• 제목/요약/키워드: second fundamental form

검색결과 145건 처리시간 0.024초

ROTATIONAL HYPERSURFACES CONSTRUCTED BY DOUBLE ROTATION IN FIVE DIMENSIONAL EUCLIDEAN SPACE 𝔼5

  • Erhan Guler
    • 호남수학학술지
    • /
    • 제45권4호
    • /
    • pp.585-597
    • /
    • 2023
  • We introduce the rotational hypersurface x = x(u, v, s, t) constructed by double rotation in five dimensional Euclidean space 𝔼5. We reveal the first and the second fundamental form matrices, Gauss map, shape operator matrix of x. Additionally, defining the i-th curvatures of any hypersurface via Cayley-Hamilton theorem, we compute the curvatures of the rotational hypersurface x. We give some relations of the mean and Gauss-Kronecker curvatures of x. In addition, we reveal Δx=𝓐x, where 𝓐 is the 5 × 5 matrix in 𝔼5.

COMPLETE NONCOMPACT SUBMANIFOLDS OF MANIFOLDS WITH NEGATIVE CURVATURE

  • Ya Gao;Yanling Gao;Jing Mao;Zhiqi Xie
    • 대한수학회지
    • /
    • 제61권1호
    • /
    • pp.183-205
    • /
    • 2024
  • In this paper, for an m-dimensional (m ≥ 5) complete non-compact submanifold M immersed in an n-dimensional (n ≥ 6) simply connected Riemannian manifold N with negative sectional curvature, under suitable constraints on the squared norm of the second fundamental form of M, the norm of its weighted mean curvature vector |Hf| and the weighted real-valued function f, we can obtain: • several one-end theorems for M; • two Liouville theorems for harmonic maps from M to complete Riemannian manifolds with nonpositive sectional curvature.

Spectral Computed Tomography: Fundamental Principles and Recent Developments

  • Aaron So;Savvas Nicolaou
    • Korean Journal of Radiology
    • /
    • 제22권1호
    • /
    • pp.86-96
    • /
    • 2021
  • CT is a diagnostic tool with many clinical applications. The CT voxel intensity is related to the magnitude of X-ray attenuation, which is not unique to a given material. Substances with different chemical compositions can be represented by similar voxel intensities, making the classification of different tissue types challenging. Compared to the conventional single-energy CT, spectral CT is an emerging technology offering superior material differentiation, which is achieved using the energy dependence of X-ray attenuation in any material. A specific form of spectral CT is dual-energy imaging, in which an additional X-ray attenuation measurement is obtained at a second X-ray energy. Dual-energy CT has been implemented in clinical settings with great success. This paper reviews the theoretical basis and practical implementation of spectral/dual-energy CT.

학령기 여아의 상반신 체형특성-체형구성인자를 중심으로- (Somatometric Characteristics on Upper Body of Elementary School Girls -Focusing somatometric factors-)

  • 장정아;배은아;권영숙
    • 한국의류학회지
    • /
    • 제24권6호
    • /
    • pp.850-860
    • /
    • 2000
  • The purposes of this study was to provide the fundamental data for children's wear standardizing sizes of ready-made clothes by analyzing the elementary school girls’somatotype. The subjects for anthropometic measurements were 434 elementary school girls’by age groups < ‘(1st age(1ㆍ2 grade)’,‘2nd age(3ㆍ4 grade)’, and 3rd(5ㆍ6 grade)’ > living in Pusan. According to the analysis of upper bodies by the age groups 1. According to the analysis to draw somatometric factors by the age groups, sevenㆍseven and six actors in 1st . End and 3rd age groups are obtained from measurements of upper body. 2. The 1st & 2nd age groups: As the result of factor analysis for the factor, the first and second factors which explain more than 70% of the whole variance represent“horizontal size”and“vertical size”, which characterize more aspects of the body shape of girls at elementary school ages. 3. The 3rd age groups: As the result of factor analysis for the factor, 6 factor which explain 74.39% of variance were extracted form anthropometic data. The first factor represented the items of circumference, breadth and depth related to“sectional size the front length of the upper body”, The second factor described the items of "heights & the back length of the upper body”.

