਀㰀琀椀琀氀攀㸀䄀甀琀漀戀椀漀最爀愀瀀栀礀        䠀攀爀戀攀爀琀 䄀⸀ 䠀愀甀瀀琀洀愀渀   ⸀ 吀栀攀 一漀戀攀氀 倀爀椀稀攀 椀渀 䌀栀攀洀椀猀琀爀礀  ਀  㰀䴀䔀吀䄀 栀琀琀瀀ⴀ攀焀甀椀瘀㴀䌀漀渀琀攀渀琀ⴀ匀琀礀氀攀ⴀ吀礀瀀攀 挀漀渀琀攀渀琀㴀琀攀砀琀⼀挀猀猀㸀㰀䰀䤀一䬀 栀爀攀昀㴀∀猀琀礀氀攀⸀挀猀猀∀ 琀礀瀀攀㴀琀攀砀琀⼀挀猀猀 爀攀氀㴀猀琀礀氀攀猀栀攀攀琀㸀㰀栀攀愀搀㸀㰀⼀栀攀愀搀㸀 ਀ ਀

਀吀栀攀 一漀戀攀氀 倀爀椀稀攀 椀渀 䌀栀攀洀椀猀琀爀礀  ㄀㤀㠀㔀 㰀⼀栀㈀㸀

Herbert A. Hauptman

਀㰀瀀㸀㰀栀㌀㸀倀爀漀琀攀椀渀 挀爀礀猀琀愀氀 猀琀爀甀挀琀甀爀攀 搀攀琀攀爀洀椀渀愀琀椀漀渀⸀

਀吀栀攀 搀攀琀攀爀洀椀渀愀琀椀漀渀 漀昀 愀 渀漀瘀攀氀 瀀爀漀琀攀椀渀 猀琀爀甀挀琀甀爀攀 戀礀 堀ⴀ爀愀礀 挀爀礀猀琀愀氀氀漀最爀愀瀀栀椀挀 愀渀愀氀礀猀椀猀 椀渀瘀漀氀瘀攀猀 琀栀攀 昀漀氀氀漀眀椀渀最 猀琀攀瀀猀⸀ 椀⤀ 倀爀漀琀攀椀渀 瀀甀爀椀昀椀挀愀琀椀漀渀 愀渀搀 挀爀礀猀琀愀氀氀椀猀愀琀椀漀渀 漀昀 琀栀攀 渀愀琀椀瘀攀 瀀爀漀琀攀椀渀Ⰰ 椀椀⤀ 洀攀愀猀甀爀攀洀攀渀琀 漀昀 渀愀琀椀瘀攀 搀椀昀昀爀愀挀琀椀漀渀 搀愀琀愀Ⰰ 椀椀椀⤀ 漀戀琀愀椀渀椀渀最 栀攀愀瘀礀 愀琀漀洀 搀攀爀椀瘀愀琀椀瘀攀猀Ⰰ 椀瘀⤀ 洀攀愀猀甀爀攀洀攀渀琀 愀渀搀 愀渀愀氀礀猀椀猀 漀昀 搀攀爀椀瘀愀琀椀瘀攀 搀愀琀愀Ⰰ 瘀⤀ 挀愀氀挀甀氀愀琀椀漀渀 漀昀 瀀栀愀猀攀猀Ⰰ 瘀椀⤀ 洀愀瀀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀 愀渀搀 洀漀搀攀氀 戀甀椀氀搀椀渀最 愀渀搀 瘀椀椀⤀ 洀漀搀攀氀 爀攀昀椀渀攀洀攀渀琀⸀ 

਀䌀爀礀猀琀愀氀氀椀猀愀琀椀漀渀 椀猀 漀昀琀攀渀 琀栀攀 爀愀琀攀 氀椀洀椀琀椀渀最 猀琀攀瀀 椀渀 瀀爀漀琀攀椀渀 挀爀礀猀琀愀氀氀漀最爀愀瀀栀礀⸀ 匀攀瘀攀爀愀氀 洀攀琀栀漀搀猀 漀昀 挀爀礀猀琀愀氀氀椀猀愀琀椀漀渀 愀爀攀 渀漀眀 眀攀氀氀 攀猀琀愀戀氀椀猀栀攀搀 戀甀琀 愀瀀瀀氀椀挀愀琀椀漀渀 漀昀 琀栀攀猀攀 洀攀琀栀漀搀猀 椀猀 猀琀椀氀氀 瘀攀爀礀 洀甀挀栀 琀爀椀愀氀 愀渀搀 攀爀爀漀爀⸀ 䌀爀礀猀琀愀氀氀椀猀愀琀椀漀渀 漀昀 愀 渀攀眀氀礀 椀猀漀氀愀琀攀搀 瀀爀漀琀攀椀渀 挀愀渀 琀愀欀攀 眀攀攀欀猀Ⰰ 洀漀渀琀栀猀 漀爀 礀攀愀爀猀⸀ 

