• 제목/요약/키워드: Tangent Curve

검색결과 107건 처리시간 0.021초

DOUBLE COVERS OF PLANE CURVES OF DEGREE SIX WITH ALMOST TOTAL FLEXES

  • Kim, Seon Jeong;Komeda, Jiryo
    • 대한수학회보
    • /
    • 제56권5호
    • /
    • pp.1159-1186
    • /
    • 2019
  • In this paper, we study plane curves of degree 6 with points whose multiplicities of the tangents are 5. We determine all the Weierstrass semigroups of ramification points on double covers of the plane curves when the genera of the covering curves are greater than 29 and the ramification points are on the points with multiplicity 5 of the tangent.

On Ruled Surfaces with a Sannia Frame in Euclidean 3-space

  • Senyurt, Suleyman;Eren, Kemal
    • Kyungpook Mathematical Journal
    • /
    • 제62권3호
    • /
    • pp.509-531
    • /
    • 2022
  • In this paper we define a new family of ruled surfaces using an othonormal Sannia frame defined on a base consisting of the striction curve of the tangent, the principal normal, the binormal and the Darboux ruled surface. We examine characterizations of these surfaces by first and second fundamental forms, and mean and Gaussian curvatures. Based on these characterizations, we provide conditions under which these ruled surfaces are developable and minimal. Finally, we present some examples and pictures of each of the corresponding ruled surfaces.

ON C-PARALLEL LEGENDRE AND MAGNETIC CURVES IN THREE DIMENSIONAL KENMOTSU MANIFOLDS

  • MAJHI, PRADIP;WOO, CHANGHWA;BISWAS, ABHIJIT
    • Journal of applied mathematics & informatics
    • /
    • 제40권3_4호
    • /
    • pp.587-601
    • /
    • 2022
  • We find the characterizations of the curvatures of Legendre curves and magnetic curves in Kenmotsu manifolds with C-parallel and C-proper mean curvature vector fields in the tangent and normal bundles. Finally, an illustrative example is presented.

THE FLOW-CURVATURE OF CURVES IN A GEOMETRIC SURFACE

  • Mircea Crasmareanu
    • 대한수학회논문집
    • /
    • 제38권4호
    • /
    • pp.1261-1269
    • /
    • 2023
  • For a fixed parametrization of a curve in an orientable two-dimensional Riemannian manifold, we introduce and investigate a new frame and curvature function. Due to the way of defining this new frame as being the time-dependent rotation in the tangent plane of the standard Frenet frame, both these new tools are called flow.

2차원 벡터 필드의 효율적인 가시화 방법 (An Efficient Visualization Method of Two-Dimensional Vector Fields)

  • 정일홍
    • 한국멀티미디어학회논문지
    • /
    • 제12권11호
    • /
    • pp.1623-1628
    • /
    • 2009
  • 본 논문에서는 2차원 벡터 필드의 탄젠트 곡선을 계산하는 효율적이고 정확한 방법을 제안한다. 탄젠트 곡선 상의 정확한 값을 구하지 못하고 단지 탄젠트 곡선의 근사치를 구하는 Runge-Kutta 같은 종래의 방법과는 달리 여기서 제안한 방법은 2D 삼각형에서 벡터 필드가 선형적으로 변한다는 가정 하에 탄젠트 곡선상의 정확한 값을 계산한다. 새로 제안한 방법은 벡터 필드가 2D 삼각형에서 선형적으로 변한다고 가정한다. 우선 이 방법은 2D에서 사각형 셀을 2개의 삼각형 셀로 분해하는 것을 요구한다. 임계점은 각 삼각형의 간단한 선형 시스템을 풀어서 간단하게 구할 수 있다. 이 방법은 이전 삼각형에서 계산된 탄젠트 곡선상의 점들을 기초로 다음 삼각형에서 탄젠트 곡선상의 계속적인 점들을 생성함으로써 출구 점을 구한다. 탄젠트 곡선상의 점들은 각 삼각형의 명시해에 의해서 계산되었기 때문에 새로운 방법은 2D 벡터 필드를 가시화하는데 정확한 위상을 마련한다.

  • PDF

3차원 벡터 필드의 위상 공간 분석 (The Phase Space Analysis of 3D Vector Fields)

  • 정일홍;김용수
    • 디지털콘텐츠학회 논문지
    • /
    • 제16권6호
    • /
    • pp.909-916
    • /
    • 2015
  • 본 논문에서는 위상 공간 분석을 통해 3D 벡터 필드를 표현하는 방법을 제안한다. 이 방법은 상미분 방정식과 벡터 필드 위상과의 연결에 기초를 두고 있다. 위상 공간 분석은 위상 공간 형태의 자율 방정식 시스템의 기하학적 보간법이 되어야 한다. 이 방정식 시스템의 모든 해는 공간에서의 곡선이 아니라 곡선을 따라가는 점의 움직임과 일치한다. 이러한 분석은 이 논문의 기반이다. 새로운 방법은 3차원 벡터필드에서 육면체 셀을 5 또는 6개의 사면체 셀로 분해하는 것을 요구한다. 임계점은 각 사면체의 간단한 선형 시스템을 풀어서 간단하게 구할 수 있다. 각 사면체의 일반해에 의해 그려지는 전체 곡선과 사면체의 한 면을 포함하는 평면과의 교차점을 계산함으로써 탄젠트 곡선은 구해진다.