  • PDF

Vector form intrinsic finite-element analysis of static and dynamic behavior of deep-sea flexible pipe

  • Wu, Han;Zeng, Xiaohui;Xiao, Jianyu;Yu, Yang;Dai, Xin;Yu, Jianxing
    • International Journal of Naval Architecture and Ocean Engineering
    • /
    • 제12권1호
    • /
    • pp.376-386
    • /
    • 2020
  • The aim of this study was to develop a new efficient strategy that uses the Vector form Intrinsic Finite-element (VFIFE) method to conduct the static and dynamic analyses of marine pipes. Nonlinear problems, such as large displacement, small strain, and contact and collision, can be analyzed using a unified calculation process in the VFIFE method according to the fundamental theories of point value description, path element, and reverse motion. This method enables analysis without the need to integrate the stiffness matrix of the structure, because only motion equations of particles established according to Newton's second law are required. These characteristics of the VFIFE facilitate the modeling and computation efficiencies in analyzing the nonlinear dynamic problem of flexible pipe with large deflections. In this study, a three-dimensional (3-D) dynamical model based on 3-D beam element was established according to the VFIFE method. The deep-sea flexible pipe was described by a set of spatial mass particles linked by 3-D beam element. The motion and configuration of the pipe are determined by these spatial particles. Based on this model, a simulation procedure to predict the 3-D dynamical behavior of flexible pipe was developed and verified. It was found that the spatial configuration and static internal force of the mining pipe can be obtained by calculating the stationary state of pipe motion. Using this simulation procedure, an analysis was conducted on the static and dynamic behaviors of the flexible mining pipe based on a 1000-m sea trial system. The results of the analysis proved that the VFIFE method can be efficiently applied to the static and dynamic analyses of marine pipes.

奚琴의 音響學的 特性 (The Acoustical Characteristics of the Hae-keum)

  • 임무열;윤화중
    • 한국음향학회지
    • /
    • 제9권3호
    • /
    • pp.11-23
    • /
    • 1990
  • 奚琴 音質의 音響學的 特性을 조사하기 위해 奚琴音의 파워스펙트럼과 時間波形을 FFT Analyzer를 이용하여 분석하였다. 奚琴絃의 張力과 遠山(bridge)의 위치, 腹板(top plate)의 두께등을 변화시키면서 분석을 하였다. 실험에 의하여 다음과 같은 결론을 얻었다. 腹板의 共振周波數가 絃의 基音의 周波數보다 높기 때문에, 基音의 音壓보다 腹板의 共振周波數 부근의 上音들의 音壓이 더 큼을 알았다. 絃의 張力이 강할 때와 遠山이 腹板의 중앙에 위치하였을 때가 音質이 보다 우수하였다. 奚琴 遊絃의 inharmonicity 계수는 0.049 cents/$n^2$이었다. 5kHz 이상의 上音은 발견할 수 없었으며, 奚琴의 inharmonicity가 violin의 inharmonicity보다 큰 값을 나타내었는데 이를 통해 奚琴음의 明瞭度와 豊富性이 부족하다는 것을 알 수 있었다. 奚琴筒의 共振周波數(MAR)와 腹板의 共振周波數(MWR)의 周波數比는 1 octave 정도일 때 奚琴이 가장 좋은 음색을 갖는다는 것을 밝혔으며 이때 腹板의 두께는 4.5mm 정도이다.

  • PDF

주파수 체배기를 이용한 K-Band용 Hair-pin 발진기 (A K-band Hair-pin Oscillator Using a Frequency Doubler)

  • 현안선;김훈석;김종헌;이종철;김남영;정원채;홍의석
    • 한국전자파학회논문지
    • /
    • 제9권6호
    • /
    • pp.833-842
    • /
    • 1998
  • 본 논문에서는 hair-pin 공진기, GaAs MESFET, 그리고 주파수 체배기로 구성된 K-Band용 발진기가 제안 되며, 하이브리드 초고주파 집적회로(HMIC) 형태로 제작되고 그 마이크로파 동작 특성이 발표된다. $\lambda_g$/4 개방 스터브가 벼ir-pin 공진 발진기의 출력인 9GHz의 기본 주파수를 억제하기 위해 주파수 체배기에서 사 용되며I 출력 정합 회로가 2차 고조파 주파수인 18 GHz에서 최적화된다. 제안된 발진기는 -083dBm의 출력, -23 dBc의 기본 주파수 억압, 그리고 18.2 GHz에서 -86 dBc/Hz의 위상 잡음을 갖는다

