Two Corollaries Of Holditch's Theorem For One-Parameter Closed Spatial Motions

One - Parameter Closed Dual Spherical Motions and Holditch ’ s Theorem

In this paper, for one-parameter closed dual spherical motions, we define the dual versions of the area vector of a given closed space curve, and the area projection of this curve in the direction of a given unit vector. The relationship between the above dual versions and the dual Steiner vector of the motion is used to give a generalization for Holditch’s theorem of planar kinematics into spa...

A limit theorem for one-parameter alteration of two knots of B-spline curves∗

Knot modification of B-spline curves is extensively studied in the past few years. Altering one knot value, curve points move on well-defined paths, the limit of which can be computed if the knot value tends to infinity. Symmetric alteration of two knot values can also be studied in a similar way. The extension of these limit theorems for general synchronized modification of two knots is discus...

A Spectral Mapping Theorem for Representations of One-parameter Groups

In this paper we present some generalization (at the same time a new and a short proof in the Banach algebra context) of the Weak Spectral Mapping Theorem (WSMT) for non-quasianalytic representations of oneparameter groups.

The uniqueness theorem for a two-parameter extended relative entropy

Shannon entropy [1] is one of fundamental quantities in classical information theory and uniquely determinded by the Shannon-Khinchin axiom or the Faddeev axiom. One-parameter extensions for Shannon entropy have been studied by many researchers. The Rényi entropy [2] and the Tsallis entropy [3] are famous. In the paper [4], the uniqueness theorem for the Tsallis entropy was proved. Also, in our...

Cauchy ’ s theorem , Cauchy ’ s formula , corollaries Paul