Optimal multi-degree reduction of Bézier curves with constraints of endpoints continuity
|
|
- Albert Rich
- 8 years ago
- Views:
Transcription
1 Computer Aded Geometrc Desg 19 ( wwwelsevercom/locate/comad Optmal mult-degree reducto of Bézer curves wth costrats of edpots cotuty Guo-Dog Che, Guo-J Wag State Key Laboratory of CAD&CG, Isttute of Computer Images ad Graphcs, Zhejag Uversty, Hagzhou , Cha Abstract Gve a Bézer curve of degree, the problem of optmal mult-degree reducto (degree reducto of more tha oe degree by a Bézer curve of degree m(m< 1 wth costrats of edpots cotuty s vestgated Wth respect to L 2 orm, ths paper presets oe approxmate method (MDR by L 2 that gves a explct soluto to deal wth t The method has good propertes of edpots terpolato: cotuty of ay r, s (r, s 0 orders ca be preserved at two edpots respectvely The method the paper performs mult-degree reducto at oe tme ad does ot eed the stepwse computg Whe appled to the mult-degree reducto wth edpots cotuty of ay orders, the MDR by L 2 obtas the best least squares approxmato Comparso wth aother method of mult-degree reducto (MDR by L, whch acheves the early best uform approxmato wth respect to L orm, s also gve The approxmate effect of the MDR by L 2 s better tha that of the MDR by L Explct approxmate error aalyss of the mult-degree reducto methods s preseted 2002 Publshed by Elsever Scece BV Keywords: Degree reducto; Bézer curve; Optmal approxmato; Edpot cotuty 1 Itroducto The exchagg of product model data betwee varous CAD/CAM systems s ofte eeded However the represetato schemes of parametrc curves ad surfaces are vared dfferet geometrc modelg systems Such as, the maxmum degree, whch dfferet computer systems ca deal wth, vares qute dramatcally Therefore for the data commucato betwee dverse CAD/CAM systems, curves of hgh degree must be approxmated by curves of lower degree due to varato the maxmum degree allowed * Correspodg author E-mal address: wgj@mathzjueduc (G-J Wag /02/$ see frot matter 2002 Publshed by Elsever Scece BV PII: S (
2 366 G-D Che, G-J Wag / Computer Aded Geometrc Desg 19 ( Thus the problem of how to optmally approxmate a gve parametrc curve by a lower degree curve wth a certa error boud has arse CAGD I recet years, may methods have bee used to reduce the degree of Bézer curves The problem of degree reducto s vewed as the verse process of degree elevato (Forrest, 1972; Far, 1983; Pegl ad Tller, 1995 I geeral, degree reducto s ot exactly possble cotract to the reverse process of degree elevato Thus degree reducto approxmato of parametrc curves ad surfaces has bee wdely studed Dscrete pots ad dervatve formato of orgal curve are used degree reducto approxmato (Daeberg ad Nowack, 1985; Hoschek, 1987 The degree reducto of Bézer curves ca also bee doe by usg Chebyshev polyomals approxmato (Watks ad Worsey, 1988; Lachace, 1988 A smple geometrc costructve method of degree reducto wth costraed Chebyshev polyomals s preseted (Eck, 1993, whle a least squares method of degree reducto wth costraed Legedre polyomals s preseted (Eck, 1995 Usg coverso of bases betwee Chebyshev ad Berste bases, a method of degree reducto wth the reducto matrx s developed (Bogack et al, 1995 From the practcal pot of vew, whe trasmttg geometrc formato from oe system to aother, t s our geeral am to esure a hgh degree of accuracy ad the least possble loss of geometrc formato Moreover degree reducto schemes ofte eed to be combed wth the subdvso algorthm, e, a hgh degree curve s approxmated by a umber of lower degree curve segmets ad cotuty betwee adjacet lower degree curve segmets should be mataed Ufortuately, all methods kow up-to-ow have some dsadvatages Frst, they have o explct solutos for optmal mult-degree reducto wth costrats of edpots cotuty of hgh order ad have to be determed by umerc algorthms such as Remes-type algorthm Secodly, for the multdegree reducto, most methods eed stepwse approxmato ad hece a lot of tme for computg s spet Thrdly, most methods geeral caot acheve the optmal approxmato ay more The am of ths paper s to fd out the method of optmal mult-degree reducto wth edpots cotuty of hgh order Based o the verse of degree elevato ad orthogoal polyomal approxmato theory, a method called MDR by L 2 s preseted ths paper, whch gves a explct soluto ad has the optmal precso for mult-degree reducto wth costras of edpot cotuty wth respect to L 2 orm The method ca perform the degree reducto of more tha oe degree at a tme ad avod the stepwse computg The geometrc terpolato formato of edpots betwee the orgal curve ad the degree-reduced curve ca be preserved, e, cotuty of ay r, s (r, s 0 orders ca be preserved at two edpots respectvely I ths paper aother method called MDR by L s troduced, whch also gves a explct soluto for mult-degree reducto wth respect to L orm ad whch s compared wth the MDR by L 2 For the costrats of edpot cotuty of ay orders, the MDR by L 2 ca obta the best least squares approxmato of mult-degree reducto ad the MDR by L acheves early best uform approxmato The approxmate effect of the MDR by L 2 s obvously better tha that of the MDR by L ad the computatoal examples also dsplay t The orgazato of the paper s as follows The secod secto s prelmares I the thrd secto the best least square mult-degree reducto of Bézer curves wth costras of edpots cotuty (MDR by L 2 ad the approxmate error are preseted The fourth secto compares the MDR by L 2 wth the MDR by L Secto fve presets the cocluso
3 G-D Che, G-J Wag / Computer Aded Geometrc Desg 19 ( Prelmares I ths paper, Π deotes all real polyomals of degree at most The deotato deotes the Eucldea vector orm v v,v, add (, deotes as the dstace fucto wth respect to L orm Gve a degree Bézer curve P (t P B (t, t [0, 1], (1 B (t ( t (1 t s the Berste polyomal of degree ad {P } are the cotrol pots The problem of degree reducto s to fd out a Bézer curve Q(t, t [0, 1], ofdegreem(m< such that a sutable dstace fucto d(p, Q s mmzed Obvously the approxmate result of degree reducto wll vary much accordg to the chose dstace fucto I ths paper, we use the least squares (L 2 orm ad the uform (L orm to measure the approxmate error The dstace fuctos betwee P (t ad Q(t wth respect to L 2 ad L orms o the terval [a,b] are defed as follows respectvely: b d 2 (P, Q P (t Q(t 2 dt, (2 a d (P, Q max P (t Q(t (3 t [a,b] Now the optmal mult-degree reducto wth costras of edpot cotuty ca be descrbed as follows Defto 1 Gve a degree Bézer curve P (t, approxmate t optmally by a degree m(m< 1 Bézer curve Q m (t wth respect to dfferet dstace fucto ad avod the stepwse computg, by cotuty of ay r, s (r, s 0 orders should be preserved at two edpots respectvely Ths problem s called optmal mult-degree reducto wth costras of edpot cotuty The key of the optmal mult-degree reducto the paper s the costrats of edpot cotuty ad the mmzato of the approxmate error dstace fucto, e, fd the best least squares ad best uform approxmato wth respect to the dstace fuctos d 2 ad d, respectvely We frst preset the followg property of Berste polyomals: Lemma 1 Berste polyomal B m (t of degree m, 0 t 1, ca be represeted by + m B m (t,j Bj (t, > m, 0, 1,,m, (4,j j ( m ( m j /( j (5
