Method for solving an optimization problem

Abstract

The invention pertains to a computer-implemented method for solving an optimization problem using an analog quantum computer. The method comprises the steps of: (a) training a Physics-Informed Neural Network (PINN) to obtain a complete decomposition of a Gauge potential using a plurality of training samples to address a Counter-Diabatic driving problem in a quantum system, wherein training the PINN comprises: - defining a temporal domain as the input of the PINN, - constructing the PINN on the basis of the temporal domain, - obtaining outputs from the PINN and derivating them, - updating the temporal domain with derivated outputs; and (b) obtaining a set of counterdiabatic terms as the solution for the counter-diabatic driving problem from the PINN; (c) differentiating at least one partial differential equation characterizing a time-dependent behavior of the system; (d) minimizing a loss function; and (e) solving, using the set of counterdiabatic terms, the optimization problem.

Description

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nn. nm .rxm, m m v m n m rm ,nrrrr m n nrm r nn r .rxm, m m rxm, m m v nr₂n,,nmrrr ,n wrnr.₂. n ..nnvnmm ,nnnvnnnrrvv n n mnmznrn mn nrrn w nm v nm nr n nrmn nw .r n rv nm , rm mn - rr, mnnmmz.n rmmnn,nn r nvrr nwr ' nnv,n'nnmnr wrnnwn ' nnvrm ,'rmn m. nnrm mrnr nr nwrn r n v mznrmrnn mn wn n n vn m ^ ^^. nr rmn nm w nnrr n rnrmnrnn m , v r nm vrn, nrw. nrnnnnrnn m mn v m m n m' nm. v rrr,m wn,nnnn, m vrmrnnr mmnn,m r rw.mr, rr rnn m w r nr n rnm vr. n,rv , m rnn m nxv .n r n rn rm rvv nnn nr nnvnn, mr rn n . nmmn, w r nvnn mnmz nnnnv nn,rvn rnrr nnnrr mnmzn w nrnnrrnz m n n rr. w n rrnz.n nrrn m nr w , w n mnnrnn m n n rnrrnmnnnrnnrnv n nn, n. rr r rnrmnnr nnrv n r.nnr nrnn m , w w n mnmzn , v nrmr mnmn r , w nnnnn r rnn rn n rnn m. nn rn nr rnrmn n .. mnnrmm n mrrnmrrnrnrnnr m n n mr rmr rn. mnnr wr mnmznv,nn,n nnn n n mn rm nnvrrm,n rnwnnn n =.wr. nvnnrmn 'm' n n, rmrrnn m nnmrz.r rr ,nrnnnnrn . vnxrn v m nn nrmn nz nn m n rr w rnnnrr vrm, r.n n r rn nnn n nrnn nvnnnmr wnrrnxmmmnxrn nrmrnm m nn nrrrnz,n rmnn n m nn vxrrnn w nrnrn.r m nn nr mr nrnrvmnnn, ,vrnrn n mz nr n.nz r nnnr w nrrr m-nrm nrvnnwrrmrnn rnrrmmnrrr