Advanced Mathematical and Computational Tools in Metrology V by P. Ciarlini, M. G. Cox, E. Filipe, F. Pavese, D. Richter

By P. Ciarlini, M. G. Cox, E. Filipe, F. Pavese, D. Richter

A set of the revised contributions from the 5th workshop on complex mathematical and computational instruments in metrology, held in Caparica, Portugal, in may possibly of 2000. contains papers from certain curiosity teams in metrology software program and knowledge fusion. DLC: Mensuration--Congresses.

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Deg q δ = ÁÒ Ô ÖØ ÙÐ Ö¸ ÓÖ X = P ¸ Û Ú ÒÓ ÕÙ ÒØÙÑ ÓÖÖ Ø ÓÒ Ø ÖÑ׸ ÓÖ Ú × Ù× Ø Ö Ò ÔÖ × ÒØ Ø ÓÒ 2 c1 (TX ). δ deg q = c (T ) line 1 X Ö Ö ×ÓÒ×µ¸ Ò º ËÓ ´Û Ø ºÌ × =3 h2 = [pt] 3 h = h ∗ [pt] = q QH ∗ (P2 ) = Z[h, q]/(h3 − q). ÆÓØ Ø Ø Ø Ð ×× Ð ÔÖ × ÒØ Ø ÓÒ × H (P ) = Z[h]/h º ÁØ × Ò Ö Ð Ô ÒÓÑ ÒÓÒ Ø Ø ´ ÓÖ ÓÙÖ Ú Ö Ø × X µ Ø ÕÙ ÒØÙÑ Ó Ó¹ ÑÓÐÓ Ý Ö Ò QH (X) × Ò Ö Ø Ý Ø Ð ×× Ð Ò Ö ØÓÖ× ØÓ Ø Ö Û Ø Ø q ¹Ô Ö Ñ Ø Ö׸ Û Ø Ú ÖÝ Ð ×× Ð Ö Ð Ø ÓÒ Ö ÔÐ Ý q¹ ÓÖÑ Ö Ð Ø ÓÒ Û ÓÐ × Ò Ø ÕÙ ÒØÙÑ Ó ÓÑÓÐÓ Ýº ∗ 2 3 ∗ ¾º Ö ××Ñ ÒÒ Ò× Ä Ø X = Gr(k, n) = {Λ ⊂ C } Ø Ö ××Ñ ÒÒ Ò Ó k¹ÔÐ Ò × Ò n¹ Ñ Ò× ÓÒ Ð ×Ô º Ð ×× ÐÐݸ Ø × ÒÓÛÒ Ø Ø × Ò Ð Ò ÖÓÙÔ¸ k n H ∗ (X) = ⊕Zσλ , Û Ö Ø ×ÙÑ × ÓÚ Ö Ô ÖØ Ø ÓÒ× λ ⊂ ((n − k) ) Ò Ë Ù ÖØ ×Ù Ú Ö Ø × Ó X k σλ Xλ = {Λ | dim(Λ ∩ En−k+i−λi ) ≥ i}, Ö Ø Ð ×× × Ó ÉÍ ÆÌÍÅ ÇÀÇÅÇÄÇ ¾½ Û Ö E ⊂ · · · × ÓÑÔÐ Ø Ó ×Ù ×Ô × Ó C º Ì Ô ÖØ Ø ÓÒ× λ Ö Ò¹ Ø Û Ø Ø Ö ÓÙÒ Ö Ñ× Ó ÓÜ × × ØØ Ò Ò Ö Ø Ò Ð ((n − k) ) Û Ø n−k ÓÐÙÑÒ× Ò k ÖÓÛ׺ Ê ÐÐ Ø Ø dim(X) = k(n−k) Ò codim(X ) = |λ|¸ Ø ×ÙÑ Ó Ø Ô ÖØ× Ó λº Ò ÐÐݸ n 1 k λ µ = λ∨ 1 0 ÓØ ÖÛ × , Û Ö λ ÒÓØ × Ø × Ø Ó ÓÜ × Ò ((n − k) ) ÒÓØ Ò λ ´ÖÓØ Ø ½ ¼ Ö × ×Ó × ØÓ ÓÑ ÒÓØ Ö Ô ÖØ Ø ÓÒµº Ì × Ú × Ø ÈÓ Ò Ö Ù Ð ØÝ ÒÚÓÐÙØ ÓÒ ÓÒ Ø × Ø Ò Ü Ò Ø Ë Ù ÖØ Ð ×× ×º Ì ×ØÖÙ ØÙÖ ÓÒ×Ø ÒØ× ÓÖ ÑÙÐØ ÔÐ Ø ÓÒ Ò H (X) Ö ÐÐ Ä ØØÐ ÛÓÓ ¹ σλ ∪ σµ = ∨ Ê k Ö ×ÓÒ Ó ∗ ÒØ× σλ ∪ σµ = cνλµ σν .

