Numero 049 - Rudi Mathematici
Transcript
Numero 049 - Rudi Mathematici
!" # $%& !"# & ' ' ( $ % ) # & * + * & " # $ % $ ' % & ) & !! & ( & * ' + / , ( ( "& 2 ( 6, 3( ) ! 7 . + ' ! ( 01 ' 8( ' ( ) 4 5 67 & ) 7 ' ( 8( ' ( ' ) ' " 1 9 !! :; ( & ) ( 9 & & * & ' ' & ' ' & ( ! ( ! & :; ' , < & !( ) & ' = ) & " & ' & ) 9 ! ( & , ' + ? & > ' ! > & ! ) - ! & & 9 ) ( ! = ( ) ( & !! ( ' ' %) ' &@ ! & ! & ) !! ! ( ) ' ( & 7 > 9 * ( ) ' ) : & # !! ( #( # $ ( # ' ! $ A( ) 9 ? ( ( # ? & * 3 B ( ! ! 6 K 2 C:; D ? 6 ' ( , 0 ' !! 5 /GH ' 6 8 : ' 0 82 & & & ( ( C1 ( E ( !! 4 ) & ' ) 9 ' %7 0 5L 8 & E 9 625 4F & ' !! 8 2 6$ & I 0 84 ' +J ( ? ! ) 4 ( ' L ' ( ' & ? & ' ' & , & ' = ) ( ) ! * & : ? + ( M ( ( ( & ) & ( 9 ( ? * ' H , ' * /NHH & 5 1 L & & ( ) & % ( *' # 5 & O % P M . ' ) F - & & H #( 1 ) ) () !! & ( ' & ' & 1 # ! B & ( 9) ) ' : & ! ! F % ! ( ' , ' ) & ' ! & ( ) &( ( ) !! ' . 9 ( ' ) & % ' ! ( * ) ( ) ) ( ' ( 9 ' ' & B & & 2 ' ( ! ' ') & ' # ' 9 6> . N D & Q 5 ( ( !! 2 & ) & 9 8 ( !! 0 ' 2 & 0 & ! 8 & ' ' D( ? #& L 6 & 2 & ' '( ( 6 8 H 4 ( . G 4 > $ ! & ) & : = 4 0 ( , ( ) 9 ' 5 &9 M $ ! ) ! +4 . ! ( 0 ' ' Q & D /H ( ( & + ! ( R *' ( R *' ' ! & R Q # * ( ) Q ( ( ' 1 & ) ( ' ( & ' ) # ( / / Q * Q ( & ) P & * # ( O , & ! & #( ' O & 1 & S 5 ( ' / ' $ . ' ) ' ! ! + ( ( O ' > ) ! ! # O A( ' ) ( & ( ) ! + 1 & ( O & #( *) 9 B&( 2/ U 4V2/ U/ 4V/H / *< F ) & ( ( & ' #R & ) 9 . ( O () O ( * ! 1 $ ' ( ' ( ' G ! & ! / ( &@ & ) # T & () R$ & &( ( & O 9 ' O ( * & & ' ( # ( ( ' ( O & ( ( ' 2 4 ' ( & ) & ) . ( = ! ) # ' ( ' BD O !! + B & ! & ) /N 4% ' ' 2 ( ' ) T ( ! & ' 5 ( ! B T ) O ) O # ( & ( & & @ !! ( ' O ' % ( &@ > ! O " & 49 ( ' ) ) = ( ' # T & ) #T 2 ) , ( ) & % ! ( / H 2 & #4 F & 5 ) ( ( ) & !! & O ' / ( ( 9 ' > ( #T 5 B ( & /N & # * 1 O ' ! > ' //% & ( & # & & # ! ( : ( ( ( ( ( B ) # ( ' ! & ) O P & * ' ! #( % ( ' $ ' ) 5 ! O > ( !! ( ( * = 9 ( ) = & ( ( // / ) B # O ' ) B ( ( F & ( & ' ( $ & ) () & : 2 ? 4 ( K & # ! ' ' & 5 WW 9 5 & ( * ! & ! & & ) ' 7 2 ( ( > ) / / 4 > * 5 ! & B I ( ! ! 