zn nr nrn rmr n-n mn,. rm rr, m n, r-rn n nn , rnrmn m n - 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m nn, nrvr-vnwr nnnn r rwr mnnrr ^^ ^^n ’nrm nrnwn.nxrnn,, nw ^^ ^^ ^^ ^^ ^^ =r>r n ^^ n mnnrrnrn n mnnnn?n rm. n rm - rnrrr,nrn ^^nn ^^>, rnnv.nnn,rxm,n - rvrnn mnrnv m m r .nnnr,n ^^, r w n, rn nn, m nnrmn nr nmm .. rr.n rm mnn rrnrr nr ^ n n nn n ^^ = ^^ ^^ + ^^ ^^ + ^^. nn^>. , rnmmn n> >m v w n r nn. m m nr nwr r mr - mznr. w nr n nrw nrw vrr r nn rn r rn nrn. wr mnmz nn.. - rnrr rr m rxmm nnmrnvrrnn m r... w nnn, rn, r rmnv nmmrnv r , m n nrr wrx mnnn. m nnrm mnnnrrrrn, nvnn rr m rrnrn.r r mmrn wnn, wrn,nvnn rr mrrrmr mrnnrn mrrmrxrn. mr, mr rrnnrnr , nvnn rr mr-r r mmmrn mn w,r wnxrn. mr, mr rr nnr r vrv w mrvnnnnr,nnn ^^:= ^^ ^^, ^^ n w rrvv,r mnn m nr nwnr. wn vrm, nr ^^vr mnrv, n nn: ^^.n n, wr wn ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ r ^^n .. w rmrmn mnn rmn ^^ ⊂ ^^*. rr ^^ nnrnn nn n z mrnv n r rnnrn n m, w. w mr nn ,nnrrn nnrrnn, vmnnrmmnnr n ,wn nn: nn^^ ^^ ^^, ^^ =, ^^, ^^ ∈ × ^^,rnnr nrmnn,nn mnnnnwn vnr: m^^ ^^, ^^ =, ^^, ^^ ∈× ^^ ^^.n n rmnn nn, r rn nn nrn, nmnn nnnnr wnnn nmmrnrmnwrn.,rr n r xrmn mrmnv rmr, rnrr.n n, rnn r mn, n nw rrn nrn”,n rn mn rr r rmrrr “ nrm nnr w ^^,nn n:nn^ ^ ^^ ^^ ^^ ^^wrn>^^rr , ^^ , …n rrn mr wrnn nnrnrm wmn m,x w nnrr>,^^ ^^, ^r^ ^^:m= ^^ ^n m n vrr., nwr r:r^n, ^^, wrrnn ^^nrm :.n rn rmr n w rrnn r-wr v , ^^ ^^, ^^ ≈ ^^ ^^, ^^n., m mnnrnxrrnn m.rmnn mrn,rnrmn nn mrr . rmnn n n rrrr r w n r w ^^>n n '^^ ^^ nmm .. '^^ ^^ ^^ ^^ ^^ ^^ mr,nnr ,B,>rrn nmr nn m r r v m v. n, ^^4n mn nrn n m , m .r zn nmn m m w vnrmm.nr m nrn n “rmnrmn” n ,rnv r , r r m ,r mn nr nwr nr nn nnrnrmnrrnnrvnrnn mr n nwr. nnn rm n. r rrn, n n nnn nrnn w ^ r v rnv rn mn m . ^H,n ^^,, ...nnvv. rn m r wn rrrvnnn nmn. rnrnnn rn w r v nr nvnrmn. r nrzrnm-nnn mv , wrr rrmmnnn n nn nn mnn. wn rmn rm m rv xr -: nrvn wrnnmnnrnr n nr mr - nrn nr nw nr nwr. nrnrr r n nn nwr r w - nn . nn, nr nwr vr mrn mrrnrn rmn n -nmnnmrn n. n mm mrnnnn,rrrvrvvnrmn - nr . nn. nnr,n nr nrmrrm nr nwr mnm wr w mz rmrnrr n zr rnnn.rr,n nmr nmwr wn.rn w rmr nmm .. - rn rrn.n r nvrn vr mxmm nmr rnm wrm-nnnnn mrr mn .rv r w rvr rnm, rnrmmn vrmn , rmr mzn wnn rm n n nm rr. mnn nn w rn n rm.n mnnrrn rmmnnnn n - m ,nnvrnnn,rn ^^mn nrmw wn nvnr wn - rrnn. r n zn rrr.