਀䄀 瀀爀攀爀攀焀甀椀猀椀琀攀 漀昀 琀栀攀 猀漀氀甀琀椀漀渀 漀昀 琀栀攀 洀愀樀漀爀椀琀礀 漀昀 瀀爀漀琀攀椀渀 挀爀礀猀琀愀氀 猀琀爀甀挀琀甀爀攀猀 椀猀 琀漀 昀椀渀搀 愀渀 椀猀漀洀漀爀瀀栀漀甀猀 栀攀愀瘀礀 愀琀漀洀 搀攀爀椀瘀愀琀椀瘀攀 漀昀 琀栀攀 渀愀琀椀瘀攀 瀀爀漀琀攀椀渀⸀ 䤀猀漀洀漀爀瀀栀漀甀猀Ⰰ 椀渀 琀栀椀猀 猀攀渀猀攀Ⰰ 洀攀愀渀猀 琀栀愀琀 琀栀攀 搀攀爀椀瘀愀琀椀瘀攀 瀀爀漀琀攀椀渀 挀爀礀猀琀愀氀 猀琀爀甀挀琀甀爀攀 猀栀漀甀氀搀 戀攀 椀搀攀渀琀椀挀愀氀 琀漀 琀栀攀 渀愀琀椀瘀攀 瀀爀漀琀攀椀渀 猀琀爀甀挀琀甀爀攀 攀砀挀攀瀀琀 昀漀爀 琀栀攀 瀀爀攀猀攀渀挀攀 漀昀 漀渀攀 漀爀 洀漀爀攀 栀攀愀瘀礀 愀琀漀洀猀 戀漀甀渀搀 琀漀 瀀爀漀琀攀椀渀 洀漀氀攀挀甀氀攀猀Ⰰ 椀⸀攀⸀ 琀栀攀 氀愀琀琀椀挀攀Ⰰ 猀瀀愀挀攀 最爀漀甀瀀Ⰰ 挀攀氀氀 搀椀洀攀渀猀椀漀渀猀 愀渀搀 瀀漀猀椀琀椀漀渀 愀渀搀 挀漀渀昀漀爀洀愀琀椀漀渀 漀昀 琀栀攀 瀀爀漀琀攀椀渀 洀漀氀攀挀甀氀攀 眀椀琀栀椀渀 琀栀攀 甀渀椀琀 挀攀氀氀 猀栀漀甀氀搀 戀攀 瀀爀攀猀攀爀瘀攀搀⸀ 吀栀攀 洀漀猀琀 挀漀洀洀漀渀 洀攀琀栀漀搀 漀昀 栀攀愀瘀礀 愀琀漀洀 椀渀挀氀甀猀椀漀渀 椀猀 琀漀 猀漀愀欀 琀栀攀 渀愀琀椀瘀攀 瀀爀漀琀攀椀渀 挀爀礀猀琀愀氀猀 椀渀 愀 猀漀氀甀琀椀漀渀 挀漀渀琀愀椀渀椀渀最 愀 栀攀愀瘀礀 愀琀漀洀 挀漀洀瀀漀甀渀搀⸀ 伀琀栀攀爀 洀漀爀攀 爀攀挀攀渀琀 洀攀琀栀漀搀猀 椀渀瘀漀氀瘀攀 琀栀攀 瀀爀漀搀甀挀琀椀漀渀 漀昀 瀀爀漀琀攀椀渀 眀椀琀栀 洀漀搀椀昀椀攀搀 愀洀椀渀漀 愀挀椀搀 爀攀猀椀搀甀攀猀Ⰰ 攀⸀最⸀ 洀攀琀栀椀漀渀椀渀攀 挀漀渀琀愀椀渀椀渀最 瀀爀漀琀攀椀渀猀 挀愀渀 戀攀 攀渀最椀渀攀攀爀攀搀 眀栀攀爀攀 猀攀氀攀渀椀甀洀 爀攀瀀氀愀挀攀猀 琀栀攀 猀甀氀瀀栀甀爀 漀昀 琀栀攀 洀攀琀栀椀漀渀椀渀攀 嬀㔀 崀⸀ 

਀伀渀挀攀 猀甀椀琀愀戀氀攀 渀愀琀椀瘀攀 愀渀搀 搀攀爀椀瘀愀琀椀瘀攀 瀀爀漀琀攀椀渀 挀爀礀猀琀愀氀猀 戀攀挀漀洀攀 愀瘀愀椀氀愀戀氀攀Ⰰ 堀ⴀ爀愀礀 搀椀昀昀爀愀挀琀椀漀渀 搀愀琀愀 愀爀攀 挀漀氀氀攀挀琀攀搀⸀ 伀渀攀 漀昀 猀攀瘀攀爀愀氀 瀀爀漀挀攀搀甀爀攀猀 洀愀礀 戀攀 愀搀漀瀀琀攀搀 昀漀爀 搀愀琀愀 挀漀氀氀攀挀琀椀漀渀⸀ 䴀漀猀琀 猀椀渀最氀攀 挀爀礀猀琀愀氀 搀椀昀昀爀愀挀琀椀漀渀 搀愀琀愀 愀爀攀 洀攀愀猀甀爀攀搀 甀猀椀渀最 洀漀渀漀挀栀爀漀洀愀琀椀挀 堀ⴀ爀愀礀猀 昀爀漀洀 攀椀琀栀攀爀 愀 猀攀愀氀攀搀 琀甀戀攀 最攀渀攀爀愀琀漀爀Ⰰ 愀 爀漀琀愀琀椀渀最 愀渀漀搀攀 最攀渀攀爀愀琀漀爀 漀爀 昀爀漀洀 愀 猀礀渀挀栀爀漀琀爀漀渀 猀漀甀爀挀攀⸀ 吀栀攀 愀瘀愀椀氀愀戀椀氀椀琀礀 漀昀 猀礀渀挀栀爀漀琀爀漀渀 爀愀搀椀愀琀椀漀渀 栀愀猀 氀攀搀 琀漀 琀栀攀 愀瀀瀀氀椀挀愀琀椀漀渀 漀昀 琀栀攀 氀攀猀猀 眀椀搀攀氀礀 甀猀攀搀 䰀愀甀攀 洀攀琀栀漀搀 漀昀 搀愀琀愀 挀漀氀氀攀挀琀椀漀渀 琀漀 瀀爀漀琀攀椀渀 挀爀礀猀琀愀氀氀漀最爀愀瀀栀礀⸀ 䤀琀 甀琀椀氀椀猀攀猀 琀栀攀 渀漀渀ⴀ挀栀愀爀愀挀琀攀爀椀猀琀椀挀 瀀漀氀礀挀栀爀漀洀愀琀椀挀 爀愀搀椀愀琀椀漀渀 瀀爀漀搀甀挀攀搀 戀礀 愀 猀礀渀挀栀爀漀琀爀漀渀⸀ 䄀 搀攀琀愀椀氀攀搀 搀攀猀挀爀椀瀀琀椀漀渀 漀昀 琀栀攀 䰀愀甀攀 洀攀琀栀漀搀 洀愀礀 戀攀 昀漀甀渀搀 椀渀 嬀㐀㜀崀⸀ 

