Differential properties of Feynman amplitudes.—I

This paper develops the differential properties of ruled surfaces in a form which is applicable to spatial kinematics. Derivations are presented for the three curvature parameters which define the local shape of a ruled surface. Related parameters are also developed which allow a physical representation of this shape as generated by a cylindric-cylindric crank. These curvature parameters are then used to define all the lines in the moving body which instantaneously generate speciality shaped trajectories. Such lines may be used in the synthesis of spatial motions in the same way that the points on the inflection circle and cubic of stationary curvature are used to synthesize planar motion. As an example of this application several special sets of lines are defined: the locus of all lines which for a general spatial motion instantaneously generate helicoids to the second order and the locus of lines generating right hyperboloids to the third order.

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Differential Properties of ${x\mapsto x^{2^{t}-1}}$

IEEE Transactions on Information Theory ◽

10.1109/tit.2011.2169129 ◽

2011 ◽

Vol 57 (12) ◽

pp. 8127-8137 ◽

Cited By ~ 20

Author(s):

Céline Blondeau ◽

Anne Canteaut ◽

Pascale Charpin

Keyword(s):

Differential Properties

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Differential Properties of Aspergillus niger Tannase Produced Under Solid-State and Submerged Fermentations

Applied Biochemistry and Biotechnology ◽

10.1007/s12010-011-9258-3 ◽

2011 ◽

Vol 165 (1) ◽

pp. 382-395 ◽

Cited By ~ 20

Author(s):

Jaqueline Renovato ◽

Gerardo Gutiérrez-Sánchez ◽

Luis V. Rodríguez-Durán ◽

Carl Bergman ◽

Raúl Rodríguez ◽

...

Keyword(s):

Solid State ◽

Aspergillus Niger ◽

Differential Properties

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On Motion of Robot End-Effector Using the Curvature Theory of Timelike Ruled Surfaces with Timelike Rulings

Mathematical Problems in Engineering ◽

10.1155/2008/362783 ◽

2008 ◽

Vol 2008 ◽

pp. 1-19 ◽

Cited By ~ 3

Author(s):

Cumali Ekici ◽

Yasin Ünlütürk ◽

Mustafa Dede ◽

B. S. Ryuh

Keyword(s):

Ruled Surface ◽

Ruled Surfaces ◽

End Effector ◽

Timelike Ruled Surface ◽

Curvature Theory ◽

Differential Properties

The trajectory of a robot end-effector is described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way, the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The curvature theory of a ruled surface generated by a line fixed in the end-effector referred to as the tool line is used for more accurate motion of a robot end-effector. In the present paper, we first defined tool trihedron in which tool line is contained for timelike ruled surface with timelike ruling, and transition relations among surface trihedron: tool trihedron, generator trihedron, natural trihedron, and Darboux vectors for each trihedron, were found. Then differential properties of robot end-effector's motion were obtained by using the curvature theory of timelike ruled surfaces with timelike ruling.

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Designing and Mapping Trimming Curves on Surfaces Using Orthogonal Projection

16th Design Automation Conference: Volume 1 — Computer Aided and Computational Design ◽

10.1115/detc1990-0029 ◽

1990 ◽

Author(s):

Joseph Pegna ◽

Franz-Erich Wolter

Keyword(s):

Differential Equation ◽

Orthogonal Projection ◽

Broad Class ◽

Design Tool ◽

Space Curve ◽

Computationally Efficient ◽

Curves On Surfaces ◽

Surface Representations ◽

Differential Properties ◽

Surface Curve

Abstract In the design and manufacturing of shell structures it is frequently necessary to construct trimming curves on surfaces. The novel method introduced in this paper was formulated to be coordinate independent and computationally efficient for a very general class of surfaces. Generality of the formulation is attained by solving a tensorial differential equation that is formulated in terms of local differential properties of the surface. In the method proposed here, a space curve is mapped onto the surface by tracing a surface curve whose points are connected to the space curve via surface normals. This surface curve is called to be an orthogonal projection of the space curve onto the surface. Tracing of the orthogonal projection is achieved by solving the aforementionned tensorial differential equation. For an implicitely represented surface, the differential equation is solved in three-space. For a parametric surface the tensorial differential equation is solved in the parametric space associated with the surface representation. This method has been tested on a broad class of examples including polynomials, splines, transcendental parametric and implicit surface representations. Orthogonal projection of a curve onto a surface was also developed in the context of surface blending. The orthogonal projection of a curve onto two surfaces to be blended provides not only a trimming curve design tool, but it was also used to construct smooth natural maps between trimming curves on different surfaces. This provides a coordinate and representation independent tool for constructing blend surfaces.

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