₂ m ,vrrmnvvnrmnn rn nrn rn w n n ^^*rrn m n,nrr nrnnn,nrmz -nrmrmrr wr n. r wr n ₂r m r nn ,nn n n nv . ' nm r₂ mrnmn nw rnrmn.n,r,nmmn, n rnm rnrnm.,,, w n n n wnw r rrn nr-m n mnr. mn w rnmr n n z-x, r rnr m rrrzr w, rm n : - rmnn m 'rn nrn rnrr. -nnrn -nrm m r. wr nrr rvn -rmzn nwr.nnnm n n _ rr,CD nrn .. -xnmm , nvn,rnmnm n m r ’ nmrr,nn mr . nnn v nn nmnwr.nmmn,n n nrwr znrn nnrnmmmrn v,r m ^^,nz wnvrnnrv ^^,v . rmr ,. vr mr7,-^^789^ w rm. n, nr m- nn nr mzn n rrrn m, rnrrnmmmnnn ^n^ ^,^=w>, w n v rm. mnnrnmn nn?n m n nrn. nnnrmrnmrmnw,r m,nnmr nm rrmrr - nrnrr ^^. r r ^^n nmr mx4rm rrmrrr rmnn n nrn m .rrmr, m m mn m r vnn-rmnnrvn, w. mn n rrr nn nrrnnmrmnr ^^, mz rrmr nmr r ^^ wr4r -nrm r wr ,n m r w m , nnn mr nmr nrn, n n vxw m r m n.rnn-v n- m r w nwr rnnn nrz rm. n m-vn n m m rr rrmn r rn nr., wrrn-rnnn,mnnrn mrn nrrnr r,rr m m nmzn, w r nrn, mrvn rv r .r r ,vrn m mnr – n m rrm wnrnn rn nr r wr r m mmn r rr nn -n r rzn r n rnn nwr'r n m r. rv m rnm r. rrmrrmnn rn nmm .. rn m nrm n . nm m m m nr rn mzn rrn m.rmr vrm.nnnnn, rrrnnnn v n m. n, m r nr- m rrn mx r rm ^^*^^ n m, m-r,x w.r ^z^ n mmrxr rmn nmr vr m n n ^^ .nrnn m n ^^ ^^nr , w rrn m'*nmrmr n mr.n vrrrrvmmnnn.rmn rn m nrm rrrmn v n. n . nwrn mrmrmrnrmnm mmn:nn nr n nn:n mr vr wn =>nrv,,,. mnn : n mnn ^^n rmmnn ^^?. r. nrn: rrmr nmr rn nrnr mn : mnrmrnrvnrn. rnnn n:z n rn w n. mzn:mz rrmr nrr m rrmn. rm ^^*^^.nrn:m nnn m n nr- m .r n: rmn nr rmn n rwr zn rrnnr r nmrwr rmr nm nmnmnr .rmmnrn nvnn,nr r rrr v n n n nnr rnnn nr m . mznrm n nnr rm m nn ..nrnmmmmnn,r,.mrnrv mnr n r rmn rr r nn n n n-rmrnnnmnn. z rnr n r mn n r mmr rnr nrnm nrm rnn r v. , nwnnrnmnxmrmrrr v,r mvvnv .m mrn rnxnrn-nmrm r wr ,r r nn w m .mnnr v mnn m nmn rn n,r n nnnr r w,xr r rr n m n rr nn nwr. nrn r nmx m,nr.rrx mn r n r r n , w r wm- nr. xnnvmn r rn rnr nr nwr mrxn vr rnnn rnnvnvrnmzn nwrrn w, w nnn nmrnr m rnn. nn m n, m rr mrrnnrm r mnr r nrvr mn. n v wn -mnnrmmmn nmr mr n, wr nnvvr nn mxnm nnnv. n, r nr r rrnn nwr nrm nn m n ,m n r nrn -rvn mnn. w-rmnn, nwn n, m nrn -rnm nn .'n r n nmr m rrnm n r r n -mnn nmrnrnnrnnnnnnr mm ,n.mrr ,n vr m n m , nrnn,rrnrmn nr n.wr, w nvv n rn n xnv mrxr rv n rm n wr rvv nnnn m rnn rr rmn mnnrr w r nn.. r n nrn nmm .. vrrmn nrn rmn nnn nn .rnnnnnvn,vnr-r rm,n n rn m n nnvnr x nnn m.znr z, wrwr mnn nwnr.n r rnnr r nr ,wnr nnvrn n,nvnnnnrnnr- nrmxr,nn nn r ,. m rrnnnrr w vnrn r mrmn nmrmnr , mn rrm n r nmr v mxnmm nn mzn rm.. nmn n mzn

