High-order fundamental and general solutions of convection-diffusion equation and their applications with boundary particle method
|
|
- Mary Chase
- 8 years ago
- Views:
Transcription
1 Hgh-order fndaental and general soltons of convecton-dffson eqaton and ther alcatons wth bondary artcle ethod W. Chen * Sla Research Laboratory, P. O. Bo. 34, 325 Lysaer, Norway E-al: wenc@sla.no (sbtted Oct. 2, revsed 8, Feb. 22) Abstract In ths stdy, we resented the hgh-order fndaental soltons and general soltons of convecton-dffson eqaton. To deonstrate ther effcacy, we aled the hghorder general soltons to the bondary artcle ethod (BPM) for the solton of soe nhoogeneos convecton-dffson robles, where the BPM s a new trly bondaryonly eshfree collocaton ethod based on ltle recrocty rncle. For the sae of coleteness, the BPM s also brefly descrbed here. Keyword: convecton-dffson eqaton, hgh-order fndaental solton; hgh-order general solton; bondary artcle ethod; radal bass fncton; eshfree; ltle recrocty ethod.. Introdcton The hgh-order fndaental soltons lay a votal role n the ltle recrocty BEM (MR-BEM) []. On the other hand, the bondary artcle ethod (BPM), recently ntrodced by the resent athor [2], also reqres the se of the hgh-order general soltons. In addton, an nderlyng relatonsh between the radal bass fncton (RBF) and Green second dentty hghlghts the ortance of these oerator-deendent soltons [3]. A ernel RBF-creatng strategy [3,4], whch eloys these hgh-order fndaental or general soltons as the RBF, s resented for the dal recrocty BEM * Ths research s sorted by Norwegan Research Concl.
2 [5], bondary not ethod [6], and Kansa s ethod [7]. To the athor s best nowledge, the elct hgh-order fndaental soltons are now avalable only for the Lalace [], Helholtz and odfed Helholtz oerators [8]. Based on the nderlyng relatonsh between the convecton-dffson eqaton and the odfed Helholtz eqaton [9], we derve the hgh-order fndaental and general soltons of the convecton-dffson eqaton []. In ths stdy, we wll gve a systeatc descrton of ths recent advance. In addton, to deonstrate the effcacy of these hgh-order soltons, we aly the to the bondary artcle ethod for the solton of soe nhoogeneos convecton-dffson robles. The BPM s develoed based on the ltle recrocty rncle [2,], whch ses ether hgh-order nonsnglar general soltons or snglar fndaental soltons to evalate hgh-order hoogeneos soltons, and then ther s aroates the artclar soltons. Le the MR-BEM, the BPM does not reqre any nner nodes for nhoogeneos robles and therefore s a trly bondary-only technqe. Unle the MR-BEM, the BPM does not need to generate ore than one nterolaton atr snce we develoed the effcent recrsve ltle recrocty forlas, whch treendosly redces cotng effort and eory reqreents. In addton, the BPM s essentally eshfree, sectral convergence, easy-to-se, and syetrc technqe. The rest of ths aer s organzed nto 4 sectons. We dscss the dfference between the snglar fndaental solton and nonsnglar general solton and then ntrodce the hgh-order fndaental and general soltons of the convecton-dffson eqaton n secton 2. The bondary artcle ethod s brefly descrbed n secton 3, and followed by the leentaton sses: overflow and ll condtonng n secton 4. Fnally, Secton 5 resented nercal testng the convecton-dffson hgh-order general soltons wth the BPM to soe 2D nhoogeneos convecton-dffson robles nder colcated geoetres. 2
