Diffraction of Elastic PP-, SV- and SH- Waves on the Arbitrary Deep-founded Cavities in the Anisotropic Rock Massif
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1 Dffcto of Etc PP- SV- S- W o th ty D-fou Ct th otoc oc Mf Lyzzt B tyty Zhu K Mo Bt E Yy tct Th ot to ch th yc t-t ho of ttoc f wth fw ct fou fo th ufc C of oto ffcto of tc PP- SV- S-w co ytc oou tho y u thoy of cyc fucto fo o th ft th co fut o of chc th c of ttoy ffcto of tc w o th fw ct wth ty fo octo fuc of hyc chc ot of uou f f tc w to t-t tt of ttoc f wth -fou ct ott I T ttoc f fou ct tu ft ffcto PP-w SV-w S-w I ITODUCTIO Th thu o wth foo u th cyco tu t whch yt c th fo o t fu ffct of thu c f w u th cht of o thoy ctc of yc c tty of u Th cht y t to th ot cotucto of fct o th ou Mwh ct oct c th uou c fu of u w oct oth fct Th uou uwy tto tu fctu ouy y wth co tuctu ut My ot ct o th wth c ctty Thy ut y uou o f th t two of fft of hozot tc o tu I outou o to c hoc ou tu: o hyo ut ty ot Uou tuctu cy ct o ut t th ut of thu tc But th coct t Coty u to th fct tht th c o cf y th yc ffct Lyzzt B tyty wth th Kzh-Bth Tchc Uty ty uc of Kzht ho: ; f: : tyty@co tyty@tuz Zhu K Mo wth th Ittut of Mchc E Scc ft U Zhoo ty uc of Kzht ho: ; f: Bt E Yy wth th Ittut of Mchc E Scc ft U Zhoo ty uc of Kzht ho: ; f: : ty@co ccut cto of th tu tu of th c ot c cu of th co hooouyy tuctu of th oc f U th coto th ctc y of t t f oto o th ho of uou tuctu u thu h t O th of tu tchoc coto o th of tu of ct of c ffct o uou tuctu fo ou uo w c tuh two-c fct: how-fou -fou Moo th octo of how-fou tuctu tcu c u to th fct tht th ccuto of th c tty cy to couct ct ot oy fo ou w ut o fo ufc w It hou o co th w fct fo Eth Sufc Th -fou tuctu c oct wth th t co of w tot hyuc tu wth fouto cty- o ch t ot tc Th fuc of thu ut oo to th t-t tt of -fou tuctu oct oy wth th ct fuc of th otu t w wthout y fuc of th ufc Thu th c of cut ch to t to ccout o fuy th ffct of y th yc t f t to w oto oto th ttc t f whch w fo th c-y oc hozot uou tuctu of ty fouto fo th oc of th tto f oto u th ct of th yc ffct So w h oty to t uty th ttc yc o o tuctu t of u Th ot fuy o th o of t th ttc t f th oc th fct Th ffcut ccut th yc f of t o ty of tuctu u to w oc y oc f II EVIEW OF ESECES OF TE POBLEMS OF WVE DIFFCTIO O TE O-OMOEEITIES To y of t ch th f of w ffcto o th o-hoot of o of c tty of uou tuctu w c o ot to t o th cto of ch of ctt of th t ctuy uch I Pth ] D E D u ] Zh S Ezho ShM ty L y ] uz VD Kuo M Cho V ooch Shu 456] S
2 Kooy VI Stoozh LB Oooy 78] Y Po CCMow L Mt Cho CC 9] Bf oth] Sh tz] Foty 4] K Mo 5] S Lhty 6] S 7] S Koo 8] Ooto C Kto K M9] Wt Wtt Bt Pu Cu Ech ] th foow whch h co t of th fut fouto of chc fo u of oto ffcto of w otoc otoc oc chc fo o of c tty of uou tuctu W wou to to o c th o of w ffcto wth o-hooto ct o th u of oou ytc tho fo th tu whch t c ct y Th o of w ctt o th o-hoot ct wth u of th tho of th co thoy th tho of ouy t uto tu y th utho u F Kh Lou ] Th f uou th oct co otoc ] o othotoc ] Th wo of utho uo W Du Lu ] c th ch of th tuto ctt of S-w o th ut ccu ct hf-c Thy co otoc u th tho of uto coot yt ctt tho w tchu of fucto fo ot of coot Th o of ctt oto of h w th hf-c tfo to th o of w oto c Th ft yt of