LIPSCHITZ ESTIMATES FOR MULTILINEAR COMMUTATOR OF MARCINKIEWICZ OPERATOR

Size: px
Start display at page:

Download "LIPSCHITZ ESTIMATES FOR MULTILINEAR COMMUTATOR OF MARCINKIEWICZ OPERATOR"

Transcription

1 Reseh d ouiios i heis d hei Siees Vo. Issue Pges -46 ISSN Puished Oie o Deee 7 Joi Adei Pess h://oideiess.e IPSHITZ ESTIATES FOR UTIINEAR OUTATOR OF ARINKIEWIZ OPERATOR DAZHAO HEN Dee o Siee d Ioio Siee Shog Uivesi Hu Shog 4 P. R. hi e-i: As I his e we wi sud he oiui o uiie ouo geeed iiewiz oeo d o Tiee-izoi se Hd se d Hez-Hd se whee he uio eogs o ishiz se. The iiewiz oeo Sei [4]. Sei oved h. Ioduio (iodued eow) ws is deied is ouded o ( R ) o whe is oiuous d sisies i ( S )( ) odiio. uhos hve ioved he esu. O he ohe hd Tohis d Wg (see [5]) osideed he oudedess o he ouo heis Sue ssiiio: 4B 4B5. Kewods d hses: uiie ouo Tiee-izoi se Hez-Hd se Hez se ishiz se. ouied iu zhe. Reeived Augus

2 DAZHAO HEN o. The oved he ouo [ ] is ouded o ( w) BO w A whe is oiuous d sisies i ( S )( ) odiio. Foowig he he i uose o his e is o disuss he oudedess o uiie ouo geeed iiewiz oeo d o Tiee-izoi se Hd se d Hez-Hd se whee i. o. Peiiies d Deiiios Thoughou his e ( ) wi deoe he Hd-iewood i uio o d wie ( ) ( ( )) o wi deoe ue o d R wih sides e o he es. e # d su d. Deoe he Hd ses ( R H ). I is we ow h H ( R )( ) he oi deoosiio heizio (see [] [8] []). Fo > hs d > e F e he hoogeeous Tiee-izoi se. The ishiz se i ( R ) is he se o uios suh h i su R. e (See []). Fo we hve F su d su i d.

3 IPSHITZ ESTIATES FOR UTIINEAR e (See []). Fo we hve su i d su d. e (See []). Fo d > e ( )( ) su d suose h d he ( ). e 4 (See [4]). I B( ) d ( B( ) ). The ( ) ( ). γ γ Deiiio. e. A uio o R is ed H -o i () Su B( ) o soe d o soe > (o o soe ); () B( ) ; () d. R

4 4 DAZHAO HEN e 5 (See [7] []). e. A disiuio o R is i H ( R ) i d o i e wie s i he disiuio sese whee eh is H - o d eh is os. oeove H i wih he iiu e ove deoosiios o s ove. Deiiio. e R B { R } E B \ B d χ χ o Z. whee E () The hoogeeous Hez se is deied K o ( R ) { ( R \{ }) : } K K χ. whee () The ohoogeeous Hez se is deied K o ( R ) { ( R ) : } K K ( R ) χ χb. Deiiio. e R. () The hoogeeous Hez e Hd se is deied HK ( R ) { S ( R ) : G( ) K ( R )}

5 IPSHITZ ESTIATES FOR UTIINEAR 5 d G( ). HK K () The ohoogeeous Hez e Hd se is deied ( R ) { S ( R ) : G( ) K ( R )} HK d G( ) HK K whee G ( ) (see []) is he gd i uio o. The Hez e Hd ses hve he oi deoosiio heizio. Deiiio 4. e R. A uio o R is ed e ( ) -o (o e ( ) -o o esi e) i () Su B( ) o soe > (o o soe ); () B( ) ; () d R η o η [ ( ) ]. e 6 (See [9]). e d ( ). A eee disiuio eogs o HK ( R )( o HK ( R )) i d o i hee eis e ( ) -os (o e ( ) -os o esi e) suoed o B B( ) d oss suh h ( o ) i he S ( R ) sese d HK ( o HK ) ~.

6 6 DAZHAO HEN Deiiio 5 (See []). e R. () A esue uio is sid o eog o hoogeeous we Hez se ( R W ) i K WK > su ( { E : > } ). () A esue uio is sid o eog o ihoogeeous we Hez se ( R WK ) i WK : > su ( { E > } { B : > } ). Deiiio 6. e γ d e hoogeeous o degee zeo o R suh h ( ) d( ). S Assue h i ( S ) γ h is hee eiss os > suh h o S γ ( ). The iiewiz uiie ouo is deied whee Se F d F ( ) ( ) ( ) d. F ( ) ( ) d

7 we so deie h IPSHITZ ESTIATES FOR UTIINEAR 7 d F whih is he iiewiz oeo (see []). e H e he se H h : h ( ) h d. The i is e h ( ) F ( ) d ( ) F ( ). Noe h whe is us he ode ouo. I is we ow h ouos e o ge iees i hoi sis d hve ee wide sudied uhos (see [5] [6] [9] [] []). Ou i uose is o esish he oudedess o he uiie ouo o Tiee-izoi se Hd se d Hez-Hd se. Give osiive iege d we se i d deoe i he i o iie suses { () () } o { } o diee eees is he eee ue o. Fo se { } \. Fo ( ) d { () ()} se ( () ()) () () d (). i i i. Theoes d Poos Theoe. e i( γ ) ( ) wih i ( R ) o d e he uiie ouo o iiewiz oeo s i Deiiio 6. The

8 8 DAZHAO HEN () () is ouded o ( R ) o F ( R ). is ouded o ( R ) o ( R ) o d >. Poo. () Fied ue ( ) d ~. Se ( ( ) ) whee ( ) d. Wie whee χ χ we hve R \ ( ) F ( ) ( ) ( ) R ( ( ) ) ( ( ) ) F ( ) ( ) F (( ( ) ) ( ( ) ) ) ( ) ( ) d ( ) ( ) d ( ( ) ) ( ( ) ) F ( ) ( ) F (( ( ) ) ( ( ) ) ) ( ) F (( ( ) ) ( ( ) ) ) ( ) ( ) F (( ) )

9 IPSHITZ ESTIATES FOR UTIINEAR 9 he (( ) ( ) ) (( ) ( ) ) F F ( ) ( ) F ( ) ( ) F (( ) ( ) ) F (( ) ( ) ) F (( ) ( ) ) F 4 I I I I hus ( ) ( ) ) d d I d I d I d I 4 IV. III II I Fo I usig e we hve d I su d i

10 DAZHAO HEN ( ). ~ i Fi. Fo II usig he Höde s ieui d he oudedess o o d e we ge ( ) ( ) d II ( ) d ( ) d ( ) d ( ) d i i d. ~ i Fo III Höde s ieui we hve (( ) ( ) ) d III

11 IPSHITZ ESTIATES FOR UTIINEAR ( ( ) ) R d ( ) d i d. ~ i Fo IV sie o we hve (( ) ( ) ) F I 4 (( ) ( ) ) F ( ( ) d ( ) ) d d ( ) > d d ( ) > d d ( ) d d. J J J

12 DAZHAO HEN Fo J sie ( ) d d J ( ) d ( ) d ( ) d \ d i i ~. ~ i Fo J sii o J we hve. ~ i J Fo J usig es 4 d γ ( ) d d J ( ) d d γ γ

13 IPSHITZ ESTIATES FOR UTIINEAR ( ) ( ) d γ γ \ ( ) d i γ γ ( ) i ~ γ. ~ i Thus. ~ IV i We u hese esies ogehe usig e d ig he sueu ove suh h we oi. i F This oee he oo o (). () B soe gue s i he oo o () we hve (( ) ( ) ) d d I d I d I d I 4 ( ( ) ) i hus ( ) ( ( ) ). # i

14 4 DAZHAO HEN B usig e d he oudedess o we hve ( ) ( ( )) # i ( ( ( )) ( ) ( ) ). This oee he oo o (). Theoe. e i( γ ) ( ) ( ) wih ( i R ) o. The is ouded o H ( R ) o ( R ). Poo. B e 5 i suies o show h hee eiss os > suh h o eve H -o Wie ( ). ( ) ( ) d ( ) > d I II. Fo I hoose d suh h. B R he oudedess o o o ( R ) (see Theoe ) he size odiio o d Höde s ieui we ge I ( ) ( ) i i.