4 368 G-D Che, G-J Wag / Computer Aded Geometrc Desg 19 ( Proof From the defto of Berste polyomals, we have ( ( m m B m (t (1 t m t (1 t m t (1 t + t m m ( ( m m (1 t m t (1 t m j t j j j0 m (( m j0 ( m j /( + j ( + m (1 t (+j t +j + j j,j B j (t I the followg theorem, a part of the cotrol pots of the approxmate degree reduced Bézer curve are frstly derved to satsfy the geometrc terpolato costrats of two edpots Theorem 1 Gve a degree Bézer curve P (t P B (t, t [0, 1], ad let r + s<m< 1, the the curve ca be expressed as P (t Q(t r f ad oly f Eqs (7 (9 s satsfed: s 1 Q B m (t + P I B (t + r+1 m m s Q B m (t, (6 Q 0 1 Q m 1 Q m j 0,0 b m,m (m, ( P 0, Q j 1 j,j P, 1 m j, j Whe m s>+ r m, ( P j P j j 1 j 1 max(0,j ( m m, j Q m max(0,j ( m,j Q, j 1, 2,,r,, j 1, 2,,s r P I j P j,j Q, j r + 1,r + 2,,+ r m, P I j P j, m s 1 >+ r m; j + r m + 1,+ r m + 2,,m s 1, s P I j P j m,j Q m, j m s,m s + 1,, s 1 (7 (8
5 G-D Che, G-J Wag / Computer Aded Geometrc Desg 19 ( Whe m s + r m, r P I j P j,j Q, m s 1 >r; j r + 1,r + 2,,m s 1, P I j P j r,j Q s m,j Q m, j m s,m s + 1,,+ r m, s P I j P j m,j Q m, m s 1 >r; j + r m + 1,+ r m + 2,, s 1 (9 Where {Q } r, {Q } m m s are the part cotrol pots of degree reduced curve Q m(t of degree m, are the ukow accessoral cotrol pots, ad the followg two equatos must be satsfed {P I } s 1 r+1 d λ Q m (0 dt λ dλ P (0 dt λ, λ 0, 1,,r, d µ Q m (1 dt µ dµ P (1 dt µ, µ 0, 1,,s (10 Proof By Lemma 1, we have B m (t + m j,j Bj (t Substtute t to the rght sde of Eq (6 ad express t matrx form Let,j 0 (j < or j > m,the (Q 0, Q 1,,Q r 0,0 0,1 0, m 1,1 1, m + ( P I r+1, P I r+2,,p I s 1 r,r B r+1 B r+2 B s 1 b(m, 1, m+1 r,r+1 r, m+r + (Q m s,,q m 1, Q m m s,m s m s, s m 1,m 1 m 1, 1 b m,m (m, m, 1 (P 0, P 1,,P r, P r+1,,p s 1, P s,,p B 0 B 1 B m, B m s B 1 B B 0 B 1 B +r m wth the lear depedet property of Berste bases {B }, the ecessary ad suffcet codtos of Eqs (7 (9 ca be derved I addto, from Lemma 1 ad Eq (7, we have,
6 370 G-D Che, G-J Wag / Computer Aded Geometrc Desg 19 ( m Q B m (t m + m j,j Q Bj (t r s 1 P j Bj (t + j0 jr+1 [ m(j,m max(0,j ( m ],j Q Bj (t + j s P j B j (t The Eqs (10 ca be derved from the above equato ad the symmetrcal property of the Bézer curves That s the ed of the proof Remark 1 The process theorem 1 essece s the part verse process of degree elevato (Far, 1991 Remark 2 Let m r + s + 1ad{Q } m s show as (7 The the approxmate degree reduced curve Q m (t of degree m wth cotrol pots {Q } m s the smplest Hermte terpolat, whch preserves the terpolato of r, s orders at two edpots repectvely I fact all cotrol pots {Q } m ca be derved from terpolato codtos Remark 3 Let m 1, r s [(m 1/2] Whem s odd {Q } m s show as (7 ad whe m s eve, {Q } m/2 1 ad {Q } m m/2+1 are show as (7 ad Q m/2 ( Q L s + QR r /2, Q L s P r+1 (r + 1Q r (r + 1, Q R r P m s ( m + sq m s m s The the approxmate curve Q m (t wth cotrol pots {Q } m s the degree reduced Bézer curve the paper of (Pegl ad Tller, Best least squares mult-degree reducto (MDR by L 2 I the approxmate theory, the orthogoal polyomal bass fuctos are always used to solve least squares approxmate problems We wll use costraed Jacob polyomals to mmze the least squares dstace fucto The Jacob polyomals J (r,s (x (Szego, 1975 are orthogoal o the doma ad ca be explctly represeted Berste forms as ( +r ( +s ( J (r,s (x ( 1 + x + 1 ( B, 0, 1,, (11 2 x [ 1, 1] ad r, s > 1 These Jacob polyomals are orthogoal o [ 1, 1] wth respect to the weght fucto w (r,s (x (1 + x r (1 x s Defe the costraed Jacob polyomals J,r,s as J,r,s (x (1 + x r+1 (1 x s+1 J (2r+2,2s+2 r s 2 (x, r + s + 2,r + s + 3, (12
7 G-D Che, G-J Wag / Computer Aded Geometrc Desg 19 ( It forms the orthogoal bass o [ 1, 1] wth respect to the weght w(x 1, ad has roots of multplcty r + 1, s + 1atx 1, +1, respectvely If the fucto f(x (x [ 1, 1] ca be represeted as f(x (1 + x r+1 (1 x s+1 f(x,the Π, the polyomal J (r,s (x a J,r,s (x (13 r+s+2 s the best least squares approxmato of degree to f(x o x [ 1, 1], >r+ s + 1, a 1 δ 1 1 J,r,s (xf (x dx, δ The least squares approxmate error s 1 d 2 (f, J f(x J (x 2 dt f 2 (t dt ( J,r,s (x 2 dx r+s+2 δ a 2 (14 If f(xs defed o the terval [a,b], we ca trasform t to the [ 1, 1] terval by a lear trasform as t (2x b a/(b a From the propertes of Berste polyomals ad Jacob polyomals, we have Lemma 2 For k 0, 1,, let J (r,s k (2t 1 (0 t 1 be the Jacob polyomal of degree k The the lear relato betwee Jacob polyomals ad Berste polyomals {B (t} (0 t 1 ca be expressed the matrx form as follows: J (r,s J (r,s L (r,s B, B ( L (r,s 1J (r,s E (r,s J (r,s, (15 ( J (r,s 0 (2t 1, J (r,s 1 (2t 1,,J (r,s (2t 1 T, (16 B ( B0 (t, B 1 (t,, B (t T, (17 L (r,s ( m(j,k L (r,s k,j (+1 (+1, (( ( /( k + r k + s k L(r,s k,j ( 1 k+ b (k,,j, (18 k ad b (k,,j s show as Eq (5 max(0,j+k Proof By (11, the Jacob polyomals ca be represeted Berste form as (( ( /( + r + s J (r,s (2t 1 ( 1 + B (t, 0, 1,, o the terval [ 1, 1] The from Lemma 1 ad the lear depedet property of Jacob bases ad Berste bases, the cocluso ca be easly derved Now we preset the best least squares mult-degree reducto (MDR by L 2 as follows