[0002] nmm .. r rrn:nwr:n vmrm ^n, m w nrr r wrm,nrr n n ^, nnnn vr nr, mr wr nr. m ,nrnmmn, rr rrrnnmn:nr-r vrrm rn,nxrnn ^ ^^ ^^, mnnr nnnn ,n ^*^^, w nr m n n rr ^^xr n ^^ ^^n nr r nrm rnrr*nrmnn mrn n mrxn rrrm wn rr rr nr mnn,n ^^. n, m n nrn m m rn m ^^,rrr .r nrn r,nr r, n,nnnv . nn,nn rn mnmm n, n nn rnrnrrm, rrmnr r n.rmm nn,n ^^. nnn n nr n rnnr r rn r rmnrrrr n,rvx.m, nm:nn vmnnnnrnnnrn r,n ^nr .n r.n r r, nv n^,nnn,n rn,rrnn rn nrn ^^>, n rm ^^ n n , rmrn. mrn n=IJ7,1,K,1Lnnnn nr rnn. rmn rn wn ^^*n ^^ / 0?M,-Nrr r mrmv r vvnz.nr ,rn r n rv :n nnn ^^n mrrvvrnrn m rnnr . rvn rv rn n nrrnnzvn,n ^^x,nvrrwrr rnmrnvrm nn.wvr, ≈ rvv:nv nvrmr mnnnnv ^^nnnr ^^ mn wn n .. - mm v nn rnrxrnn..n r, m r^^ ^^r:^^v n r nmnr mnn mnn rrnm xmn n n n ^^ =.. nr vrn r rrnmn.nrnrn, r v,n nr rn v rv n nn v rmrnrmmnn., r ,v, nrr mmrrmnnmmrrrr. r n nm:mnvrv ^^ ^^n, rn r mmnn ^^ nnn nr v, - . -m nrn r wvnr vm zn n n, ^^. mrvn nr v nrr r nrm r n rw,x rn,wnrm m m w rnnn mn rw.v n nr v mnr nn x rr =.rnn nwr r , nmnn m r rrnn ^^ ^^n =r..nv :mr- mnn vrrnm ^^, rmrnnrm-nnnrnnvn ^^- ^^- r .n m r nn nm w nr:nmn r ww.rnnrmrw, r,n ,mnrrn rmrnrnn zrxr , mn rnnnnrnrOmP, nrn . n r ^^: mmv nn r-nmnnrmnnn n ^^*^^ r vn n nw n ^^ =.^, rrn x vrnr rnrr m rn . rv v nmmrr nr n. , nrmmrn rr. n mnnvrm rm :m r rww mrv n n ^^ ^^ r nrm nrnnn - r.rn ^^*^^wr rw,r ^^r mr zvnr v- nmm .. n ^^nn,rrnmmnr nnnrrr ^r mn. vn r"#nrr ,w ^^, ^^%^"n#^^xr. m nnn :% ""nvnnrr ^nv n nmmn m mrn^r m, r n - .r n n rn -n rrnr nm n ^^nr n r. r , n nmr n ^^nr mn rnn r-n r w>m rr wnmmn ^^ ∈n ^^r7,-, ^^789. r , nrmz mnmmm. x rnn . rmn wrn nn :wr w nmmn m nvnn. n:nnrr, mn nnnmn,nn w wrrr rn r n nm nrr n. m n mrr n r mnnm nnr mr wr m nrr n m .. wrrrr n mzn.n nmr mr. rmmnnxmwmmrrrnmn,rnnn mnrnnn rmrnmm wrvrmr,nnnrn,nwmmrrmmr m n .nnrrnnnrmr nr .nrrn mnrrmrrrnn mmr rn rnr nr rn n rnnmn.m n m n nr mrr r n mmr r r n r r . nnrnr r r n m r m rm rrnr. r n m n mvmnr r nr m.n,n m , mvmn nmnn mrnnrnnmm. nnm,rxm, mnn