16-dimensional compact projective planes with a large group by Hahl H., Salzmann H.

By Hahl H., Salzmann H.

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CATIA V5 - Grundkurs für Maschinenbauer: Bauteil- und Baugruppenkonstruktion, Zeichnungsableitung

Dieses Lehrbuch enthält ein nahezu komplettes Übungsprogramm für eine CAD-Grundausbildung für Maschinenbauer in CATIA V5. Die Modellierung von Bauteilen und komplexen Baugruppen sowie die Zeichnungsableitung und -aufbereitung werden detailliert und einfach nachvollziehbar dargestellt. Auf eine verständliche, methodisch zweckmäßige Vorgehensweise wird besonderer Wert gelegt.

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Over Q with coefficients. of SU~ then involved of standard every last in v is s t a n d a r d . 9 COROLLARY If v e S ~ and the c o e f f i c i e n t s of the tabloids i n v o l v e d in v are all inte~ers~ then v is an i n t e g r a l linear combina- tion of s t a n d a r d p o l y t a b l o i d s . Proof: We may assume that v is non-zero. the < order) Let {t} be the last (in tabloid i n v o l v e d in v, with c o e f f i c i e n t aE Z, say. By the last corollary, {t} is standard. 3 shows that the {t}, so by i n d u c t i o n v - a e t is an i n t e g r a l linear c o m b i n a t i o n of s t a n d a r d p o l y t a b l o i d s .

And (ii)_CTl ~ 0 for some Proof: Part (i)T* = (j)T*. Since (i) S u p p o s e We wish that TI~ in the s a m e that CT, column of t, and = O. Kt(i,j ) =-Kt, T*(i,j) If c h a r sing tableau i # j are to p r o v e 7 c T T(i,j) Because semistandard = T*, it F = 2 and the o r d e r of = {t}K t 8(i,j) follows I is that CT, 2-regular, the n u m b e r s in e a c h = --E C T T = 0 when let ~ be row of c h a r F ~ 2. the p e r m u t a t i o n t. 5, appears Part tableau {t}

H-tableau (cf. the p r o o f of L e m m a and s u p p o s e If ~ ~ u , or if i = p and that t is a h - t a b l e a u {tl} is not i n v o l v e d and t I is in et, 50 then some column pair of numbers of t. 18 < e t 0 , { t I} involves > e t. COROLLARY This tabloids column > = sgn Thus Unless > . > = O. only to t h e ~-l,{t} > proves involved stabilizer 0 = 0 if I = ~. o f t, t h e n ~ < et@,{t} 0 is m u l t i p l i c a t i o n char F = 2 and that in e t w h e n > by and this shows that a constant.

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