• Title/Summary/Keyword: minimal surface

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A CHARACTERIZATION OF MAXIMAL SURFACES IN TERMS OF THE GEODESIC CURVATURES

  • Eunjoo Lee
    • Journal of the Chungcheong Mathematical Society
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    • v.37 no.2
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    • pp.67-74
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    • 2024
  • Maximal surfaces have a prominent place in the field of differential geometry, captivating researchers with their intriguing properties. Bearing a direct analogy to the minimal surfaces in Euclidean space, investigating both their similarities and differences has long been an important issue. This paper is aimed to give a local characterization of maximal surfaces in 𝕃3 in terms of their geodesic curvatures, which is analogous to the minimal surface case presented in [8]. We present a classification of the maximal surfaces under some simple condition on the geodesic curvatures of the parameter curves in the line of curvature coordinates.

Synthesis and Surface Activity of New Quaternary Ammonium Salts Prepared from 2-Chloromethyl-5-(2-Phenylthiazol-4-yl)-1,3,4-Oxadiazole (2-클로로메틸-5-(2-Phenylthiazol-4-yl)-1,3,4-옥사디아졸의 새로운 4급 암모늄염의 합성과 계면활성도)

  • Bae, Sun Kun;Yeon, Young Heum
    • Applied Chemistry for Engineering
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    • v.17 no.3
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    • pp.286-290
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    • 2006
  • New quaternary ammonium chlorides, [alkyldimethyl-[5-(2-phenylthiazol-4-yl]-1,3,4-oxadizol-2-ylmethyl]quaternary ammonium chlorides (ADOQACs): 6] were obtained with high yields by the reaction of compound 5 with N,N-dimethylalkyl amines in isopropyl alcohol. The structures and physical properties of the synthesized compounds were investigated and those surface-active properties were measured. The surface tension ($\gamma_{cmc}$) and the minimal inhibitory concentration (MIC) of compound 6 were found to be influenced by the number of alkyl chain carbon. Especially, compounds 6c and 6d exhibited high anti-bacterial activities and good surface-active properties.

Fabrication of an Ultralow Density Material Based on Wire-Weaving (와이어 직조에 기반한 극저밀도 재료의 제조법)

  • Choi, Jung Myung;Gang, Liu;Kang, Kiju
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.41 no.8
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    • pp.737-744
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    • 2017
  • A new ultralow density material (ULDM) named Shellular was recently introduced. Shellular has a periodic cellular structure with smooth-curved shells. The template for the first Shellular was fabricated using lithography and its shape was similar to the P-surface, a type of triply periodic minimal surface (TPMS). In this paper, a new fabrication method of Shellular with D-surface, named W-Shellular, is described. W-Shellular is fabricated based on weaving of polymer wires. The compressive properties are evaluated by experiments and analysis in comparison with the previous ULDMs.

Constructing Nonlinear Sliding Surface for Spacecraft Attitude Control Problems

  • Cheon, Yee-Jin
    • 제어로봇시스템학회:학술대회논문집
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    • 1999.10a
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    • pp.41-44
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    • 1999
  • Nonlinear sliding surface design in variable structure systems for spacecraft attitude control problems is studied. A robustness analysis is performed for regular form of system, and calculation of actuator bandwidth is presented by reviewing sliding surface dynamics. To achieve non-singular attitude description and minimal parameterization, spacecraft attitude control problems are considered based on modified Rodrigues parameters(MRP). It is shown that the derived controller ensures the sliding motion in pre-determined region irrespective of unmodeled effects and disturbances.

