• Title, Summary, Keyword: Hamiltonian reduction

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EXISTENCE OF SIX SOLUTIONS OF THE NONLINEAR HAMILTONIAN SYSTEM

  • Jung, Tack-Sun;Choi, Q-Heung
    • Honam Mathematical Journal
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    • v.30 no.3
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    • pp.443-468
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    • 2008
  • We give a theorem of existence of six nontrivial solutions of the nonlinear Hamiltonian system $\.{z}$ = $J(H_z(t,z))$. For the proof of the theorem we use the critical point theory induced from the limit relative category of the torus with three holes and the finite dimensional reduction method.

EQUIVARIANT MATRIX FACTORIZATIONS AND HAMILTONIAN REDUCTION

  • Arkhipov, Sergey;Kanstrup, Tina
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.5
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    • pp.1803-1825
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    • 2017
  • Let X be a smooth scheme with an action of an algebraic group G. We establish an equivalence of two categories related to the corresponding moment map ${\mu}:T^{\ast}X{\rightarrow}g^{\ast}$ - the derived category of G-equivariant coherent sheaves on the derived fiber ${\mu}^{-1}(0)$ and the derived category of G-equivariant matrix factorizations on $T^{\ast}X{\times}g$ with potential given by ${\mu}$.

Simulation Study on Search Strategies for the Reconnaissance Drone (정찰 드론의 탐색 경로에 대한 시뮬레이션 연구)

  • Choi, Min Woo;Cho, Namsuk
    • Journal of the Korea Society for Simulation
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    • v.28 no.1
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    • pp.23-39
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    • 2019
  • The use of drone-bots is demanded in times regarding the reduction of military force, the spread of the life-oriented thought, and the use of innovative technology in the defense through the fourth industrial revolution. Especially, the drone's surveillance and reconnaissance are expected to play a big role in the future battlefield. However, there are not many cases in which the concept of operation is studied scientifically. In this study, We propose search algorithms for reconnaissance drone through simulation analysis. In the simulation, the drone and target move linearly in continuous space, and the target is moving adopting the Random-walk concept to reflect the uncertainty of the battlefield. The research investigates the effectiveness of existing search methods such as Parallel and Spiral Search. We analyze the probabilistic analysis for detector radius and the speed on the detection probability. In particular, the new detection algorithms those can be used when an enemy moves toward a specific goal, PS (Probability Search) and HS (Hamiltonian Search), are introduced. The results of this study will have applicability on planning the path for the reconnaissance operations using drone-bots.

Luminescence and Crystal-Field Analysis of Europium and Terbium Complexes with Oxydiacetate and 1,10-Phenanthroline

  • Kang, Jun-Gill;Kim, Tack-Jin
    • Bulletin of the Korean Chemical Society
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    • v.26 no.7
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    • pp.1057-1064
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    • 2005
  • Photoluminescence (PL) spectra of Eu(III) and Tb(III) complexes with mixed oxydiacetate (ODA) and 1,10-phenanthroline (phen) ligands and with homoleptic ODA reveal characteristic line-splitting at 10 K, depending on the site-symmetry of the lanthanide ion in the complex. The energy-level schemes of the $^7F_J$ states and the emitting levels for Eu(III) and Tb(III) ions have been proposed by simulating the line splitting in the framework of crystal-field Hamiltonian. The sets of refined crystal-field parameters for the experimentally determined sitesymmetry satisfactorily reproduce the experimental energy-level schemes. In addition, the PL quantum yield and the decay time were determined at room temperature. The PL quantum yields of [$Eu(ODA){\cdot}(phen){\cdot}4H_2O]^+$ and [Tb$(ODA){\cdot}(phen){\cdot}4H_2O]^+$ in the crystalline state (Q = 17.7 and Q = 56.6%, respectively) are much greater than those of [Eu($ODA)_3]^{3-}and\;[Tb(ODA)_3]^{3-}$(Q = 1.1 and Q = 1.3, respectively), due to the energy transfer from phen to the lanthanide ion. In the aqueous state, the relaxation of the phen moiety due to the solvent results in the reduction of the quantum yield and the shortening of the lifetime.

Travelling Salesman Problem Based on Area Division and Connection Method (외판원 문제의 지역 분할-연결 기법)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.15 no.3
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    • pp.211-218
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    • 2015
  • This paper introduces a 'divide-and-conquer' algorithm to the travelling salesman problem (TSP). Top 10n are selected beforehand from a pool of n(n-1) data which are sorted in the ascending order of each vertex's distance. The proposed algorithm then firstly selects partial paths that are interconnected with the shortest distance $r_1=d\{v_i,v_j\}$ of each vertex $v_i$ and assigns them as individual regions. For $r_2$, it connects all inter-vertex edges within the region and inter-region edges are connected in accordance with the connection rule. Finally for $r_3$, it connects only inter-region edges until one whole Hamiltonian cycle is constructed. When tested on TSP-1(n=26) and TSP-2(n=42) of real cities and on a randomly constructed TSP-3(n=50) of the Euclidean plane, the algorithm has obtained optimal solutions for the first two and an improved one from that of Valenzuela and Jones for the third. In contrast to the brute-force search algorithm which runs in n!, the proposed algorithm runs at most 10n times, with the time complexity of $O(n^2)$.