9 ' ' & ( ) ' * +J G ! ( F R " F ( & ! ) ! & ' & + & & $ & ) ( % : # ! & & ' '( OM( ( E ( & % ) ( ( ( 9 ) / 9 5 5 & ( ( 5 2 ) & 4 ' = & & ' ( ! ! ? ! "#$ - & ( "%( + 2 ) & ) & & ( % & ) ' ' ( !! ( ) !! # ' & + & ( ) ' + & H 4 ( , = + & ( , 9 1 !! ( ( (& ! ' $ = & '9 " " ) $ ) % ! ' . ! # ! ) E ! # ' ( !! ( & & &'# ( # L & ( # & ( & % )))'( &( & & !! ) ' ( & EF (5 " ( > ! ( ' ( ' & *+ 2 ' , ' & 4 * ( ( - (( ( ( - . ( "" " # ) * # ( # ( ( ( ( ( ) * # ( ) "" " # " # ( ( - ( ( ) ( # ( " # *'+', / ( ( ( ( # ) " - ( ( " )/ # " ( ( ) " # 0 ( # ) N *'-',) * " # # # "" 1 + # ( # 2 ( ) " 345 6 745 8 "" # 5 ) ) , (( "" 2 , ) (( ( +9 "" ( "" 8: ( " ( : ( *. -', / 9 "" ( 8: * -', "" )* # 9 8: &9-8 + - ( ( " & # &'#0( (( ( ) F &( ) 5 + ( " ( ( & # " " & ( ! # * ( ( 7 # $ E $& & O & ' ( ') R ( ) #/ O ' ! 25 ( & ( ( ' 4 ; "" " (( < & I " - =, ( ( 5> ( @ ( (( ( ? -< ( ( ( " " " ( ( # ( ( " / ( " " B ( " # "" ) ( " - )* ( " " " ( ) " (( "" 65 " ( F " " " ( # 6?) " " ( " )@ ( ( " ) " ( ) " E5 ' O 2 4( ( ## # ( " ( A ) " ( =, ( - = 1 ) " ( " >) * " ( " ## ( " ? A ) # - " " " & ( +J4) " ) ," * 2= 1 !! ( & ( ( ) & & & # &'#1( 5 ) O ( ? / 5 ( . ) & & & ) # 2 ( ( ( ! ' & ( / ( & & & & 4 $ 2 , '" E & & # ' ( F ) 2 - ) 4 $ ) ( R 5 ? # # ' ( ? > E 2 ? & ) ' & 5 $ ! ( #& ! ! ! & " ))) F &( ' & ' ' &( ' 9 ; *& ( & & ' ( # # &'#3( ## 4 !! ( ) ! . ! & ( 2 & & 9 ' ( & !! ( ) ' & & ' $ ( ! 2, ( " 9 (( # ; ( - + " 9 -- " ( ( -- " ( ' ' ' & & 2 ( B ( 4 ! ( & ! & ) # ( ' ( # C & + ( # ) ' ( ' " ( ( + 2 & ( 4( + ( > & 2 ( 4 - ( 2 4 ( # ( ' D'C ( +( ! $ ) 9 2? & # " - ! ) F !! " ' ) 2> & ' & & '4 > I !! E4( ? # ( +J4 O & & # ) ( ) + !! & & 1 $ + // ) ( ( ( & 2 (( ( - ( + + ( (( " ( ))) ( ( ( - " ( - " 5 # " 8 5) . ( ( & 8 # EB E&E+ ) & ) & , ' ( 55 - (( )* $ + B : ( ( - # E E (( " " ') E ( ( " ) ( +J) ( &) ; - ) ( 3E ( # # # + # E )@ ( ( ( BE BE3 ( - E C ( ! ) ! ( (( & ( E E ( & " ( & ' + ( ( ( # # -- E # ( E ) # & ( ' & # E E E # ( %) E # E ( E E ( -- ) E ( / ) - ( ( I E ( ; ( # ( -" " & I +J " + F & +J " -- ( ( # ! I + ( 5) * 1 " & ( ' - ( ) / ( - " ( "" E -- E E E # ( -- ( E ( 8 " & ( @ - A $ " # ' $ & ( +J) I # - & ( E + ' ( 3E E7A ) ( ) ! 2 & 9 ' ( 5 ) ( ' 5 ? ! F &( ! ( " ! ( 9 ( " ; -- ( -- " # " " ' # ( ( (" # " ) ( # ( *( ( " " " + - # 7 - - " ( ( - ) ( " '@ ( - ( - 2 " ))) # " % ' F+ " ' ( - " - ) @ " F+ ( " ) ') ) A B ## ( ( # %' ( ( / - " ); ( - " # + ( )+ ( " ( ( " '@ - ( - # " ( " ( ) ( - A / # 0 '( ( ( " ))) ( " " ' ( - ( ( (( )B ( ( - ) ' ( ( # ) - + ( " " " -- ) ( ) ; & ( ) " # - ,G - ( " ) ( -" -- " # ( ' F+ ( ) " , ( - ( " ' ' " ) , ( -- # ( ( - 0 ( ( " A * - (( " @ "" ; ) ) @ ( " ) # ' " '))) ( "- ' ' ' C ( ' (( ' '&' ' '( - 'BB' ' ' - ' # # ( - " " ' ( ' ( " ( "" ( ( " ) ; " ( ' " ( ( ( ' # - ( ) * # - ' ( ( - 0 ## - (( ))) ))) ) ' ( - ( - ( ( ) ( ' ( 0 # ( ) ( ' ' " "" )+ '( " ( ( ( ( )@ - ( 'A & " ') ( ( '8 ( (( " 8' ( " - 8 ' / ( " ' 'C ( ( ) 'F - ## " (( (( ' " " ( ' %) (( " 8 ' ( # ( - # - - ( D) ' ( ( ( ( - " ( " ( "" - ' ' ( A& 'BB' ' ' ' B') ( " ( " - A 2 " ' B') ( ( ( ) # " ) ') - ) * ( F+ ( ))))' @ ( ( ( ' ' ' " ( ) ( ' ( ( ( - ( "" # - @ " ( ( " ( - ' ( "" " " & " # * ' ))) - (( ; ' - ( ') 2 ( - ' ( ( ))) ( - ' # - - %' 8 - (" ( - # ( # 0 (( " " ( "" ( ( '" ( ## ( ( " ') ' ) ( - " ( -# ( " B BB ) " " " (( # )') " " H # ( ( )* ( 8*( # ## ( ( ( " " -0 ( - # ) ) ( ( ' " ( ) ( " " ( ( "" - ( (" # ) D ( " - A& # # " " ) # ( " 'B @ '( ( ) EB ) 1 ( ' # ( ))) ? ' # ( ( ( - ## (( # " ) ( ( ( 0 ( ) + ) ( & ! " ( ( & () F ( 9 2 ) ( ) :I ( ' " 9 E 2 +4J - J ? ( %) 9 # ( " - I R # 5E:I) ( " ' ) 4 ' 3 ' & ' & ( ! ( - 69' ( - - !! ) & " 3 L ( ) " " & ( /K 0 -- ( & & ( * ( ( 6.7 () + ' /K ( + E ( " & ' ( ' G ! ) /K & & ' G I+ T ' ! +J 2 4 ) ( @ ( K: ) ( ( * ) ( ( - - ( $ ( 2 5 " ( - ) ' ) G ( ( O 3 / " " " ( " ; ( ' ( ( < # ') ( - = ) * ( ( - - ' ( - # ' -- ) * ( '( ( - - ( G # ( & ( ( " # ( ) ' 6: C /G " ' " = ( "" ( - - ( ) ( " # &)* ( G C (M ( ) ( ) ( ( - ' ( # ' ( - ( ( MC " < L( 5) " " % " :E< = % ' " " ' ## :) = <) ( ( 8 * ( ( 1 > :< = " ( - - )* ( % " "" ' ( - ( - - " # # / 9 ( ( - = L ( # / -( 4 & / ( # ( ( " ?) ; -- # ) 5 ( N ( - ( ( - - ' ( ( + # = " # ' ( - - ') ( = - 9: ( # ') ( ( : L" - "" ( ( " + + + + + + + + + + " 4 ( - ) ( 8 ) * ( ( - - ( " " ) ( ( (MM9: ) ( ) "" ( / - ( ( ( ( ( O ( ( ) ( L) + ( " "" ) ( : ) ( - ( - ' ( (( : M ( ) ( - " ( ( - ( - ) ( + ) / ( :EL ) + + ( " L # ( ' M9: :EL ( " ( "" ( ) ( (( 2 ( " # " 'Q' 5( & ) L ( ( Q ) P ( !! ! $ " " # AAAAA I. 2 ( # " ) ( R ( " & ' +4J ( - ( ( /H ( " " " " ) ) + (( " " O ( " - # ( - O&* " -- " ( ))) & ( " ( G 2 @ - " $ ( -- ( - ( * I ( ( H "" ( $ ( ( - ( $ ( ( ( ( ( . 7))) ( " ( ))) ( (( ( " ( ( " ( -- ( ( ( " ( ( ( ( ( " ( ## ( ))) -- ))) - ( ( " - - " $ ) - ( - ( ) @ " "" / " ( - - " " >: $ > ) +4J) ( $ # -- - ( ( " -( ( & ( ( 7 " " & ) F &( " & + ))) 7 $ 9 2 ! ! 1 ( ( + ) & ' ( ! 9 ( 2 ) ( ' ) 4 ( & 4 " & & ' ' ' B O ' & N848N ( ( " " 9B ) ) ( -- ( ) + & ) & ( ( ( & ! S # & T ) 1 ( ' ' ) T D ' & ) ( 4 !! O ( ' , ? ( 1 2 !