of subsets of TM: Note that i) 8 (p;Xp) 2 TM , as p 2M ) there exists (U ; ) 2 S such that p 2 U ; i.e. (p;Xp) 2 TU , and we have TU =  1 (R) 2 : ii) If we de…ne F : TpM ! R by F (Xp) = (Xp(x); Xp(x); :::::; Xp(x)) where x; x; ::::; x are local coordinates on (U ; ), then clearly F is an isomorphism, so  (p; Xp) = ( (p); F ( Xp)); and  1 = ( 1 ; F 1 ): Now take  1 (U);  1 (V ) 2 and suppos...

A point P ∈ R is represented in Parallel Coordinates by a polygonal line P̄ (see [Ins99] for a recent survey). Earlier [Ins85], a surface σ was represented as the envelope of the polygonal lines representing it’s points. This is ambiguous in the sense that different surfaces can provide the same envelopes. Here the ambiguity is eliminated by considering the surface σ as the envelope of it’s tang...

This paper presents a new form of quartic equation based on Lagrange’s extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid. A very explicit and concise formulae of the quartic equation by Ferrari’s line is found, which avoids the need of a good starting guess for iterative methods. A new expli...

Multichannel tracking radars with phased antenna arrays are widely used to track air targets. The use of a array in combination digital computing technology allows control the radar radiation pattern and several targets time distribution mode. Air target multichannel is provided by subsystems for measuring range, radial velocity angular coordinates, most cases, without adaptation external influ...

We consider a system of differential equations the behavior of which solutions possesses several properties characteristic of the blood pressure distribution. The system can be used for a compartmental modeling [8, 15] of the cardiovascular system. It admits a unique bounded solution such that all coordinates of the solution are separated from zero by positive numbers, and which is periodic, ev...

Chromatography is a technique used to separate and quantify the components in a complex chemical mixture. We have created a 3D visualization system capable of comparing the chemical properties of chromatographic systems. The visualization system combines scatter plots, parallel coordinates, and specialized glyphs to assist in the analysis of chromatographic data and comparisons of multiple syst...

In this chapter we will study the differential structure of discrete images in detail. This is the structure described by the local multi-scale derivatives of the image. We start with the development of a toolkit for the definitions of heightlines, local coordinate systems and independence of our choice of coordinates. << FrontEndVision`FEV`; Off@General::spellD; Show@Import@"Spiral CT abdomen....