표준압밀시험에 의한 점토의 초기탄성계수 산정 (The Estimation of Initial Elastic Modulus of Clay by Standard Consolidation Test)

  • 권병해;임성훈
    • 한국농공학회논문집
    • /
    • 제66권1호
    • /
    • pp.15-24
    • /
    • 2024
  • Unlike artificially created homogeneous materials, the process of calculating the elastic modulus of natural soil involves the possibility of errors. Because the stress-strain behavior of soil is nonlinear, the secant modulus of elasticity is often used based on 1/2 of the stress at failure. Since soil has the property of changing its elastic modulus depending on the confining pressure, numerical analysis models that analyze its behavior inevitably include complex elements. The hyperbolic model, which relatively accurately simulates the behavior immediately after loading in soft ground, assumes that the stress-strain curve of the consolidated undrained triaxial test is hyperbolic and requires the slope of the tangent line at the starting point. However, the slope of the initial tangent in the stress-strain curve obtained from an actual triaxial test is difficult to have regularity according to changes in confining pressure. Additionally, due to the characteristics of a hyperbola, even small changes in related factors cause large changes in the hyperbola. Therefore, there is a lot of randomness in the process of calculating model parameters from the triaxial test results, which causes large differences in the results. Therefore, the method of calculating the initial elastic modulus by the consolidation test presented in this study is also used to verify the method by the triaxial test. It can be applied. However, since this study was applied to only one sample showing typical consolidation characteristics, it is necessary to check samples with various physical properties in the future.

한국 젊은이의 안면미 선호경향에 관한 연구 : 얼굴의 측모평가를 중심으로 (A STUDY ON THE FACIAL ESTHETIC PREFERENCES AMONG KOREAN YOUTHS: ASSESSMENT OF PROFILE PREFERENCES)

  • 송세진;최익찬
    • 대한치과교정학회지
    • /
    • 제22권4호
    • /
    • pp.881-920
    • /
    • 1992
  • This study was designed to assess profile preferences among Korean youths in the year 1992. Facial esthetics was evaluated by means of silhouette profiles, eliminating the influence of a number of aspects that may affect judgment when normal lateral photographs are used. The main points of preference to be clarified here are as follows. First, on facial convexity, Second, on nasion depth, Third, on mentolabial sulcus depth, Fourth, on the position of upper and lower lips, Fifth, on facial type according to Angle's classification of malocclusion, Sixth, on Song's tangents. The 54 subjects printed in questionnaire as black and white silhouettes were selected from 300 tracings from cephalometric radiographs of people whose age ranging from 11 to 20 years. Photographs of six female subjects were retouched by computer graphic software and printed in color and black/white photographs which were used for adaptation of eyes of participants in selecting profiles in silhouette. They constitute 2 questions. The 54 subjects were grouped as 22 questions, each of them composed of 6 subjects, according to the aspects to be clarified. Twenty four questions in total were asked to assess profile preferences. For the assessment, the profile line, the facial esthetic triangle, Song's tangents, and Angle's classification of malocclusion were introduced. The profile line is composed of 11 component points which are Trichion, Glabella, Nasion, Pronasale, Subnasale, Labrale superius, Stomion, Labrale inferius, Supramentale, Pogonion, and Gnathion. The facial esthetic triangle is composed of 3 tangents: A-tangent which is the tangent of dorsum of nose, B-tangent which is the line passing through Sn and Ls, and C-tangent which is drawn on the turning point of the curve which lies between mentolabial sulcus (Sm) and pogonion (Pg). Angle's classification has 3 types of malocclusion which are Class I, Class II, and Class III. Class II malocclusion is subdivided into Division 1 and Division 2. The participants of the survey were composed of 861 college students (448 male students, 413 female students) whose majors grouped as Fine Arts. Liberal Arts, and Natural Sciences, and whose mean age 21.8 years. The statistics program SPSS/PC + of SPSS Inc. was used to analyze answers of participants. Crosstabulation, Chi-square test, and Kendall test were done. The conclusions are as follows: First, Korean youths have a tendency to prefer the slightly convex face to the flat or concave face. Second, they prefer a moderately deep nasion. Third, they prefer a moderately deep mentolabial sulcus. Fourth, they prefer the position of lips which are near to Ricketts' E-line. The position of the upper lip which is slightly posterior to E-line is preferred. The upper lip which lies too far anterior or posterior to the lower lip is not perferred. Fifth, they prefer most, according to Angle's Classification of Malocclusion, Class I facial profile which has a slight inclination to Class II division 2. The order of preference is Class I, Class II division 2, Class III, and Class II division 1. Sixth, they prefer the type 2 and 3 of Song's tangents. The facial profile within which A-and B-tangent meet is preferred. The facial profile which has Cotangent that .meets with A-tangent slightly posterior to the crossing point of A-and B-tangent or that parallels with B-tangent is preferred.

  • PDF

CENTROID OF TRIANGLES ASSOCIATED WITH A CURVE

  • Kim, Dong-Soo;Kim, Dong Seo
    • 대한수학회보
    • /
    • 제52권2호
    • /
    • pp.571-579
    • /
    • 2015
  • Archimedes showed that the area between a parabola and any chord AB on the parabola is four thirds of the area of triangle ${\Delta}ABP$, where P is the point on the parabola at which the tangent is parallel to the chord AB. Recently, this property of parabolas was proved to be a characteristic property of parabolas. With the aid of this characterization of parabolas, using centroid of triangles associated with a curve we present two conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be a parabola.