• Ocean and Polar Research
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• 제32권3호
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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.

• 충청수학회지
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• 제17권1호
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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.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2016년도 학술발표회
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• pp.201-201
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• 2016

The asymptotic extreme value distributions of maxima are a natural choice when designing against future extreme events like flood peaks or wave heights, given a stationary time series. The generalized extreme value distribution (GEV) is often utilised in this context because it is seen as a convenient single expression for extreme event analysis. However, the GEV has a drawback because the location of the distribution bound relative to the data is a discontinuous function of the GEV shape parameter. That is, for annual maxima approximated by the Gumbel distribution, the data is also consistent with a GEV distribution with an upper bound (no lower bound) or a GEV distribution with a lower bound (no upper bound). A more consistent single extreme value expression for design purposes is proposed as the Weibull distribution of smallest extremes, as applied to transformed annual maxima. The Weibull distribution limit holds here for sufficiently large sample sizes, irrespective of the extreme value domain of attraction applicable to the untransformed maxima. The Gumbel, Type 2, and Type 3 extreme value distributions thus become redundant, together with the GEV, because in reality there is only a single asymptotic extreme value distribution required for design purposes - the Weibull distribution of minima as applied to transformed maxima. An illustrative synthetic example is given showing transformed maxima from the normal distribution approaching the Weibull limit much faster than the untransformed sample maxima approach the normal distribution Gumbel limit. Some New Zealand examples are given with the Weibull distribution being applied to reciprocal transformations of annual flood maxima, where the untransformed maxima follow apparently different extreme value distributions.

• 대한수학회논문집
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• 제10권2호
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• pp.461-469
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• 1995

Some bounds for anisotropic torsional rigidity with one plane of elastic symmetry perpendicular to the axis of the beam are derived by making use of the isoperimetric inequalities, complementary variational principles, and the maximum principle. Upper and lower bounds are obtained by applying the isoperimetric inequalities. While the upper bound investigated by the variational principles and maximum principle. The analysis is patterned after the work of Payne and Weinbeger [J. Math. Anal. Appl. 2(1961). pp. 210-216].

• East Asian mathematical journal
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• 제17권1호
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• pp.93-101
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• 2001

We give an equivalent formulation to the $Erd\"{o}s'$ conjecture on the lower bound of the greatest element in a set having distinct subset sums. On this basis we suggest a possible approach towards $ERD\"{O}S'$ conjecture. Also we reproduce L. Moser's result by means of an analytic method.

• 한국CDE학회논문집
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• 제15권1호
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• pp.24-32
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• 2010

This paper introduces a B-spline based branch & bound algorithm for global optimization. The branch & bound is a well-known algorithm paradigm for global optimization, of which key components are the subdivision scheme and the bound calculation scheme. For this, we consider the B-spline hypervolume to approximate an objective function defined in a design space. This model enables us to subdivide the design space, and to compute the upper & lower bound of each subspace where the bound calculation is based on the LHS sampling points. We also describe a search tree to represent the searching process for optimal solution, and explain iteration steps and some conditions necessary to carry out the algorithm. Finally, the performance of the proposed algorithm is examined on some test problems which would cover most difficulties faced in global optimization area. It shows that the proposed algorithm is complete algorithm not using heuristics, provides an approximate global solution within prescribed tolerances, and has the good possibility for large scale NP-hard optimization.

• 한국통신학회논문지
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• 제37권2B호
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• pp.87-96
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• 2012

본 논문에서는 2-홉 릴레이 시스템에서 릴레이 노드와 목적지 노드가 모두 임의의 수를 갖는 간섭원들의 영향을 받는 상황을 고려한다. 특히 릴레이 채널과 액세스 채널, 그리고 간섭 채널들이 모두 레일리 페이딩을 겪는다고 가정할 때, 증폭-후-전달(amplify-and-forward: AF) 릴레이 시스템의 불능 확률에 대한 정확한 수식을 도출하고, 나아가 불능 확률의 상한 식(upper bound)과 하한 식(lower bound)을 도출한다. 또한 도출된 불능 확률의 상한 식과 하한 식을 이용하여 AF 릴레이 시스템의 비트 오류율 성능에 대한 상한 식과 하한 식을 도출한다. 그리고 도출된 AF 릴레이 시스템의 불능 확률과 비트 오류율 성능에 대한 상한 식과 하한 식의 정확도를 모의실험을 통해 확인한다.

• Geomechanics and Engineering
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• 제8권5호
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• pp.741-756
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• 2015

The prediction of impending collapse of deep tunnel is one of the most difficult problems. Collapse mechanism of deep tunnel in layered soils is derived using a new curved failure mechanism within the framework of upper bound theorem, and effects of seepage forces are considered. Nonlinear failure criterion is adopted in the present analysis, and the possible collapse shape of deep tunnel in the layered soils is discussed in this paper. In the layered soils, the internal energy dissipations along velocity discontinuity are calculated, and the external work rates are produced by weight, seepage forces and supporting pressure. With upper bound theorem of limit analysis, two different curve functions are proposed for the two different soil stratums. The specific shape of collapse surface is discussed, using the proposed curve functions. Effects of nonlinear coefficient, initial cohesion, pore water pressure and unit weight on potential collapse are analyzed. According to the numerical results, with the nonlinear coefficient increase, the shape of collapse block will increase. With initial cohesion of the upper soil increase, the shape of failure block will be flat, and with the lower soil improving, the size of collapsing will be large. Furthermore, the shape of collapsing will decrease with the unit weight decrease.

• 한국경영과학회지
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• 제22권3호
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• pp.59-80
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• 1997

Designing highly survivable interoffice telecommunication networks is considered. The problem is formulated as a minimum-cost network design problem with three node connectivity constraints. These valid and facet-defining inequalities for the convex hull of the solution are presented. A branch and cut algorithm is proposed based on the inequalities to obtain the optimal solution. With the lower bound by the cutting plane algorithm, a delete-ink heuristic is proposed to otain a good upper bound in the branch and bound procedure. The effeciveness of the branch and cut algorithm is demonstrated with computational results for a variety of problem sets : different lower bounds, two types of link costs and large number of links. The cutting plane procedure based on the three inequalities provides excellent lower bounds to the optimal solutions.

• Journal of applied mathematics & informatics
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• 제3권2호
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• pp.245-252
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• 1996

We described a relationship of the $L_2$ norm of the $L_2$norm of a Bzier curve and l2 norm of its confrol points. The use of Bezier curves finds much application in the general description of curves and surfaces and provided the mathematical basis for many computer graphics system. We define the $L_2$ norm for Bezier curves and find a upper and lower bound for many computer graphics system. We define the $L_2$ norm for Bezier curves and find a upper and lower bound for the $L_2$ norm with respect to the $L_2$ norm for its control points for easy computation.