By Ethel Sara Wolper

**Read or Download Cities and Saints: Sufism and the Transformation of Urban Space in Medieval Anatolia PDF**

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**Extra resources for Cities and Saints: Sufism and the Transformation of Urban Space in Medieval Anatolia**

**Example text**

36) we can individualize a correspondence of {f(q, p)} to the set of the associated Lie operators {ki}" A A {f(q,p)} ~ {kf}. 41) A A A to obtain yet a Lie operator. Notably, the operators {kl} span a Lic algebra with respect to the commutation between operators. We recall that the commutator of two operators F and G is defined by the antisyinmetric product A A A A A A IF, G] - A A FG - A GF. , {f,g}} - A - k{:,,} - k{g,f}. 43) The cominutator of two Lie operators is therefore a Lie operator as well.

Il~g t,l~e ray l)atl~ i~ a, l)laa~(~ tl~r()~gl~ the ()t)ti(:al axis. 17) in t11(; llm,ri(li()lla,1 1)lml( ~, ill(livi(llm,liz(~,(l t)y t,ll( ~, illl)llt ray. F. lysis ()f a r(~,fi'a,(:l,illg sl)lm, re 1)y lisillg a, t)()wer s(wies exl)a,llSi()]l ill l,lle ()if-axis (lista,n(:es an(t a,ngh~,s. xia,l ()I)ti(:s ()r first-()r(ter ()t)ti(:s. tion of para,xia,1 (Ilmri(ti()lm,1) ra,ys t h r o u g h simt)le astignmti(: and stigma,ti(: optical devi(:es can t)e trea,te(t as a, 1D d y n a m i c a l prot)lem, with the "plane of the motion" t)eing respe(:tively any one of the two pla,nes of s y m m e t r y of the s y s t e m ()r any ()ne of the infinite meridional pla, nes.

We consider now the set of dynamical variables {f(q, p)}, which, as previously remarked, configures as a Lie algebra under the Poisson bracket operation. 36) we can individualize a correspondence of {f(q, p)} to the set of the associated Lie operators {ki}" A A {f(q,p)} ~ {kf}. 41) A A A to obtain yet a Lie operator. Notably, the operators {kl} span a Lic algebra with respect to the commutation between operators. We recall that the commutator of two operators F and G is defined by the antisyinmetric product A A A A A A IF, G] - A A FG - A GF.