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Combined Percutaneous and Minimal on Internal Fixation of Calcaneal Fractures Using Extensile Lateral Approach (광범위 외측 도달법을 이용한 종골 골절의 경피적 및 최소 내고정술)

  • Yu, Sun-O;Kim, Joo-Sung;Kim, Jong-Jin
    • Journal of Korean Foot and Ankle Society
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    • v.6 no.2
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    • pp.201-207
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    • 2002
  • Purpose: To present the clinical analysis of the results obtained in 38 cases of displaced intraarticular calcaneal fractures undergone combined percutaneous axial pin fixation of calcaneal body and minimal internal fixation using extensile lateral approach. Materials and Methods: From March 2000 to February 2002, thirty-eight displaced intraarticular fractures of the calcaneus in 35 patients were fixed with 3.5mm cannulated screws and percutaneous 2.5mm K-wires. The extensile lateral approach was used in all cases. The average follow-up period was 16 months. Clinical evaluation was assessed according to the Ankle-Hind Foot Scale of American Orthopedic Foot and Ankle Society. Results: The clinical results were graded as excellent in 8 cases(21%), good in 22 cases(58%), fair in 6 cases(16%), and poor in 2 cases(5%). Two cases of poor result were type IV of Sanders classification. The postoperative reduction status of the articular surface was analyzed by computed tomography in all cases and was found to be less 2mm of step off in 30 cases and between 2 and 4mm in 8 cases. Unsatisfactory results were correlated with severity of articular comminution and failure to obtain accurate reduction of the articular surface. Using early functional postoperative care, all fractures healed without secondary displacement except 1 case on an average of ten weeks. Two cases had superficial necrosis of the wound margins, however, secondary wound healing was uneventful and skin grafting was not needed. Conclusion: Combined minimal internal fixation and percutaneous pin fixation using extensile lateral approach is useful operative method of intraarticular calcaneal fractures because providing enough stability to permit functional aftercare and allowing excellent anatomical reduction. In addition, this method diminishes the risk of lateral soft tissue problems.

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Effectiveness of Minimal Quantity Lubrication in Machining Processes

  • Suda, S.;Yokota, H.;Inasaki, I.;Wakabayashi, T.
    • Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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    • 2002.10b
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    • pp.309-310
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    • 2002
  • A minimal quantity lubrication (MQL) machining is able to achieve both functions of cooling and lubrication with an extremely low quantity of a cutting fluid and a large amount of air blow. Using a biodegradable ester oil, turning tests were carried out to evaluate the effectiveness of the MQL system. It was found that the performance of MQL cutting was equivalent to, or better than, that of conventional cutting, because the MQL system tends to prevent the heat damage of the tool tip and, if an effective lubricant such as a particular polyol ester is applied to the system, it can avoid the extensive transfer of workpiece materials on to the tool surface.

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Planar harmonic mappings and curvature estimates

  • Jun, Sook-Heui
    • Journal of the Korean Mathematical Society
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    • v.32 no.4
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    • pp.803-814
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    • 1995
  • Let $\Sigma$ be the class of all complex-valued, harmonic, orientation-preserving, univalent mappings defined on $\Delta = {z : $\mid$z$\mid$ > 1}$ that map $\infty$ to $\infty$.

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Microstructural Characteristics of Al-Cr Coated Zr Alloy Fabricated by Laser Surface Melting Process (레이저 표면 용융공정으로 Al-Cr 코팅한 Zr합금의 미세조직 특성)

  • Kim, Jeong-Min;Lee, Jae-Cheol;Kim, Il-Hyun;Kim, Hyun-Gil
    • Korean Journal of Materials Research
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    • v.27 no.10
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    • pp.563-568
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    • 2017
  • In this study, the coating of an Al-Cr layer on the surface of a Zircaloy-4 alloy was carried out through plasma pretreatment coating and a laser surface melting process. Two different conditions for laser treatment, severe or minimal surface melting of the Zr alloy substrate, were applied to form the final coating. When there was significant surface melting of the Zr alloy, the solidification microstructure of the newly formed coating layer was mainly composed of needle-shaped $Al_3Zr$, Al(Cr) and $Al_7Cr$ phases. On the other hand, the solidification microstructure of the coating layer was mainly composed of Al(Cr) and $Al_7Cr$ phases when there was minimal surface melting of Zr base in the laser process. However, when the coating was maintained at $1100^{\circ}C$ for 2 hours, significant inter-diffusion occurred between the phases in the coating. As a result, the upper part of the coating layer was observed to mainly consist of $Al_3Zr$ and $Al_8Cr_5$ phases, regardless of the laser treatment conditions.