• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.709-716
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• 1996

Nielsen coincidence theory is concerned with the determinatin of a lower bound of the minimal number MC[f,g] of coincidence points for all maps in the homotopy class of a given map (f,g) : X $\to$ Y. The Nielsen Nielsen number $N_R(f,g)$ (similar to [9]) is introduced in [3], which is a lower bound for the number of coincidence points in the relative homotopy class of (f,g) and $N_R(f,g) \geq N(f,g)$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.67-77
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• 2011

Let M be a compact orientable closed 3-manifold, and F a non-separating incompressible closed surface in M. Let M' = M - ${\eta}(F)$, where ${\eta}(F)$ is an open regular neighborhood of F in M. In the paper, we give a lower bound of genus of self-amalgamation of minimal Heegaard splitting $V'\;{\cup}_{S'}\;W'$ of M' under some conditions on the distance of the Heegaard splitting.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.143-150
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• 2004

In this paper we study the estimation problem of individual weights of objects using an A-optimal chemical balance weighing design. We assume that in this model errors are correlated and they have the same variances. The lower bound of tr$(X'G^{-1}X)^{-1}$ is obtained and a necessary and sufficient condition for this lower bound to be attained is given. There is given new construction method of A-optimal chemical balance weighing design.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.283-290
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• 2003

Andras Bezdek proved that if a convex n-gon and n points are given, then the points and the sides of the polygon can be renumbered so that at least[${\frac{n}{3}}$] triangles spanned by the ith point and the ith side (i = 1,2,...n) are mutually non-overlapping. In this paper, we show that at least [${\frac{n}{2}}$] mutually non-overlapping triangles can be constructed. This lower bound is best possible.

• Journal of Korean Institute of Industrial Engineers
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• v.14 no.2
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• pp.41-51
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• 1988

In this paper an efficient heuristic for the generalized assignment problem(GAP) is presented. A new lower bound that is slightly improved by adding the feasibility constraint is used to measure the quality of solutions obtained by the heuristic. The heuristic was tested on a number of large-scale random problems and a large sample of small problems. The heuristic appears to be better than the best previously existing heuristic for GAP. Its effectiveness in comparison of running times and closenesses to lower bound is discussed.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.725-732
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• 2021

This paper aims to present a new lower bound for some inequalities related to Frames in Hilbert space. Some refinements of the inequalities for general frames and alternate dual frames under suitable conditions are given. These results refine the remarkable results obtained by Balan et al. and Gavruta.

• Ocean and Polar Research
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• v.32 no.3
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• pp.177-186
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• 2010

A sequential extraction technique was used to study sediment phosphorus speciation and its relative importance in the intertidal flat of Keunso Bay during summer and winter for a better understanding of the phosphorus cycle and bioavailability in intertidal sediments. Loosely sorbed P contents were the lowest among the five P-pools and showed little seasonal or spatial variation. Although Fe-bound P contents were almost constant in winter, they decreased rapidly with sediment depth in summer. The dissolution of Fe oxides, used as an oxidant for the anaerobic respiration, ascribed the rapid decrease of Fe-bound P in summer. Al-bound P contents displayed little seasonal variation, but showed a large spatial variation, with higher values in the upper intertidal flat. Comprising about 50% of total P, Ca-bound P contents were the highest among the five P-pools. Ca-bound P contents were higher in winter than summer, but did not exhibit a clear spatial variation. Organic P contents were higher in summer than winter, which was associated with higher primary production and clam biomass in summer. Organic P contents were higher in the lower intertidal flat than the upper intertidal flat. In Keunso Bay, bioavailable P contents of the intertidal flat comprising about one third of total P ranged from 2.41 to 5.09 ${\mu}molg^{-1}$ in summer and 3.82 to 5.29 ${\mu}molg^{-1}$ in winter. The bioavailability of P contents was higher in the lower intertidal flat than the upper intertidal flat, which was attributed to the large clam production in the lower intertidal flat.

• Journal of the Korean Geotechnical Society
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• v.30 no.11
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• pp.51-60
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• 2014

Load and Resistance Factor Design (LRFD) is one of the limit state design methods, and has been used worldwide, especially in North America. Also, the study for LRFD has been actively conducted in Korea. However, the data for LRFD in Korea were not sufficient, so resistance factors suggested by AASTTO have been used for the design in Korea. But the resistance factors suggested by AASHTO represent the characteristics of bedrocks defined in the US, therefore, it is necessary to determine the resistance factors for designs in Korea, which can reflect the characteristics of bedrocks in Korea. Also, the calculated probabilities of failure from conventional reliability analyses which commonly use log-normal distribution are not realistic because of the lower tail that can be extended to zero. Therefore, it is necessary to calibrate the resistance factors considering the lower-bound resistance. Thus, this study calculates the resistance factors using thirteen sets of drilled shaft load test results, and then calibrates the resistance factors considering the lower-bound resistance corresponding to a target reliability index of 3.0. As a result, resistance factors from conventional reliability analyses were determined in the range of 0.13-0.32 for the shaft resistance, and 0.19-0.29 for the base resistance, respectively. Also, the lower bounds of resistance were determined based on the Hoek-Brown failure criteria (2002) and GSI downgrading. Considering the lower-bound resistances, resistance factors increased by 0~8% for the shaft, and 0~13% for the base, respectively.

• Korean Journal of Computational Design and Engineering
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• v.15 no.2
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• pp.115-123
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• 2010

We present an efficient algorithm for computing the Hausdorff distance between two planar curves. The algorithm is based on an efficient trimming technique that eliminates the curve domains that make no contribution to the final Hausdorff distance. The input curves are first approximated with biarcs within a given error bound in a pre-processing step. Using the biarc approximation, the distance map of an input curve is then approximated and stored into the graphics hardware depth-buffer by rendering the distance maps (represented as circular cones) of the biarcs. We repeat the same procedure for the other input curve. By sampling points on each input curve and reading the distance from the other curve (stored in the hardware depth-buffer), we can easily estimate a lower bound of the Hausdorff distance. Based on the lower bound, the algorithm eliminates redundant curve segments where the exact Hausdorff distance can never be obtained. Finally, we employ a multivariate equation solver to compute the Hausdorff distance efficiently using the remaining curve segments only.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.47-56
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• 2004

The nonlinearity of a Boolean function f on $GF(2)^n$ is the minimum hamming distance between f and all affine functions on $GF(2)^n$ and it measures the ability of a cryptographic system using the functions to resist against being expressed as a set of linear equations. Finding out the exact value of the nonlinearity of given Boolean functions is not an easy problem therefore one wants to estimate the nonlinearity using extra information on given functions, or wants to find a lower bound or an upper bound on the nonlinearity. In this paper we extend the notion of auto-correlations of Boolean functions to vector Boolean functions and obtain upper bounds and a lower bound on the nonlinearity of vector Boolean functions in the context of their auto-correlations. Also we can describe avalanche characteristics of vector Boolean functions by examining the extended notion of auto-correlations.