15 IPSHITZ ESTIATES FOR UTIINEAR 5 Fo II sie > we hve ( ( ) ) d d ( ( ) ) d d J. J Oseve h o > d B B i oows h. ~ ~ B he iowsi ieui d γ S S i we oi d d J R d B i d B i d B i. i Noie h o d B i oows we oi ( ( ) ) d d J

16 DAZHAO HEN 6 ( ( ) R ( ) ) d d ( ( ) ( R ) ) d d ( ) B ( ) d d ( B ) d d γ γ d B i ( ) i γ γ i

17 IPSHITZ ESTIATES FOR UTIINEAR 7 ( ). i γ γ Theeoe sie > > > d >. γ > i d II > i d > i d > i d γ > γ. i oiig he esies o I d II he eds o he desied esu. I is we-ow h he du se o R H is. R BO Fo his d Theoe du gue we esi dedue he oowig ousio: oo. e. i R i γ The s R oiuous io. R BO Theoe. e wih R i o. The is ouded o R K H o. K

18 DAZHAO HEN 8 Poo. B e 6 e R HK d B B su e e -o d. The we hve K χ χ I. I Fo I he oudedess o o (see Theoe ) i is es o vei h i I ( ) i i ( )( ). i

19 Fo I oe h IPSHITZ ESTIATES FOR UTIINEAR 9 ( ) d ( ) ( ( ) d ) Whe ( ) d ( ( ) d ) E J J. d wih i oows o h ~ ~. The he iowsi ieui J R d d ( ) i R d i ( ) d B ( ) [( ) ]. i B he ehod o he esie o J i he oo o he Theoe we ge ( ) J i ( ) i ( ) γ γ ) ( sie ( ) he ( ) χ J J

20 4 i DAZHAO HEN [ ( ( ) ( ) ) ] d E i E [ ( ( ) ( ) ) d ] i [ ( E ( ) d ) ] γ γ ( ) [ ( ) ] i d E i ( ) (( ) ) ( ) (( ) ) ( ) i ( ) (( ) ) ( ) ( ) i (( γ ) ) γ ( ) ( ) i ( ) ( ) ( ( ) ) i i ( ) ( )( ( ) γ) i. i Thus I [ ( i ( )( ( ) ) ) ( )( ( ) ) ) (

21 IPSHITZ ESTIATES FOR UTIINEAR 4 ( ( ( )( ( ) ) ) ( )( ( ) γ ) ) ]. Whe I ( )( ( ) ) [ i ( )( ( ) ) ( )( ( ) ) ( )( ( ) γ) ] i. Whe > I [ ( i ( )( ( ) ) ) ( ( )( ( ) ) ) ( ( )( ( ) ) ( )( ( ) ) )( )

22 4 DAZHAO HEN ( ( )( ( ) ) ( )( ( ) ) )( ) ( ( )( ( ) γ) ( )( ( ) γ) )( ) i. The esies o I d I ed o ( ) K i ( ) d desied esie oows o ig iiu ove deoosiios o. Whe ( ) his id o oudedess is. I [5] u d Xu ove i whe. Now we give esie o we e. Theoe 4. e i( γ ) ( ) wih ( i R ) o. The ( ) s HK ( ) ( R ) oiuous io WK ( R ). Poo. We wie whee eh is e ( ( ) ) o suoed o B d. Wie ( ( ) ) ( ) WK { su > { } E : > }

23 IPSHITZ ESTIATES FOR UTIINEAR 4 ( ( ) ) su { > 4 { } E : > } G G. B he ( ) oudedess o I i Theoe we ge d esie sii o h o G ( ( ) ) ( ) χ. i To esie G e us ow use he esie ( ) ( ) ( ) i ( ) i ( ) ( ) i γ γ ( ) ( ) i whih we ge i he oo o Theoe. Noe h whe E ( ) 4 4 ( ) [ ( ) i ( )

24 44 DAZHAO HEN ( ) ( ) ( ) γ γ ( ) ( ) ] 4 i 4 [( ) ( ) 4 ( ) ( ) ( ) 4 ( ) ( ) ( ) 4 γ γ ( ) ( ) ( ) ] 4 ( ) (( ) ) i ( ( ) ) i ( ) o > e e he i osiive iege sisig he i > we hve ( ) i 4 { E : ( ) > }.

25 So we oi IPSHITZ ESTIATES FOR UTIINEAR 45 G su { > ( ( ) ) su { ( ) > ( ) su > ( ) } ( ) } i ( ). Now oiig he ove esies o G d G we oi ( ) ( ) WK i ( ). Theoe 4 oows ig he iiu ove e oi deoosiios. Reeees [] S. hio A oe o ouos Idi Uiv. h. J. (98) 7-6. [] W. G. he Besov esies o ss o uiie sigu iegs A h. Sii 6 () [] R. A. Devoe d R.. Sh i uios esuig soohess e. Ae. h. So. 47 (984). [4] J. Gi-uev d. J.. Heeo A heo o Hd ses ssoied o Hez ses Po. odo h. So. 69 (994) [5] G. E. Hu S. Z. u d D.. Yg The weed Hez ses J. Beiig No. Uiv. (N. Si.)(hi) (997) 7-4. [6] S. Jso e osiio d ouos o sigu ieg oeos A. h. 6 (978) 6-7. [7]. Z. iu Boudedess o uiie oeo o Tiee-izoi ses Ie. J. h. & h. Si. 5 (4) 59-7.

26 46 DAZHAO HEN [8]. Z. iu The oiui o ouos o Tiee-izoi ses Ieg Euios d Oeo Theo 49 (4) [9] S. Z. u. Wu d D.. Yg Boudedess o ouos o Hd e ses Si. i hi (Se. A) 45 () [] S. Z. u d. F. Xu Boudedess o ouos eed o iiewiz iegs o Hd e ses Asis i Theo d Aiios (4) 5-. [] S. Z. u d D.. Yg The deoosiio o he weighed Hez ses d is iios Si. i hi (Se. A) 8 (995) [] S. Z. u d D.. Yg The weighed Hez e Hd ses d is iios Si. i hi (Se. A) 8 (995) []. Puszsi heizio o he Besov ses vi he ouo oeo o oi Roheg d Weiss Idi Uiv. h. J. 44 (995) -7. [4] E.. Sei Hoi Asis: Re-Vie ehods Ohogoi d Osio Iegs Pieo Uiv. Pess Pieo 99. [5] A. Tohis d S. Wg A oe o he iiewiz ieg oo. h. 6/6 (99) 5-4. g

4.1 Schrödinger Equation in Spherical Coordinates

4.1 Schrödinger Equation in Spherical Coordinates Phs 34 Quu Mehs D 9 9 Mo./ Wed./ Thus /3 F./4 Mo., /7 Tues. / Wed., /9 F., /3 4.. -. Shodge Sphe: Sepo & gu (Q9.) 4..-.3 Shodge Sphe: gu & d(q9.) Copuo: Sphe Shodge s 4. Hdoge o (Q9.) 4.3 gu Moeu 4.4.-.