3 2. Hgh-order fndaental and general soltons of Convecton-dffson oerator The general solton satsfes { } R, () where R s a dfferental oerator. The general solton at orgn s eqal to a lt vale rather than zero and nfnty. In contrast, the fndaental solton * has to satsfy * { } + R, (2) where reresents the Drac delta fncton whch goes to nfnty at the orgn ont and s eqal to zero elsewhere. Accordng to the above defntons, the essental dstnctness between the general solton and fndaental solton of a dfferental oerator s that the forer s nonsnglar whle the latter s snglar. 2.. Hgh-order general soltons Consder a hoogeneos sotroc regon Ω. The steady convecton-dffson eqaton s gven by 2 v D ( ) ( ) κ( ), n Ω (3) where v v denotes a velocty vector, D s the dffsvty coeffcent, κ reresents the reacton coeffcent. The varable can be nterreted as teeratre for heat transfer robles, concentraton for dserson robles [5]. Assng that convectve velocty v v eonental varable transforaton [9] and dffsvty D are constant, we have an 3
4 v v ν r 2D e w, (4) where w() s an nteredate feld varable, and r v s the dstance vector between the sorce and feld onts. Convecton-dffson eqaton (3) can be accordngly rewrtten as a odfed Helholtz eqaton where 2 2 w τ w n Ω, (5) 2 [( v 2D) κ D] 2 τ v +. (6) Accordng to Itaga s three-densonal hgh-order fndaental soltons of the odfed Helholtz eqaton [8], t s very easy to get the corresondng hgher-order general soltons,.e. w n 2+ + () r A ( r) I ( τr) τ n 2+, n 2, (7) where A A - /(2τ 2 ), A ; n s the denson of the roble; denotes the order of general solton; r s the Ecldean dstance nor; I reresents the odfed Bessel fncton of the frst nd, whch can be transfored to the odfed shercal Bessel fncton when n3. Usng coter software Male, we verfed that those hgherorder fndaental and general soltons are also establshed for ore than 3 densons. Throgh an nverse transforaton rocess, we derve the hgh-order general soltons of the convecton-dffson eqaton v v r τ n 2+ 2D n 2+ + () r A e ( r) I ( τr), n 2, (8) where τ s defned by forla (6). 4
5 The above hgh-order general soltons of the convecton-dffson eqaton are also valdated by atheatcal dedcton aroach wth the hel of coter algebrac acage Male. Naely, frst we rove the zero-order general solton, and then, t s fond that R } conssts only of (-)th or lower order general soltons of oerator R. { Therefore, the -order general solton s roved. It s noted that the general soltons (7) and (8) are nonsnglar at the orgn and actally nfntely contnos bt grow eonentally as r. Ths, t s often regarded as roer soltons []. In contrast, the fndaental solton decays eonentally and s consdered as roer solton. However, f or roble s to handle the data or PDEs on the bonded doans,.e. nteror robles, the growth at nfnty s no longer an sse, snce the eanson ters always rean fnte []. We have soe ersasve nercal deonstratons of the tlty of these general soltons wth the bondary not ethod [7,] n solvng nteror robles. In later secton, we wll show these general soltons n conncton wth the BPM cold be very sccessflly aled to evalaton of soe tycal convecton-dffson robles on bonded doans. In general, the fndaental soltons can be aled to both eternal and nteror robles, whle the general soltons are bt the solton of nteror robles. Bt the general soltons ay nevertheless be alcable even to eteror robles f we se the trncated doan aroach, e.g., for eteror wave robles wth a roer nonreflectng bondary condton at trncated bondary Hgh-order fndaental soltons The fndaental solton of steady convecton-dffson eqaton s deterned by 2 v D ( ) ( ) κ( ), n Ω (9) 5
6 where reresents the Drac delta fncton at a sorce ont. Followng the recedng rocedre for hgh-order general soltons, we can easly derve the -order fndaental solton * v v r τ n 2+ 2D n 2+ + () r B e ( r) K ( τr), n 2, () where K reresents the odfed Bessel fncton of the second nd. As n the odfed Helholtz case, the hgh-order fndaental solton of convecton-dffson eqaton has the snglarty order of (r 2-n ) ecet the 2D case where the only snglarty occrs n the zero-order fndaental solton. For nstance, the snglarty for 3D case s always r - rresectve of the order of fndaental solton. In other words, the snglarty order has nothng to do wth the order of a fndaental solton Evalatng fndaental and general soltons It s worth ontng ot that we can greatly slfy the above-gven standard fors of hgh-order soltons nvolvng soe Bessel fnctons. Ths, the cotng effort for the cold be trval. For eale, the zero-, frst-, and second-order general soltons of 3D convecton-dffson eqaton are resectvely slfed va coter algebra acage Male as () r 2 2 v v ( τr) v r A snh D e, () π τr () r A ( τr) snh( τr) r 2 v v r cosh D e 2, (2) π τr 2 () r ( τr) + 3snh( τr) 3r cosh( τr) r A 2 v v 2 2 r snh 2D e, (3) π τr 6
