• Honam Mathematical Journal
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• v.43 no.4
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• pp.679-689
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• 2021

The first author suggested an exact volume formula of the hypercubes [0, 1]ⁿ clipped by several hyperplanes expressed directly in terms of linear coefficients of the hyperplanes. However, it requires awkward assumptions to apply the formula to various situations. We suggest a concrete method to overcome those restrictions for two or three hyperplanes using 𝜖-perturbation, which gives an exact value applicable for any kind of arrangement of hyperplanes with no consideration.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.853-868
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• 2015

Let G be a complex semisimple simply connected linear algebraic group. The main result of this note is to give several equivalent criteria for the untwistedness of the twisted cubes introduced by Grossberg and Karshon. In certain cases arising from representation theory, Grossberg and Karshon obtained a Demazure-type character formula for irreducible G-representations as a sum over lattice points (counted with sign according to a density function) of these twisted cubes. A twisted cube is untwisted when it is a "true" (i.e., closed, convex) polytope; in this case, Grossberg and Karshon's character formula becomes a purely positive formula with no multiplicities, i.e., each lattice point appears precisely once in the formula, with coefficient +1. One of our equivalent conditions for untwistedness is that a certain divisor on the special fiber of a toric degeneration of a Bott-Samelson variety, as constructed by Pasquier, is basepoint-free. We also show that the strict positivity of some of the defining constants for the twisted cube, together with convexity (of its support), is enough to guarantee untwistedness. Finally, in the special case when the twisted cube arises from the representation-theoretic data of $\lambda$ an integral weight and $\underline{w}$ a choice of word decomposition of a Weyl group element, we give two simple necessary conditions for untwistedness which is stated in terms of $\lambda$ and $\underline{w}$.

• Journal of Korea Water Resources Association
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• v.47 no.9
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• pp.743-752
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• 2014

Delay time for groundwater recharge means the travel time from the bottom of soil layer to groundwater through vadose zone after infiltration from rainfall. As it is difficult to measure delay time, we suggested an empirical formula which is derived by using linear regression between altitude and delay time. For the regression analysis, 4 major gauging watersheds were chosen (Hancheon, Kangjeongcheon, Oedocheon, Cheonmicheon) with 18 measured groundwater level stations. To verify this empirical formula, derived equation from linear reservoir theory was applied to compute delay time and to compare estimated amounts of groundwater recharge using both methods. The result showed good agreement. Furthermore, if derived empirical formula would be linked with SWAT model, the spatial time delay effect in the watershed could be reflected properly.

• Journal of Navigation and Port Research
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• v.45 no.3
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• pp.165-172
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• 2021

Breaking wave is one of the important design factors in the design of coastal and port structures as they are directly related to various physical phenomena occurring on the coast, such as onshore currents, sediment transport, shock wave pressure, and energy dissipation. Due to the inherent complexity of the breaking wave, many empirical formulas have been proposed to predict breaker indices such as wave breaking height and breaking depth using hydraulic models. However, the existing empirical equations for breaker indices mainly were proposed via statistical analysis of experimental data under the assumption of a specific equation. In this study, a new Munk-type empirical equation was proposed to predict the height of breaking waves based on a representative linear supervised machine learning technique with high predictive performance in various research fields related to regression or classification challenges. Although the newly proposed breaker height formula was a simple polynomial equation, its predictive performance was comparable to that of the currently available empirical formula.

• Journal of the Korean GEO-environmental Society
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• v.12 no.10
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• pp.13-22
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• 2011

In this study, features of correlation between S-velocity and N value are derived from 9 suspension PS layers in Chungcheong Buk-do. S-velocity to be measured on Chungcheong Buk-do is classified into 5 as conditions of stratum that are ; cohesive soil layer, sandy soil layer, gravel layer, weathering soil layer, weathered rock layer. Each correlation formulas between N value by SPT and S-velocity is proposed from these classifications. And correlation formula for whole soil body except weathered rock layer also is proposed for reference. Corelation formulas developed this study formed square expression considering existing formulas produced internationally. Strength parameter converted to linear if N value is more than 50. Features of proposed formula which came up with comparative analysis of international result of cohesive soil layer and sandy soil layer and gravel layer show similar to existing ones. But there is deference that result of correlation formula for weathered rock layer is a little smaller than domestic formula's one. Because correlations of weathered rock layer above the N value of 50 is converted into a linear formation.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.492-499
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• 2004

