By Rafal Ablamowicz, P. Lounesto

This quantity is devoted to the reminiscence of Albert Crumeyrolle, who died on June 17, 1992. In organizing the quantity we gave precedence to: articles summarizing Crumeyrolle's personal paintings in differential geometry, basic relativity and spinors, articles which provide the reader an idea of the intensity and breadth of Crumeyrolle's study pursuits and impact within the box, articles of excessive medical caliber which might be of basic curiosity. In all of the components to which Crumeyrolle made major contribution - Clifford and external algebras, Weyl and natural spinors, spin buildings on manifolds, precept of triality, conformal geometry - there was enormous growth. Our desire is that the quantity conveys the originality of Crumeyrolle's personal paintings, the continued power of the sphere he motivated, and the iconic appreciate for, and tribute to, him and his accomplishments within the mathematical neighborhood. It isour excitement to thank Peter Morgan, Artibano Micali, Joseph Grifone, Marie Crumeyrolle and Kluwer educational Publishers for his or her assist in preparingthis quantity

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**Sample text**

By varying the constants Av, 1J = I, 2, ... , flows around various shapes can be obtained. On the other hand, it is often necessary to determine constants Av to yield a flow which approximates 4 S. Bergman: The approximation of function satisfying a linear partial differential equation. Journal, Vol. 6 (1940), pp. 537-561. 5 S. Bergman: Methods for determination and computation of flow patterns of a compressihle fluid. N. A. C. , T. N. No. 1018 (1946). 42 IV. Transonic Flow that about a prescribed boundary curve, the equation of which is, say, F (x, y) = o.

10) seems to be valid: T=[~ (l_h2 /'IAI '/'+ ... ]0) 30 III. 8), we have: 8=[! '/a[! (k+1)(k+l) + ... '/3+ ... 2. 5) a choice of parameters that leads to the asymptotic behavior of the physical gas for M = 1, i. 5) with !. For this value of (2. 3. 8) takes the different form: 2)-I. 12) 2 D (1 - L ( 2)-I. 13) D S-l (1 - 82 ( one gets: dL de = ! Suppose we fix y so that D = y6 = 0,606; this choice leads to curves that agree with the corresponding curves for a physical gas quite well for higher Mach numbers.

Sci. 6, 399-407 (1939). 26 II. Simplified Pressure-Density Relation ° obtain a better agreement between the hypothetical and the physical gas. :.. 5) 8'/(2~) y-l/~, (2 0)-1 y-l/~ 8'/(2~)-1~. de On the other hand, equation (1. 6) (section 1. 2) lead to ~~ = + 12- ~: = 0, and thus P )-'/2 q (drIe = (1 - 82 122 )'1" we h ave = 12 q-l 8. From the Bernoulli equation we have q ~~ d)' d)' dq dp S' . rIe o btam = --a;q rIe = - 8 q-2 de' mce M = 1 d)' M -2=_8(1_ 82 122)-1. 8), calculate M (12), i. , one of our desired relations between the variables of the gas.