• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.209-224
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• 2006

This paper presents an optimization model with performance constraints for two kinds of graph elements layout problem. The layout problem is partitioned into finite subproblems by using graph theory and group theory, such that each subproblem overcomes its on-off nature about optimal variable. Furthermore each subproblem is relaxed and the continuity about optimal variable doesn't change. We construct a min-max problem which is locally equivalent to the relaxed subproblem and develop the first order necessary and sufficient conditions for the relaxed subproblem by virtue of the min-max problem and the theories of convex analysis and nonsmooth optimization. The global optimal solution can be obtained through the first order optimality conditions.

• Coupled systems mechanics
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• 제10권6호
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• pp.521-544
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• 2021

In this work, we present the development of a 3D lattice-type model at microscale based upon the Voronoi-cell representation of material microstructure. This model can capture the coupling between mechanic and electric fields with non-linear constitutive behavior for both. More precisely, for electric part we consider the ferroelectric constitutive behavior with the possibility of domain switching polarization, which can be handled in the same fashion as deformation theory of plasticity. For mechanics part, we introduce the constitutive model of plasticity with the Armstrong-Frederick kinematic hardening. This model is used to simulate a complete coupling of the chosen electric and mechanics behavior with a multiscale approach implemented within the same computational architecture.

• Smart Structures and Systems
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• 제20권1호
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• pp.99-114
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• 2017

In cognitive science, it is illustrated how the collective opinions of a group of individuals answers to questions involving quantity estimation. One example of this approach is introduced in this article as Star Graph (SG) algorithm. This graph describes the details of communication among individuals to share their information and make a new decision. A new labyrinthine network of neighbors is defined in the decision-making process of the algorithm. In order to prevent getting trapped in local optima, the neighboring networks are regenerated in each iteration of the algorithm. In this algorithm, the normal distribution is utilized for a group of agents with the best results (guidance group) to replace the existing infeasible solutions. Here, some new functions are introduced to provide a high convergence for the method. These functions not only increase the local and global search capabilities but also require less computational effort. Various benchmark functions and engineering problems are examined and the results are compared with those of some other algorithms to show the capability and performance of the presented method.

• Bulletin of the Korean Chemical Society
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• 제25권1호
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• pp.90-96
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• 2004

The conformations of dicyclopropyl, isopropyl cyclopropyl, and diisopropylcarbenes were optimized using density functional theory (B3LYP/6-31G(d)). We showed that the optimized geometries of carbenes with cyclopropyl groups are fully in accord with those expected for bisected W-shaped conformations, in which the effective hyperconjugation of a cyclopropyl group with singlet carbene can occur. The stabilization energies were evaluated at the B3LYP/6-311+G(3df, 2p)//B3LYP/6-31G(d) + ZPE level using an isodesmic equation. The relative stability of carbenes is in the order $(c-Pr)_2$C: > (i-Pr)(c-Pr)C: > $(i-Pr)_2$C:, and a cyclopropyl group stabilizes carbene more than an isopropyl group by nearly 9 kcal/mol. Energies for the decomposition of diazo compounds to carbenes increase in the order $(c-Pr)_2$ < (i-Pr)(c-Pr) < $(i-Pr)_2$ by ~9 kcal/mol each. From a singlettriplet energy gap ($E_{ST}$) calculation, the singlet level is lower than the triplet level and the $E_{ST}$ shows a trend similar to the stabilization energy calculations. For comparison, the optimized geometries and stabilization energies for the corresponding carbocations were also studied at the same level of calculation. The greater changes in geometries and the higher stabilization energies for carbocations compared to carbenes can explain the greater hyperconjugation effect.

• Bulletin of the Korean Chemical Society
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• 제30권2호
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• pp.423-428
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• 2009

The comparative study of three calix[4]heterocycles (calix[4]pyrrole, calix[4]furan, and calix[4]thiophene) has been theoretically performed by using high-level density functional theory (DFT) at the MPWB1K/6-311G$^{**}$//B3LYP/6- 311G$^{**}$ level. The effect of different hetero-atoms (nitrogen, oxygen, and sulfur) placed in the heterocycles on the conformational flexibility, thermodynamic stability order, cavity sizes, charge distributions, and binding propensities are examined. The thermodynamic stability differences between the conformers are found to be much greater in calix[4]pyrrole compared to those in calix[4]furan and calix[4]thiophene. Relatively larger NH group and higher dipole of a pyrrole ring in calix[4]pyrrole contribute to the higher energy barrier for the conformational conversions and relatively rigid potential energy surface compared to the case of calix[4]furan and calix[4]thiophene. The computational results herein provide theoretical understanding of the conformational flexibility and the thermodynamic nature which can be applied to understand the complexation behavior of the three calix[4]heterocycles.

