• Title, Summary, Keyword: convex body

Search Result 66, Processing Time 0.044 seconds

MIXED VOLUMES OF A CONVEX BODY AND ITS POLAR DUAL

  • Chai, Y. D.;Lee, Young-Soo
    • Bulletin of the Korean Mathematical Society
    • /
    • v.36 no.4
    • /
    • pp.771-778
    • /
    • 1999
  • In this paper, we obtain some geometric inequalities for mixed volumes of a convex body and its polar dual. We also develop a lower bound of the product of quermassintegral of a convex body and its polar dual and give a lower bound for the product of the dual quermassintegral of any index of centrally symmetric convex body and that of its polar dual.

  • PDF

A NEW LOWER BOUND FOR THE VOLUME PRODUCT OF A CONVEX BODY WITH CONSTANT WIDTH AND POLAR DUAL OF ITS p-CENTROID BODY

  • Chai, Y.D.;Lee, Young-Soo
    • Honam Mathematical Journal
    • /
    • v.34 no.3
    • /
    • pp.403-408
    • /
    • 2012
  • In this paper, we prove that if K is a convex body in $E^n$ and $E_i$ and $E_o$ are inscribed ellipsoid and circumscribed ellipsoid of K respectively with ${\alpha}E_i=E_o$, then $\[({\alpha})^{\frac{n}{p}+1}\]^n{\omega}^2_n{\geq}V(K)V({\Gamma}^{\ast}_pK){\geq}\[(\frac{1}{\alpha})^{\frac{n}{p}+1}\]^n{\omega}^2_n$. Lutwak and Zhang[6] proved that if K is a convex body, ${\omega}^2_n=V(K)V({\Gamma}_pK)$ if and only if K is an ellipsoid. Our inequality provides very elementary proof for their result and this in turn gives a lower bound of the volume product for the sets of constant width.

Study of Convex Cyclone with Continuous Curve (연속적인 곡선으로 정의 되는 볼록한 형상의 사이클론에 대한 연구)

  • Heo, Kwang-Su;Seol, Seoung-Yun;Li, Zhen-Zhe
    • Proceedings of the KSME Conference
    • /
    • /
    • pp.2757-2762
    • /
    • 2007
  • A cyclone design concept named Convex cyclone was developed to reduce pressure losses. Contrary to conventional cylinder-on-con type cyclone, inner wall of Convex cyclone are defined with a continuous curve and it has convex shape body. The discontinuity of inner diameter variation rate of cylinder-on-con type cyclone cause additional pressure loss. Continuous wall of Convex cyclone prevent additional pressure loss. In order to verify Convex cyclone design concept, we make a comparative experiments between Stairmand HE and Convex cyclone. Experimental Convex cyclone designed based on Stairmand HE model, and inner wall are defined with circular arch. The experimental result clearly shows that Convex cyclone can achieve maximum 50% pressure loss reduction with a few percent of collection efficiency drop. In addition, the experimental results indicated the existence of optimum convexity, minimum pressure loss, of cyclone wall.

  • PDF

Assessment of Uterine Internal Temperature according to the Time of Convex Probe Injection using a Self-made Uterine Model Phantom (자체 제작한 자궁모형팬텀을 이용한 Convex probe 주사시간에 따른 자궁내부온도 평가)

  • Lee, Hyun-Kyung;Heo, Yeong-Cheol
    • Journal of the Korean Society of Radiology
    • /
    • v.13 no.6
    • /
    • pp.895-900
    • /
    • 2019
  • Ultrasound is known to be harmless to the human body and is widely used in obstetrics and gynecology to confirm the diagnosis and development status of fetus. Diagnosis Although long - term use of ultrasound may cause changes in body temperature, studies on the uterine temperature changes due to ultrasound have been lacking. The purpose of this study was to investigate the change of temperature according to ultrasonic scanning time using a self - produced uterine model phantom. Ultrasound equipment and a 4MHz convex probe were used to construct the uterine model phantom similar to the human uterus using acrylic and pig uterus, which are tissue equivalents. Three probe type thermometers were installed to measure the inside of the acrylic water tank, the uterus, and the atmospheric temperature. The temperature of the uterine phantom was ascertained by measuring the temperature of the subject for 6 hours, 361 times. In this study, the possibility of human body temperature elevation due to ultrasound could be confirmed and this study will be used as the basic data of ultrasonic heat absorption study.

Gait Planning of Quadruped Walking and Climbing Robot in Convex Corner Environment

  • Loc, Vo Gia;Kang, Tae-Hun;Song, Hyun-Sup;Choi, Hyouk-Ryeol
    • 제어로봇시스템학회:학술대회논문집
    • /
    • /
    • pp.314-319
    • /
    • 2005
  • When a robot navigates in the real environment, it frequently meets various environments that can be expressed by simple geometrical shapes such as fiat floor, uneven floor, floor with obstacles, slopes, concave or convex corners, etc. Among them, the convex corner composed of two plain surfaces is the most difficult one for the robot to negotiate. In this paper, we propose a gait planning algorithm to help the robot overcome the convex environment. The trajectory of the body is derived from the maximum distance between the edge boundary of the corner and the bottom of the robot when it travels in the convex environment. Additionally, we find the relation between kinematical structure of the robot and its ability of avoiding collision. The relation is realized by considering the workspace and the best posture of the robot in the convex structure. To provide necessary information for the algorithm, we use an IR sensor attached in the leg of the robot to perceive the convex environment. The validity of the gait planning algorithm is verified through simulations and the performance is demonstrated using a quadruped walking robot, called "MRWALLSPECT III"( Multifunctional Robot for WALL inSPECTion version 3).

  • PDF