By Benz W.

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**Additional info for A Beckman-Quarles type theorem for finite desarguesian planes**

**Example text**

G(~) connections elastic materials Lie a l g e b r a a s s o c i a t e d to any r e f e r e n c e = {O}; f r o m T h e o r e m on such b o d i e s atlas II-3 we are c h a r a c - t e r i z e d by the c o n d i t i o n s Fj -i ~ jm ik = - ~ m (II-18) i -] where ~ = y -. It is a s i m p l e m a t t e r to c o m p u t e that R = 0 (the c u r v a t u r e (II-18)) t e n s o r b a s e d on the F symbols so that m a t e r i a l are b o t h u n i q u e w o r k of N o l l connections on s o l i d c r y s t a l b o d i e s and c o m p l e t e l y i n t e g r a b l e .

There is a vector-valued all points stress on CoB is given function t(x,n) x in St(C) and all unit vectors defined for n such that the acting on C is given by t(x; C) = t(x,n) where n is the exterior boundary unit normal of C in the configuration stress vector at x and the above stress principle at the point x on the ~t" We call t(x,n) concept the is known as the of Cauchy. , of moment 25 of momentum. If the momentum M(C) of C in the configuration ~t is given by / x dm then the principle of balance of ~t(C ) ~ momentum requires that f(C) = M(C) and implies, under suitable continuity conditions, the existence of a tensor field ~S such that t(~,n) = Ts(x)n for all xs~t(~C); the superposed dot above indicates, respect to time.

Material a c c o r d i n Z to w h i c h must ference esl} where relation characterizes The , K0r~), ~ = GO and the It can be if ~ is a r e f e r e n c e in this way by some to ~, w h i c h from the simple [ 7 ]) that isomorphisms isomorphisms relative on B are not unique. bodies (i) their d e f i n i n g satisfy and in c o n t i n u u m these c o n s t i t u t i v e e q u a t i o n s formulation mechanics was we give b e l o w Definition isomorphism 11-4 + B P [28], essentially, Let pEB, i: B (or isotropy) a simple is a m e m b e r q equations, frame-indif@roups which The first truly r i g o r o u s of the i s o t r o p y given by Noll are due, of m a t e r i a l admit.

### A Beckman-Quarles type theorem for finite desarguesian planes by Benz W.

by Ronald

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