K º Å Ô× ØÓ X Ö Ö ÕÙ Ö ØÓ ØÓÖ ÐÓ ÐÐÝ Ø ÖÓÙ ÓÒ Ó Ø U ³×º À Ö Ö ×ÓÑ ×ÙÖ Ü ÑÔÐ × [A /µ ]¸ Ø ÓÒ Ý (x , x ) → (−x , −x ) Ú × ÕÙ Ö ÓÒ Û Ø Z/2¹ÓÖ ÓÐ ÔÓ ÒØ Ø Ú ÖØ Ü Ø × ×ÑÓÓØ × ×Ø º P = U ∪ U ∪ U Ø ×Ø Ò Ö Ò ÓÔ Ò ÓÚ Ö Ò U ∼= A º ÆÓÛ ∼ ÓÚ Ö P Ý U ¸ U = A /µ ¸ Ò U ∼= A /µ ¸ Û Ö µ Ø× Ý (x , x ) → (−x , x )º Ï Ø P Û Ø Ò ÓÖ ÓÐ ×ØÖÙ ØÙÖ ÐÓÒ Ø Ð Ò Ø Ò Ò Øݺ ÁÒ Ø × Ü ÑÔÐ Ø Ö × Ö ÒØ ×Ø ×ØÖÙ ØÙÖ ÓÚ Ö Ø Ð Ò Ø Ò Ò ØÝ Ø Ò Ù×Ø P × B(Z/2)º ÇÒ ×Ø ×¸ ÔÓ ÒØ× Ú ×Ø Ð Þ Ö ÖÓÙÔ× ØØ ØÓ Ø Ñº Å ÒÝ ×Ø × ÓÑ ÖÓÑ ÑÓ ÙÐ ÔÖÓ Ð Ñ׸ ×Ù × M ¸ Û Ö ÔÓ ÒØ× ÓÖÖ ×ÔÓÒ ØÓ ×ÓÑÓÖÔ ×Ñ ØÓ ÔÓ ÒØ × Ø Ð ×× × Ó ÒÙ× g ÙÖÚ ×º Ì Ò Ø ×Ø Ð Þ Ö ÖÓÙÔ ØØ ÙØÓÑÓÖÔ ×Ñ ÖÓÙÔ Ó Ø ÓÖÖ ×ÔÓÒ Ò ÙÖÚ º ÖØ Ò ×Ø × ÐÐÓÛ Ò Ò Ø ÖÓÙÔ× × ×Ø Ð Þ Ö ÖÓÙÔ× ´ º º¸ GL (k)µº Ð Ò ¹ÅÙÑ ÓÖ ×Ø × Ö ×ØÖ Ø ØÓ Ò Ø ÖÓÙÔ× ´Û × ÖÓÙÔ × Ñ × ÑÙ×Ø ÙÒÖ Ñ × Û Ðи º º¸ Ò Ö Ø Ö ×Ø p ÒÓ α ¸ µ ¸ Ø ºµ Ì ×Ø × ÐÐ Ö Ø ×Ø Ð Þ Ö ÖÓÙÔ × ÒÓÒÚ ÖÝ Ò º n i=1 i i i i i i 1 k ni i 2 2 2 1 1 0 2 1 1 2 2 0 2 2 1 1 2 i 2 2 2 2 2 2 2 2 1 g n p p Ü ÑÔÐ ½º¾ º × Ö ÓÚ Ö ÔÓ Òغ Ì Ö Ö ØÛÓ ´ ×ÓÑÓÖÔ ×Ñ Ð ×× × Ó µ Z/2¹ Ö × ÓÚ Ö P º ÅÓÖ Ò Ö ÐÐݸ Z/2¹ Ö × ÓÚ Ö X Ö Ð ×× Ý H (X, Z/2)º Ö ×¸ Ð ×× Ý H (−, G )º Ì Ó ÓÑÓÐÓ Ð ÓÒ× Ö G ¹ Ò ÒØ ÖÔÖ Ø Ø ÓÒ Ó Br(X) × BG 1 2 et 2 m m 2 Br(X) → Het (X, Gm ).

0) Yn−1 ↑ (0) Z1 (0) → Z0 .

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