08.04.2014 Views

On the growth problem for skew and symmetric conference matrices

On the growth problem for skew and symmetric conference matrices

On the growth problem for skew and symmetric conference matrices

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

u„vwxzDr ; Ž¡ Vw z ; ‡ zzsyv+} #F*'>3Nü<br />

U<br />

A X-`S”F`S”F`Fc`<br />

<br />

. `<br />

<br />

`<br />

<br />

`\7Cp%7 A X-`S”F`S”FÀ¦F`<br />

<br />

, `<br />

<br />

`<br />

<br />

`\7C ”<br />

¢<br />

<br />

X/” X7X A X-`S”F`S”FÀ¦F` [¡<br />

<br />

` [<br />

<br />

¨ ` [4[ ,<br />

` [4[ ` [4[ ` [4[<br />

<br />

¨<br />

¨ .<br />

, ` [4[<br />

A X-`S”F`S”F`FcÀ¦F` , ` [ ¤<br />

¨ ` [4[ . ` [4[ ` [4[ `/X7X CW%7<br />

[¡<br />

N¨ [¡<br />

[<br />

<br />

¨<br />

¨ ` [4[<br />

<br />

X-`S”F`S”FÀ¦FÀ¦F`Fc` [4[ , ` [4[ , ` [4[ . ` [4[<br />

` [4[<br />

`/X7X C<br />

A<br />

X A X-`S”F`S”FÀ¦F` [¡, ` [ ¤<br />

¨ `<br />

,".<br />

`Fc•£cc'X¢F`•••ž`Fc• F` [<br />

¨<br />

, ` [<br />

¨<br />

. ` [<br />

¨<br />

X'<br />

<br />

`/X7X CW%7 ¦<br />

<br />

`<br />

¨<br />

`/X&C [<br />

%7 A X-`S”F`S”FÀ¦F` [¡<br />

<br />

` [ ¤<br />

¨ ` [4[<br />

<br />

`••• `Fc•*+FÀF` [<br />

¨<br />

, ` [<br />

¨<br />

. ` [<br />

¨<br />

` [<br />

¨<br />

`/X&C<br />

, ,<br />

<br />

X X-`S”F`S”F`FcÀ¦F`<br />

<br />

` [ ¤<br />

¨ `•••/ÀF•À”+¢F` [<br />

”+ A , ` [, ` [. ` [ ` [ `/X&CW%7<br />

[¡<br />

<br />

,".<br />

N¨ [¡<br />

,<br />

X-`S”F`S”FÀ¦F` [¡, ` [ ¤<br />

¨ `<br />

A<br />

X-`S”F`S”F`Fc`<br />

¨ ,".<br />

A<br />

` [ ¤<br />

¨ `<br />

”¢ ” A X-`S”F`S”FÀ¦F` <br />

, ` [ ¤<br />

[¡<br />

X-`S”F`S”F`FcÀ¦F` [¡, ` [ ¤<br />

A<br />

X-`S”F`S”F`Fc`<br />

¨ ,".<br />

A<br />

[ `•••/ÀF•À”+¢F`<br />

N¨ , ` [, ` [. ` [<br />

[¡<br />

¦c^¦¢F` [, ` [, ` [. ` [ ` [<br />

`•••¡ÀF•<br />

`Fc`•••¡` <br />

<br />

¨<br />

`•••/` <br />

<br />

¨<br />

` [ ¤<br />

¨ `<br />

¦' ¦ A X-`S”F`S”F`FcÀ¦F` <br />

, ` [ ¤<br />

¨ `•••/` [¡<br />

<br />

`<br />

<br />

`<br />

<br />

` <br />

<br />

` <br />

<br />

` <br />

<br />

`S”7Cp%7<br />

<br />

<br />

. . . <br />

` <br />

<br />

` <br />

<br />

` <br />

<br />

` <br />

<br />

. . ` .<br />

¨ ¨<br />

c'X/”F` <br />

<br />

`•••¡`\•"XFXF`\• ` <br />

<br />

. ` <br />

<br />

<br />

, ¨ , ¨ , ¨ , ¨ , ¨ , ¨ <br />

<br />

À¦&Cp%7<br />

, ¨ , ¨ , ¨ <br />

[ ` `/X&CW%7<br />

<br />

`/X&C<br />

`S”7Cp%7<br />

<br />

<br />

`S”7C `<br />

` ` ` . ` `<br />

. .<br />

[¡<br />

<br />

` [ ¤<br />

¨ `<br />

,".<br />

`•••/ÀF• -”7”7”F`<br />

, ¨<br />

A X-`S”F`S”FÀ¦F` , `<br />

, ¨<br />

, ` . ` ` À¦&C<br />

<br />

[¡ N¨ ,<br />

X-`S”F`S”F`FcÀ¦F` [¡, ` [ ¤<br />

¨ `•••/`<br />

. ,<br />

. `<br />

. ,<br />

. `<br />

. ,<br />

`<br />

. ,<br />

. `<br />

. ,<br />

`<br />

. ,<br />

`Fc^¦&Cp%7<br />

A c^¦ cc<br />

X-`S”F`S”FÀ¦F` [¡, ` [ ¤<br />

¨ `<br />

A<br />

MX A X-`S”F`S”FÀ¦F` [¡, ` [ ¤<br />

7”<br />