The purpose of this paper is to present a design procedure of coulomb friction dampers for controlling elastic and inelastic responses of building structures. The equivalent damping and frequency increased by the friction damper are estimated using ATC-40 and ATC-55 procedures which provide equivalent linear system for bilinear one, and then a design formula to achieve target performance response level by friction damper is presented. It is identified that there exists error between the responses obtained by this formula and by performing nonlinear analysis and the features of the error vary according to the hardening ratio, yield strength ratio, and structural period. Equations for compensating this er개r are reposed based on the least square method, and the results from numerical analyses indicate that the error is significantly reduced, and the proposed formula can be used without much error for designing coulomb friction damper for retrofitting a structure showing elastic or inelastic behavior.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1853-1878
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• 2017

Let $\{U(t,s)\}_{t{\geq}s}$ be a periodic evolutionary process with period ${\tau}$ > 0 on a Banach space X. Also, let L be the generator of the evolution semigroup associated with $\{U(t,s)\}_{t{\geq}s}$ on the phase space $P_{\tau}(X)$ of all ${\tau}$-periodic continuous X-valued functions. Some kind of variation-of-constants formula for the solution u of the equation $({\alpha}I-L)^nu=f$ will be given together with the conditions on $f{\in}P_{\tau}(X)$ for the existence of coefficients in the formula involving the monodromy operator $U(0,-{\tau})$. Also, examples of ODEs and PDEs are presented as its application.

• Journal of the Korean Ceramic Society
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• v.53 no.5
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• pp.535-540
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• 2016

Effects of compositions and sintering conditions on glaze properties are shown in the diagram constructed by using the unity molecular formula (UMF) method in this study. Glossy characteristics of glaze were clearly differentiated by compositional area in the diagram and sintering process. As alumina and silica contents were increased, texture of the glaze became rough and opaque, akin to having been devitrified or underfired. The correlation between glossiness and surface roughness was found to be non-linear and inversely proportionate. Crystalline phases formed in the glaze were also influenced by the compositional area. Due to the high concentration of CaO, anorthite and wollastonite were formed depending on the compositions. Hardness was increased with an increase of alumina and silica concentrations in the glaze.

• Proceedings of the Korea Information Processing Society Conference
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• 2010.11a
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• pp.295-298
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• 2010

Linear Temporal Logic synthesis 는 LTL formula 로 표현된 요구 사항으로부터 그것을 만족하는 시스템을 만들어낸다. 이러한 synthesis 과정은 2EXPTIME-complete 이 요구 되지만 GR formula 라는 특수한 형태를 사용함으로써 복잡도를 Polynomial 시간으로 줄일 수 있다. LTL synthesis 는 작업 공간, 로봇이 취하는 센서 정보와 액션의 종류, 상위 수준의 작업 명세를 입력으로 받아 GR formula 형태로 변환하고, 기대되는 작업이 실현 가능하다면 그것을 성취할 수 있는 오토마타를 생성해낸다. Synthesis 알고리즘을 구현한 LTLMoP 라는 도구를 이용하여 LTL synthesis 과정을 보이고 화성 행궁의 미아 찾기 로봇 작업 계획을 구현한다. 마지막으로 시뮬레이션 과정을 통해 기대하는 작업을 성공적으로 성취할 수 있음을 보인다.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.7
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• pp.1462-1470
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• 2003

According to the necessity about information security as well as the advance of IT system and the spread of the Internet, a variety of cryptography algorithms are being developed and put to practical use. In addition the technique about cryptography attack also is advanced, and the algorithms which are strong against its attack are being studied. If the linear transformation matrix in the block cipher algorithm such as Substitution Permutation Networks(SPN) produces the Maximum Distance Separable(MDS) code, it has strong characteristics against the differential attack and linear attack. In this paper, we propose a new algorithm which cm estimate that the linear transformation matrix produces the MDS code. The elements of input code of linear transformation matrix over GF$({2_n})$ can be interpreted as variables. One of variables is transformed as an algebraic formula with the other variables, with applying the formula to the matrix the variables are eliminated one by one. If the number of variables is 1 and the all of coefficient of variable is non zero, then the linear transformation matrix produces the MDS code. The proposed algorithm reduces the calculation time greatly by diminishing the number of multiply and reciprocal operation compared with the conventional algorithm which is designed to know whether the every square submatrix is nonsingular.