More information

). So the estimators mainly considered here are linear

). So the estimators mainly considered here are linear 6 Ioic Ecooică (4/7 Moe Geel Cedibiliy Models Vigii ATANASIU Dee o Mheics Acdey o Ecooic Sudies e-il: vigii_siu@yhooco This couicio gives soe exesios o he oigil Bühl odel The e is devoed o sei-lie cedibiliy

More information

ON THE EXTENSION OF WEAK ARMENDARIZ RINGS RELATIVE TO A MONOID

ON THE EXTENSION OF WEAK ARMENDARIZ RINGS RELATIVE TO A MONOID wwweo/voue/vo9iue/ijas_9 9f ON THE EXTENSION OF WEAK AENDAIZ INGS ELATIVE TO A ONOID Eye A & Ayou Eoy Dee of e Nowe No Uvey Lzou 77 C Dee of e Uvey of Kou Ou Su E-: eye76@o; you975@yooo ABSTACT Fo oo we

More information

Physics 232 Exam II Mar. 28, 2005

Physics 232 Exam II Mar. 28, 2005 Phi 3 M. 8, 5 So. Se # Ne. A piee o gl, ide o eio.5, h hi oig o oil o i. The oil h ide o eio.4.d hike o. Fo wh welegh, i he iile egio, do ou ge o eleio? The ol phe dieee i gie δ Tol δ PhDieee δ i,il δ

More information

Coefficient Inequalities for Certain Subclasses. of Analytic Functions

Coefficient Inequalities for Certain Subclasses. of Analytic Functions I. Jourl o Mh. Alysis, Vol., 00, o. 6, 77-78 Coeiie Iequliies or Ceri Sulsses o Alyi Fuios T. Rm Reddy d * R.. Shrm Deprme o Mhemis, Kkiy Uiversiy Wrgl 506009, Adhr Prdesh, Idi reddyr@yhoo.om, *rshrm_005@yhoo.o.i

More information

Physics 232 Exam I Feb. 13, 2006

Physics 232 Exam I Feb. 13, 2006 Phsics I Fe. 6 oc. ec # Ne..5 g ss is ched o hoizol spig d is eecuig siple hoic oio. The oio hs peiod o.59 secods. iiil ie i is oud o e 8.66 c o he igh o he equiliiu posiio d oig o he le wih eloci o sec.

More information

BINOMIAL THEOREM OBJECTIVE PROBLEMS in the expansion of ( 3 +kx ) are equal. Then k =

BINOMIAL THEOREM OBJECTIVE PROBLEMS in the expansion of ( 3 +kx ) are equal. Then k = wwwskshieduciocom BINOMIAL HEOREM OBJEIVE PROBLEMS he coefficies of, i e esio of k e equl he k /7 If e coefficie of, d ems i e i AP, e e vlue of is he coefficies i e,, 7 ems i e esio of e i AP he 7 7 em

More information

Parametric Methods. Autoregressive (AR) Moving Average (MA) Autoregressive - Moving Average (ARMA) LO-2.5, P-13.3 to 13.4 (skip

Parametric Methods. Autoregressive (AR) Moving Average (MA) Autoregressive - Moving Average (ARMA) LO-2.5, P-13.3 to 13.4 (skip Pmeti Methods Autoegessive AR) Movig Avege MA) Autoegessive - Movig Avege ARMA) LO-.5, P-3.3 to 3.4 si 3.4.3 3.4.5) / Time Seies Modes Time Seies DT Rdom Sig / Motivtio fo Time Seies Modes Re the esut

More information

Degree of Approximation of Fourier Series

Degree of Approximation of Fourier Series Ieaioal Mahemaical Foum Vol. 9 4 o. 9 49-47 HIARI Ld www.m-hiai.com h://d.doi.og/.988/im.4.49 Degee o Aoimaio o Fouie Seies by N E Meas B. P. Padhy U.. Misa Maheda Misa 3 ad Saosh uma Naya 4 Deame o Mahemaics

More information

NECESSARY AND SUFFICIENT CONDITIONS FOR NEAR- OPTIMALITY HARVESTING CONTROL PROBLEM OF STOCHASTIC AGE-DEPENDENT SYSTEM WITH POISSON JUMPS

NECESSARY AND SUFFICIENT CONDITIONS FOR NEAR- OPTIMALITY HARVESTING CONTROL PROBLEM OF STOCHASTIC AGE-DEPENDENT SYSTEM WITH POISSON JUMPS IJRRS 4 M wwweom/vome/vo4ie/ijrrs_4 NCSSRY N SUFFICIN CONIIONS FOR NR- OPIMLIY RVSING CONROL PROBLM OF SOCSIC G-PNN SYSM WI POISSON JUMPS Xii Li * Qimi Z & Jiwei Si Soo o Memi Come Siee NiXi Uiveiy YiC

More information

The sphere of radius a has the geographical form. r (,)=(acoscos,acossin,asin) T =(p(u)cos v, p(u)sin v,q(u) ) T.

The sphere of radius a has the geographical form. r (,)=(acoscos,acossin,asin) T =(p(u)cos v, p(u)sin v,q(u) ) T. Che 5. Dieeil Geome o Sces 5. Sce i meic om I 3D sce c be eeseed b. Elici om z =. Imlici om z = 3. Veco om = o moe geel =z deedig o wo mees. Emle. he shee o dis hs he geoghicl om =coscoscossisi Emle. he

More information

Physics 232 Exam I Feb. 14, 2005

Physics 232 Exam I Feb. 14, 2005 Phsics I Fe., 5 oc. ec # Ne..5 g ss is ched o hoizol spig d is eecuig siple hoic oio wih gul eloci o dissec. gie is i ie i is oud o e 8 c o he igh o he equiliiu posiio d oig o he le wih eloci o.5 sec..

More information

-HYBRID LAPLACE TRANSFORM AND APPLICATIONS TO MULTIDIMENSIONAL HYBRID SYSTEMS. PART II: DETERMINING THE ORIGINAL

-HYBRID LAPLACE TRANSFORM AND APPLICATIONS TO MULTIDIMENSIONAL HYBRID SYSTEMS. PART II: DETERMINING THE ORIGINAL UPB Sc B See A Vo 72 I 3 2 ISSN 223-727 MUTIPE -HYBRID APACE TRANSORM AND APPICATIONS TO MUTIDIMENSIONA HYBRID SYSTEMS PART II: DETERMININ THE ORIINA Ve PREPEIŢĂ Te VASIACHE 2 Ace co copeeă oă - pce he

More information

Primal and Weakly Primal Sub Semi Modules

Primal and Weakly Primal Sub Semi Modules Aein Inenionl Jounl of Conepoy eeh Vol 4 No ; Jnuy 204 Pil nd Wekly Pil ub ei odule lik Bineh ub l hei Depen Jodn Univeiy of iene nd Tehnology Ibid 220 Jodn Ab Le be ouive eiing wih ideniy nd n -ei odule

More information

PROPOSED SIGNAL HEADS 4 SECTION WITH BACK PLATE 12" CLEARANCE CHART 12" PRESENT SP-8 TYP. TYP. FDC WMV 24"OAK 24"OAK PAINTED WHITE LINE EOI.

PROPOSED SIGNAL HEADS 4 SECTION WITH BACK PLATE 12 CLEARANCE CHART 12 PRESENT SP-8 TYP. TYP. FDC WMV 24OAK 24OAK PAINTED WHITE LINE EOI. I I I I I I I I I I I I I I I I I I I I I 0 0 I I 0 0 0 arwick lvd IO I K " OO I IO I K " I 0 & 0 OO QU / / / 0 & 0 / 0 & 0 0 & 0 0 & 0 (V) (V) / V V / / V V V I OI UI IO I O O OI UI IO V O 0" " OI OI

More information

African Journal of Science and Technology (AJST) Science and Engineering Series Vol. 4, No. 2, pp GENERALISED DELETION DESIGNS

African Journal of Science and Technology (AJST) Science and Engineering Series Vol. 4, No. 2, pp GENERALISED DELETION DESIGNS Af Joul of See Tehology (AJST) See Egeeg See Vol. 4, No.,. 7-79 GENERALISED DELETION DESIGNS Mhel Ku Gh Joh Wylff Ohbo Dee of Mhe, Uvey of Nob, P. O. Bo 3097, Nob, Key ABSTRACT:- I h e yel gle ele fol

More information

Suggested Solution for Pure Mathematics 2011 By Y.K. Ng (last update: 8/4/2011) Paper I. (b) (c)

Suggested Solution for Pure Mathematics 2011 By Y.K. Ng (last update: 8/4/2011) Paper I. (b) (c) per I. Le α 7 d β 7. The α d β re he roos o he equio, such h α α, β β, --- α β d αβ. For, α β For, α β α β αβ 66 The seme is rue or,. ssume Cosider, α β d α β y deiiio α α α α β or some posiive ieer.