7 where snh and cosh resectvely denote the sne-hyerbolc and cosne-hyerbolc fnctons. 3. Bondary artcle ethods In secton 4 the above-derved hgh-order general soltons of convecton-dffson eqaton are aled wth the bondary artcle ethod to soe 2D nhoogeneos robles. For the coleteness and very recent orgn of the BPM, we gve a bref descrton of the ethod n ths secton. Consder a steady convecton-dffson syste 2 v D ( ) ( ) κ( ) f, Ω, (4) R, S, (5) n N, S T, (6) where n s the nt otward noral. The syste solton can be slt as h +, (7) where h and are the zero-order hoogeneos and artclar soltons, resectvely. The ltle recrocty rncle asses that the sffcently sooth artclar solton can be aroated by hgher-order hoogeneos soltons,.e. + h + h h, (8) 7
8 where serscrt s the order nde of hoogeneos solton. Throgh an ncreental dfferentaton oeraton va the convecton-dffson oerator, we have sccessvely hgher order bondary dfferental eqatons: R R R R h h n ( ) R( ) ( ) ( ) N ( ) n ( ) { h( )} f ( ) R { ( )} { ( )} ( f ( ) R { ( )}) h n n 2 { h ( )} R { f ( )} R { ( )} 2 { ( )} ( R { f ( )} R { ( )}) h n n, (9a), (9b), 2,3,, (9c) where R {} denotes the -th order of convecton-dffson eqaton, say R {}RR {}, and R {}R{}, and are nots ndces resectvely on Drchlet and Neann bondary. The -order hoogeneos solton can be aroated n ters of the - order general solton bass fncton h L ( r ), (2) where L s the nber of bondary nodes, and denotes the nde of sorce onts on bondary. are the desred coeffcents. Note that we can se the fndaental solton * nstead of general solton n Eq. (2). However, the se of fndaental solton reqres a fcttos bondary otsde hyscal doan as encontered n the MFS [2]. Collocatng Eqs. (9a,b,c) at all bondary nots n ters of reresentaton (2), we have the BPM bondary dscretzaton eqatons : 8
9 b n N n r R r L L, (2a) { } { } { } { } b n f n r f r L L R R R R, (2b) { } { } { } { } { } { } L L b n f n r f r R R R R R R 2 2, 2,3, (2c) Whenever the ed bondary condtons are resent, the resent BPM nterolaton atr s nsyetrc even for self-adont oerator. By analogy wth Fasshaer s Herte RBF nterolaton [3] the resent athor also roosed a syetrc BPM forlaton for self-adont oerator [2]. Snce the convecton-dffson eqaton s not self-adont, ths stdy sly ses the resent nsyetrc BPM schee. As n the MR-BEM [], the sccessve rocess s ternated at soe order M, naely, { } R M M. (22) The ractcal solton rocedre s a reversal recrsve rocess: L M M. (23) It s noted that de to 9
10 { () r } () r R, (24) the coeffcent atrces of all sccessve eqatons (2a,b,c) are the sae,.e., let Q b, M,M-,,,. (25) The LU decooston algorth s stable for ths tas. Then we can eloy the obtaned eanson coeffcents to calclate the BPM solton at any not,.e. M L ( ) ( ). (26) It s noted that the BPM solton (26) s also a RBF wavelet eanson seres, where the dfferental eqaton order s sed as the dlaton araeter and s the translaton araeter. It s also worth ontng ot that the above ltle recrocty solton rocedre s n fact eqvalent to that wthn the MR-BEM. The dstncton s that the resent one has a atheatcal rocedre cotatonally ore effcent snce t s a recrsve teraton solton whch does not need to evalate costly nterolaton atrces of hgh order artal dfferental eqatons. We wll gve a detaled dscsson on ths sse and resent the MR-BEM forlatons based on the general solton and the fndaental solton n a sbseqent aer. 4. Ileentaton sses: overflow and ll-condtonng As the araeter τ n forla (6) grows, the condton nber of the BPM dscretzaton atr Q n (25) ncreases qcly and the a and n entres resectvely assocated wth the general solton and the fndaental solton becoe rone to overflow. Conseqently, the solton blows at ed vale of τ. Wth the noral
11 nercal algebrac rocedre, the overflow and ll-condtonng are two aor bottlenecs n alyng the BPM to convecton robles wth large τ vale. To avod the overflow, ths stdy odfes the BPM nterolaton atr Q n (25) by ltlyng t wth an eonental araeter to scale down the a entry wth the general solton,.e. τ L Lc { e ( r )}{ e } c τ b, M,M-,,,, (27) where L c denotes a characterstc length. The entres of nterolaton atr n (27) s actally calclated n the followng anner: e τl c v v r [ n 2 τlc + + τr 2D n 2+ τr ( r ) A e ( τr ) e I ( τr ) ], n 2. (28) Here τr e I τ ) s seen as a new fncton, whch s never overflow and ch ore n 2( r sooth than the odfed Bessel fncton I ( τ ) n 2 r. Many software acages nclde the sbrotne or secal fncton for calclatng τr n 2( r e I τ ). It s worth notng that corresondng to (27), the forla (26) s revsed as M L τlc τlc ( ) ( e )[ e ( )], (29) where e τl c v v [ n 2+ v r τlc + + τr 2D n 2+ + τr ( r ) A e ( τr) e I ( τr )], n 2. (3) If the BPM ses the fndaental solton, we need to scale the n entry n coarson to (28),.e.
12 e τl c v v v r [ r ], n 2. (3) τlc + τr 2D n 2+ τr () r B e ( τr) e K ( τ ) * n 2 The reander of the rocedre s slar to that of the BPM sng the general solton. On the other hand, we stll lac a good devse to deal wth the ll-condtonng sse. Here we resent a concetal aroach called Hadaard rodct recondtonng. Defnton 4. Let atrces P[ ] and Q[q ] C N M, the Hadaard rodct of atrces s defned as Po Q [ q ] C N M, where C N M denotes the set of N M real atrces. Observng the BPM nterolaton atr Q n (25), we note that Q can be decoosed va the Hadaard atr rodct,.e. Q v v v r τr 2D n 2 r + τ { e } A e ( τr ) [ e I ( τr )] H Qˆ n 2 o. (32) Ths, the forlaton (25) s restated as [ H Qˆ ] b o, M,M-,,,. (33) Note that the atr Q ˆ wll never be overflow and s well condtoned. At sse s how to anlate and recondton the agented H, whch s a oorly-condtoned eonental fncton atr. Albet etreely sle n ts for, the Hadaard rodct s qte hard to analyze and anever [4-6]. For the te beng, the ll-condtonng s stll an oen sse n the BPM solton of the convecton-dffson roble. 2
13 5. Nercal valdatons The tested case s a 2D steady convecton-dffson roble descrbed by D 2 v η( y κ e + ) ( 2 4η + 2σ ) (34) wth the bondary condtons of the Drchlet tye (5) and Neann tye (6), where η σ + σ + κ. The eact solton s D, v v y -σ, κ3σ 2 2 /2, ( 2 ) 2 η ( + y 2 e ). (35) The Peclet nber Pe s defned as v ν Lc Pe. (36) D The Peclet nber ndcates the relatve ortance of convecton verss dffson. Fg.. llstrates the 2D rreglar geoetry. Ecet secfed Neann bondary condtons at and y edges, the otherwse bondary are all of the Drchlet tye. Eqally saced nots were aled on the bondary. The L 2 nors of relatve errors are calclated based on the nercal soltons at 46 nner and bondary nodes. The absolte error s taen as the relatve error f the absolte vale of the solton s less than.. Table dslays the eerental reslts, where L reresents the nber of the sed bondary nots. It s seen that the BPM schee based on the hgh-order general soltons rodces stable soltons wth ncreasng nber of bondary nodes for the resent nhoogeneos convecton-dffson robles. In artclar, the BPM soltons are fond very accrate even wth a sall nber of bondary nodes. It s stressed that we dd not se any nner nodes here. For hgher Peclect nber robles, the BPM soltons becoe nstable de to very oor condton of the BPM nterolaton atr. As n the 3
