also find bounds for $^{\delta}^*_T(A,B)$ defined by $$^{\delta}^*_T(A,B)=jnf\{{\delta}&gt;0:B{\subset}TN_{\delta}(f)\;for\;all\;f{\in}A\}$$ where A, B are given subsets of $\mathcal{A}$.

• ETRI Journal
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• v.15 no.3
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• pp.47-59
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• 1994

A capacity expansion planning problem with buy-or-lease decisions is considered. Demands for capacity are deterministic and are given period-dependently at each period. Capacity additions occur by buying or leasing a capacity, and leased capacity at any period is reconverted to original source after a fixed length of periods, say, lease period. All cost functions (buying, leasing and idle costs) are assumed to be concave. And shortages of capacity and disposals are not considered. The properties of an optimal solution are characterized. This is then used in a tree search algorithm for the optimal solution and other two algorithms for a near-optimal solution are added. And these algorithms are illustrated with numerical examples.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.141-148
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• 1986

In [1], M. Guignard considered a constraint set in a Banach space, which is similar to that in [2] and gave a first order necessary optimality condition which generalized the Kuhn-Tucker conditions [3]. Sufficiency is proved for objective functions which is either pseudoconcave [5] or quasi-concave [6] where the constraint sets are taken pseudoconvex. In this note, we consider a psedoconvex programming problem in a Hilbert space. Constraint set in a Hillbert space being pseudoconvex and the objective function is restrained by an operator equation. Then we use the methods similar to that in [1] and [6] to obtain a necessary and sufficient optimality condition.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.3
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• pp.71-79
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• 1993

Dynamic production planning problems are to determine the optimal production times and production quantities of product for discrete finite periods. In previous many researches, the solutions for these problems have been developed through the algorithms using dynamic programming. The purpose of this research is to suggest the new algorithm using linear programming. This research is to determine optimal production quantities of product in each period to satisfy dynamic for discrete finite periods, minimizing the total of production cost and inventory holding cost. Cost functions are concave, and no backlogging for product is allowed. The new algorithm for capacity constrained problem is developed.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1141-1145
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• 2005

In this note, we show that Theorem 2.1[Kybernetika, 28(1992) 45-49], a result of a functional relationship between the membership function of LR fuzzy numbers of T-sum and T-product, remains valid for convex additive generator and concave shape functions L and R with simple proof. We also consider the case for 0-symmetric R fuzzy numbers.