਀匀攀瘀攀爀愀氀 搀愀琀愀 挀漀氀氀攀挀琀椀漀渀 最攀漀洀攀琀爀椀攀猀 洀愀礀 戀攀 甀猀攀搀 愀氀漀渀最 眀椀琀栀 洀漀渀漀挀栀爀漀洀愀琀椀挀 爀愀搀椀愀琀椀漀渀⸀ 䄀 挀漀渀瘀攀渀琀椀漀渀愀氀 搀椀昀昀爀愀挀琀漀洀攀琀攀爀 洀攀愀猀甀爀攀猀 攀愀挀栀 爀攀昀氀攀挀琀椀漀渀 椀渀搀椀瘀椀搀甀愀氀氀礀 眀椀琀栀 愀 猀挀椀渀琀椀氀氀愀琀椀漀渀 挀漀甀渀琀攀爀⸀ 䄀 最漀渀椀漀洀攀琀攀爀 爀漀琀愀琀攀猀 琀栀攀 挀爀礀猀琀愀氀 猀漀 愀猀 琀漀 猀愀琀椀猀昀礀 琀栀攀 䈀爀愀最最 挀漀渀搀椀琀椀漀渀 昀漀爀 攀愀挀栀 爀攀昀氀攀挀琀椀漀渀 椀渀搀椀瘀椀搀甀愀氀氀礀 眀栀椀氀攀 琀栀攀 搀攀琀攀挀琀漀爀 猀椀洀甀氀琀愀渀攀漀甀猀氀礀 爀攀挀漀爀搀猀 琀栀攀 搀椀昀昀爀愀挀琀攀搀 堀ⴀ爀愀礀 椀渀琀攀渀猀椀琀礀⸀ 䐀椀昀昀爀愀挀琀漀洀攀琀攀爀猀 愀爀攀 猀琀椀氀氀 眀椀搀攀氀礀 甀猀攀搀 昀漀爀 猀洀愀氀氀 洀漀氀攀挀甀氀攀 眀漀爀欀 戀甀琀 栀愀瘀攀 爀攀挀攀渀琀氀礀 戀攀攀渀 猀甀瀀攀爀猀攀搀攀搀 戀礀 愀爀攀愀 搀攀琀攀挀琀漀爀猀 眀栀椀挀栀 愀爀攀 愀戀氀攀 琀漀 洀攀愀猀甀爀攀 攀焀甀椀瘀愀氀攀渀琀 焀甀愀渀琀椀琀椀攀猀 漀昀 搀愀琀愀 椀渀 愀 洀甀挀栀 猀栀漀爀琀攀爀 琀椀洀攀㬀 愀渀 椀洀瀀漀爀琀愀渀琀 昀愀挀琀漀爀 眀栀攀渀 挀爀礀猀琀愀氀 猀愀洀瀀氀攀猀 愀爀攀 栀椀最栀氀礀 猀攀渀猀椀琀椀瘀攀 琀漀 琀栀攀 搀漀猀愀最攀 漀昀 堀ⴀ爀愀礀猀 搀攀氀椀瘀攀爀攀搀 搀甀爀椀渀最 琀栀攀 攀砀瀀攀爀椀洀攀渀琀⸀ 吀栀椀猀 椀猀 瀀愀爀琀椀挀甀氀愀爀氀礀 爀攀氀攀瘀愀渀琀 昀漀爀 戀椀漀氀漀最椀挀愀氀 猀愀洀瀀氀攀猀⸀ 

਀吀栀攀爀攀 愀爀攀 琀眀漀 愀爀攀愀 搀攀琀攀挀琀漀爀 最攀漀洀攀琀爀椀攀猀 眀栀椀挀栀 愀爀攀 愀琀 瀀爀攀猀攀渀琀 眀椀搀攀氀礀 甀猀攀搀 ⴀ 爀漀琀愀琀椀漀渀 最攀漀洀攀琀爀礀 愀渀搀 圀攀椀猀猀攀渀戀攀爀最 最攀漀洀攀琀爀礀⸀ 䤀渀 戀漀琀栀 洀攀琀栀漀搀猀 琀栀攀 䈀爀愀最最 挀漀渀搀椀琀椀漀渀 椀猀 猀愀琀椀猀昀椀攀搀 戀礀 爀漀琀愀琀椀渀最 琀栀攀 猀愀洀瀀氀攀 挀爀礀猀琀愀氀 愀戀漀甀琀 愀 昀椀砀攀搀 愀砀椀猀⸀ 䄀 猀攀爀椀攀猀 漀昀 搀椀昀昀爀愀挀琀椀漀渀 椀洀愀最攀猀 愀爀攀 洀攀愀猀甀爀攀搀 眀栀攀爀攀戀礀 攀愀挀栀 椀洀愀最攀 爀攀挀漀爀搀猀 愀氀氀 爀攀昀氀攀挀琀椀漀渀猀 猀愀琀椀猀昀礀椀渀最 琀栀攀 䈀爀愀最最 挀漀渀搀椀琀椀漀渀 愀猀 琀栀攀 挀爀礀猀琀愀氀 椀猀 爀漀琀愀琀攀搀 琀栀爀漀甀最栀 愀 猀瀀攀挀椀昀椀攀搀 愀渀最氀攀 ⸀ 䄀 氀椀洀椀琀攀搀 瘀愀氀甀攀 漀昀  椀猀 渀攀挀攀猀猀愀爀礀 猀漀 愀猀 琀漀 愀瘀漀椀搀 漀瘀攀爀氀愀瀀 漀昀 搀椀昀昀爀愀挀琀攀搀 爀攀昀氀攀挀琀椀漀渀猀 漀渀 愀渀 椀洀愀最攀⸀ 

਀吀栀攀 攀猀猀攀渀琀椀愀氀 搀椀昀昀攀爀攀渀挀攀 椀猀 琀栀愀琀 愀 圀攀椀猀猀攀渀戀攀爀最 挀愀洀攀爀愀 挀漀甀瀀氀攀猀 琀栀攀 猀愀洀瀀氀攀 爀漀琀愀琀椀漀渀 眀椀琀栀 愀 琀爀愀渀猀氀愀琀椀漀渀 漀昀 琀栀攀 愀爀攀愀 搀攀琀攀挀琀漀爀⸀ 吀栀椀猀 栀攀氀瀀猀 愀瘀漀椀搀 琀栀攀 瀀爀漀戀氀攀洀 漀昀 漀瘀攀爀氀愀瀀瀀椀渀最 猀瀀漀琀猀 愀渀搀 甀猀攀猀 琀栀攀 愀瘀愀椀氀愀戀氀攀 猀瀀愀挀攀 漀渀 琀栀攀 愀爀攀愀 搀攀琀攀挀琀漀爀 洀漀爀攀 攀昀昀椀挀椀攀渀琀氀礀 愀渀搀 挀愀渀 昀甀爀琀栀攀爀 爀攀搀甀挀攀 琀栀攀 漀瘀攀爀愀氀氀 琀椀洀攀 昀漀爀 搀愀琀愀 挀漀氀氀攀挀琀椀漀渀⸀ 吀栀攀 甀猀攀 漀昀 氀愀爀最攀爀 愀渀最甀氀愀爀 爀漀琀愀琀椀漀渀 爀愀渀最攀猀 昀漀爀 攀愀挀栀 搀椀昀昀爀愀挀琀椀漀渀 椀洀愀最攀 椀渀 琀栀攀 圀攀椀猀猀攀渀戀攀爀最 最攀漀洀攀琀爀礀 椀洀瀀氀椀攀猀 琀栀攀 愀挀挀甀洀甀氀愀琀椀漀渀 漀昀 洀漀爀攀 戀愀挀欀最爀漀甀渀搀 爀愀搀椀愀琀椀漀渀 瀀攀爀 椀洀愀最攀Ⰰ 栀漀眀攀瘀攀爀 氀愀爀最攀 猀愀洀瀀氀攀 琀漀 搀攀琀攀挀琀漀爀 搀椀猀琀愀渀挀攀猀Ⰰ Ⰰ 愀爀攀 愀氀猀漀 琀礀瀀椀挀愀氀氀礀 甀猀攀搀 眀栀椀挀栀 爀攀搀甀挀攀 琀栀攀 氀攀瘀攀氀 漀昀 爀攀挀漀爀搀攀搀 戀愀挀欀最爀漀甀渀搀 爀攀氀愀琀椀瘀攀 琀漀 琀栀攀 椀渀琀攀渀猀椀琀礀 漀昀 搀椀昀昀爀愀挀琀攀搀 堀ⴀ爀愀礀猀 戀礀 愀 昀愀挀琀漀爀 漀昀 ⸀ 

਀䤀渀 愀 搀椀昀昀爀愀挀琀椀漀渀 攀砀瀀攀爀椀洀攀渀琀 漀渀攀 挀愀渀 漀渀氀礀 洀攀愀猀甀爀攀 琀栀攀 椀渀琀攀渀猀椀琀椀攀猀 愀渀搀 搀椀昀昀爀愀挀琀椀漀渀 愀渀最氀攀猀 漀昀 琀栀攀 搀椀昀昀爀愀挀琀攀搀 戀攀愀洀猀⸀ 䄀氀氀 椀渀昀漀爀洀愀琀椀漀渀 愀戀漀甀琀 琀栀攀 瀀栀愀猀攀猀 漀昀 琀栀攀 搀椀昀昀爀愀挀琀攀搀 堀ⴀ爀愀礀猀 椀猀 氀漀猀琀⸀ 吀栀椀猀 瀀栀愀猀攀 椀渀昀漀爀洀愀琀椀漀渀 愀氀漀渀最 眀椀琀栀 琀栀攀 愀洀瀀氀椀琀甀搀攀猀 漀昀 琀栀攀 搀椀昀昀爀愀挀琀攀搀 堀ⴀ爀愀礀猀 椀猀 攀猀猀攀渀琀椀愀氀 昀漀爀 琀栀攀 猀漀氀甀琀椀漀渀 漀昀 挀爀礀猀琀愀氀 猀琀爀甀挀琀甀爀攀猀 愀渀搀 洀甀猀琀 戀攀 爀攀挀漀瘀攀爀攀搀⸀ 

਀吀栀攀爀攀 愀爀攀 昀漀甀爀 愀瀀瀀爀漀愀挀栀攀猀 眀栀椀挀栀 洀愀礀 戀攀 琀愀欀攀渀 椀渀 爀攀挀漀瘀攀爀椀渀最 瀀栀愀猀攀 椀渀昀漀爀洀愀琀椀漀渀 椀渀 愀 搀椀昀昀爀愀挀琀椀漀渀 攀砀瀀攀爀椀洀攀渀琀⸀ 吀栀攀 栀攀愀瘀礀 愀琀漀洀 洀攀琀栀漀搀 洀愀欀攀猀 琀栀攀 愀猀猀甀洀瀀琀椀漀渀 琀栀愀琀 椀昀 愀 猀椀最渀椀昀椀挀愀渀琀 挀漀渀琀爀椀戀甀琀椀漀渀 漀昀 琀栀攀 猀挀愀琀琀攀爀椀渀最 昀爀漀洀 愀 猀琀爀甀挀琀甀爀攀 椀猀 洀愀搀攀 戀礀 愀 栀攀愀瘀礀 愀琀漀洀 琀栀攀渀 琀栀攀 瀀栀愀猀攀猀 漀昀 琀栀攀 搀椀昀昀爀愀挀琀攀搀 堀ⴀ爀愀礀猀 眀椀氀氀 戀攀 挀氀漀猀攀 琀漀 琀栀漀猀攀 瀀栀愀猀攀猀 眀栀椀挀栀 眀漀甀氀搀 戀攀 漀戀猀攀爀瘀攀搀 眀攀爀攀 漀渀氀礀 琀栀攀 栀攀愀瘀礀 愀琀漀洀猀 瀀爀攀猀攀渀琀⸀ 吀栀攀 瀀爀漀戀氀攀洀 椀猀 琀栀甀猀 爀攀搀甀挀攀搀 琀漀 昀椀渀搀椀渀最 琀栀攀 瀀漀猀椀琀椀漀渀猀 漀昀 琀栀攀 栀攀愀瘀礀 愀琀漀洀猀 眀椀琀栀椀渀 琀栀攀 猀琀爀甀挀琀甀爀攀⸀ 吀栀椀猀 愀瀀瀀爀漀愀挀栀 椀猀 椀渀 最攀渀攀爀愀氀 渀漀琀 愀瀀瀀氀椀挀愀戀氀攀 琀漀 瀀爀漀琀攀椀渀猀 猀椀渀挀攀 琀栀攀 栀攀愀瘀礀 愀琀漀洀 挀漀渀琀爀椀戀甀琀椀漀渀 琀漀 猀挀愀琀琀攀椀渀最 椀猀 猀洀愀氀氀 眀椀琀栀 爀攀猀瀀攀挀琀 琀漀 琀栀攀 瀀爀漀琀攀椀渀⸀ 吀栀攀 搀椀爀攀挀琀 洀攀琀栀漀搀猀 愀瀀瀀爀漀愀挀栀 挀愀渀 洀愀欀攀 攀猀琀椀洀愀琀攀猀 愀戀漀甀琀 琀栀攀 爀攀昀氀攀挀琀椀漀渀 瀀栀愀猀攀猀 甀猀椀渀最 愀猀猀甀洀瀀琀椀漀渀猀 愀戀漀甀琀 琀栀攀 椀渀琀攀爀渀愀氀 猀琀爀甀挀琀甀爀攀 漀昀 琀栀攀 挀爀礀猀琀愀氀⸀ 䐀椀爀攀挀琀 洀攀琀栀漀搀猀 愀爀攀 爀漀甀琀椀渀攀氀礀 甀猀攀搀 昀漀爀 琀栀攀 猀漀氀甀琀椀漀渀 漀昀 猀洀愀氀氀 猀琀爀甀挀琀甀爀攀猀 愀渀搀 栀愀瘀攀 漀渀氀礀 爀攀挀攀渀琀氀礀 戀攀攀渀 愀瀀瀀氀椀攀搀 琀漀 琀栀攀 猀漀氀甀琀椀漀渀 漀昀 猀洀愀氀氀 瀀爀漀琀攀椀渀猀 挀漀渀琀愀椀渀椀渀最 愀戀漀甀琀 㔀  愀洀椀渀漀 愀挀椀搀 爀攀猀椀搀甀攀猀 嬀㄀ ㈀崀⸀ 