14 BEM, soe recondtonng technqes cold be sed to handle ths sse, whch s beyond the resent stdy. Now one can conclde that the resented hgh-order general soltons of convecton-dffson eqaton do wor well n ths nercal eerent. Table. L 2 nor of relatve errors for 2D nhoogeneos convecton-dffson roble. L Pe24 9.e-3.4e-3 3.6e-4 3.6e-4 L Pe72.2e-2 4.5e-2 2.2e-3 4.5e-4 4
15 References. Nowa AJ, Neves AC (ed.). The Mltle Recrocty Bondary Eleent Method. Sothaton: Cot. Mech. Pbl., Chen W. New RBF collocaton schees and ther alcatons. Internatonal Worsho Meshfree Methods for Partal Dfferental Eqatons, Bonn, Gerany, Set Chen W, Tanaa M. Relatonsh between bondary ntegral eqaton and radal bass fncton. The 52th Syos of Jaan Socety for Cotatonal Methods n Engneerng on BEM. Toyo, Chen W, He J. A stdy on radal bass fncton and qas-monte Carlo ethods. Int. J. Nonlnear Sc. & Ner. Slaton, (4); :2. 5. Partrdge PW, Brebba CA, Wrobel LW. The Dal Recrocty Bondary Eleent Method. Sothaton: Cot. Mech. Pbl., Chen W, Tanaa M. A eshless, eonental convergence, ntegraton-free, and bondary-only RBF technqe. Cot. Math. Al. (n ress), Kansa EJ. Mltqadrcs: A scattered data aroaton schee wth alcatons to cotatonal fld-dynacs. Cot. Math. Al. 99;9: Itaga M. Hgher order three-densonal fndaental soltons to the Helholtz and the odfed Helholtz eqatons. Engng Anal. Bondary eleents. 995;5: L BQ, Evans JW. Bondary eleent solton of heat convecton-dffson robles. J. Co. Phy. 99;93: Chen W. RBF-based eshless bondary not ethod and bondary artcle ethod. Proc. of Chna Congress on Cotatonal Mechancs 2, Gangzho, Chna, Dec. 2.. Dffy DG. Transfor Methods for Solvng Partal Dfferental Eqatons, CRC Press, Florda, Golberg MA, Chen CS. The ethod of fndaental soltons for otental, Helholtz and dffson robles. In Bondary Integral Methods - Nercal and Matheatcal Asects, (Ed. by M.A. Golberg),. 3-76, Cot. Mech. Pbl., 5
16 Fasshaer GE. Solvng artal dfferental eqatons by collocaton wth radal bass fnctons. Proceedngs of Chaon, 996, (Mehate, A. and Rabt, C. and Schaer, L. ed.), Horn RA. The Hadaard rodct, n Matr Theory and Alcatons, Seres: Proc. Of Syosa n aled atheatcs, V. 4, 87-69, Johnson C.R. Ed., Aercan Matheatcal Socety, Provdence, Rhode Island, 99. Acadec Press, Chen W. Relatonsh theore between nonlnear olynoal eqaton and the corresondng Jacoban atr, Int. J. of Nonlnear Scences and Nercal Slaton,, 5-4, Chen W, Sh C, He W, Zhong TX. The DQ solton of geoetrcally nonlnear bendng of orthotroc rectanglar lates by sng Hadaard and SJT rodct, Coters & Strctres, 74(), 65-74, 2. 6
Least Squares Fitting of Data
Least Squares Fttng of Data Davd Eberly Geoetrc Tools, LLC http://www.geoetrctools.co/ Copyrght c 1998-2016. All Rghts Reserved. Created: July 15, 1999 Last Modfed: January 5, 2015 Contents 1 Lnear Fttng
More information1. Introduction to CFD
. Introdcton to CFD Ths s a qck ntrodcton to the basc concepts nderlyng CFD. The concepts are llstrated by applyng them to a smple D example. We dscss the followng topcs brefly:. Applcatons of CFD. The
More informationA Study on Secure Data Storage Strategy in Cloud Computing
Journal of Convergence Informaton Technology Volume 5, Number 7, Setember 00 A Study on Secure Data Storage Strategy n Cloud Comutng Danwe Chen, Yanjun He, Frst Author College of Comuter Technology, Nanjng
More informationHow To Understand The Results Of The German Meris Cloud And Water Vapour Product
Ttel: Project: Doc. No.: MERIS level 3 cloud and water vapour products MAPP MAPP-ATBD-ClWVL3 Issue: 1 Revson: 0 Date: 9.12.1998 Functon Name Organsaton Sgnature Date Author: Bennartz FUB Preusker FUB Schüller
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationA Prediction System Based on Fuzzy Logic
Proceedngs of the World Congress on Engneerng and Comuter Scence 2008 WCECS 2008, October 22-24, 2008, San Francsco, USA A Predcton System Based on Fuzzy Logc Vadeh.V,Monca.S, Mohamed Shek Safeer.S, Deeka.M
More informationv a 1 b 1 i, a 2 b 2 i,..., a n b n i.
SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationPSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12
14 The Ch-squared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationRing structure of splines on triangulations
www.oeaw.ac.at Rng structure of splnes on trangulatons N. Vllamzar RICAM-Report 2014-48 www.rcam.oeaw.ac.at RING STRUCTURE OF SPLINES ON TRIANGULATIONS NELLY VILLAMIZAR Introducton For a trangulated regon
More informationThe Subtraction Rule and its Effects on Pricing in the Electricity Industry
Dscusson Paer No 04- The Subtracton Rule and ts Effects on Prcng n the Electrcty Industry Walter Elberfeld Dscusson Paer No 04- The Subtracton Rule and ts Effects on Prcng n the Electrcty Industry Walter
More informationFinite difference method
grd ponts x = mesh sze = X NÜÆ Fnte dfference method Prncple: dervatves n the partal dfferental eqaton are approxmated by lnear combnatons of fncton vales at the grd ponts 1D: Ω = (0, X), (x ), = 0,1,...,
More informationAn Electricity Trade Model for Microgrid Communities in Smart Grid
An Electrcty Trade Model for Mcrogrd Countes n Sart Grd Tansong Cu, Yanzh Wang, Shahn Nazaran and Massoud Pedra Unversty of Southern Calforna Departent of Electrcal Engneerng Los Angeles, CA, USA {tcu,
More informationApplied Research Laboratory. Decision Theory and Receiver Design
Decson Theor and Recever Desgn Sgnal Detecton and Performance Estmaton Sgnal Processor Decde Sgnal s resent or Sgnal s not resent Nose Nose Sgnal? Problem: How should receved sgnals be rocessed n order
More informationQuantization Effects in Digital Filters
Quantzaton Effects n Dgtal Flters Dstrbuton of Truncaton Errors In two's complement representaton an exact number would have nfntely many bts (n general). When we lmt the number of bts to some fnte value
More informationDynamic Load Balancing of Parallel Computational Iterative Routines on Platforms with Memory Heterogeneity
Dynamc Load Balancng of Parallel Comutatonal Iteratve Routnes on Platforms wth Memory Heterogenety Davd Clare, Alexey Lastovetsy, Vladmr Rychov School of Comuter Scence and Informatcs, Unversty College
More informationEnergy-based Design of Steel Structures According to the Predefined Interstory Drift Ratio 1
Dgest 01, December 01, 1573-1593 Energy-based Desgn of Steel Structures Accordng to the Predefned Interstory Drft Rato 1 Onur ERTER* Özgür BOZDAĞ** ustafa DÜZGÜ*** ABSTRACT The methods whch take lace n
More informationTailoring Fuzzy C-Means Clustering Algorithm for Big Data Using Random Sampling and Particle Swarm Optimization
Internatonal Journal of Database Theory and Alcaton,.191-202 htt://dx.do.org/10.14257/jdta.2015.8.3.16 Talorng Fuzzy -Means lusterng Algorth for Bg Data Usng Rando Salng and Partcle Swar Otzaton Yang Xanfeng
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationLoop Parallelization
- - Loop Parallelzaton C-52 Complaton steps: nested loops operatng on arrays, sequentell executon of teraton space DECLARE B[..,..+] FOR I :=.. FOR J :=.. I B[I,J] := B[I-,J]+B[I-,J-] ED FOR ED FOR analyze
More informationBANDWIDTH ALLOCATION AND PRICING PROBLEM FOR A DUOPOLY MARKET
Yugoslav Journal of Operatons Research (0), Nuber, 65-78 DOI: 0.98/YJOR0065Y BANDWIDTH ALLOCATION AND PRICING PROBLEM FOR A DUOPOLY MARKET Peng-Sheng YOU Graduate Insttute of Marketng and Logstcs/Transportaton,
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationA hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm
Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(7):1884-1889 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel
More informationFinite Math Chapter 10: Study Guide and Solution to Problems
Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount
More informationDescription of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t
Indeternate Analyss Force Method The force (flexblty) ethod expresses the relatonshps between dsplaceents and forces that exst n a structure. Prary objectve of the force ethod s to deterne the chosen set
More informationDamage detection in composite laminates using coin-tap method
Damage detecton n composte lamnates usng con-tap method S.J. Km Korea Aerospace Research Insttute, 45 Eoeun-Dong, Youseong-Gu, 35-333 Daejeon, Republc of Korea yaeln@kar.re.kr 45 The con-tap test has the
More informationBERNSTEIN POLYNOMIALS
On-Lne Geometrc Modelng Notes BERNSTEIN POLYNOMIALS Kenneth I. Joy Vsualzaton and Graphcs Research Group Department of Computer Scence Unversty of Calforna, Davs Overvew Polynomals are ncredbly useful
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationA New Technique for Vehicle Tracking on the Assumption of Stratospheric Platforms. Department of Civil Engineering, University of Tokyo **
Fuse, Taash A New Technque for Vehcle Tracng on the Assumton of Stratosherc Platforms Taash FUSE * and Ehan SHIMIZU ** * Deartment of Cvl Engneerng, Unversty of Toyo ** Professor, Deartment of Cvl Engneerng,
More informationRESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL. Yaoqi FENG 1, Hanping QIU 1. China Academy of Space Technology (CAST) yaoqi.feng@yahoo.
ICSV4 Carns Australa 9- July, 007 RESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL Yaoq FENG, Hanpng QIU Dynamc Test Laboratory, BISEE Chna Academy of Space Technology (CAST) yaoq.feng@yahoo.com Abstract
More informationA NEW ACTIVE QUEUE MANAGEMENT ALGORITHM BASED ON NEURAL NETWORKS PI. M. Yaghoubi Waskasi MYaghoubi@ece.ut.ac.ir. M. J. Yazdanpanah Yazdan@ut.ac.
A NEW ACTIVE QUEUE MANAGEMENT ALGORITHM BASED ON NEURAL NETWORKS M. Yaghoub Waskas MYaghoub@ece.ut.ac.r M. J. Yazdananah Yazdan@ut.ac.r N. Yazdan Yazdan@ut.ac.r Control and Intellgent Processng Center
More informationwww.engineerspress.com Neural Network Solutions for Forward Kinematics Problem of Hybrid Serial-Parallel Manipulator
www.engneersress.com World of Scences Journal ISSN: 307-307 Year: 03 Volume: Issue: 8 Pages: 48-58 Aahmad Ghanbar,, Arash ahman Deartment of Mechancal Engneerng, Unversty of Tabrz, Tabrz, Iran School of
More informationA Secure Password-Authenticated Key Agreement Using Smart Cards
A Secure Password-Authentcated Key Agreement Usng Smart Cards Ka Chan 1, Wen-Chung Kuo 2 and Jn-Chou Cheng 3 1 Department of Computer and Informaton Scence, R.O.C. Mltary Academy, Kaohsung 83059, Tawan,
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationEfficient Computation of Optimal, Physically Valid Motion
Vol. xx No. xx,.1 5, 200x 1 Effcent Comutaton of Otmal, Physcally Vald Moton Anthony C. Fang 1 and Nancy S. Pollard 2 1 Deartment of Comuter Scence, Natonal Unversty of Sngaore 2 Robotcs Insttute, Carnege
More informationA Statistical Model for Detecting Abnormality in Static-Priority Scheduling Networks with Differentiated Services
A Statstcal odel for Detectng Abnoralty n Statc-Prorty Schedulng Networks wth Dfferentated Servces ng L 1 and We Zhao 1 School of Inforaton Scence & Technology, East Chna Noral Unversty, Shangha 0006,
More informationMaximizing profit using recommender systems
Maxzng proft usng recoender systes Aparna Das Brown Unversty rovdence, RI aparna@cs.brown.edu Clare Matheu Brown Unversty rovdence, RI clare@cs.brown.edu Danel Rcketts Brown Unversty rovdence, RI danel.bore.rcketts@gal.co
More informationJ. Parallel Distrib. Comput.
