Special curves

Noether s normalization lemma, 2-6 Non-degenerate curve, 11 -5 Non-special curve, 11 -6... 

According to the definition, if in a special point on the surface of c = c(x, t) for a reviewing special curve from that point, the slope of the projected curve on the x-t plane is equal with the quantity of the curve of that point, the passing direction of that point is known as the characteristic direction. We have in mathematical expression ... 

These equations for the special curves of the underlying space correspond exactly with the equations of chap. VI (33), that we obtained for the case M 0, therefore a four-dimensional associated space. Thereby we have found a geometrical meaning of the world hue of an electrical particle also in the five-dimensional associated spaces. 

Refractory bricks—the selection will depend on the service temperature in the furnace, the shape (special curved bricks are tailor made and cost more) and size and intended use as lining of surfaces or as arches for roofs or manholes with 45 or 65 %... 

Spines and rails control the shape of elementary surfaces. At the creation of a swept surface, a generator curve (Cg) is moved along a path curve (Cf. The normal of the plane of the generator curve is defined at each point along the path curve by the tangent of a control curve called a spine (Csp) (Figure 3-37e). The shape of surfaces can be controlled by curves outside of them. A special curve called a sculpt curve controls the shape... 

A special curve is obtained with the border line to the instability region, i.e., the spinodal curve, for which the second derivative in Equation [4.4.57] is equal to zero. If one applies again the one-parameter approach with an empirical %(T)-fimction, the following simple result can be derived ... 

Critical exponents indicate how fluid properties behave near a critical point. They arc defined by Sengers and Anisimov, these proceedings. By inspecting Fig. lb, one would guess that the simplest forms the special curves could take would be a parabola for the density or volume dilTerence along the coexistence curve, and a cubic for the pressure along the critical isotherm as function of volume or density ... 

A new type of mica with a special curved form develops in this BIOVERIT Il-type glass-ceramics (Fig. 3-15, see also Section 3.2.7). 

We will use a special curved bouncing arrow to show which carbon makes a bond to H. 

---