਀䤀昀 愀 爀攀氀愀琀攀搀 漀爀 猀椀洀椀氀愀爀 瀀爀漀琀攀椀渀 猀琀爀甀挀琀甀爀攀 椀猀 愀氀爀攀愀搀礀 欀渀漀眀渀 琀栀攀渀 琀栀攀 洀攀琀栀漀搀 漀昀 䴀漀氀攀挀甀氀愀爀 刀攀瀀氀愀挀攀洀攀渀琀 ⠀䴀刀⤀ 嬀㤀㠀崀 洀愀礀 戀攀 甀猀攀搀⸀ 吀栀攀 椀搀攀愀 椀猀 琀漀 昀椀渀搀 琀栀攀 爀漀琀愀琀椀漀渀 愀渀搀 琀爀愀渀猀氀愀琀椀漀渀 眀栀椀挀栀 瀀漀猀椀琀椀漀渀 琀栀攀 洀漀搀攀氀 猀琀爀甀挀琀甀爀攀 椀渀 琀栀攀 甀渀椀琀 挀攀氀氀 猀漀 愀猀 琀漀 最椀瘀攀 琀栀攀 栀椀最栀攀猀琀 挀漀爀爀攀氀愀琀椀漀渀 戀攀琀眀攀攀渀 攀砀瀀攀爀椀洀攀渀琀愀氀 搀椀昀昀爀愀挀琀椀漀渀 洀攀愀猀甀爀攀洀攀渀琀猀 愀渀搀 琀栀漀猀攀 挀愀氀挀甀氀愀琀攀搀 昀爀漀洀 琀栀攀 洀漀搀攀氀⸀ 吀栀椀猀 洀攀琀栀漀搀 爀攀氀椀攀猀 漀渀 琀栀攀 攀砀椀猀琀攀渀挀攀 漀昀 愀 欀渀漀眀渀 爀攀氀愀琀攀搀 猀琀爀甀挀琀甀爀攀 愀渀搀 椀猀 琀栀攀爀攀昀漀爀攀 氀椀欀攀氀礀 琀漀 戀攀挀漀洀攀 洀漀爀攀 愀渀搀 洀漀爀攀 愀瀀瀀氀椀挀愀戀氀攀 愀猀 琀栀攀 渀甀洀戀攀爀 漀昀 猀漀氀瘀攀搀 瀀爀漀琀攀椀渀 猀琀爀甀挀琀甀爀攀猀 椀渀挀爀攀愀猀攀猀 椀渀 琀栀攀 昀甀琀甀爀攀⸀ 

਀吀栀攀 琀栀椀爀搀 愀渀搀 洀漀猀琀 瀀爀漀洀椀渀攀渀琀 漀昀 琀栀攀 猀漀氀甀琀椀漀渀猀 琀漀 琀栀攀 瀀栀愀猀攀 瀀爀漀戀氀攀洀 椀渀 洀愀挀爀漀洀漀氀攀挀甀氀愀爀 挀爀礀猀琀愀氀氀漀最爀愀瀀栀礀 椀猀 椀猀漀洀漀爀瀀栀漀甀猀 爀攀瀀氀愀挀攀洀攀渀琀 愀渀搀 爀攀氀愀琀攀搀 洀攀琀栀漀搀猀⸀ 䤀渀 琀栀攀猀攀 洀攀琀栀漀搀猀 瀀栀愀猀攀 椀渀昀漀爀洀愀琀椀漀渀 椀猀 爀攀琀爀椀攀瘀攀搀 戀礀 洀愀欀椀渀最 椀猀漀洀漀爀瀀栀漀甀猀 猀琀爀甀挀琀甀爀愀氀 洀漀搀椀昀椀挀愀琀椀漀渀猀 琀漀 琀栀攀 渀愀琀椀瘀攀 瀀爀漀琀攀椀渀Ⰰ 甀猀甀愀氀氀礀 戀礀 椀渀挀氀甀搀椀渀最 愀 栀攀愀瘀礀 愀琀漀洀 漀爀 挀栀愀渀最椀渀最 琀栀攀 猀挀愀琀琀攀爀椀渀最 猀琀爀攀渀最琀栀 漀昀 愀 栀攀愀瘀礀 愀琀漀洀 愀氀爀攀愀搀礀 瀀爀攀猀攀渀琀 愀渀搀 琀栀攀渀 洀攀愀猀甀爀椀渀最 琀栀攀 搀椀昀昀爀愀挀琀椀漀渀 愀洀瀀氀椀琀甀搀攀猀 昀漀爀 琀栀攀 渀愀琀椀瘀攀 瀀爀漀琀攀椀渀 愀渀搀 攀愀挀栀 漀昀 琀栀攀 洀漀搀椀昀椀攀搀 挀愀猀攀猀⸀ 䤀昀 琀栀攀 瀀漀猀椀琀椀漀渀 漀昀 琀栀攀 愀搀搀椀琀椀漀渀愀氀 栀攀愀瘀礀 愀琀漀洀 漀爀 琀栀攀 挀栀愀渀最攀 椀渀 椀琀猀 猀挀愀琀琀攀爀椀渀最 猀琀爀攀渀最琀栀 椀猀 欀渀漀眀渀 琀栀攀渀 琀栀攀 瀀栀愀猀攀 漀昀 攀愀挀栀 搀椀昀昀爀愀挀琀攀搀 堀ⴀ爀愀礀 挀愀渀 戀攀 搀攀琀攀爀洀椀渀攀搀 戀礀 猀漀氀瘀椀渀最 愀 猀攀琀 漀昀 猀椀洀甀氀琀愀渀攀漀甀猀 瀀栀愀猀攀 攀焀甀愀琀椀漀渀猀⸀ 䴀攀琀栀漀搀猀 眀栀椀挀栀 甀猀攀 猀甀挀栀 愀 猀琀爀愀琀攀最礀 愀爀攀 匀椀渀最氀攀 䤀猀漀洀漀爀瀀栀漀甀猀 刀攀瀀氀愀挀攀洀攀渀琀 ⠀匀䤀刀⤀Ⰰ 䴀甀氀琀椀瀀氀攀 䤀猀漀洀漀爀瀀栀漀甀猀 刀攀瀀氀愀挀攀洀攀渀琀 ⠀䴀䤀刀⤀Ⰰ 匀椀渀最氀攀 䤀猀漀洀漀爀瀀栀漀甀猀 刀攀瀀氀愀挀攀洀攀渀琀 眀椀琀栀 䄀渀漀洀愀氀漀甀猀 匀挀愀琀琀攀爀椀渀最 ⠀匀䤀刀䄀匀⤀ 愀渀搀 眀椀琀栀椀渀 琀栀攀 氀愀猀琀 ㄀㔀 礀攀愀爀猀Ⰰ 琀栀攀 䴀甀氀琀椀瀀氀攀 眀愀瘀攀氀攀渀最琀栀 䄀渀漀洀愀氀漀甀猀 䐀椀昀昀爀愀挀琀椀漀渀 洀攀琀栀漀搀 ⠀䴀䄀䐀⤀⸀ 

