Powerful curves

TENSION QUARTIC TRIGONOMETRIC BÉZIER CURVES PRESERVING INTERPOLATION CURVES SHAPE

In this paper simple quartic trigonometric polynomial blending functions, with a tensionparameter, are presented. These type of functions are useful for constructing trigonometricB´ezier curves and surfaces, they can be applied to construct continuous shape preservinginterpolation spline curves with shape parameters. To better visualize objects and graphics atension parameter is included. In th...

The powerful placebo.

are not particularly noted for the pleasure which they give to their recipients. One meaning of the word dummy is a "counterfeit object." This seems to me the right word to describe a form of treatment which is intended to have no effect and I follow those who use it. A placebo is something which is intended to act through a psychological mechanism. It is an aid to therapeutic suggestion, but t...

How Powerful isUnconditional

We prove that every recursively enumerable language can be generated by a programmed grammar with context-free core rules using unconditional transfer with leftmost derivation of type 3 or type 2. We show that every recursively enumerable tally language can be generated by a programmed grammar with context-free core rules using unconditional transfer or by some k-limited ET0L system, where k 2 ...

Powerful Arithmetic Progressions

We give a complete characterization of so called powerful arithmetic progressions, i.e. of progressions whose kth term is a kth power for all k. We also prove that the length of any primitive arithmetic progression of powers can be bounded both by any term of the progression different from 0 and ±1, and by its common difference. In particular, such a progression can have only finite length.

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups