scholarly journals On extension of functions, being integrable with weight on interval and satisfying conditions of Lipschitz type

2016 ◽  
Vol 24 ◽  
pp. 23
Author(s):  
S.V. Goncharov
Keyword(s):  
Extension Of Functions ◽  
Differential Properties

We show the method to expand functions being integrable with a weight on the interval, and satisfying conditions of integral Lipschitz type, on the whole line. We prove that the differential properties of such functions are kept at the expansion.

scholarly journals Proposals on calculating the differential properties of concrete

2021 ◽  
Vol 1083 (1) ◽  
pp. 012009
Author(s):  
L R Mailyan ◽  
S A Stel‘makh ◽  
E M Shcherban‘ ◽  
A P Korobkin ◽  
E A Efimenko
Keyword(s):  
Differential Properties

The Curvature Theory of Line Trajectories in Spatial Kinematics

1981 ◽  
Vol 103 (4) ◽  
pp. 718-724 ◽  
Author(s):  
J. M. McCarthy ◽  
B. Roth
Keyword(s):  
Planar Motion ◽  
Spatial Motion ◽  
Third Order ◽  
Local Shape ◽  
The Third ◽  
Moving Body ◽  
Physical Representation ◽  
Curvature Theory ◽  
Spatial Kinematics ◽  
Differential Properties

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.

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

2011 ◽  
Vol 57 (12) ◽  
pp. 8127-8137 ◽  
Author(s):  
Céline Blondeau ◽  
Anne Canteaut ◽  
Pascale Charpin
Keyword(s):  
Differential Properties

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

2011 ◽  
Vol 165 (1) ◽  
pp. 382-395 ◽  
Author(s):  
Jaqueline Renovato ◽  
Gerardo Gutiérrez-Sánchez ◽  
Luis V. Rodríguez-Durán ◽  
Carl Bergman ◽  
Raúl Rodríguez ◽  
...  
Keyword(s):  
Solid State ◽  
Aspergillus Niger ◽  
Differential Properties

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

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
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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