਀圀椀琀栀 愀渀 攀砀瀀攀爀椀洀攀渀琀愀氀 猀攀琀 漀昀 瀀栀愀猀攀猀 漀戀琀愀椀渀攀搀 昀爀漀洀 攀椀琀栀攀爀 搀椀爀攀挀琀 洀攀琀栀漀搀猀 漀爀 䤀猀漀洀漀爀瀀栀漀甀猀 刀攀瀀氀愀挀攀洀攀渀琀 爀攀氀愀琀攀搀 洀攀琀栀漀搀猀 漀渀攀 挀愀渀 挀愀氀挀甀氀愀琀攀 愀 ㌀ⴀ搀椀洀攀渀猀椀漀渀愀氀 攀氀攀挀琀爀漀渀 搀攀渀猀椀琀礀 洀愀瀀 漀昀 琀栀攀 瀀爀漀琀攀椀渀 猀琀爀甀挀琀甀爀攀⸀ 吀栀椀猀 椀猀 渀漀琀 愀氀眀愀礀猀 爀攀愀搀椀氀礀 椀渀琀攀爀瀀爀攀琀愀戀氀攀 愀猀 愀 猀椀渀最氀攀 瀀漀氀礀瀀攀瀀琀椀搀攀 挀栀愀椀渀 愀渀搀 洀攀琀栀漀搀猀 愀爀攀 甀猀甀愀氀氀礀 攀洀瀀氀漀礀攀搀 琀漀 椀洀瀀爀漀瘀攀 琀栀攀 搀攀渀猀椀琀礀 洀愀瀀 甀猀椀渀最 欀渀漀眀氀攀搀最攀 愀戀漀甀琀 琀栀攀 挀漀洀洀漀渀 挀栀愀爀愀挀琀攀爀椀猀琀椀挀猀 漀昀 瀀爀漀琀攀椀渀 挀爀礀猀琀愀氀猀⸀ 攀⸀最⸀ 琀栀攀礀 渀攀愀爀氀礀 愀氀眀愀礀猀 挀漀渀琀愀椀渀 戀攀琀眀攀攀渀  愀渀搀  猀漀氀瘀攀渀琀Ⰰ 愀爀攀 洀愀搀攀 漀昀 椀渀搀椀瘀椀搀甀愀氀 愀洀椀渀漀 愀挀椀搀 爀攀猀椀搀甀攀猀 眀椀琀栀 欀渀漀眀渀 猀琀爀甀挀琀甀爀攀猀 愀渀搀 栀愀瘀攀 瀀爀攀搀椀挀琀愀戀氀攀 猀攀挀漀渀搀愀爀礀 猀琀爀甀挀琀甀爀攀猀 攀⸀最⸀ ⴀ栀攀氀椀砀 漀爀 ⴀ瀀氀攀愀琀攀搀 猀栀攀攀琀⸀ 䐀攀渀猀椀琀礀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀 愀渀搀 洀漀搀攀氀 戀甀椀氀搀椀渀最 栀愀瘀攀 戀攀攀渀 猀攀洀椀ⴀ愀甀琀漀洀愀琀攀搀 眀椀琀栀 琀栀攀 爀攀挀攀渀琀 搀攀瘀攀氀漀瀀洀攀渀琀 漀昀 瀀漀眀攀爀昀甀氀 最爀愀瀀栀椀挀愀氀 挀漀洀瀀甀琀攀爀 栀愀爀搀眀愀爀攀 愀渀搀 猀漀昀琀眀愀爀攀 愀椀洀攀搀 猀瀀攀挀椀昀椀挀愀氀氀礀 愀琀 洀愀挀爀漀洀漀氀攀挀甀氀愀爀 洀漀搀攀氀氀椀渀最Ⰰ 攀⸀最⸀ 琀栀攀 瀀爀漀最爀愀洀 伀 嬀㘀㄀崀⸀ 䄀昀琀攀爀 愀渀搀 搀甀爀椀渀最 琀栀攀 洀愀椀渀 瀀栀愀猀攀 漀昀 洀漀搀攀氀 戀甀椀氀搀椀渀最Ⰰ 爀攀昀椀渀攀洀攀渀琀 漀昀 琀栀攀 洀漀搀攀氀 椀猀 挀愀爀爀椀攀搀 漀甀琀 愀最愀椀渀猀琀 琀栀攀 攀砀瀀攀爀椀洀攀渀琀愀氀氀礀 洀攀愀猀甀爀攀搀 椀渀琀攀渀猀椀琀椀攀猀⸀ 吀栀椀猀 猀琀愀最攀 洀愀礀 椀渀挀氀甀搀攀 琀栀攀 愀搀搀椀琀椀漀渀 漀昀 漀爀搀攀爀攀搀 猀漀氀瘀攀渀琀 洀漀氀攀挀甀氀攀猀 愀渀搀 椀昀 瘀攀爀礀 栀椀最栀 爀攀猀漀氀甀琀椀漀渀 堀ⴀ爀愀礀 搀愀琀愀 愀爀攀 愀瘀愀椀氀愀戀氀攀 攀瘀攀渀 琀栀攀 愀搀搀椀琀椀漀渀 漀昀 栀礀搀爀漀最攀渀 愀琀漀洀猀Ⰰ 愀氀琀栀漀甀最栀 琀栀椀猀 椀猀 爀愀爀攀 昀漀爀 洀愀挀爀漀洀漀氀攀挀甀氀愀爀 猀琀爀甀挀琀甀爀攀猀⸀ ਀㰀⼀瀀㸀㰀瀀㸀 ਀ ਀ ਀ I was born in New York City on February 14, 1917, the oldest child of Israel Hauptman਀愀渀搀 䰀攀愀栀 刀漀猀攀渀昀攀氀搀⸀ 䤀 栀愀瘀攀 琀眀漀 戀爀漀琀栀攀爀猀Ⰰ 䴀愀渀甀攀氀 愀渀搀 刀漀戀攀爀琀⸀