8 372 G-D Che, G-J Wag / Computer Aded Geometrc Desg 19 ( Deote P I (t s 1 r+1 P I B (t The the problem of optmal approxmato of P (t wth costrats of edpots cotuty of ay r, s (r, s 0,r + s< 1 orders s equal to fdg out the optmal approxmato of P I (t wthout costrats of edpots cotuty By the propertes of Berste polyomals, we have s 1 r+1 P I B (t (1 ts+1 t r+1 N (r + s + 2, Deote P II N N ( P II P I r+1+ II ( P 0, P II 1,, P II N, P II P II P II BN (t (1 t s+1 t r+1 P II N (t, (19 r The from (19, there s P I (t (1 ts+1 t r+1 P II N (t (1 ts+1 t r+1 P II N B N O the other had, by Lemma 2, there s P II N B N P II N E(2r+2,2s+2 N N N Suppose r + s<m 1, deote M m (r + s + 2, the t s easy to kow that J (2r+2,2s+2 P III N /( N, 0, 1,,N, 0, 1,,N, P II N (t N P III N J (2r+2,2s+2 N III ( P 0, P III 1 J (r,s m (t (1 ts+1 III t r+1 P M J (2r+2,2s+2 M s the best least squares approxmato of degree to J (r,s (t P I (t (1 ts+1 III t r+1 P N J (2r+2,2s+2 N o the terval [ 1, 1] III,, P N P II N E(2r+2,2s+2 N N, Now we try to derve the correspodg Berste form of (1 t s+1 t there s P III M J (2r+2,2s+2 M P III M L(2r+2,2s+2 M M B M P IV M B M, P IV IV M ( P 0, P IV 1,, P IV M P III M L(2r+2,2s+2 M M The (1 t s+1 III t r+1 P M J (2r+2,2s+2 M (1 t s+1 t r+1 P m s 1 IV M B M Q B m (t, ( M Q P IV r 1 r 1 /( m r+1 P II BN (t r+1 P III M J (2r+2,2s+2 M By Lemma 2,, r + 1,r + 2,,m s 1 (20
9 G-D Che, G-J Wag / Computer Aded Geometrc Desg 19 ( The best least squares approxmate error ca be derved as follows: ( ε 2 d 2 P (t, Q m (t ( 1/2 d 2 ( J (r,s (t, J (r,s m (t δ P III 2 (21 m+1 Legedre polyomals are specal cases of Jocob polyomals Therefore, covertg a polyomal Bézer bass to Jacob bass s very smlar to that from Bézer to Legedre Ad as for the detaled covertg process, oe ca refer to (L ad Zhag, 1998 Ths covertg process s smple ad stable To sum up, we ca obta the followg theorem: Theorem 2 Gve a degree Bézer curve P (t, whe{q } m s show as (7 ad (20, m< 1, the mult-degree reduced Bézer curve Q m (t m Q B m (t of degree m s ts best least squares approxmato, by the cotuty of r, s (r, s 0,r + s<m 1 orders ca be preserved at two edpots, respectvely The best least squares error of approxmate mult-degree reducto s ε 2 As compared wth most degree reducto methods, such as the methods by Eck (1993, 1995, the MDR by L 2 possesses a seres of advatages Frst, It avods stepwse approxmato for the mult-degree reducto so that the computg tme ca correspodgly be decreased ad there are o accumulatve calculatve errors Secodly, t ca satsfy costrat codtos of edpot cotuty of ay orders at the same tme of mult-degree reducto, thus the degree reducto computato ca combe wth the subdvso algorthm to crease the precso Furthermore, t acheves the optmal approxmato usg the orthogoal polyomals ad acqures the explct soluto of degree reducto curves Example 1 Let P 12 (t be a Bézer curve of degree 12 wth cotrol pots ( 14, 8, ( 10, 5, ( 7, 5, ( 5, 7, (1, 3, ( 3, 5, (1, 11, (4, 9, (7, 7, (10, 4, (12, 9, (14, 11, (19, 0 The best least squares 3-degree reductos wth dfferet edpot costrats are show Fg 1 Fg 2 shows the 6-degree reducto wth C 1 cotuty after oe subdvso As ca be see from the example, the MDR by L 2 the paper obtas the good approxmato of mult-degree reducto ad ca be combed wth the subdvso algorthm effectvely 4 Comparso betwee the MDR by L 2 ad the MDR by L I the paper (Che ad Wag, 2000, we preset oe smple method (MDR by L to the mult-degree reducto wth respect to L orm ad the MDR by L obtas the early best uform approxmato I the followg we troduce the MDR by L brefly ad compare t wth the MDR by L 2 ths paper by some umercal examples Chebyshev polyomals are oe of the classcal orthogoal polyomals that have bee studed extesvely Let T (x deote the Chebyshev polyomal of degree, whch s defed by T (x cos( arccos x ( 1 x 1 The we ca obta the followg explct Berste represetato (Eck, 1993 T (x ( 1 + (( 2 2 /( B ( x + 1 2, 0, 1, (22
10 374 G-D Che, G-J Wag / Computer Aded Geometrc Desg 19 ( (a (b Fg 1 Reducto from degree 12 (sold to degree 9 (dash (a (r, s (2, 2 (b(r, s (3, 3 (a (b Fg 2 Reducto from degree 12 (sold to degree 6 (dash ((r, s (1, 1 (a Wthout subdvso (b Wth oe subdvso Oe of the mportat propertes of Chebyshev polyomals T (x s the so-called equoscllatg property, e, that the Chebyshev polyomals have + 1 extremal values ( 1 at x cos(π/, 0, 1,, Chebyshev polyomals have bee used wdely degree reducto the past The costraed Chebyshev polyomal s frstly troduced to deal wth degree reducto wth costrats of edpots cotuty (Lachace, 1988 Ufortuately, these costraed Chebyshev polyomals have o explct represetatos except certa specal cases ad have to be determed umercally by a modfed Remez algorthm (Davs, 1963
11 G-D Che, G-J Wag / Computer Aded Geometrc Desg 19 ( From the propertes of Berste polyomals ad Chebyshev polyomals, we have Lemma 3 For k 0, 1,,, the lear relato betwee Chebyshev polyomals {T (2t 1} (0 t 1 ad Berste polyomals {B (t} (0 t 1 ca be expressed matrx form as follows: T C B, B C 1 T A T, (23 T ( T 0 (2t 1, T 1 (2t 1,,T (2t 1 T, (24 C (C k,j (+1 (+1, C k,j ad b (k,,j s show as Eq (5 m(j,k max(0,j+k ( 1 k+ b (k,,j ( /( 2k k, (25 2 The proof of Lemma 3 s smlar to the proof of Lemma 2 Thus the MDR by L ca be descrbed as follows Deote P I (t (1 ts+1 t r+1 P II N (t (1 ts+1 t r+1 P II II N ( P 0, P II 1,, P II N, P II P II, The by (19 ad Lemma 3, there s P II N B N P II N A N N T N P III N T N Let r + s<m 1, deote M m (r + s + 2, P III N III ( P 0, P III 1 N P II BN (t (1 t s+1 t r+1 P II N B N, 0, 1,,N III,, P N P II N A N N By Chebyshev polyomal approxmato theory (Fox ad Parker, 1968, P III M T M s the early best uform approxmato of P II N B N amog all polyomals of degree M o the terval [ 1, 1] Now we derve the correspodg Berste form of (1 t s+1 III tr+1 P M T M By Lemma 3, there s (1 t s+1 III t r+1 P M T M (1 t s+1 t r+1 P m s 1 IV M B M Q B m (t, P IV M IV ( P 0, P IV 1,, P IV M P III ( /( M m r 1 Q P IV r 1 M C M M, r+1, r + 1,r + 2,,m s 1 (26
12 376 G-D Che, G-J Wag / Computer Aded Geometrc Desg 19 ( (a (b Fg 3 The comparso betwee the MDR by L 2 (dash ad the MDR by L (dot (the sold curve s the orgal curve (a Reducto from degree 12 to 6 ((r, s (0, 0 (b Reducto from degree 12 to 8 ((r, s (2, 2 The error boud of early best uform approxmato s preseted as follows: ( d P (t, Q m (t ( ε max (1 t s+1 t r+1 N P III 0 t 1 M+1 (r + 1r+1 (s + 1 s+1 N P III (r + s + 2 r+s+2 (27 M+1 Therefore we ca obta the followg theorem: Theorem 3 Let Q m (t m Q B m (t,{q } m s show as (7 ad (26, the the mult-degree reduced Bézer curve Q m (t of degree m(m< 1 ca approxmate the gve degree Bézer curve P (t wth that the cotuty of r, s (r, s 0,r + s<m 1 orders ca be preserved at two edpots, respectvely It s the early best uform approxmato uder the codtos of edpot terpolao ad the correspodg error boud of degree reducto approxmato s ε Fg 3 presets the comparso of the MDR by L wth the MDR by L 2 usg the put curve the Example 1 of Secto 3 Obvously, the MDR by L 2 s better tha the early best uform approxmate method (MDR by L uder the codtos of edpot cotuty 5 Coclusos By usg the costraed Jacob orthogoal polyomal bass fuctos, ths paper derves oe best least squares approxmato method for mult-degree reducto of Bézer curves wth costrats of edpots cotuty The approxmate degree reduced Bézer curve s show as a explct soluto