  • PDF

Topology and geometry optimization of different types of domes using ECBO

  • Kaveh, A.;Rezaei, M.
    • Advances in Computational Design
    • /
    • 제1권1호
    • /
    • pp.1-25
    • /
    • 2016
  • Domes are architectural and elegant structures which cover a vast area with no interrupting columns in the middle, and with suitable shapes can be also economical. Domes are built in a wide variety of forms and specialized terms are available to describe them. According to their form, domes are given special names such as network, lamella, Schwedler, ribbed, and geodesic domes. In this paper, an optimum topology design algorithm is performed using the enhanced colliding bodies optimization (ECBO) method. The network, lamella, ribbed and Schwedler domes are studied to determine the optimum number of rings, the optimum height of crown and tubular sections of these domes. The minimum volume of each dome is taken as the objective function. A simple procedure is defined to determine the dome structures configurations. This procedure includes calculating the joint coordinates and element constructions. The design constraints are implemented according to the provision of LRFD-AISC (Load and Resistance Factor Design-American Institute of Steel Constitution). The wind loading act on domes according to ASCE 7-05 (American Society of Civil Engineers). This paper will explore the efficiency of various type of domes and compare them at the first stage to investigate the performance of these domes under different kind of loading. At the second stage the wind load on optimum design of domes are investigated for Schwedler dome. Optimization process is performed via ECBO algorithm to demonstrate the effectiveness and robustness of the ECBO in creating optimal design for domes.

현대패션에 나타난 픽셀의 표현 경향과 특성 (Expression Trend and Characteristics of Pixel in Contemporary Fashion)

  • 김선영
    • 한국생활과학회지
    • /
    • 제24권3호
    • /
    • pp.407-421
    • /
    • 2015
  • This study examined the pixel's expression trend and nature featured in contemporary fashion, which works as a basic unit symbolizing the digital image, paying attention to its formativeness. The work through this process aimed at suggesting an opportunity for recognition about pixel image utilized as a formative component beyond its simple meaning of unit and providing the fundamental materials for usage in creative fashion design reflecting the digital emotion in the future, In research method, literature review was followed on pixel and the empirical study about its image was also performed that was found in the modern fashion. As a result, the trend in pixel has these characteristics. Its first nature lies in its plane expression. It was printed as mosaic or graphic grid image or expressed through patchwork technique. Also, rather than a certain form or figure, its unique image was emphasized according to the applied color, size, and position. Second, a stepwise pattern in pixel was applied to external format for part of clothing, eye glass and necktie, indicating some interest and wit. Third, in application to plane and external shape, the graphically modernized effect was realized, not to mention the illusive image with cubic expression. As shown, the characteristics in contemporary fashion via pixel expression were given in fantastic image, optical humor, and reflection of digital value.

HYPERSURFACES IN THE UNIT SPHERE WITH SOME CURVATURE CONDITIONS

  • Park, Joon-Sang
    • 대한수학회논문집
    • /
    • 제9권3호
    • /
    • pp.641-648
    • /
    • 1994
  • Let M be a minimally immersed closed hypersurface in $S^{n+1}$, II the second fundamental form and $S = \Vert II \Vert^2$. It is well known that if $0 \leq S \leq n$, then $S \equiv 0$ or $S \equiv n$ and totally geodesic hypersheres and Clifford tori are the only possible minimal hypersurfaces with $S \equiv 0$ or $S \equiv n$ ([6], [2]). From these results, Chern suggested some questions on the study of compact minimal hypersurfaces on the sphere with S =constant: what are the next possible values of S to n, and does in the ambient sphere\ulcorner By the way, S is defined extrinsically but, in fact, it is an intrinsic invariant for the minimal hypersurface, i.e., S = n(n-1) - R, where R is the scalar, curvature of M. Some partial answers have been obtained for dim M = 3: Assuming $M^3 \subset S^4$ is closed and minimal with S =constant, de Almeida and Brito [1] proved that if $R \geq 0$ (or equivalently $S \leq 6$), then S = 0, 3 or 6, Peng and Terng ([5]) proved that if M has 3 distint principal curvatures, then S = 6, and in [3] Chang showed that if there exists a point which has two distinct principal curvatures, then S = 3. Hence the problem for dim M = 3 is completely done. For higher dimensional cases, not much has been known and these problems seem to be very hard without imposing some more conditions on M.

  • PDF