nn n n n- r r rn mr n mwr rnnr rmxnrmnw mnrnmnnrm vrn.. n ..nnnmm rrnwm, rnnnrnm .nnmnnnm xm, rmr rn r rr m ,r m . mn mnnrrmnnrnnrnrnv nrnn rn m,n r rz nr nw r w.rxm, n mn m.rrnrnn,r nr n rnn xm,rnrrnnr n rr rmrr mnnrr nn m .r m r mv mnnr mr mnwnn mnrnnm: m.n mnnrmrr n:r, rm m m, w mn v rmn. n. rr n n,nn .m rm n:x, rm r nn v n, vmn,nn r rnvnn vmr..n vr v m mn m, n v m mnn. r r r n .mrnnn v n: rnn rnnm . n mvm mn nrn n mn vrn mzn m mnnr r . m rn nn mrnrrrrm,wn r rnrn n, v mn.mz m nn, w r nr nrz nw,nn. v n mvmmnnrn rmnnm.rxm m,n r m mvmrnn,nn vr r nn v m mnn nm.rn nr nr n m ,n vr rr n rwr. r v n mr w mrmn rrmr, m nmr. mrr n nn r nnr nnwmrrv nn r rznrnrrnn r ,r n mv mrv .r m rnn. w nw nmm ..nrmnxnm, nrnr nr rrnn m vr m mrn mnmrznn nnn.rrzn m- nn rn : mrrnn n :rnn m :r n m :r r :mr :rnnm : rnr :nr mrr r : m :vmnr r

[0003] nmm .. x - m nvnn, ^^m rm w nvnr wn - rrn,nn.rn rnn n wn r n zn nmr nr ^^rn rm mn nmrmn rnn w n rn ^^ m n - rrn n n wr,nr r - r . mnm r nnn rxm mn wnn. r w - nrnnrn mnn^^ ^^ ^^' ^^ ^^ ^^' ^^' ^^ ^^' ^^ ^^ ^^' ' ' ' ' ' ^^ ^^ ^^" ^^" ^^ ^^wr v n vr w n n. rrrrnn nrrnm mmnnn..n nx, nmr nrnr n wrnrrrn m n nr r nnn mr w n. wrn r w rnmrrrr.nrrmr,rrrn nr m ,vn mrxrmv mn n rnmn wrnn rn. mnnn. n r rrr,nrrmrvnmnn rr.r , w mrmx,rm wrr- rxmnmnn,. vnw m mnrnr ^^"rn-v r ^^%.nnnr.m. n w n mrx,n ^^,n ^^ ^^ ^^'^^ ^^' ^^'^^'^^ ^^'^^ ^^ ^^'^^'^^ ^^' nmm .. n r nn rrnn.n mnnrr^^ ^^ ^ ^^ ^^^^ ^^ ^^ ^^^ ^^^^ wn^^,-rn: = ^^ nn^^n: =n^^ =mnnrnrnrn wnwnn.,-^^,1,8M^^ ^^=>^^ ^^S,-^^8^M^>^^r mrmrnnv mnn mnvnvnmn nrr nr nwr n ^^. n n n r, w nmr r nmr nrn, n r. rn vr nnn ^ r^.rnv ^n^4,nnn rmrrz mmn vn vn r r4. ^^4 ∈ ^^!*×!*+n,nwnr nrn wn ^^ −- r ^^- r,n ^^4 ∈ ^^!* vmrrxrnnnn n, ^^- r,4^^- r.n vnnn ^ n ^^:,n xr w n ^,4n wn.m. rv r, ^^ ^^ ^^ ^^ ^^nrm mrnnr,nn wnnnn mrmnnnrnrn, n nwr w rnr, rn v n.vr ,n nvnn nwr,n r w m nn r r m ^^ rn rm n.rnn,rnr v vr rn mrmn mnnn wnr nn. rn, w v .nnrnxm x nrv, n v wn rv nr w nnrn,r nnr .n nx r rm, nmnn n .. v mr m .nm,m nr, nwnrn.xn mmnnn n nr nm vr r rn wrvn ^^ m ∈nn, ^^r.,nnxr^ ^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^'^^n.rn nwr nwr mnm m rrnnvnn rxmnr rnmx, m ∘ rrn nmwnnrmn. r.nn rrnnrm.n nn rrrmn nrrnn rrn r w rnnr nr n m vnnn vr n n r nrn.wvr,r rmrn r ^^ w n wnvnnvnn wnn ^^ n4, wwr.nnrmn, nr r rr. nv n mzn m, w wnvnnnnvrvr,nrnrnnmvmn,nmrnrn m n nr nwr. nrrnnn nr w n rm . v , mrnnrn vrnn nrn nwrn m nvnn wnnr n vr^^: ^^: = ^^, ^^* , ^^:rnmr,nrz,nx nm ^^ wrn nwrr n w m n mn n. rmn m n r n r, ^^ ∈ ^r^mn v n,nn ^n^ ∈ ^^n,- w.r ^r^*∈n ^^-.