13 G-D Che, G-J Wag / Computer Aded Geometrc Desg 19 ( form ad ca preserve cotuty of ay r, s (r, s 0 orders at two edpots, respectvely The error boud s gve ad the degree of accuracy for the approxmato s optmal wth respect to L 2 orm accordg to the tradtoal approxmate theory The method the paper avods stepwse computg for the mult-degree reducto so that the computg tme ca obvously be reduced The method ths paper ca be effectvely combed wth the subdvso algorthm for the approxmato of mult-degree reducto wth a prescrbed error tolerace Ackowledgemets Ths work s supported by the Natoal Natural Scece Foudato of Cha (No ad the Foudato of State Key Basc Research 973 Item (No G Refereces Bogack, P, Weste, S, Xu, Y, 1995 Degree reduto of Bézer curves by uform approxmato wth edpot terpolato Computer-Aded Desg 27 (9, Che, G-D, Wag, G-J, 2000 Multdegree reducto of Bézer curves wth codtos of edpot terpolatos J Software 11 (9, I Chese Daeberg, L, Nowack, H, 1985 Approxmate coverso of surface represetatos wth polyomal bases Computer Aded Geometrc Desg 2 (2, Davs, PJ, 1963 Iterpolato ad Approxmato Dover, New York Eck, M, 1993 Degree reducto of Bézer curves Computer Aded Geometrc Desg 10 (4, Eck, M, 1995 Least squares degree reducto of Bézer curves Computer-Aded Desg 27 (11, Far, G, 1983 Algorthms for ratoal Bézer curves Computer-Aded Desg 15 (2, Far, G, 1991 Curves ad Surfaces for Computer Aded Geometrc Desg, A Practcal Gude Academc Press, New York Forrest, AR, 1972 Iteractve terpolato ad approxmato by Bézer curve Computer J 15 (1, Fox, L, Parker, IB, 1968 Chebyshev Polyomals Numercal Aalyss Oxford Uversty Press, Lodo Hoschek, J, 1987 Approxmato of sple curves Computer Aded Geometrc Desg 4 (1, Lachace, MA, 1988 Chebyshev ecoomzato for parametrc surfaces Computer Aded Geometrc Desg 5 (3, L, Y-M, Zhag, X-Y, 1998 Bass coverso amog Bézer, Tchebyshev ad Legedre Computer Aded Geometrc Desg 15, Pegl, L, Tller, W, 1995 Algorthm for degree reducto of B-sple curves Computer-Aded Desg 27 (2, Szego, G, 1975 Orthogoal Polyomals, 4th ed Amerca Mathematcal Socety, Provdece, RI Watks, M, Worsey, A, 1988 Degree reducto for Bézer curves Computer-Aded Desg 20 (7,
APPENDIX III THE ENVELOPE PROPERTY
Apped III APPENDIX III THE ENVELOPE PROPERTY Optmzato mposes a very strog structure o the problem cosdered Ths s the reaso why eoclasscal ecoomcs whch assumes optmzg behavour has bee the most successful
More informationNumerical Methods with MS Excel
TMME, vol4, o.1, p.84 Numercal Methods wth MS Excel M. El-Gebely & B. Yushau 1 Departmet of Mathematcal Sceces Kg Fahd Uversty of Petroleum & Merals. Dhahra, Saud Araba. Abstract: I ths ote we show how
More information6.7 Network analysis. 6.7.1 Introduction. References - Network analysis. Topological analysis
6.7 Network aalyss Le data that explctly store topologcal formato are called etwork data. Besdes spatal operatos, several methods of spatal aalyss are applcable to etwork data. Fgure: Network data Refereces
More informationAbraham Zaks. Technion I.I.T. Haifa ISRAEL. and. University of Haifa, Haifa ISRAEL. Abstract
Preset Value of Autes Uder Radom Rates of Iterest By Abraham Zas Techo I.I.T. Hafa ISRAEL ad Uversty of Hafa, Hafa ISRAEL Abstract Some attempts were made to evaluate the future value (FV) of the expected
More informationChapter Eight. f : R R
Chapter Eght f : R R 8. Itroducto We shall ow tur our atteto to the very mportat specal case of fuctos that are real, or scalar, valued. These are sometmes called scalar felds. I the very, but mportat,
More informationFractal-Structured Karatsuba`s Algorithm for Binary Field Multiplication: FK
Fractal-Structured Karatsuba`s Algorthm for Bary Feld Multplcato: FK *The authors are worg at the Isttute of Mathematcs The Academy of Sceces of DPR Korea. **Address : U Jog dstrct Kwahadog Number Pyogyag
More informationModels for Selecting an ERP System with Intuitionistic Trapezoidal Fuzzy Information
JOURNAL OF SOFWARE, VOL 5, NO 3, MARCH 00 75 Models for Selectg a ERP System wth Itutostc rapezodal Fuzzy Iformato Guwu We, Ru L Departmet of Ecoomcs ad Maagemet, Chogqg Uversty of Arts ad Sceces, Yogchua,
More informationIDENTIFICATION OF THE DYNAMICS OF THE GOOGLE S RANKING ALGORITHM. A. Khaki Sedigh, Mehdi Roudaki
IDENIFICAION OF HE DYNAMICS OF HE GOOGLE S RANKING ALGORIHM A. Khak Sedgh, Mehd Roudak Cotrol Dvso, Departmet of Electrcal Egeerg, K.N.oos Uversty of echology P. O. Box: 16315-1355, ehra, Ira sedgh@eetd.ktu.ac.r,
More information1. The Time Value of Money
Corporate Face [00-0345]. The Tme Value of Moey. Compoudg ad Dscoutg Captalzato (compoudg, fdg future values) s a process of movg a value forward tme. It yelds the future value gve the relevat compoudg
More informationA Study of Unrelated Parallel-Machine Scheduling with Deteriorating Maintenance Activities to Minimize the Total Completion Time
Joural of Na Ka, Vol. 0, No., pp.5-9 (20) 5 A Study of Urelated Parallel-Mache Schedulg wth Deteroratg Mateace Actvtes to Mze the Total Copleto Te Suh-Jeq Yag, Ja-Yuar Guo, Hs-Tao Lee Departet of Idustral
More informationADAPTATION OF SHAPIRO-WILK TEST TO THE CASE OF KNOWN MEAN
Colloquum Bometrcum 4 ADAPTATION OF SHAPIRO-WILK TEST TO THE CASE OF KNOWN MEAN Zofa Hausz, Joaa Tarasńska Departmet of Appled Mathematcs ad Computer Scece Uversty of Lfe Sceces Lubl Akademcka 3, -95 Lubl
More informationA New Bayesian Network Method for Computing Bottom Event's Structural Importance Degree using Jointree
, pp.277-288 http://dx.do.org/10.14257/juesst.2015.8.1.25 A New Bayesa Network Method for Computg Bottom Evet's Structural Importace Degree usg Jotree Wag Yao ad Su Q School of Aeroautcs, Northwester Polytechcal
More informationPreprocess a planar map S. Given a query point p, report the face of S containing p. Goal: O(n)-size data structure that enables O(log n) query time.