uto o y th ucto tho Muty of otoc u t to ccout y w L o Zh Vct W L 4 5] I th wo thy tu th outo fo y of ct o th ufc th c of uou tu otoc u u th fuc of SV-w 4] PP-w 5] Souto ouht th Fou-B fucto Th uc ut how th fuc of uou tu oto th ct o th ufc Th of B-zh 6] ot to o of u of co fucto tho fo o o of ffcto of tc w f th yc t co th c of y-coct uty coct otoc u th o of cc I th 7] Lu Du Lu ow co c ' fucto fo th tuy of cyc cty otoc hf- ffcto of S-w By u of E Fho t uto thy tfo hf- to I th of Xu P XI T- To-ch 8] w c tuy th o of ctt of th coo w PP- wt-tut otoc u o th utho t th o of Bot t th tu uto fo th ott fucto of th ctt fcto of w whch o ucy yz K D C Coh 9] tt tho to uc c th tu thouh th foct of th tu oft th It how tht th tu th oc wth oft th h oy o of fo whch ow to ut th ut ffct wth t u of y t V W L M E Moo S Ch ] tu th o of yc tt fy fouto th c of uou ccu tu t th c of S-w ffcto th otoc u By of ct ytc outo fo two-o S-w th tu th fouto th utho yz ct t fo th ct of fft yc ffct Th tt of th ct tu how co w tuto I th wo ] o u-yu L Zh-y Qu Ch tt th ffct of yh w oto o ytc to of L o th thoy of tc w ctt Thy ch th ctt of yh w fo ut u otc otoc u Th y oth ch th of w ffcto fft ut th ctt ffcto of w oc f wth o-hoot h y c chcttc tht w hou t to ccout t w of th ttu o how tht ch of th yc of uou tuctu th u of ffcto of w o th uou fct otoc y ot fuy o I tcu th o of ffcto of tc w ttoc y yc tty of ty ot uou fct ot of whch t c u th cut coto of uou cotucto uffcty tu I th w ty to f th ch co th yc t-t tt of hozot uou tuctu whch ut y ct otoc y u u th coto of ttoy ffcto of tc otu PP t SV S w III DIFFCTIO OF ELSTIC WVES O TE BITY DEEP-FOUDED CVITIES I TE ISOTOPIC OCK MSSIF Lt u co th o of otoc oc f y t t -y ttoc f wth c of otoy th uto of whch tfy th z oo' w 5]: D D ; th tcty coffct whch o th tc cott of th ot E E th fo c of otoy Oct of uou cotucto c o y ct fft fo fo ccu to occu thouh th u of th fucto ]: z z 4
3 I th c of f th ttoy w of fft tu ty - otu t w uto c t ]: t u u * * * u U ] W uto ff oy y w tu y w u Schtcy th oc of f th ttoy w to ttoc f wth o-hooty o o-hoot c how Fu F Th ch of oto of tc w y ttoc f wth o-hoot Lt co th c of ut ct of ty of ut th -fou hozoty t o w oth uou tuctu F D o th coto of f th ou of th ct w c o th ft th co fut o of chc y w co th c wh th ouy of th ct f of o ft fut o th ouy of th ct outy y f co fut o Fo th fft coto of f th ou w c ut fft ouy uto I tcu fo th ft fut o th coto o t of t: * * * 4 Fo th co fut o coto o th ct: * u 5 u IV SOLUTIOS FO TE FIST D TE SECOD FUDMETL POBLEMS Lt tuy th u of w ffcto th oc f wth o-hoot o th oo uto W c ut tht th o y o y tfo th uto of oto z oo' w Cuchy uto ] to th uto of th foow fo: B B B B u u u u 6 B B B B fo otu t PP- SV- w 45 / / 55 u 8 / 55 - u fucy - fo hft S- w I th c of coto of th tt of t foto of ct ttoc f th coot yt O th uto 6 8 u th foow ff tfoto: ' 9 t tht - ot ft ytc t - th oot of th chcttc uto of th co y uc to th hotz uto t fo th coot : 6 E B B u u * * I th c c wh th tc coffct 6 = = th c of hozot tc ttfcto of th f uto c t ut w ot th foow two uto: / u / 66 u I th ot O tht ct of oc coot yt th of S L L-u of ct u th tfoto 9 co th ot O Thy w co th of th oc Ct yt wth ot o th coot o coot wth th out of th o fo th O Souto of uto ct u u u u u ccoc wth th c of z uoto 4] c t ft fo th uow coffct th cyc t fucto ]: L u By u th tho of to of cyc fucto 4] w c ot o u u y of th coot yt :