×-.^^ rrnnn wnr- mnrr-m rmnnr m nn nrn^^*mrn rrnrn mr nrr mxrmnnnm wmn zr!n .,×^^, ^^!"., ^^r w#, ^n^%^.^3nnnr, wrn .. nm mm x nn,r vrn.rvr, nw nn nn m n m.n, nwr nmrrnrm nrrnnrnnnmn.n nn.rnn nnr nw mr w mz nnr -mn “nnnmr, wmn” nnnrnnr mrrnnn m r nm mnrrvm ^.^ ∈ ^ , n n n. n , r v. ^7,-, ^^789r ^^ ^^ ^^ ^^ − ^^ n nn v, ^^ ^^ r w mxrn wn rmnr , w n r nn nw n nnnn, r>rn nmr m n n ^^ ^^ v. rn nnn rm, nr n, nnr-n rn rr n n nnm wr ^^ m n.. n mnn, nn,n w rr ^^^zr,.., ^^ ^^ =.mr, rmn rm nn. rmnn^789nm n,.., ^^ ^^789 =, rrnrn n r wnnn rrn mn n ^^ = ^^, nr. n mmn, r nmn7,-nrr.nnnvnnr n zrn, wrnrnrr- rn mn,n ^^ ^^7,-= ^^=>. n,nrrn nr- rm, nnrnrr. rnnn r m nmx^^?J / ,TMI7w,vr, nm nw n mnnnwnn m v vn nmr m nrr,mnr .n n,mnn w rrmn nnn m m nvnn.v n, v n nnn mn nmm ..nrrm nm rn wnnnnnvr x , vrnn rmnn mnn, v . n rn mnnr n rmnrrn nr m rn, rxrrvnnr rmr, rn vn..wvr,r r rr n. n rnn^ ^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^mnrvnmr- nrmn nvr nwmr r nrwn vn nr. n n n rnn n n vnm n n vn rnrn m mrrvmnm, r nrr,v*^^n,rn nn,nm n r. r vmn xrmn ,mn r rn n. r m nn rvrn r- nr vn nnnn,rmmnn w nr nwr m,nmzr n .nrvr, mr r n;<n·. rr nnn,n;1: = ^^, mn vrrn r w nnm-nnrmrn.nnrvnv n rwvvvr,rnr zr,.r., ^^·=,nr-nvnnrm mnn, r wvnr. nrr, rr x r w rxrnr n, rmnn m mmmrnvv ^ mnnnn. r rn ^ rmnmr, n.n.r n .^^ ^^ ^^ ^^ ^^ rmn , r × r n mvrvn. rvm nnr r mrr*rnrnmm nr. nmm .. mrr,, n nrnnrmnn-nrr nvvn rr n ^^ ∈ ^^ . mn wn mn rv mn rm rr. rr, mr nxnr n. nmrrrmn znnmnnmnr m .^ ^ ^^ ^^ ^^ ^^ ^^n xnn, w rm nrmrnm. n n rv n . v , vnn,rm rr nrmn nn nr nwr nr n n n ^^ ^^ ..n n, w, r rn rnnr nrr rmrnm rr. mn r rnnrrn m n m x rn nnrrn rrmn, mmn r nrmrnrv. nn r,nnrn,rnnnnnnm.r^ ^ ^^ ^^ ^^^n r mnnrmrv n ., , , m nnrn wrnm n.nn r mnnx,nr v.r, w ^^ w6Kn1, / -, ^ ^ n ^^ wrm.nr, nrmr,n.rmnnnwnn r- mxr w r rwr. nrr w nrn. m nn., w mrnrn nrn n .,.n n, n nn m nnmr mznr , n vr nrvr mr m mnmz. nwr wn^^>: = ^^I8\16K1, / - + ^^6;,8T81,K,1L + ^^ / 0?M,-N.^^:= ^^ + ^^> + ^^> . nm ..nrrn,rm nmwrvn nxn n rvrnnn nnrrmnn.n nwmnmzr nnrnr^^*− ^.