( ( !! ( 4 L ( !! & 9 + 5 2 ( - ) 2 ( ! 4 ( 2 > T5 2+ #( R4 ' ( F &( /N L ' $ ( = ( & ( ) ( ' & C C " ( ( 4% 2 ! . ) ! O , ) 1 ( O 2 ! 4 " & ' ' " - " " ( ( 2 ' OM " & ) & ( ! ! & ! O ( ( )& ' )* *!*#*$*+*, 2 ' ! ! & ! 4 ( 9 2)* *)*)( )* *!*#( D ! ( & ) 9 . O 4 4( & - *( & 9 / $ " K H / N ) & & & 4( 4 / / / / K / !! O / /K /G /H K / K / & ) 2+.#))-+$ ( & ) & ( ( R 89: ( () & ' ( (( " ( ) # # A ! ( ! ! # = = M M & : , ? #% * ( A I $ ' ' $ ) ( 2 - " @ ( - / +4J + ( ( ' # ? :4>5Q<:>INL?I<QN?5) ( & ' // 2 O ' & F / * / (( + N ' . " / H & ! " 0 ) G ( " ( & 3 ! " (( # , ( - .# 2 ( (( ; ( " ) ( - ) " . . . " ( ( ( # . ( - :L @ ( :L ( " " " " < / " :L * 4 I. ( ( / 2 ( "" %%% ( " ( 5:4>5Q<:>INL?I<QN? ## ) " ( ( G R . ( ( " 5 5) 2 ( / 0 ' 4 /+0 /#0 2 ) ) "3 :4 "" ( +4J " " ( 5 5 :4 ( # :N # + )2 ( & & ' ! 4( ( ) / 0 " ( " ' ) ' ) ( "" ( ( " 4 ' " ) $ +!)$- 5#-!+ # ) ( 7 " # ' '( ( ( :4>5Q<:>INL?I<QN?) ' ) / 1)2!0 :IC # ( ( ( :4>5Q<:>INL?I<QN?5 ( (( ( ( ' ( :4U:I ( -- ) ))) 5 ( ) - ( ( ( ( ( ; # # ( # " $ ( 0 ) $ - 5 ( + & ( . ( " ( ) " ( ( ( $& ) ' & = > = $? 4 ( (( 5 9 " 1 = ( 2 ' ) 4( ) 9 " ( " ( ( ( "" 2 & ( C " * ( 2 ' . & ' ! " C - ( & E 1 ' # /G( ( ( ( ( 5 1 ( ( & ( ( ? ( ( " ' ' 4 * ( #= O ( 5 '- 2 4 ' # ))) ' 6 ! % ! 9 $& ' 9 .. B ( 1 & 2 4 55 69 .. ( 5 2 . ) ) 6 ! # ( ( 2)( & 1 26255 & 9 .. . /G 5 (& ? . . & ) ' & / L R $& ! . ( ( = & 9 . B 52 & )) *) ' ) ) ? 5 + ( )) *) . ( 9 . ' $ 54 .. ' . ' .. . ( ( $& 2 ! ( ! . ( ( $ ( $& ! ! ( ( ! ' ) 16 16*) .. ( .. .. $& ' 3 3 + " @ 2 7 ( . ' ( &'' ( ( . " " " 4 9 F ! ( =T?% + L ( ' ' & ) ( ( 6 ( & ' ( 2 ( A ) ' B % 2 4 G ( ' % K " 4 ' B 2/4 6 ' & % ) ' G L K ! !! ! 6 *D ) ( & ) ) $ ( % ) ( ' . & . ( 6 & + ' % & ( ! + L ( ! & ) & % ) ( & $ ( 2 4 ( ( ( ) & ( % // / $ = ( ' & 9 $ 2 B E 1 ( B % ( E5 ( A E ) $ 4 ( ( ! ( . 5 ! ' F ( ') . ' & % & ! ( ) % . ( ( % ( ' !! ( ( & ( ! ( ' ! ( * ' ' L : 5 ) . O . ' ( $ & & ( 2 ( 4 : ) $ ' ) ( ( & 2 & 9 % & '( 4 & 2 ( & & ) & & ( ' ( & ) 4 . ( & ' ' ' !! ) ( ( %) ') ( 5 ( + & ! ( & ( ! ! ' ' L 2 ! & & ' & ! ( 9 4 ( ( % % ) ( & & ! ( ( ( 4 1 & & 4 ) ) K ( 2 2 / K 9 & . ( / - ! % ) ' ( ) L & E F &( % ) " ( & & ) = ( ? ( ' 5 ! ( , '( & ( ! ) ( % (( 2 ! * "% % 7 !! 9 ' & ( & ( ( & !*" '( ' -- 2 ! !* " ( # !! * " * " 4 & ) !*" . 4 !*" !* " 4 5 F ( ' ! 9 & '( & 1 ( " * 1 ! + '( ( 9 ! 2 E4 . () 2 = & & ( ' K ) ( ( !* " '