Three Near Points Method for Calculating Generalized Curvature and Torsion

Abstract

The aim of this paper is to establish a new method for calculating generalized curvature and generalized torsion. This method depends on at least three points infinitely close to the considered point. The established method is characterize from other methods by using only dot and cross product of vectors combined from this points, without any parameter that interacts in the defined curve by using some concepts of nonstandard analysis given by Robinson A. and axiomatized by Nelson E.

Benzyl Esters of Vegetable Oils as Processing Oil in Carbon Black–Filled SBR Compounding: Chemical Modification, Characterization, and Performance

“…The processing oil retards the onset of vulcanization by restraining the formation of cross-links between the macromolecular chains of rubber. 7 This is beneficial to the rubber-manufacturing process: There must be sufficient delay or scorch resistance to allow shaping, forming, and flow in the mold. In Table VI, it is also seen that the palm benzyl ester had the highest cure rate index and the lowest cure and scorch times.…”

“…5 The vegetable oils in rubber vulcanizates reinforced with carbon black tend to form an oil monolayer at the interfaces of carbon black and rubber, and this coupling action improves elasticity and reduces tan δ. 6,7 Various vegetable oils and petroleum-based oils have been applied in rubber compounds. Both castor and vegetable oil enhanced the physical and the mechanical properties relative to saturated paraffin oil.…”