More information

Viewing in 3D. Viewing in 3D. Planar Geometric Projections. Taxonomy of Projections. How to specify which part of the 3D world is to be viewed?

Viewing in 3D. Viewing in 3D. Planar Geometric Projections. Taxonomy of Projections. How to specify which part of the 3D world is to be viewed? Viewig i 3D Viewig i 3D How o speci which pa o he 3D wo is o e viewe? 3D viewig voume How o asom 3D wo cooiaes o D ispa cooiae? Pojecios Cocepua viewig pipeie: Xom o ee coos 3D cippig Pojec Xom o viewpo

More information

_ J.. C C A 551NED. - n R ' ' t i :. t ; . b c c : : I I .., I AS IEC. r '2 5? 9

_ J.. C C A 551NED. - n R ' ' t i :. t ; . b c c : : I I .., I AS IEC. r '2 5? 9 C C A 55NED n R 5 0 9 b c c \ { s AS EC 2 5? 9 Con 0 \ 0265 o + s ^! 4 y!! {! w Y n < R > s s = ~ C c [ + * c n j R c C / e A / = + j ) d /! Y 6 ] s v * ^ / ) v } > { ± n S = S w c s y c C { ~! > R = n

More information

T h e C S E T I P r o j e c t

T h e C S E T I P r o j e c t T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T

More information

P a g e 3 6 of R e p o r t P B 4 / 0 9

P a g e 3 6 of R e p o r t P B 4 / 0 9 P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J

More information

Clicks, concurrency and Khoisan

Clicks, concurrency and Khoisan Poooy 31 (2014). Sueey ei Cic, cocuecy Koi Jui Bie Uiveiy o Eiu Sueey ei Aeix: Tciio Ti Aeix y ou e coex ei ioy o oio ue o e ou o!xóõ i e iy ouce. 1 Iii o-cic Te o-cic iii e oy ii o oe ue, o ee i ie couio

More information

Simple Methods for Stability Analysis of Nonlinear Control Systems

Simple Methods for Stability Analysis of Nonlinear Control Systems Poeeig of he Wol Coge o Egieeig Coe Siee 009 Vol II WCECS 009, Ooe 0-, 009, S Fio, USA Sile Meho fo Sili Ali of Nolie Cool Se R. Moek, Mee, IAENG, I. Sv, P. Pivoňk, P. Oe, M. Se A Thee eho fo ili li of

More information

Computer Aided Geometric Design

Computer Aided Geometric Design Copue Aided Geoei Design Geshon Ele, Tehnion sed on ook Cohen, Riesenfeld, & Ele Geshon Ele, Tehnion Definiion 3. The Cile Given poin C in plne nd nue R 0, he ile ih ene C nd dius R is defined s he se

More information

RAKE Receiver with Adaptive Interference Cancellers for a DS-CDMA System in Multipath Fading Channels

RAKE Receiver with Adaptive Interference Cancellers for a DS-CDMA System in Multipath Fading Channels AKE v wh Apv f Cs fo DS-CDMA Ss Muph Fg Chs JooHu Y Su M EEE JHog M EEE Shoo of E Egg Sou o Uvs Sh-og Gw-gu Sou 5-74 Ko E-: ohu@su As hs pp pv AKE v wh vs og s popos fo DS-CDMA ss uph fg hs h popos pv

More information

IJRET: International Journal of Research in Engineering and Technology eissn: pissn:

IJRET: International Journal of Research in Engineering and Technology eissn: pissn: IJRE: Iiol Joul o Rh i Eii d holo I: 39-63 I: 3-738 VRIE OF IME O RERUIME FOR ILE RDE MOWER EM WI DIFFERE EO FOR EXI D WO E OF DEIIO VI WO REOLD IVOLVI WO OMOE. Rvihd. iiv i oo i Mhi R Eii oll RM ROU ih

More information

ABSOLUTE INDEXED SUMMABILITY FACTOR OF AN INFINITE SERIES USING QUASI-F-POWER INCREASING SEQUENCES

ABSOLUTE INDEXED SUMMABILITY FACTOR OF AN INFINITE SERIES USING QUASI-F-POWER INCREASING SEQUENCES Available olie a h://sciog Egieeig Maheaics Lees 2 (23) No 56-66 ISSN 249-9337 ABSLUE INDEED SUMMABILIY FACR F AN INFINIE SERIES USING QUASI-F-WER INCREASING SEQUENCES SKAIKRAY * RKJAI 2 UKMISRA 3 NCSAH

More information

Technical Appendix for Inventory Management for an Assembly System with Product or Component Returns, DeCroix and Zipkin, Management Science 2005.

Technical Appendix for Inventory Management for an Assembly System with Product or Component Returns, DeCroix and Zipkin, Management Science 2005. Techc Appedx fo Iveoy geme fo Assemy Sysem wh Poduc o Compoe eus ecox d Zp geme Scece 2005 Lemm µ µ s c Poof If J d µ > µ he ˆ 0 µ µ µ µ µ µ µ µ Sm gumes essh he esu f µ ˆ > µ > µ > µ o K ˆ If J he so

More information

Swords/Airport Ú City Centre Route Maps

Swords/Airport Ú City Centre Route Maps /p Ú p lb p b l v b f p Ú lb EWOW O l b l l E l E l pl E Þ lf IO bl W p E lb EIWY V WO p E IIE W O p EUE UE O O IEE l l l l v V b l l b vl pp p l W l E v Y W IE l bb IOW O b OE E l l ' l bl E OU f l W

More information

Generating Function for

Generating Function for Itetiol Joul of Ltest Tehology i Egieeig, Mgemet & Applied Siee (IJLTEMAS) Volume VI, Issue VIIIS, August 207 ISSN 2278-2540 Geetig Futio fo G spt D. K. Humeddy #, K. Jkmm * # Deptmet of Memtis, Hidu College,

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

e*s EU[8tr r'glt il IIM IITTT D Cl : L25119AP1984PLiC XL719 New GIN: L27029APl 984PLC Bikrafi Keshari Prusty An ISO 9001 Company

e*s EU[8tr r'glt il IIM IITTT D Cl : L25119AP1984PLiC XL719 New GIN: L27029APl 984PLC Bikrafi Keshari Prusty An ISO 9001 Company [8 i M D S 91 Cpy C : 2119198iC X719 ew : 27029 98C71 9 2 /, M C RD 12, BR HS, HDRBD(x0,D h6 : +91 0 260661 x : +91 0 260660 : hi iid. webib : w.iiih. /SC/ 1 807 0 7h uy, 2018 M. ii bue Vie eide i Seuiie

More information

GREEN ACRES TRIBUTARY B/W BEGIN RETAINING WALL T/W

GREEN ACRES TRIBUTARY B/W BEGIN RETAINING WALL T/W W PK UV S IU PK VI II. HIHW -. /W................................ S IU P..S SU HKS:.... US U... US U IS U S I PPI. SUHWS H I HS HWS.. H I PK UV. VI =. (V ).... /W......'. PPS II... /W..'.'..' W (SI HS)..'.'.'..