4 u L / 66 / L - th coot of th ot O coot yt I o cyc fucto w u th ft fucto c th t c y th ut t outo of th o chctz y th w ttch to fty ot to tto of ct u u th fo th o fo th t coot c fou u th z oo' w th coo tfoto th foow fo: ] ] ] ] L ow u th fucto ff tfoto 9 w c f th o fo ot o th cotou of th ct: - I c of o-ccu cty: - I c of ccu cty: L ; th f th f E th f th f E To t th co ott o th cotou of ct w to u th tho of to of cyc fucto u th tto of foow coto: 4 Th coto tf cu th t > ot ft th t t th zo > thfo I to w co th fct tht th t t t hc th oc cot th foow o c t: ow y th tho of to of cyc fucto uty w c wt th tto of co fucto fo ot o th cotou of th ct: Q P 5 th c of o-ccu of of th cty w c u th foow to: Q 6 P ] ] ; u o f u f L o 7 I c of ccu ct th o o c tfo to uch to Q P 6
5 ; o f u f o u 7 ow ct u o th cotou of ct c t y th o u Q P L 8 By u th fou fo th o tt t o th tfo wth th o w tfo th ouy coto 4 5 to th foow uto: * ' ' * ' ' * ' ' 4 * u 5 u Cotou o fo t y u th cotou to fo ct fou fo cotou fucto of t 4 5] y f foow: ' ' 9 ' - co fucto fo fft fo of cty cotou tht to thouh th cyc fucto 4] to fo th ct t o th cotou of th cty o th ct w ' * * ' * ' u * u u u PP SV S y ot y u th fou of o of ot fucto th hoc : * * u U Q * * ' U 4 * * ' U 4 * * ' U ; Q - co fucto tht cu cyc fucto o4] By u th ouy coto 4 5 fo th ft co fut o y ut coffct o th u of w c ot yt of c uto fo th uow coffct tht c o y ucto tho 4 5]: 4 * U * U 4 * U V LYSIS OF ESULTS To yz th t-t chcttc of th ct th ttoc f w co tto wth tc t E =74* 5 /c E = 5* 5 /c =4 =98 =* 5 /c th tc w t cu to th otu of th ct t of = fucy ch th fo to z I ccoc wth th ot thotc outo w o oth oftw y u Po Eot MtL 7 fo th ccuto of u of t ct th ct of fft fo fo ccu to o-ccu W tt o to t th ouy coto wth o th % fo th tu u of th t fct w wth ct to th coo tu u of t th ct w t th c of o of th ft fut o w w chc o to t th ouy coto fo th ct fct w wth ct to th tu u of th ct th ct w - th c of th o co fut o It h o tt th coc of ou ut wth th ow ut of th ch of ffcto of tc w Lt u you of ch of ct of fft of w PP- SV-S- to th t-t tt F F Ict of fft of w to th t-t tt of ct ttoc oc f ft fut o Fu how th tuto of ct fo fft of w t th c of o th ft fut o of of otoy of f w u ch oth - fucy =5 z
6 VI COCLUSIO I cocuo w c tht th wo o cot y oth ch ut to yz th t-t ho of oc f o th ou hyc otc t of f w ct W co th fuc of co-cto fo of ct th utu fuc ct of ch of th of otoy oc f ch of th of cc fucy of tc w oto th t-t tt of ttoc f wth ct W o c tht th wo t of ch tht h th Kzh-Bth Tchc Uty th Ittut of Mchc E Scc ft U Zhoo uc of Kzht o th t c 4 5 6] EFEECES ] I Pth Poto of w otoc tc u L u 98-8 u ] E D D u Etc w o Mocow u u ] ZhSEzho ShMty L Dyc of tu uou -t Puh ou u 989 u 4] uz VDKuo MCho Dffcto of tc w K Puh ou uo u 978 u 5] uz VTooch Dffcto of tc w utcoht o K Puh ou uo u 97 u 6] Shu VI Coo Dffcto of S-w o occu cyc cty chc 984 Vo7 o u 7] SKoo VIStoozh Dyc t of tcty thoy fo otoc ot K Puh ou uo u 985 u 8] SKoo LBOooVIStoozh Dffcto of tc w o otoc cyc cuo th utcoht Poc of Scc