Computatoal Geometry Chapter 6 Pot Locato 1 Problem Defto Preprocess a plaar map S. Gve a query pot p, report the face of S cotag p. S Goal: O()-sze data structure that eables O(log ) query tme. C p E
More informationProjection model for Computer Network Security Evaluation with interval-valued intuitionistic fuzzy information. Qingxiang Li
Iteratoal Joural of Scece Vol No7 05 ISSN: 83-4890 Proecto model for Computer Network Securty Evaluato wth terval-valued tutostc fuzzy formato Qgxag L School of Software Egeerg Chogqg Uversty of rts ad
More informationT = 1/freq, T = 2/freq, T = i/freq, T = n (number of cash flows = freq n) are :
Bullets bods Let s descrbe frst a fxed rate bod wthout amortzg a more geeral way : Let s ote : C the aual fxed rate t s a percetage N the otoal freq ( 2 4 ) the umber of coupo per year R the redempto of
More informationConstrained Cubic Spline Interpolation for Chemical Engineering Applications
Costraed Cubc Sple Iterpolato or Chemcal Egeerg Applcatos b CJC Kruger Summar Cubc sple terpolato s a useul techque to terpolate betwee kow data pots due to ts stable ad smooth characterstcs. Uortuatel
More informationThe analysis of annuities relies on the formula for geometric sums: r k = rn+1 1 r 1. (2.1) k=0
Chapter 2 Autes ad loas A auty s a sequece of paymets wth fxed frequecy. The term auty orgally referred to aual paymets (hece the ame), but t s ow also used for paymets wth ay frequecy. Autes appear may
More informationMaintenance Scheduling of Distribution System with Optimal Economy and Reliability
Egeerg, 203, 5, 4-8 http://dx.do.org/0.4236/eg.203.59b003 Publshed Ole September 203 (http://www.scrp.org/joural/eg) Mateace Schedulg of Dstrbuto System wth Optmal Ecoomy ad Relablty Syua Hog, Hafeg L,
More informationSecurity Analysis of RAPP: An RFID Authentication Protocol based on Permutation
Securty Aalyss of RAPP: A RFID Authetcato Protocol based o Permutato Wag Shao-hu,,, Ha Zhje,, Lu Sujua,, Che Da-we, {College of Computer, Najg Uversty of Posts ad Telecommucatos, Najg 004, Cha Jagsu Hgh
More informationAverage Price Ratios
Average Prce Ratos Morgstar Methodology Paper August 3, 2005 2005 Morgstar, Ic. All rghts reserved. The formato ths documet s the property of Morgstar, Ic. Reproducto or trascrpto by ay meas, whole or
More informationOn Error Detection with Block Codes
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 9, No 3 Sofa 2009 O Error Detecto wth Block Codes Rostza Doduekova Chalmers Uversty of Techology ad the Uversty of Gotheburg,
More informationThe Gompertz-Makeham distribution. Fredrik Norström. Supervisor: Yuri Belyaev
The Gompertz-Makeham dstrbuto by Fredrk Norström Master s thess Mathematcal Statstcs, Umeå Uversty, 997 Supervsor: Yur Belyaev Abstract Ths work s about the Gompertz-Makeham dstrbuto. The dstrbuto has
More informationApplications of Support Vector Machine Based on Boolean Kernel to Spam Filtering
Moder Appled Scece October, 2009 Applcatos of Support Vector Mache Based o Boolea Kerel to Spam Flterg Shugag Lu & Keb Cu School of Computer scece ad techology, North Cha Electrc Power Uversty Hebe 071003,
More informationSHAPIRO-WILK TEST FOR NORMALITY WITH KNOWN MEAN
SHAPIRO-WILK TEST FOR NORMALITY WITH KNOWN MEAN Wojcech Zelńsk Departmet of Ecoometrcs ad Statstcs Warsaw Uversty of Lfe Sceces Nowoursyowska 66, -787 Warszawa e-mal: wojtekzelsk@statystykafo Zofa Hausz,
More informationAnalysis of one-dimensional consolidation of soft soils with non-darcian flow caused by non-newtonian liquid
Joural of Rock Mechacs ad Geotechcal Egeerg., 4 (3): 5 57 Aalyss of oe-dmesoal cosoldato of soft sols wth o-darca flow caused by o-newtoa lqud Kaghe Xe, Chuaxu L, *, Xgwag Lu 3, Yul Wag Isttute of Geotechcal
More informationThe Digital Signature Scheme MQQ-SIG
The Dgtal Sgature Scheme MQQ-SIG Itellectual Property Statemet ad Techcal Descrpto Frst publshed: 10 October 2010, Last update: 20 December 2010 Dalo Glgorosk 1 ad Rue Stesmo Ødegård 2 ad Rue Erled Jese
More informationAn Approach to Evaluating the Computer Network Security with Hesitant Fuzzy Information
A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato Jafeg Dog A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato Jafeg Dog, Frst ad Correspodg Author
More informationON SLANT HELICES AND GENERAL HELICES IN EUCLIDEAN n -SPACE. Yusuf YAYLI 1, Evren ZIPLAR 2. yayli@science.ankara.edu.tr. evrenziplar@yahoo.
ON SLANT HELICES AND ENERAL HELICES IN EUCLIDEAN -SPACE Yusuf YAYLI Evre ZIPLAR Departmet of Mathematcs Faculty of Scece Uversty of Akara Tadoğa Akara Turkey yayl@sceceakaraedutr Departmet of Mathematcs
More informationA particle swarm optimization to vehicle routing problem with fuzzy demands
A partcle swarm optmzato to vehcle routg problem wth fuzzy demads Yag Peg, Ye-me Qa A partcle swarm optmzato to vehcle routg problem wth fuzzy demads Yag Peg 1,Ye-me Qa 1 School of computer ad formato
More informationFault Tree Analysis of Software Reliability Allocation
Fault Tree Aalyss of Software Relablty Allocato Jawe XIANG, Kokch FUTATSUGI School of Iformato Scece, Japa Advaced Isttute of Scece ad Techology - Asahda, Tatsuokuch, Ishkawa, 92-292 Japa ad Yaxag HE Computer
More informationAn Effectiveness of Integrated Portfolio in Bancassurance
A Effectveess of Itegrated Portfolo Bacassurace Taea Karya Research Ceter for Facal Egeerg Isttute of Ecoomc Research Kyoto versty Sayouu Kyoto 606-850 Japa arya@eryoto-uacp Itroducto As s well ow the
More informationThe Analysis of Development of Insurance Contract Premiums of General Liability Insurance in the Business Insurance Risk
The Aalyss of Developmet of Isurace Cotract Premums of Geeral Lablty Isurace the Busess Isurace Rsk the Frame of the Czech Isurace Market 1998 011 Scetfc Coferece Jue, 10. - 14. 013 Pavla Kubová Departmet
More informationANOVA Notes Page 1. Analysis of Variance for a One-Way Classification of Data
ANOVA Notes Page Aalss of Varace for a Oe-Wa Classfcato of Data Cosder a sgle factor or treatmet doe at levels (e, there are,, 3, dfferet varatos o the prescrbed treatmet) Wth a gve treatmet level there
More informationGreen Master based on MapReduce Cluster