More information

Extension of Hardy Inequality on Weighted Sequence Spaces

Extension of Hardy Inequality on Weighted Sequence Spaces Jourl of Scieces Islic Reublic of Ir 20(2): 59-66 (2009) Uiversiy of ehr ISS 06-04 h://sciecesucir Eesio of Hrdy Iequliy o Weighed Sequece Sces R Lshriour d D Foroui 2 Dere of Mheics Fculy of Mheics Uiversiy

More information

Posterior analysis of the compound truncated Weibull under different loss functions for censored data.

Posterior analysis of the compound truncated Weibull under different loss functions for censored data. INRNAIONA JOURNA OF MAHMAIC AND COMUR IN IMUAION Vou 6 oso yss of h oou u Wu u ff oss fuos fo so. Khw BOUDJRDA Ass CHADI Ho FAG. As I hs h Bys yss of gh u Wu suo s os u y II so. Bys sos osog ss hv v usg

More information

Outline. Review Homework Problem. Review Homework Problem II. Review Dimensionless Problem. Review Convection Problem

Outline. Review Homework Problem. Review Homework Problem II. Review Dimensionless Problem. Review Convection Problem adial diffsio eqaio Febay 4 9 Diffsio Eqaios i ylidical oodiaes ay aeo Mechaical Egieeig 5B Seia i Egieeig Aalysis Febay 4, 9 Olie eview las class Gadie ad covecio boday codiio Diffsio eqaio i adial coodiaes

More information

Hyperbolic Heat Equation as Mathematical Model for Steel Quenching of L-shape and T-shape Samples, Direct and Inverse Problems

Hyperbolic Heat Equation as Mathematical Model for Steel Quenching of L-shape and T-shape Samples, Direct and Inverse Problems SEAS RANSACIONS o HEA MASS RANSER Bos M Be As Bs Hpeo He Eo s Me Moe o See Qe o L-spe -spe Spes De Iese Poes ABIA BOBINSKA o Pss Mes es o L Ze See 8 L R LAIA e@o MARARIA BIKE ANDRIS BIKIS Ise o Mes Cope

More information

MA 1201 Engineering Mathematics MO/2017 Tutorial Sheet No. 2

MA 1201 Engineering Mathematics MO/2017 Tutorial Sheet No. 2 BIRLA INSTITUTE OF TECHNOLOGY, MESRA, RANCHI DEPARTMENT OF MATHEMATICS MA Egieeig Matheatis MO/7 Tutoia Sheet No. Modue IV:. Defie Beta futio ad Gaa futio.. Pove that,,,. Pove that, d. Pove that. & whee

More information

4/3/2017. PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103

4/3/2017. PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 PHY 7 Eleodnais 9-9:50 AM MWF Olin 0 Plan fo Leue 0: Coninue eading Chap Snhoon adiaion adiaion fo eleon snhoon deies adiaion fo asonoial objes in iula obis 0/05/07 PHY 7 Sping 07 -- Leue 0 0/05/07 PHY

More information

Classification of Equations Characteristics

Classification of Equations Characteristics Clssiiion o Eqions Cheisis Consie n elemen o li moing in wo imensionl spe enoe s poin P elow. The ph o P is inie he line. The posiion ile is s so h n inemenl isne long is s. Le he goening eqions e epesene

More information

42. (20 pts) Use Fermat s Principle to prove the law of reflection. 0 x c

42. (20 pts) Use Fermat s Principle to prove the law of reflection. 0 x c 4. (0 ts) Use Femt s Piile t ve the lw eleti. A i b 0 x While the light uld tke y th t get m A t B, Femt s Piile sys it will tke the th lest time. We theee lulte the time th s uti the eleti it, d the tke

More information

Eurasian International Center of Theoretical Physics, Eurasian National University, Astana , Kazakhstan

Eurasian International Center of Theoretical Physics, Eurasian National University, Astana , Kazakhstan Joul o Mhems d sem ee 8 8 87-95 do: 765/59-59/8 D DAVID PUBLIHIG E Loled oluos o he Geeled +-Dmesol Ldu-Lsh Equo Gulgssl ugmov Ao Mul d Zh gdullev Eus Ieol Cee o Theoel Phss Eus ol Uves As 8 Khs As: I

More information

I N A C O M P L E X W O R L D

I N A C O M P L E X W O R L D IS L A M I C E C O N O M I C S I N A C O M P L E X W O R L D E x p l o r a t i o n s i n A g-b eanste d S i m u l a t i o n S a m i A l-s u w a i l e m 1 4 2 9 H 2 0 0 8 I s l a m i c D e v e l o p m e

More information

Relation (12.1) states that if two points belong to the convex subset Ω then all the points on the connecting line also belong to Ω.

Relation (12.1) states that if two points belong to the convex subset Ω then all the points on the connecting line also belong to Ω. Lectue 6. Poectio Opeato Deiitio A.: Subset Ω R is cove i [ y Ω R ] λ + λ [ y = z Ω], λ,. Relatio. states that i two poits belog to the cove subset Ω the all the poits o the coectig lie also belog to Ω.

More information

TWO INTERFACIAL COLLINEAR GRIFFITH CRACKS IN THERMO- ELASTIC COMPOSITE MEDIA

TWO INTERFACIAL COLLINEAR GRIFFITH CRACKS IN THERMO- ELASTIC COMPOSITE MEDIA WO INERFIL OLLINER GRIFFIH RS IN HERMO- ELSI OMOSIE MEDI h m MISHR S DS * Deme o Mheml See I Ie o eholog BHU V-5 I he oee o he le o he e e o eeg o o olle Gh e he ee o he wo ohoo mel e e e emee el. he olem

More information

CAVALIER SPA & SALON UPFIT

CAVALIER SPA & SALON UPFIT 7 9 0 7 V S & SO U 0 OY O, V, V U YS SSOS, S. V., SU 0 S V, O 77--7 : 77-- S 0// O OW O V OS. U o. 00 Sheet ist Sheet umber Sheet ame S WS O US, O, O OU, WO O O W SO V WOU SSO O U YS SSOS VY - S OO - S

More information

DERIVING THE DEMAND CURVE ASSUMING THAT THE MARGINAL UTILITY FUNCTIONS ARE LINEAR

DERIVING THE DEMAND CURVE ASSUMING THAT THE MARGINAL UTILITY FUNCTIONS ARE LINEAR Bllei UASVM, Horilre 65(/008 pissn 1843-554; eissn 1843-5394 DERIVING THE DEMAND CURVE ASSUMING THAT THE MARGINAL UTILITY FUNCTIONS ARE LINEAR Crii C. MERCE Uiveriy of Agrilrl iee d Veeriry Mediie Clj-Npo,

More information

UBI External Keyboard Technical Manual

UBI External Keyboard Technical Manual UI Eer eyor ei u EER IORIO ppiio o Ue ouiio e Eer eyor rie uer 12911 i R 232 eyor iee or oeio o e re o UI Eyoer prier Eyoer 11 Eyoer 21 II Eyoer 41 Eyoer 1 Eyoer 1 e eyor o e ue or oer UI prier e e up

More information

VISCOSITY APPROXIMATION TO COMMON FIXED POINTS OF kn- LIPSCHITZIAN NONEXPANSIVE MAPPINGS IN BANACH SPACES

VISCOSITY APPROXIMATION TO COMMON FIXED POINTS OF kn- LIPSCHITZIAN NONEXPANSIVE MAPPINGS IN BANACH SPACES Joral o Maheaical Scieces: Advaces ad Alicaios Vole Nber 9 Pages -35 VISCOSIY APPROXIMAION O COMMON FIXED POINS OF - LIPSCHIZIAN NONEXPANSIVE MAPPINGS IN BANACH SPACES HONGLIANG ZUO ad MIN YANG Deare o

More information

SOME NEW SEQUENCE SPACES AND ALMOST CONVERGENCE

SOME NEW SEQUENCE SPACES AND ALMOST CONVERGENCE Faulty of Siees ad Matheatis, Uivesity of Niš, Sebia Available at: http://www.pf.i.a.yu/filoat Filoat 22:2 (28), 59 64 SOME NEW SEQUENCE SPACES AND ALMOST CONVERGENCE Saee Ahad Gupai Abstat. The sequee

More information

On Fractional Operational Calculus pertaining to the product of H- functions

On Fractional Operational Calculus pertaining to the product of H- functions nenonl eh ounl of Enneen n ehnolo RE e-ssn: 2395-56 Volume: 2 ue: 3 une-25 wwwene -SSN: 2395-72 On Fonl Oeonl Clulu enn o he ou of - funon D VBL Chu, C A 2 Demen of hem, Unve of Rhn, u-3255, n E-ml : vl@hooom

More information

NEIGHBOURHOODS OF A CERTAIN SUBCLASS OF STARLIKE FUNCTIONS. P. Thirupathi Reddy. E. mail:

NEIGHBOURHOODS OF A CERTAIN SUBCLASS OF STARLIKE FUNCTIONS. P. Thirupathi Reddy. E. mail: NEIGHOURHOOD OF CERTIN UCL OF TRLIKE FUNCTION P Tirupi Reddy E mil: reddyp@yooom sr: Te im o is pper is o rodue e lss ( sulss o ( sisyig e odio wi is ( ) p < 0< E We sudy eigouroods o is lss d lso prove

More information

RESPONSE OF A RECTANGULAR PLATE TO BASE EXCITATION Revision E W( )

RESPONSE OF A RECTANGULAR PLATE TO BASE EXCITATION Revision E W( ) RESPONSE OF A RECTANGULAR PLATE TO BASE EXCITATION Revisio E B To Ivie Eil: o@viiod.co Apil, 3 Viles A pliude coefficie E k leg id ple siffess fco elsic odulus ple ickess veue ple ss edig oe,, u, v ode

More information

X-Ray Notes, Part III

X-Ray Notes, Part III oll 6 X-y oe 3: Pe X-Ry oe, P III oe Deeo Coe oupu o x-y ye h look lke h: We efe ue of que lhly ffee efo h ue y ovk: Co: C ΔS S Sl o oe Ro: SR S Co o oe Ro: CR ΔS C SR Pevouly, we ee he SR fo ye hv pxel

More information

ÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s

ÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s MÜHENDİSLİK MEKANİĞİ. HAFTA İMPULS- MMENTUM-ÇARPIŞMA Linea oenu of a paicle: The sybol L denoes he linea oenu and is defined as he ass ies he elociy of a paicle. L ÖRNEK : THE LINEAR IMPULSE-MMENTUM RELATIN

More information

Generalized Fibonacci-Type Sequence and its Properties

Generalized Fibonacci-Type Sequence and its Properties Geelized Fibocci-Type Sequece d is Popeies Ompsh Sihwl shw Vys Devshi Tuoil Keshv Kuj Mdsu (MP Idi Resech Schol Fculy of Sciece Pcific Acdemy of Highe Educio d Resech Uivesiy Udipu (Rj Absc: The Fibocci

More information

TELEMATICS LINK LEADS

TELEMATICS LINK LEADS EEAICS I EADS UI CD PHOE VOICE AV PREIU I EADS REQ E E A + A + I A + I E B + E + I B + E + I B + E + H B + I D + UI CD PHOE VOICE AV PREIU I EADS REQ D + D + D + I C + C + C + C + I G G + I G + I G + H

More information

M5. LTI Systems Described by Linear Constant Coefficient Difference Equations

M5. LTI Systems Described by Linear Constant Coefficient Difference Equations 5. LTI Systes Descied y Lie Costt Coefficiet Diffeece Equtios Redig teil: p.34-4, 245-253 3/22/2 I. Discete-Tie Sigls d Systes Up til ow we itoduced the Fouie d -tsfos d thei popeties with oly ief peview

More information

Caputo Equations in the frame of fractional operators with Mittag-Leffler kernels

Caputo Equations in the frame of fractional operators with Mittag-Leffler kernels nvenon Jounl o Reseh Tehnoloy n nneen & Mnemen JRTM SSN: 455-689 wwwjemom Volume ssue 0 ǁ Ooe 08 ǁ PP 9-45 Cuo uons n he me o onl oeos wh M-ele enels on Qn Chenmn Hou* Ynn Unvesy Jln Ynj 00 ASTRACT: n

More information

The Nehari Manifold for a Class of Elliptic Equations of P-laplacian Type. S. Khademloo and H. Mohammadnia. afrouzi

The Nehari Manifold for a Class of Elliptic Equations of P-laplacian Type. S. Khademloo and H. Mohammadnia. afrouzi Wold Alied cieces Joal (8): 898-95 IN 88-495 IDOI Pblicaios = h x g x x = x N i W whee is a eal aamee is a boded domai wih smooh boday i R N 3 ad< < INTRODUCTION Whee s ha is s = I his ae we ove he exisece

More information

On Absolute Indexed Riesz Summability of Orthogonal Series

On Absolute Indexed Riesz Summability of Orthogonal Series Ieriol Jourl of Couiol d Alied Mheics. ISSN 89-4966 Volue 3 Nuer (8). 55-6 eserch Idi Pulicios h:www.riulicio.co O Asolue Ideed iesz Suiliy of Orhogol Series L. D. Je S. K. Piry *. K. Ji 3 d. Sl 4 eserch

More information

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9 OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at

More information

Continues Model for Vertical Vibration of Tension Leg Platform

Continues Model for Vertical Vibration of Tension Leg Platform Poeedigs o e 9 WSS Ieaioa Coeee o ppied aeais Isa e a 7-9 6 pp58-53 Coies ode o Veia Viaio o esio Leg Pao. R. SPOUR.. GOLSNI. S. SI Depae o Cii gieeig Sai Uiesi o eoog zadi e. ea P.O. ox: 365-933 IRN sa:

More information

Common Solution of Nonlinear Functional Equations via Iterations

Common Solution of Nonlinear Functional Equations via Iterations Proeedigs of he World Cogress o Egieerig Vol I WCE July 6-8 Lodo U.K. Coo Soluio of Noliear Fuioal Equaios via Ieraios Muhaad Arshad Akbar Aza ad Pasquale Vero Absra We obai oo fied ois ad ois of oiidee

More information

Executive Committee and Officers ( )

Executive Committee and Officers ( ) Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r

More information

JHC series electrical connector

JHC series electrical connector i lil oo i iouio oli wi I-- Ⅲ i i- ui ouli wi i-looi i ll iz, li i wi, i o iy I/I ili ovl i o, oo-oo i ii i viio u i u, li i vio li wi,, oi,. liio: i il ii [il] oui: luiu lloy, il l li: - y iu li lol il

More information

Yamaha Virago V-twin. Instruction manual with visual guide for Yamaha XV

Yamaha Virago V-twin. Instruction manual with visual guide for Yamaha XV Yamaha Virago V-twin Instruction manual with visual guide for Yamaha XV700-1100 PHOTO HOWN FOR ILLU TRATION PURPO E ONLY We o use a o e pie e housi g a d s all si gle to e oils fo i p o ed ope aio. If

More information

Lecture 3 summary. C4 Lecture 3 - Jim Libby 1

Lecture 3 summary. C4 Lecture 3 - Jim Libby 1 Lecue su Fes of efeece Ivce ude sfoos oo of H wve fuco: d-fucos Eple: e e - µ µ - Agul oeu s oo geeo Eule gles Geec slos cosevo lws d Noehe s heoe C4 Lecue - Lbb Fes of efeece Cosde fe of efeece O whch

More information

Review for the Midterm Exam.