cy of USS Vo 98 o 8-4u ou otozt 959 u 9] Y- Po Dyc coctto of t tc chc Poc of c Socty of C E SCE: cocto of tto 96 o u ] Mu LMt Dyc t o of cyc ufc of fo ft hoou h w chc Poc of c Socty of C E SCE: cocto of tto 96 o4 u ] CC Cho Dffcto of fu w y cty tc t I ou ] Bf oth Dffcto of ttoy tc w o th otc of ty fo // chc Poc of c Socty of C E SCE: cocto of tto 96 V - o4 - PP6-4 u ] Sh tz Sc tty of hyuc fct c coto Mocowotozt 959 u 4] Foty Ccuto of th of uou tuctu cy ct Mocow 98 u 5] ZhSEzho ShMty ZhKMo Scy t tt of uou cotucto otoc y f -t Puh ou u 98 u 6] S Lhty Etc thoy fo otoc oy Mocow u u 7] S Ifuc of to tuto of t th ow uou // ot of Ittut of oc Mchc cy of Scc of U 947 o5 u 8] S Koo St tt of hf- wth tc tc // Thotc chc Kho Uty 97 V u 9] Ooto C Kto K M Bho of Su Tu Du Ethu Poc of th 5 WOK o 97 ] Wt Wtt Bt Pu Cu Ech w ut Tu Mtho TM Stty y D Stt u Kotuto Stztouw otch Fochu u P WBI-PIT 5 VE-V ücuf E ISB ] Xu Y F Sctt of S-w y ut -cyc cyo //Dzh och yu och zho 99 Vo - -8 ] Lu D F cto of th tho of co fucto to ctt of S-w otoc //8-th Itto Co Thotc Mchc f u-8 99 f 99 P95 ] uo W Du Lu Sctt of S-w y ut ccu ct hf c // ou Ethu E E Vto Vo o u tc ID: P ] w L o Zh Vct W L outo fo ufc oto fcto u to uou tw tu: ct SV w // ou Ethu E E Vto Vo о Dc DOI: 7/ Р ] w L o Zh Vct W L outo fo ufc oto fcto u to uou ou ct: Ict P w // ct Sooc Sc Vo 7 о DOI: 7/ y Р96-7 6] B-zh O th ffcto of tc w yc t coctto //CKI:SU:LXZ ] Lu Du Lu ow Sctt yc t coctto of S-w y tfc ccu ho // CKI:ISS: ] Xu P X T- To-chu Sctt of tc w y cyc h y tut o // ct Sooc Sc - M 6 tc ID: Vo9 o- P9-98 9] D S K K Ko Sc oto ffct of tu co wth cot t //c o ] V W L M E Moo S Ch t S-foto ufc fouto o uufc ccu tu // Ethu E E Vto Vo o P7-5 DOI: 7/8--4- ] o u-yu L Zh-y Qu Ch Sctt of yh w fo u otc tc hf-c // CKI:SU:YTC5-4- ] Lyzzt tyty Zhu Mo Bt Yy uz Myzhto Sttoy ffcto of tc S-w oto utuy fuc ct of ty tuctu y ttoc f Poc of th ISME / WSES CM'8 C UK Fuy -5 8 ISB: ISS: ] Lyzzt tyty ch of yc of otoc uty f u th ct of ttoy ffcto of tc w t th c of o th ft fut o //ot of Kzht uc to cy of Scc o - 5- u 4] Lyzzt tyty ch of yc of otoc uty f u th ct of ttoy ffcto of tc w t th c of o th co fut o //ot of Kzht uc to cy of Scc o u 5] tyty L Mo Zh Yy B Myzhto Dyc of ttoc tc cotuu wth o-hoot //Poc of Wo Co o E th Itto Cofc of Mchc E Loo UK u- uy - P 4-7 6] tyty L Mo Zh Yy B Myzhto Sttoy ffcto of tc w o th tu th otoc y f // Poc of th Itto cofc Mo o of thtc chc: thoy t ctc oo u My u 4 htt://cofcu/-9/otw/666
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J. Org. Chem., 1997, 62(12), , DOI: /jo961896m
J. Org. Chem., 1997, 62(12), 392-399, DO:1.121/jo961896m Terms & Conditions Electronic Supporting nformation files are available without a subscription to ACS Web Editions. The American Chemical Society
Econometric modelling and forecasting of intraday electricity prices
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Ninth Marine Air Wing To Be Decommissioned. ment of the Transport Air Broup.
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Map A-2. Riparian Reserves, Late-Successional Reserves, and Adaptive Management Area Land Management Allocations.
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