Gree Master based o MapReduce Cluster Mg-Zh Wu, Yu-Chag L, We-Tsog Lee, Yu-Su L, Fog-Hao Lu Dept of Electrcal Egeerg Tamkag Uversty, Tawa, ROC Dept of Electrcal Egeerg Tamkag Uversty, Tawa, ROC Dept of
More informationCredibility Premium Calculation in Motor Third-Party Liability Insurance
Advaces Mathematcal ad Computatoal Methods Credblty remum Calculato Motor Thrd-arty Lablty Isurace BOHA LIA, JAA KUBAOVÁ epartmet of Mathematcs ad Quattatve Methods Uversty of ardubce Studetská 95, 53
More informationStatistical Pattern Recognition (CE-725) Department of Computer Engineering Sharif University of Technology
I The Name of God, The Compassoate, The ercful Name: Problems' eys Studet ID#:. Statstcal Patter Recogto (CE-725) Departmet of Computer Egeerg Sharf Uversty of Techology Fal Exam Soluto - Sprg 202 (50
More informationCurve Fitting and Solution of Equation
UNIT V Curve Fttg ad Soluto of Equato 5. CURVE FITTING I ma braches of appled mathematcs ad egeerg sceces we come across epermets ad problems, whch volve two varables. For eample, t s kow that the speed
More informationUsing Phase Swapping to Solve Load Phase Balancing by ADSCHNN in LV Distribution Network
Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204), pp.-4 http://dx.do.org/0.4257/jca.204.7.7.0 Usg Phase Swappg to Solve Load Phase Balacg by ADSCHNN LV Dstrbuto Network Chu-guo Fe ad Ru Wag College
More informationSettlement Prediction by Spatial-temporal Random Process
Safety, Relablty ad Rs of Structures, Ifrastructures ad Egeerg Systems Furuta, Fragopol & Shozua (eds Taylor & Fracs Group, Lodo, ISBN 978---77- Settlemet Predcto by Spatal-temporal Radom Process P. Rugbaapha
More informationECONOMIC CHOICE OF OPTIMUM FEEDER CABLE CONSIDERING RISK ANALYSIS. University of Brasilia (UnB) and The Brazilian Regulatory Agency (ANEEL), Brazil
ECONOMIC CHOICE OF OPTIMUM FEEDER CABE CONSIDERING RISK ANAYSIS I Camargo, F Fgueredo, M De Olvera Uversty of Brasla (UB) ad The Brazla Regulatory Agecy (ANEE), Brazl The choce of the approprate cable
More informationThe impact of service-oriented architecture on the scheduling algorithm in cloud computing
Iteratoal Research Joural of Appled ad Basc Sceces 2015 Avalable ole at www.rjabs.com ISSN 2251-838X / Vol, 9 (3): 387-392 Scece Explorer Publcatos The mpact of servce-oreted archtecture o the schedulg
More informationStudy on prediction of network security situation based on fuzzy neutral network
Avalable ole www.ocpr.com Joural of Chemcal ad Pharmaceutcal Research, 04, 6(6):00-06 Research Artcle ISS : 0975-7384 CODE(USA) : JCPRC5 Study o predcto of etwork securty stuato based o fuzzy eutral etwork
More informationOnline Appendix: Measured Aggregate Gains from International Trade
Ole Appedx: Measured Aggregate Gas from Iteratoal Trade Arel Burste UCLA ad NBER Javer Cravo Uversty of Mchga March 3, 2014 I ths ole appedx we derve addtoal results dscussed the paper. I the frst secto,
More informationCHAPTER 2. Time Value of Money 6-1
CHAPTER 2 Tme Value of Moey 6- Tme Value of Moey (TVM) Tme Les Future value & Preset value Rates of retur Autes & Perpetutes Ueve cash Flow Streams Amortzato 6-2 Tme les 0 2 3 % CF 0 CF CF 2 CF 3 Show
More informationWe present a new approach to pricing American-style derivatives that is applicable to any Markovian setting
MANAGEMENT SCIENCE Vol. 52, No., Jauary 26, pp. 95 ss 25-99 ess 526-55 6 52 95 forms do.287/msc.5.447 26 INFORMS Prcg Amerca-Style Dervatves wth Europea Call Optos Scott B. Laprse BAE Systems, Advaced
More informationPlastic Number: Construction and Applications
Scet f c 0 Advaced Advaced Scetfc 0 December,.. 0 Plastc Number: Costructo ad Applcatos Lua Marohć Polytechc of Zagreb, 0000 Zagreb, Croata lua.marohc@tvz.hr Thaa Strmeč Polytechc of Zagreb, 0000 Zagreb,
More informationThree Dimensional Interpolation of Video Signals
Three Dmesoal Iterpolato of Vdeo Sgals Elham Shahfard March 0 th 006 Outle A Bref reve of prevous tals Dgtal Iterpolato Bascs Upsamplg D Flter Desg Issues Ifte Impulse Respose Fte Impulse Respose Desged
More informationAn IG-RS-SVM classifier for analyzing reviews of E-commerce product
Iteratoal Coferece o Iformato Techology ad Maagemet Iovato (ICITMI 205) A IG-RS-SVM classfer for aalyzg revews of E-commerce product Jaju Ye a, Hua Re b ad Hagxa Zhou c * College of Iformato Egeerg, Cha
More informationApproximation Algorithms for Scheduling with Rejection on Two Unrelated Parallel Machines
(ICS) Iteratoal oural of dvaced Comuter Scece ad lcatos Vol 6 No 05 romato lgorthms for Schedulg wth eecto o wo Urelated Parallel aches Feg Xahao Zhag Zega Ca College of Scece y Uversty y Shadog Cha 76005
More informationA Parallel Transmission Remote Backup System
2012 2d Iteratoal Coferece o Idustral Techology ad Maagemet (ICITM 2012) IPCSIT vol 49 (2012) (2012) IACSIT Press, Sgapore DOI: 107763/IPCSIT2012V495 2 A Parallel Trasmsso Remote Backup System Che Yu College
More informationCompressive Sensing over Strongly Connected Digraph and Its Application in Traffic Monitoring
Compressve Sesg over Strogly Coected Dgraph ad Its Applcato Traffc Motorg Xao Q, Yogca Wag, Yuexua Wag, Lwe Xu Isttute for Iterdscplary Iformato Sceces, Tsghua Uversty, Bejg, Cha {qxao3, kyo.c}@gmal.com,
More informationANALYTICAL MODEL FOR TCP FILE TRANSFERS OVER UMTS. Janne Peisa Ericsson Research 02420 Jorvas, Finland. Michael Meyer Ericsson Research, Germany
ANALYTICAL MODEL FOR TCP FILE TRANSFERS OVER UMTS Jae Pesa Erco Research 4 Jorvas, Flad Mchael Meyer Erco Research, Germay Abstract Ths paper proposes a farly complex model to aalyze the performace of
More informationOptimal replacement and overhaul decisions with imperfect maintenance and warranty contracts
Optmal replacemet ad overhaul decsos wth mperfect mateace ad warraty cotracts R. Pascual Departmet of Mechacal Egeerg, Uversdad de Chle, Caslla 2777, Satago, Chle Phoe: +56-2-6784591 Fax:+56-2-689657 rpascual@g.uchle.cl
More informationOn Savings Accounts in Semimartingale Term Structure Models
O Savgs Accouts Semmartgale Term Structure Models Frak Döberle Mart Schwezer moeyshelf.com Techsche Uverstät Berl Bockehemer Ladstraße 55 Fachberech Mathematk, MA 7 4 D 6325 Frakfurt am Ma Straße des 17.