Review for the Midterm Exam. Review for he iderm Exm Rememer! Gross re e re Vriles suh s,, /, p / p, r, d R re gross res 2 You should kow he disiio ewee he fesile se d he udge se, d kow how o derive hem The Fesile Se Wihou goverme

More information

Chapter 1 Fundamentals in Elasticity

Chapter 1 Fundamentals in Elasticity Fs s ν . Po Dfo ν Ps s - Do o - M os - o oos : o o w Uows o: - ss - - Ds W ows s o qos o so s os. w ows o fo s o oos s os of o os. W w o s s ss: - ss - - Ds - Ross o ows s s q s-s os s-sss os .. Do o ..

More information

Dividing Algebraic Fractions

Dividing Algebraic Fractions Leig Eheme Tem Model Awe: Mlilig d Diidig Algei Fio Mlilig d Diidig Algei Fio d gide ) Yo e he me mehod o mlil lgei io o wold o mlil meil io. To id he meo o he we o mlil he meo o he io i he eio. Simill

More information

Fig. 1S. The antenna construction: (a) main geometrical parameters, (b) the wire support pillar and (c) the console link between wire and coaxial

Fig. 1S. The antenna construction: (a) main geometrical parameters, (b) the wire support pillar and (c) the console link between wire and coaxial a b c Fig. S. The anenna consucion: (a) ain geoeical paaees, (b) he wie suppo pilla and (c) he console link beween wie and coaial pobe. Fig. S. The anenna coss-secion in he y-z plane. Accoding o [], he

More information

c- : r - C ' ',. A a \ V

c- : r - C ' ',. A a \ V HS PAGE DECLASSFED AW EO 2958 c C \ V A A a HS PAGE DECLASSFED AW EO 2958 HS PAGE DECLASSFED AW EO 2958 = N! [! D!! * J!! [ c 9 c 6 j C v C! ( «! Y y Y ^ L! J ( ) J! J ~ n + ~ L a Y C + J " J 7 = [ " S!

More information

BOOM 60JE ELECTRIC EZ-CAL MENU SETUPS ADJUSTMENTS ENTER 5A CHANGE DEFAULTS TILT SETUPS ENTER ENTER ENTER ENTER ENTER 5A-1 CUSTOMER 1 (L60D)

BOOM 60JE ELECTRIC EZ-CAL MENU SETUPS ADJUSTMENTS ENTER 5A CHANGE DEFAULTS TILT SETUPS ENTER ENTER ENTER ENTER ENTER 5A-1 CUSTOMER 1 (L60D) djustments & Setups SS IGOSIS SS OO 0J I Z- JSS SS Z-al low hart hart of SYO KY IOS S/ OS o move back and forth between enu and sub-menu /IG OS Select menus and setting to be adjusted /O OS djust setting

More information

FRACTIONAL MELLIN INTEGRAL TRANSFORM IN (0, 1/a)

FRACTIONAL MELLIN INTEGRAL TRANSFORM IN (0, 1/a) Ieol Jol o Se Reeh Pblo Volme Ie 5 y ISSN 5-5 FRACTIONAL ELLIN INTEGRAL TRANSFOR IN / S.. Kh R..Pe* J.N.Slke** Deme o hem hh Aemy o Egeeg Al-45 Pe I oble No.: 98576F No.: -785759 Eml-mkh@gml.om Deme o

More information

Chapter 1 Fundamentals in Elasticity

Chapter 1 Fundamentals in Elasticity Fs s . Ioo ssfo of ss Ms 분체역학 G Ms 역학 Ms 열역학 o Ms 유체역학 F Ms o Ms 고체역학 o Ms 구조해석 ss Dfo of Ms o B o w oo of os o of fos s s w o s s. Of fs o o of oo fos os o o o. s s o s of s os s o s o o of fos o. G fos

More information

Angle Modulation: NB (Sinusoid)

Angle Modulation: NB (Sinusoid) gle Moulaio: NB Siuoi I uay, i he eage igal i a pue iuoi, ha i, a a i o o PM o FM The, i whee a p a o PM o FM : pea equey eviaio Noe ha i ow a oulaio ie o agle oulaio a i he aiu value o phae eviaio o boh

More information

Department of Mathematics. Birla Institute of Technology, Mesra, Ranchi MA 2201(Advanced Engg. Mathematics) Session: Tutorial Sheet No.

Department of Mathematics. Birla Institute of Technology, Mesra, Ranchi MA 2201(Advanced Engg. Mathematics) Session: Tutorial Sheet No. Dpm o Mhmics Bi Isi o Tchoog Ms Rchi MA Advcd gg. Mhmics Sssio: 7---- MODUL IV Toi Sh No. --. Rdc h oowig i homogos dii qios io h Sm Liovi om: i. ii. iii. iv. Fid h ig-vs d ig-cios o h oowig Sm Liovi bod

More information

Fractional Fourier Series with Applications

Fractional Fourier Series with Applications Aeric Jourl o Couiol d Alied Mheics 4, 4(6): 87-9 DOI: 593/jjc446 Frciol Fourier Series wih Alicios Abu Hd I, Khlil R * Uiversiy o Jord, Jord Absrc I his er, we iroduce coorble rciol Fourier series We

More information

David Randall. ( )e ikx. k = u x,t. u( x,t)e ikx dx L. x L /2. Recall that the proof of (1) and (2) involves use of the orthogonality condition.

David Randall. ( )e ikx. k = u x,t. u( x,t)e ikx dx L. x L /2. Recall that the proof of (1) and (2) involves use of the orthogonality condition. ! Revised April 21, 2010 1:27 P! 1 Fourier Series David Radall Assume ha u( x,) is real ad iegrable If he domai is periodic, wih period L, we ca express u( x,) exacly by a Fourier series expasio: ( ) =

More information

Algebra 2A. Algebra 2A- Unit 5

Algebra 2A. Algebra 2A- Unit 5 Algeba 2A Algeba 2A- Ui 5 ALGEBRA 2A Less: 5.1 Name: Dae: Plymial fis O b j e i! I a evalae plymial fis! I a ideify geeal shapes f gaphs f plymial fis Plymial Fi: ly e vaiable (x) V a b l a y a :, ze a

More information

The CFD Drag Prediction Workshop Series: Summary and Retrospective. David W. Levy Cessna Aircraft Company and the DPW Organizing Committee

The CFD Drag Prediction Workshop Series: Summary and Retrospective. David W. Levy Cessna Aircraft Company and the DPW Organizing Committee CD D icio oo i: u oci Di. C Aic Co D izi Coi o, o, oiu Dio, CA - u 1 CD D icio oo i: u oci, D izi Coi Di.. i C Aic Co w. ioco, o C., oi i, i oi Co:, Huio c,. oui Cio. u, ic A., o H. oio AA c C. o io Ci

More information

Strong Result for Level Crossings of Random Polynomials. Dipty Rani Dhal, Dr. P. K. Mishra. Department of Mathematics, CET, BPUT, BBSR, ODISHA, INDIA

Strong Result for Level Crossings of Random Polynomials. Dipty Rani Dhal, Dr. P. K. Mishra. Department of Mathematics, CET, BPUT, BBSR, ODISHA, INDIA Iteatioal Joual of Reseach i Egieeig ad aageet Techology (IJRET) olue Issue July 5 Available at http://wwwijetco/ Stog Result fo Level Cossigs of Rado olyoials Dipty Rai Dhal D K isha Depatet of atheatics

More information

Strong Result for Level Crossings of Random Polynomials

Strong Result for Level Crossings of Random Polynomials IOSR Joual of haacy ad Biological Scieces (IOSR-JBS) e-issn:78-8, p-issn:19-7676 Volue 11, Issue Ve III (ay - Ju16), 1-18 wwwiosjoualsog Stog Result fo Level Cossigs of Rado olyoials 1 DKisha, AK asigh