X-`S”F`S”F`FcÀ¦F` [¡, ` [ ¤<br />

A<br />

A X-`S”F`S”F`FcÀ¦F` [¡, ` [ ¤<br />

'+<br />

<br />

,". . . , <br />

`<br />

. ,<br />

`<br />

.<br />

`•••/`<br />

, ,<br />

`<br />

. ,<br />

`<br />

. ,<br />

`Fc^¦&C<br />

`<br />

<br />

. .<br />

¨<br />

. <br />

`<br />

¨<br />

[ `<br />

¨<br />

[ ÀMX CW%7<br />

<br />

[ . `/XF•"X/”+M`/X` .<br />

`Fc`•••¡`<br />

¨<br />

[ ¨<br />

`•••/`<br />

¨<br />

[ ¨<br />

¨ `•••/`<br />

¨<br />

X-`S”F`S”FÀ¦F` [¡, ` [ ¤<br />

¨ `Fc`•••¡`/X¢F•£c^¦+F`<br />

A<br />

' A X-`S”F`S”F`FcÀ¦F` [¡, ` [ ¤<br />

'¢<br />

<br />

`/XF•"X/”+M`/X`<br />

¨<br />

[ . `<br />

¨<br />

[<br />

<br />

.<br />

`S”7”F•"X/”+M`<br />

¨<br />

, `<br />

¨<br />

. `<br />

¨<br />

.<br />

<br />

N¨ , `<br />

¨<br />

, `<br />

¨<br />

. `<br />

¨<br />

[¡<br />

¨<br />

<br />

. `<br />

<br />

`<br />

<br />

`<br />

`•••/`<br />

<br />

. `<br />

<br />

. `<br />

<br />

<br />

¨<br />

X-`S”F`S”FÀ¦F` [¡, ` [ ¤<br />

¨ `Fc`•••¡`<br />

<br />

. `<br />

<br />

. `<br />

<br />

. `<br />

<br />

<br />

A<br />

+' + A X-`S”F`S”F`FcÀ¦F` [¡<br />

<br />

` [ ¤<br />

¨ `•••/`<br />

¨<br />

. `S”¢F•"X/”+M`S”F`<br />

¨<br />

,<br />

X-`S”F`S”FÀ¦F` [¡, ` [ ¤<br />

A<br />

¢¦ A X-`S”F`S”F`FcÀ¦F` [¡, ` [ ¤<br />

¨ `•••/` ¤ ,<br />

. ` ¤ ,<br />

. ` ¤ ,<br />

¢c<br />

`<br />

<br />

`Fc`•••¡`<br />

¨<br />

. `S”¢F•"X/”+M`S”F`<br />

¨<br />

¨<br />

` ¤ ,<br />

. ` ¤ ,<br />

<br />

A X-`S”F`S”FÀ¦F` [¡<br />

<br />

` [ ¤<br />

¨ `Fc`•••¡` ¤ ,<br />

. ` ¤<br />

¤ ¨ , ` ¤ ,<br />

, ` ¤ ,<br />

. ` ¤ ,<br />

,<br />

<br />

`<br />

¨<br />

.<br />

¤ ,<br />

`<br />

`<br />

¨<br />

[<br />

<br />

ÀMX C<br />

`<br />

¨ <br />

<br />

À'7Cp%7<br />

<br />

`<br />

`<br />

¨<br />

`<br />

¨<br />

.<br />

À'7C<br />

`<br />

¨ <br />

<br />

À¢¦&C<br />

` ¤ ,<br />

À¢¦&C<br />

<br />

<br />

X-`S”F`S”F`FcÀ¦F` [¡, ` [ ¤<br />

¨ `•••/`£ [ . `¢ [ . `¢ [<br />

7” `¢ [ . `¢ [ `¢ MX [ ÀMX C<br />

A<br />

A X-`S”F`S”FÀ¦F` [¡<br />

<br />

` [ ¤<br />

¨ `Fc`•••¡`S”¦F• ¢F`S”'F• +'c` [ ¨ `<br />

<br />

[<br />

<br />

` [<br />

. ¨<br />

,<br />

A X-`S”F`S”F`FcÀ¦F` [¡, ` [ ¤<br />

¨ `•••/` . ` . `<br />

X ` . `<br />

<br />

A X-`S”F`S”FÀ¦F` [¡<br />

<br />

` [ ¤<br />

¨ `Fc`•••¡` À¦+M• ¦+F` ¨<br />

¨<br />

,<br />

q ‡¦¥¨§Ts<br />

<br />

` À&C<br />

`<br />

<br />

` ` .<br />

À&CW%7<br />

`<br />

¨<br />

À&C<br />

<br />

¦©=#)ý(,-N§+„üh¦ŠüpR'ü/!ºü/#:ýT,7+=+mý(¨+ü1E-,7+"*+ü/!,-R'RNü/,-S"#)$9a%7ý(¨+ü1c'S!ýT!(@k3,7#'De+",7!ºý!(gkPR§@E7%9ý(!,-9 <br />

¦#¨ý(¨+ü19a%&+=+@%<br />

ýºüh,-R'R§+"6F"#')j>5ücý4S=HWH%&#9?üaü/#'H@ü<br />

>j,Áý4S"H@ü/!©%79—%7SDü2U*1<br />

'F.<br />

X<br />

<br />

<br />

`\+&C<br />

`\+&C<br />

[ `<br />

<br />

À&C<br />

ÀMX C<br />

X¢<br />

¦+<br />

X/”<br />

Dc<br />

c^'<br />

c”<br />

cc<br />

¦<br />

¦c<br />

¦MX<br />

¦+<br />

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!