More informationBayesian Network Representation
Readgs: K&F 3., 3.2, 3.3, 3.4. Bayesa Network Represetato Lecture 2 Mar 30, 20 CSE 55, Statstcal Methods, Sprg 20 Istructor: Su-I Lee Uversty of Washgto, Seattle Last tme & today Last tme Probablty theory
More informationOn formula to compute primes and the n th prime
Joural's Ttle, Vol., 00, o., - O formula to compute prmes ad the th prme Issam Kaddoura Lebaese Iteratoal Uversty Faculty of Arts ad ceces, Lebao Emal: ssam.addoura@lu.edu.lb amh Abdul-Nab Lebaese Iteratoal
More informationChapter 3. AMORTIZATION OF LOAN. SINKING FUNDS R =
Chapter 3. AMORTIZATION OF LOAN. SINKING FUNDS Objectves of the Topc: Beg able to formalse ad solve practcal ad mathematcal problems, whch the subjects of loa amortsato ad maagemet of cumulatve fuds are
More informationConversion of Non-Linear Strength Envelopes into Generalized Hoek-Brown Envelopes
Covero of No-Lear Stregth Evelope to Geeralzed Hoek-Brow Evelope Itroducto The power curve crtero commoly ued lmt-equlbrum lope tablty aaly to defe a o-lear tregth evelope (relatohp betwee hear tre, τ,
More informationOptimal Packetization Interval for VoIP Applications Over IEEE 802.16 Networks
Optmal Packetzato Iterval for VoIP Applcatos Over IEEE 802.16 Networks Sheha Perera Harsha Srsea Krzysztof Pawlkowsk Departmet of Electrcal & Computer Egeerg Uversty of Caterbury New Zealad sheha@elec.caterbury.ac.z
More informationn. We know that the sum of squares of p independent standard normal variables has a chi square distribution with p degrees of freedom.
UMEÅ UNIVERSITET Matematsk-statstska sttutoe Multvarat dataaalys för tekologer MSTB0 PA TENTAMEN 004-0-9 LÖSNINGSFÖRSLAG TILL TENTAMEN I MATEMATISK STATISTIK Multvarat dataaalys för tekologer B, 5 poäg.
More informationAnalysis of Multi-product Break-even with Uncertain Information*
Aalyss o Mult-product Break-eve wth Ucerta Iormato* Lazzar Lusa L. - Morñgo María Slva Facultad de Cecas Ecoómcas Uversdad de Bueos Ares 222 Córdoba Ave. 2 d loor C20AAQ Bueos Ares - Argeta lazzar@eco.uba.ar
More informationIP Network Topology Link Prediction Based on Improved Local Information Similarity Algorithm
Iteratoal Joural of Grd Dstrbuto Computg, pp.141-150 http://dx.do.org/10.14257/jgdc.2015.8.6.14 IP Network Topology Lk Predcto Based o Improved Local Iformato mlarty Algorthm Che Yu* 1, 2 ad Dua Zhem 1
More informationLoad Balancing Control for Parallel Systems
Proc IEEE Med Symposum o New drectos Cotrol ad Automato, Chaa (Grèce),994, pp66-73 Load Balacg Cotrol for Parallel Systems Jea-Claude Heet LAAS-CNRS, 7 aveue du Coloel Roche, 3077 Toulouse, Frace E-mal
More informationM. Salahi, F. Mehrdoust, F. Piri. CVaR Robust Mean-CVaR Portfolio Optimization
M. Salah, F. Mehrdoust, F. Pr Uversty of Gula, Rasht, Ira CVaR Robust Mea-CVaR Portfolo Optmzato Abstract: Oe of the most mportat problems faced by every vestor s asset allocato. A vestor durg makg vestmet
More informationPerformance Attribution. Methodology Overview
erformace Attrbuto Methodology Overvew Faba SUAREZ March 2004 erformace Attrbuto Methodology 1.1 Itroducto erformace Attrbuto s a set of techques that performace aalysts use to expla why a portfolo's performace
More informationSTATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS. x, where. = y - ˆ " 1
STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS Recall Assumpto E(Y x) η 0 + η x (lear codtoal mea fucto) Data (x, y ), (x 2, y 2 ),, (x, y ) Least squares estmator ˆ E (Y x) ˆ " 0 + ˆ " x, where ˆ
More informationThe simple linear Regression Model
The smple lear Regresso Model Correlato coeffcet s o-parametrc ad just dcates that two varables are assocated wth oe aother, but t does ot gve a deas of the kd of relatoshp. Regresso models help vestgatg
More informationNetwork dimensioning for elastic traffic based on flow-level QoS
Network dmesog for elastc traffc based o flow-level QoS 1(10) Network dmesog for elastc traffc based o flow-level QoS Pas Lassla ad Jorma Vrtamo Networkg Laboratory Helsk Uversty of Techology Itroducto
More informationMaximization of Data Gathering in Clustered Wireless Sensor Networks
Maxmzato of Data Gatherg Clustere Wreless Sesor Networks Taq Wag Stuet Member I We Hezelma Seor Member I a Alreza Seye Member I Abstract I ths paper we vestgate the maxmzato of the amout of gathere ata
More informationFast, Secure Encryption for Indexing in a Column-Oriented DBMS
Fast, Secure Ecrypto for Idexg a Colum-Oreted DBMS Tgja Ge, Sta Zdok Brow Uversty {tge, sbz}@cs.brow.edu Abstract Networked formato systems requre strog securty guaratees because of the ew threats that
More informationAn Operating Precision Analysis Method Considering Multiple Error Sources of Serial Robots
MAEC Web of Cofereces 35, 02013 ( 2015) DOI: 10.1051/ mateccof/ 2015 3502013 C Owe by the authors, publshe by EDP Sceces, 2015 A Operatg Precso Aalyss Metho Coserg Multple Error Sources of Seral Robots
More informationBanking (Early Repayment of Housing Loans) Order, 5762 2002 1
akg (Early Repaymet of Housg Loas) Order, 5762 2002 y vrtue of the power vested me uder Secto 3 of the akg Ordace 94 (hereafter, the Ordace ), followg cosultato wth the Commttee, ad wth the approval of
More informationCH. V ME256 STATICS Center of Gravity, Centroid, and Moment of Inertia CENTER OF GRAVITY AND CENTROID
CH. ME56 STTICS Ceter of Gravt, Cetrod, ad Momet of Ierta CENTE OF GITY ND CENTOID 5. CENTE OF GITY ND CENTE OF MSS FO SYSTEM OF PTICES Ceter of Gravt. The ceter of gravt G s a pot whch locates the resultat
More informationA Fast Algorithm for Computing the Deceptive Degree of an Objective Function
IJCSNS Iteratoal Joural of Computer See ad Networ Seurty, VOL6 No3B, Marh 6 A Fast Algorthm for Computg the Deeptve Degree of a Objetve Futo LI Yu-qag Eletro Tehque Isttute, Zhegzhou Iformato Egeerg Uversty,
More informationAutomated Event Registration System in Corporation
teratoal Joural of Advaces Computer Scece ad Techology JACST), Vol., No., Pages : 0-0 0) Specal ssue of CACST 0 - Held durg 09-0 May, 0 Malaysa Automated Evet Regstrato System Corporato Zafer Al-Makhadmee
More informationOn Cheeger-type inequalities for weighted graphs
O Cheeger-type equaltes for weghted graphs Shmuel Fredlad Uversty of Illos at Chcago Departmet of Mathematcs 851 S. Morga St., Chcago, Illos 60607-7045 USA Rehard Nabbe Fakultät für Mathematk Uverstät
More informationRQM: A new rate-based active queue management algorithm
: A ew rate-based actve queue maagemet algorthm Jeff Edmods, Suprakash Datta, Patrck Dymod, Kashf Al Computer Scece ad Egeerg Departmet, York Uversty, Toroto, Caada Abstract I ths paper, we propose a ew
More informationImpact of Mobility Prediction on the Temporal Stability of MANET Clustering Algorithms *