More information

FALL 1 PARTRIDGE TIPPETT NURSING FACILITY DATE:

FALL 1 PARTRIDGE TIPPETT NURSING FACILITY DATE: 1 IDG I IG IIY D: MODY Y G Y DY Y JI M O W MD GG OW WI O WDDY O ID GG O MI MI DY JI W G I IDY WD M O W GG/ OI DY JI IMO O DY MD GG O WI O GZD DO JI I ODO MD OO DID OO D : O J G JI GZD M O MD I Y O O :

More information

Summary: Binomial Expansion...! r. where

Summary: Binomial Expansion...! r. where Summy: Biomil Epsio 009 M Teo www.techmejcmth-sg.wes.com ) Re-cp of Additiol Mthemtics Biomil Theoem... whee )!!(! () The fomul is ville i MF so studets do ot eed to memoise it. () The fomul pplies oly

More information

On Some Hadamard-Type Inequalıtıes for Convex Functıons

On Some Hadamard-Type Inequalıtıes for Convex Functıons Aville t htt://vuedu/ Al Al Mth ISSN: 93-9466 Vol 9, Issue June 4, 388-4 Alictions nd Alied Mthetics: An Intentionl Jounl AAM On Soe Hdd-Tye Inequlıtıes o, Convex Functıons M Ein Özdei Detent o Mthetics

More information

The Non-Truncated Bulk Arrival Queue M x /M/1 with Reneging, Balking, State-Dependent and an Additional Server for Longer Queues

The Non-Truncated Bulk Arrival Queue M x /M/1 with Reneging, Balking, State-Dependent and an Additional Server for Longer Queues Alied Maheaical Sciece Vol. 8 o. 5 747-75 The No-Tucaed Bul Aival Queue M x /M/ wih Reei Bali Sae-Deede ad a Addiioal Seve fo Loe Queue A. A. EL Shebiy aculy of Sciece Meofia Uiveiy Ey elhebiy@yahoo.co

More information

Available online at J. Math. Comput. Sci. 2 (2012), No. 4, ISSN:

Available online at   J. Math. Comput. Sci. 2 (2012), No. 4, ISSN: Available olie a h://scik.og J. Mah. Comu. Sci. 2 (22), No. 4, 83-835 ISSN: 927-537 UNBIASED ESTIMATION IN BURR DISTRIBUTION YASHBIR SINGH * Deame of Saisics, School of Mahemaics, Saisics ad Comuaioal

More information

Numerical Methods. Lecture 5. Numerical integration. dr hab. inż. Katarzyna Zakrzewska, prof. AGH. Numerical Methods lecture 5 1

Numerical Methods. Lecture 5. Numerical integration. dr hab. inż. Katarzyna Zakrzewska, prof. AGH. Numerical Methods lecture 5 1 Numeril Methods Leture 5. Numeril itegrtio dr h. iż. Ktrzy Zkrzewsk, pro. AGH Numeril Methods leture 5 Outlie Trpezoidl rule Multi-segmet trpezoidl rule Rihrdso etrpoltio Romerg's method Simpso's rule

More information

Fourier Series and Applications

Fourier Series and Applications 9/7/9 Fourier Series d Applictios Fuctios epsio is doe to uderstd the better i powers o etc. My iportt probles ivolvig prtil dieretil equtios c be solved provided give uctio c be epressed s iiite su o

More information

Stability of Quadratic and Cubic Functional Equations in Paranormed Spaces

Stability of Quadratic and Cubic Functional Equations in Paranormed Spaces IOSR Joua o Matheatics IOSR-JM e-issn 8-578, p-issn 9-765. Voue, Issue Ve. IV Ju - Aug. 05, - www.iosouas.og Stabiit o uadatic ad ubic Fuctioa Equatios i aaoed Spaces Muiappa, Raa S Depatet o Matheatics,

More information

FBD of SDOF Base Excitation. 2.4 Base Excitation. Particular Solution (sine term) SDOF Base Excitation (cont) F=-(-)-(-)= 2ζω ωf

FBD of SDOF Base Excitation. 2.4 Base Excitation. Particular Solution (sine term) SDOF Base Excitation (cont) F=-(-)-(-)= 2ζω ωf .4 Base Exiaio Ipoa lass of vibaio aalysis Peveig exiaios fo passig fo a vibaig base hough is ou io a suue Vibaio isolaio Vibaios i you a Saellie opeaio Dis dives, e. FBD of SDOF Base Exiaio x() y() Syse

More information

x, x, e are not periodic. Properties of periodic function: 1. For any integer n,

x, x, e are not periodic. Properties of periodic function: 1. For any integer n, Chpr Fourir Sri, Igrl, d Tror. Fourir Sri A uio i lld priodi i hr i o poiiv ur p uh h p, p i lld priod o R i,, r priodi uio.,, r o priodi. Propri o priodi uio:. For y igr, p. I d g hv priod p, h h g lo

More information

UCT RPE INTERIOR BUILDOUT 100 % CD SET UTHSCH - UT

UCT RPE INTERIOR BUILDOUT 100 % CD SET UTHSCH - UT U P IIO UIOU U - U 07O 00 annin I P I OUIIO OU P I W I & I O U WII 00 % 07O 0.0 opyright 07 W rchitects, Inc. ouisiana th loor ouston, 70 7 whrarchitects.com U P IIO UIOU 00 % 0.0 VIIO I/PUI YO ( YO OW

More information

THIS PAGE DECLASSIFIED IAW EO 12958

THIS PAGE DECLASSIFIED IAW EO 12958 L " ^ \ : / 4 a " G E G + : C 4 w i V T / J ` { } ( : f c : < J ; G L ( Y e < + a : v! { : [ y v : ; a G : : : S 4 ; l J / \ l " ` : 5 L " 7 F } ` " x l } l i > G < Y / : 7 7 \ a? / c = l L i L l / c f

More information

Riemann Integral Oct 31, such that

Riemann Integral Oct 31, such that Riem Itegrl Ot 31, 2007 Itegrtio of Step Futios A prtitio P of [, ] is olletio {x k } k=0 suh tht = x 0 < x 1 < < x 1 < x =. More suitly, prtitio is fiite suset of [, ] otiig d. It is helpful to thik of

More information

, k fftw ' et i 7. " W I T H M A. L I O E T O W A R 3 D JSrOKTE X l S T E O H A R I T Y F O R A L L. FIRE AT^ 10N1A, foerohlng * M».

, k fftw ' et i 7.  W I T H M A. L I O E T O W A R 3 D JSrOKTE X l S T E O H A R I T Y F O R A L L. FIRE AT^ 10N1A, foerohlng * M». VOZ O } 0U OY? V O O O O R 3 D SO X S O R Y F O R 59 VO O OUY URY 2 494 O 3 S? SOS OU 0 S z S $500 $450 $350 S U R Y Sz Y 50 300 @ 200 O 200 @ $60 0 G 200 @ $50 S RGS OYS SSS D DRS SOS YU O R D G Y F!

More information

Introduction to Finite Element Method

Introduction to Finite Element Method p. o C d Eo E. Iodo o E Mod s H L p. o C d Eo E o o s Ass L. o. H L p://s.s.. p. o C d Eo E. Cos. Iodo. Appoo o os & o Cs. Eqos O so. Mdso os-es 5. szo 6. wo so Es os 7. os ps o Es 8. Io 9. Co C Isop E.

More information

THE LOWELL LEDGER, INDEPENDENT NOT NEUTRAL.

THE LOWELL LEDGER, INDEPENDENT NOT NEUTRAL. E OE EDGER DEEDE O EUR FO X O 2 E RUO OE G DY OVEER 0 90 O E E GE ER E ( - & q \ G 6 Y R OY F EEER F YOU q --- Y D OVER D Y? V F F E F O V F D EYR DE OED UDER EDOOR OUE RER (E EYEV G G R R R :; - 90 R

More information