^`*.nn ^,^ ∈ ^!.rrn n r^^ ^, n vnrm m n ^^^8n.^ rrvnrr^8,.^8.`, ^^ =nr, w n nn n r* ^^* − ^^* =xr n. mrn nrrmn.rr, nn mnrnr ^^*r,rnnn ^^=>r , ^^?.J / TMI7∈ ^^-.n×-.r ^^ n,wrrmnr rmm : rmr nr- rvn m ^^3. : mn: ^^ ∈ ^^7,-, ^^789. r:rnr vnr rnr- rm mrn nnn, m n,n ^^ ^^ ^^ ^^^^^^,n ^^ ^^n ^^" ^^ . nrrnnnrnmnn:rnnrwmrnrv n n.^^ r, w nmr nrr n nn r r n nnwr,n ^^ = ^^4, ^^4^^n^^,rnr.n zrnrznnrmrmnn nrnnr mrr ^r^n ^^nn,rmn wr mvxv;;.<1rm nr n nn nmn mr ^^ ,.r nn. ., r v. ^^>, rnv, ^^,nmrrrnnvnrnr rnrm wn rn nn, m nn , rn r rm nrr n rm wr:r n n. n,rm r^^:= ^^ + ^^> + ^^>.n nwrrn vrn mzrr: ^^:= ^^ ^^n ^^, ^ ^^4, ^^4'U4UV,4mnmz w r ^^n ^^4r r ^^^, ^^^ ^^ ^^ ^^ ^^r, wnr ^^rmrrn nmm .. r nmwrrzn ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ rmn mnmm v nn ^^ nn r-rr mx rmmr n nmmrrrn rn .nvrn nrn rnmmn nvnn,n n , n m mr: vr ^^,n wnnrv ^^7,-, ^^789^ w ,. rn mnn ^^=>,n rmmnn ^^?, w n n rr ^^rmm.rr -nrm r wr ,nn nmr mn mn nmrnrr nnrnmrrrn ^^4r. vnn-mnnv, w. mnnrrrnm n , n : nrm mrnn w n m:rnvnn nn.nr m n rrnn n nmn rnn nn:nrnvn nnrmnv.v rrmn.n m n mz nn. w nwrnv nw, n mmznnr: wnrr nrmv rrm nr n mznrm. n nmnn mrv mnn :nmrrvvnn nr v: nvnn nr n rr r rm vr mn wr rmr nmn v nrnv nrnmnmnmr.,

Claims

nmm .. .mmr-mmmnn mnmmrvr,nmnrnm:znrm,nr rn rrnn nr--nrmrvnrrmwrn nmnmr rnnm mr , wrnrnn -nn mrmn n , -nrn n mrmn, - nn rm nrvnm, - n, n mrmn w rv n rmnrnm nr rm nr nr- rvn vrrnnnm nmr rn nrrzn m- nn mnmzn nnn nvrn rmm.znrm,nr rn m m,n . m, wrn rv m nr- rm. . mr, wrn mr: - n n rrCD, - nnn,n - n m n n rr. .rm. m, wrn n rrnn nr . n m ,mrn: rmnn mrv nnnrv nm m.nmm .. .rnwnnmnm, wrm'nmrnn ^^,nnr-rxrvnvn ^r^. . n m , w& 'nn rn vnr mn .mznrmn m m rr .nr n rvnm wrn, wrnvnrm mznmzrm rmr mznrm. .rrznnm- m , wrn n r rn n nn m-nnnnnrvrn. m m rm r . rnrmnm m,x wmmrn nmrnrnmrrnmn wn rv r . vrn n. mr n. mmrn mnrrrn m . nr n m m,mrn nr-nrrmrrm nr,nrr nnwrmrrnnr:mmn n nr rnrrnnnnm,- wnrrmnr nnnr nwr-nrmn nr nwmrrmrn:r rvnrnm nmrn rn nrrzn m- nn m rnmzn rnnnmn nnnnrrrr w-nrmn nr nwr w nr n r rn nn r v r mn,n w mnmm-nnrrm nr nmwrnm.nmmr,nrmn m. nr nmr.r mmrn mnrrrnnm .. .rmrmrm xrrmrmmrrr,rmr mmrnnrn w, wn m n m . r rr m. mr,r-r mrr mrrmmrnnr mn wn, wnmx .

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