਀䤀 洀愀爀爀椀攀搀 䔀搀椀琀栀 䌀椀琀爀礀渀攀氀氀 漀渀 一漀瘀攀洀戀攀爀 ㄀ Ⰰ ㄀㤀㐀 ⸀ 圀攀 栀愀瘀攀 琀眀漀 搀愀甀最栀琀攀爀猀Ⰰ 䈀愀爀戀愀爀愀 ⠀㄀㤀㐀㜀⤀ 愀渀搀 䌀愀爀漀氀 ⠀㄀㤀㔀 ⤀⸀

਀䴀礀 椀渀琀攀爀攀猀琀 椀渀 洀漀猀琀 愀爀攀愀猀 漀昀 猀挀椀攀渀挀攀 愀渀搀 洀愀琀栀攀洀愀琀椀挀猀 戀攀最愀渀 愀琀 愀渀 攀愀爀氀礀 愀最攀Ⰰ 愀猀 猀漀漀渀 愀猀 䤀 栀愀搀 氀攀愀爀渀攀搀 琀漀 爀攀愀搀Ⰰ 愀渀搀 挀漀渀琀椀渀甀攀猀 琀漀 琀栀椀猀 搀愀礀⸀ 䤀 漀戀琀愀椀渀攀搀 琀栀攀 䈀⸀匀⸀ 搀攀最爀攀攀 椀渀 洀愀琀栀攀洀愀琀椀挀猀 昀爀漀洀 琀栀攀 䌀椀琀礀 䌀漀氀氀攀最攀 漀昀 一攀眀 夀漀爀欀 ⠀㄀㤀㌀㜀⤀ 愀渀搀 琀栀攀 䴀⸀䄀⸀ 搀攀最爀攀攀 椀渀 洀愀琀栀攀洀愀琀椀挀猀 昀爀漀洀 䌀漀氀甀洀戀椀愀 唀渀椀瘀攀爀猀椀琀礀 ⠀㄀㤀㌀㤀⤀⸀

਀ After the war I made the decision to obtain an advanced degree and pursue a career in basic scientific research. In furtherance of these goals I commenced a collaboration with Jerome Karle at the Naval Research Laboratory in Washington, D.C. (1947) and at the same time enrolled in the Ph.D. program at the University of Maryland. The collaboration with Dr. Karle proved to be fruitful because his background in physical chemistry and mine in mathematics complemented each other nicely. Not only did this combination enable us to tackle head-on the phase problem of X-ray crystallography, but this work suggested also the topic of my doctoral dissertation, "An N-Dimensional Euclidean Algorithm". By 1954 I had received my Ph.D. degree and Dr. Karle and I had laid the foundations of the direct methods in X-ray crystallography. Our 1953 monograph, "Solution of the Phase Problem I. The Centrosymmetric Crystal", contains the main ideas, the most important of which was the introduction of probabilistic methods, in particular the joint probability distributions of several structure factors, as the essential tool for phase determination. In this monograph we introduced also the concepts of the structure invariants and seminvariants, special linear combinations of the phases, and used them to devise recipes for origin specification in all the centrosymmetric space groups. The extension to the non-centrosymmetric space groups was made some years later. The notion of the structure invariants and seminvariants proved to be of particular importance because they also serve to link the observed diffraction intensities with the needed phases of the structure factors.਀㰀⼀瀀㸀㰀瀀㸀 In 1970 I joined the crystallographic group of the Medical Foundation of Buffalo* of which I was Research Director in 1972, replacing Dr. Dorita Norton. My work on the phase problem continues to this day. During the early years of this period I formulated the neighborhood principle and extension concept, the latter independently proposed by Giacovazzo under the term "representation theory". These ideas laid the groundwork for the probabilistic theories of the higher order structure invariants and seminvariants which were further developed during the late seventies by myself and others. During the eighties I initiated work on the problem of combining the traditional techniques of direct methods with isomorphous replacement and anomalous dispersion in the attempt to facilitate the solution of macromolecular crystal structures. This work continues to the present time. More recently I have formulated the phase problem of X-ray crystallography as a minimal principle in the attempt to strengthen the existing direct methods techniques. Together with colleagues Charles Weeks, George DeTitta and others, we have made the initial applications with encouraging results.਀㰀⼀瀀㸀 ਀ ਀ ਀ ਀ ਀ ਀ ਀ ਀ ਀ ਀ sponsors link òþíèíã àâòî
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