• 한국IT서비스학회지
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• 제9권4호
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• pp.219-229
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• 2010

The Green's equivalence relations have played a fundamental role in the development of semigroup theory. They are concerned with mutual divisibility of various kinds, and all of them reduce to the universal equivalence in a group. Boolean matrices have been successfully used in various areas, and many researches have been performed on them. Studying Green's relations on a monoid of boolean matrices will reveal important characteristics about boolean matrices, which may be useful in diverse applications. Although there are known algorithms that can compute Green relations, most of them are concerned with finding one equivalence class in a specific Green's relation and only a few algorithms have been appeared quite recently to deal with the problem of finding the whole D or J equivalence relations on the monoid of all $n{\times}n$ Boolean matrices. However, their results are far from satisfaction since their computational complexity is exponential-their computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices and the size of the monoid of all $n{\times}n$ Boolean matrices grows exponentially as n increases. As an effort to reduce the execution time, this paper shows an isomorphism between the R relation and L relation on the monoid of all $n{\times}n$ Boolean matrices in terms of transposition. introduces theorems based on it discusses an improved algorithm for the J relation computation whose design reflects those theorems and gives its execution results.

• 대한환경공학회지
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• 제36권6호
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• pp.442-450
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• 2014

본 연구에서는 상수원에서 문제시 되고 있는 미량오염물질의 처리에 대한 연구를 하기 위해선 많은 시간과 비용이 소요되는데, 이를 절감하기 위한 대안으로 양자화학적 기반의 범밀도함수이론(Density Functional Theory, DFT)을 활용하여 물질간의 상호 반응성 및 분해과정을 해석하였다. 본 연구에서 다루고 있는 물질은, 최근 낙동강 수계에서 빈번히 검출되고 있는 Sulfonamide 물질 3종(sulfamethazine, sulfathiazole, sulfamethoxazol)을 선정하였으며, 이론적인 연구로는 DFT모델링, 실험적 연구로는 UV-VIS 및 FT-IR 등의 분광분석을 하여 비교 및 검증을 하였다. DFT모델링을 실시한 결과 Sulfonamide물질의 HOMO(highest occupied molecular orbital)와 오존의 LUMO (lowest unoccupied molecular orbital) 사이에서 반응이 가장 유리하며, Sulfonamide 물질의 HOMO를 가시화 한 결과 Sulfanilamide기에서 전자밀도가 높게 나타나므로 Sulfanilamide기에서 반응이 활발할 것이라 예측되었다. UV-VIS 실험결과 260 nm에서 Sulfanilamide기가 검출되었으며, 오존산화시 검출된 Sulfanilamide기가 빠르게 사라짐을 알 수 있었다. FT-IR분석결과로써 Sulfanilamide기에서도 그 한 부분인 아민기(N-H)에서 가장 활발한 제거반응이 일어남을 알 수 있었으며 이러한 결과로부터 DFT모델링 방법을 통해서 정수처리 공정에 대해서 반응을 예측할 수 있음을 확인하였다.

• Bulletin of the Korean Chemical Society
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• 제35권9호
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• pp.2673-2678
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• 2014

The detailed mechanisms of the efficient $\small{L}$-proline and pyrrolidine catalyzed transamidation of acetamide with benzylamine have been investigated using density functional theory (DFT) calculations. Our calculated results show: (1) the mechanisms of two catalytic cycle reactions are similar. However, the rate-determining steps of their reactions are different for the whole catalytic process. One is the intramolecular nucleophilic addition reaction of 1-COM, the other is hydrolysis reaction of 2-C. (2) COOH group of $\small{L}$-proline is essential for efficient transamidation. The computational results are in good agreement with the experiment finding and mechanism resported by Rao et al. for $\small{L}$-proline-catalyzed synthesis of amidesin good to excellent yields.

• Journal of applied mathematics & informatics
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• 제3권2호
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• pp.279-290
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• 1996

In the present paper we study the Cauchy problem in a Banach space E for an abstract nonlinear differential equation of form $$\frac{d^2u}{dt^2}=-A{\frac{du}{dt}}+B(t)u+f(t, W)$$ where W=($A_1$(t)u, A_2(t)u)..., A_{\nu}(t)u), A_{i}(t),\;i=1,2,...{\nu}$,(B(t), t{\in}I$=[0, b]) are families of closed operators defined on dense sets in E into E, f is a given abstract nonlinear function on $I{\times}E^{\nu}$ into E and -A is a closed linar operator defined on dense set in e into E which generates a semi-group. Further the existence and uniqueness of the solution of the considered Cauchy problem is studied for a wide class of the families ($A_{i}$(t), i =1.2...${\nu}$), (B(t), $t{\in}I$) An application and some properties are also given for the theory of partial diferential equations.

• International Journal of Control, Automation, and Systems
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• 제4권4호
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• pp.466-479
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• 2006

This paper addresses a formation navigation issue for a group of mobile robots passing through an environment with either static or moving obstacles meanwhile keeping a fixed formation shape. Based on Lyapunov function and graph theory, a NN formation control is proposed, which guarantees to maintain a formation if the formation pattern is $C^k,\;k\geq1$. In the process of navigation, the leader can generate a proper trajectory to lead formation and avoid moving obstacles according to the obtained information. An evolutionary computational technique using particle swarm optimization (PSO) is proposed for motion planning so that the formation is kept as $C^1$ function. The simulation results demonstrate that this algorithm is effective and the experimental studies validate the formation ability of the multiple mobile robots system.