Impact of Moblty Predcto o the Temporal Stablty of MANET Clusterg Algorthms * Aravdha Vekateswara, Vekatesh Saraga, Nataraa Gautam 1, Ra Acharya Departmet of Comp. Sc. & Egr. Pesylvaa State Uversty Uversty
More informationDECISION MAKING WITH THE OWA OPERATOR IN SPORT MANAGEMENT
ESTYLF08, Cuecas Meras (Meres - Lagreo), 7-9 de Septembre de 2008 DECISION MAKING WITH THE OWA OPERATOR IN SPORT MANAGEMENT José M. Mergó Aa M. Gl-Lafuete Departmet of Busess Admstrato, Uversty of Barceloa
More informationLecture 7. Norms and Condition Numbers
Lecture 7 Norms ad Codto Numbers To dscuss the errors umerca probems vovg vectors, t s usefu to empo orms. Vector Norm O a vector space V, a orm s a fucto from V to the set of o-egatve reas that obes three
More informationTime Series Forecasting by Using Hybrid. Models for Monthly Streamflow Data
Appled Mathematcal Sceces, Vol. 9, 215, o. 57, 289-2829 HIKARI Ltd, www.m-hkar.com http://dx.do.org/1.12988/ams.215.52164 Tme Seres Forecastg by Usg Hybrd Models for Mothly Streamflow Data Sraj Muhammed
More informationWeb Service Composition Optimization Based on Improved Artificial Bee Colony Algorithm
JOURNAL OF NETWORKS, VOL. 8, NO. 9, SEPTEMBER 2013 2143 Web Servce Composto Optmzato Based o Improved Artfcal Bee Coloy Algorthm Ju He The key laboratory, The Academy of Equpmet, Beg, Cha Emal: heu0123@sa.com
More informationRelaxation Methods for Iterative Solution to Linear Systems of Equations
Relaxato Methods for Iteratve Soluto to Lear Systems of Equatos Gerald Recktewald Portlad State Uversty Mechacal Egeerg Departmet gerry@me.pdx.edu Prmary Topcs Basc Cocepts Statoary Methods a.k.a. Relaxato
More informationCyber Journals: Multidisciplinary Journals in Science and Technology, Journal of Selected Areas in Telecommunications (JSAT), January Edition, 2011
Cyber Jourals: Multdscplary Jourals cece ad Techology, Joural of elected Areas Telecommucatos (JAT), Jauary dto, 2011 A ovel rtual etwork Mappg Algorthm for Cost Mmzg ZHAG hu-l, QIU Xue-sog tate Key Laboratory
More information10.5 Future Value and Present Value of a General Annuity Due
Chapter 10 Autes 371 5. Thomas leases a car worth $4,000 at.99% compouded mothly. He agrees to make 36 lease paymets of $330 each at the begg of every moth. What s the buyout prce (resdual value of the
More informationEfficient Traceback of DoS Attacks using Small Worlds in MANET
Effcet Traceback of DoS Attacks usg Small Worlds MANET Yog Km, Vshal Sakhla, Ahmed Helmy Departmet. of Electrcal Egeerg, Uversty of Souther Calfora, U.S.A {yogkm, sakhla, helmy}@ceg.usc.edu Abstract Moble
More informationLocally Adaptive Dimensionality Reduction for Indexing Large Time Series Databases
Locally Adaptve Dmesoalty educto for Idexg Large Tme Seres Databases Kaushk Chakrabart Eamo Keogh Sharad Mehrotra Mchael Pazza Mcrosoft esearch Uv. of Calfora Uv. of Calfora Uv. of Calfora edmod, WA 985
More informationLoad and Resistance Factor Design (LRFD)
53:134 Structural Desg II Load ad Resstace Factor Desg (LRFD) Specfcatos ad Buldg Codes: Structural steel desg of buldgs the US s prcpally based o the specfcatos of the Amerca Isttute of Steel Costructo
More informationTHE McELIECE CRYPTOSYSTEM WITH ARRAY CODES. MATRİS KODLAR İLE McELIECE ŞİFRELEME SİSTEMİ
SAÜ e Blmler Dergs, 5 Clt, 2 Sayı, THE McELIECE CRYPTOSYSTEM WITH ARRAY CODES Vedat ŞİAP* *Departmet of Mathematcs, aculty of Scece ad Art, Sakarya Uversty, 5487, Serdva, Sakarya-TURKEY vedatsap@gmalcom
More informationOPTIMAL KNOWLEDGE FLOW ON THE INTERNET
İstabul Tcaret Üverstes Fe Blmler Dergs Yıl: 5 Sayı:0 Güz 006/ s. - OPTIMAL KNOWLEDGE FLOW ON THE INTERNET Bura ORDİN *, Urfat NURİYEV ** ABSTRACT The flow roblem ad the mmum sag tree roblem are both fudametal
More informationCapacitated Production Planning and Inventory Control when Demand is Unpredictable for Most Items: The No B/C Strategy
SCHOOL OF OPERATIONS RESEARCH AND INDUSTRIAL ENGINEERING COLLEGE OF ENGINEERING CORNELL UNIVERSITY ITHACA, NY 4853-380 TECHNICAL REPORT Jue 200 Capactated Producto Plag ad Ivetory Cotrol whe Demad s Upredctable
More informationApplication of Grey Relational Analysis in Computer Communication
Applcato of Grey Relatoal Aalyss Computer Commucato Network Securty Evaluato Jgcha J Applcato of Grey Relatoal Aalyss Computer Commucato Network Securty Evaluato *1 Jgcha J *1, Frst ad Correspodg Author
More informationVIDEO REPLICA PLACEMENT STRATEGY FOR STORAGE CLOUD-BASED CDN
Joural of Theoretcal ad Appled Iformato Techology 31 st Jauary 214. Vol. 59 No.3 25-214 JATIT & S. All rghts reserved. ISSN: 1992-8645 www.att.org E-ISSN: 1817-3195 VIDEO REPICA PACEMENT STRATEGY FOR STORAGE
More informationRESEARCH ON PERFORMANCE MODELING OF TRANSACTIONAL CLOUD APPLICATIONS
Joural of Theoretcal ad Appled Iformato Techology 3 st October 22. Vol. 44 No.2 25-22 JATIT & LLS. All rghts reserved. ISSN: 992-8645 www.jatt.org E-ISSN: 87-395 RESEARCH ON PERFORMANCE MODELING OF TRANSACTIONAL
More informationResearch on the Evaluation of Information Security Management under Intuitionisitc Fuzzy Environment
Iteratoal Joural of Securty ad Its Applcatos, pp. 43-54 http://dx.do.org/10.14257/sa.2015.9.5.04 Research o the Evaluato of Iformato Securty Maagemet uder Itutostc Fuzzy Evromet LI Feg-Qua College of techology,
More informationResponse surface methodology
CHAPTER 3 Respose surface methodology 3. Itroducto Respose surface methodology (RSM) s a collecto of mathematcal ad statstcal techques for emprcal model buldg. By careful desg of epermets, the objectve
More informationA REGULARIZATION APPROACH FOR RECONSTRUCTION AND VISUALIZATION OF 3-D DATA. Hebert Montegranario Riascos, M.Sc.
A REGULARIZATION APPROACH FOR RECONSTRUCTION AND VISUALIZATION OF 3-D DATA Hebert otegraaro Rascos,.Sc. Thess submtted partal fulfllmet of the requremets for the Degree of Doctor of Phlosophy Advsor Prof.
More informationIntegrating Production Scheduling and Maintenance: Practical Implications
Proceedgs of the 2012 Iteratoal Coferece o Idustral Egeerg ad Operatos Maagemet Istabul, Turkey, uly 3 6, 2012 Itegratg Producto Schedulg ad Mateace: Practcal Implcatos Lath A. Hadd ad Umar M. Al-Turk
More informationPolyphase Filters. Section 12.4 Porat 1/39
Polyphase Flters Secto.4 Porat /39 .4 Polyphase Flters Polyphase s a way of dog saplg-rate coverso that leads to very effcet pleetatos. But ore tha that, t leads to very geeral vewpots that are useful
More informationSTOCHASTIC approximation algorithms have several
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL 60, NO 10, OCTOBER 2014 6609 Trackg a Markov-Modulated Statoary Degree Dstrbuto of a Dyamc Radom Graph Mazyar Hamd, Vkram Krshamurthy, Fellow, IEEE, ad George
More information