J. Parallel Dstrb. Comput. 71 (2011) 62 76 Contents lsts avalable at ScenceDrect J. Parallel Dstrb. Comput. journal homepage: www.elsever.com/locate/jpdc Optmzng server placement n dstrbuted systems n
More informationHow To Write A Powerpoint Powerpoint Commandbook For A Data Center
Internatonal Journal of Innovatve Research n Scence, Engneerng and Technology (An ISO 3297: 2007 ertfed Organzaton) VM Assgnent Algorth Based ost Effectve achng n loud outng Raya.R 1 Assstant Professor,Det
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a two-stage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationMobility Control with Local Views of Neighborhood in Mobile Networks
Moblty Control wth Local Vews of Neghborhood n Moble Networks Zhen Jang Je W Robert Klne Dept. of Compter Scence Dept. of Compter Sc. and Eng. Dept. of Compter Scence West Chester Unversty Florda Atlantc
More informationScan Detection in High-Speed Networks Based on Optimal Dynamic Bit Sharing
Scan Detecton n Hgh-Speed Networks Based on Optal Dynac Bt Sharng Tao L Shgang Chen Wen Luo Mng Zhang Departent of Coputer & Inforaton Scence & Engneerng, Unversty of Florda Abstract Scan detecton s one
More informationElastic Systems for Static Balancing of Robot Arms
. th World ongress n Mechans and Machne Scence, Guanajuato, Méco, 9- June, 0 _ lastc Sstes for Statc alancng of Robot rs I.Sonescu L. uptu Lucana Ionta I.Ion M. ne Poltehnca Unverst Poltehnca Unverst Poltehnca
More informationSpatial development of urban road network traffic gridlock
Transportaton Spatal deelopent of rban road networ traffc grdloc H.S. Q, Y.Y, Dan Ha Wang, *, Y.M. Be Receed: October 3, Resed: Febrary 4, Accepted: Jne 4 Abstract Abstract: Grdloc s an extree traffc state
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159-164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? Chu-Shu L Department of Internatonal Busness, Asa Unversty, Tawan Sheng-Chang
More informationOptimal maintenance of a production-inventory system with continuous repair times and idle periods
Proceedngs o the 3 Internatonal Conerence on Aled Mathematcs and Comutatonal Methods Otmal mantenance o a roducton-nventory system wth contnuous rear tmes and dle erods T. D. Dmtrakos* Deartment o Mathematcs
More information"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *
Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789-794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC
More informationA Comprehensive Analysis of Bandwidth Request Mechanisms in IEEE 802.16 Networks
A Comrehensve Analyss of Bandwdth Reuest Mechansms n IEEE 802.6 Networks Davd Chuck, Kuan-Yu Chen and J. Morrs Chang Deartment of Electrcal and Comuter Engneerng Iowa State Unversty, Ames, Iowa 500, USA
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.
More informationResearch Article Competition and Integration in Closed-Loop Supply Chain Network with Variational Inequality
Hndaw Publshng Cororaton Mathematcal Problems n Engneerng Volume 2012, Artcle ID 524809, 21 ages do:10.1155/2012/524809 Research Artcle Cometton and Integraton n Closed-Loo Suly Chan Network wth Varatonal
More informationWe are now ready to answer the question: What are the possible cardinalities for finite fields?
Chapter 3 Fnte felds We have seen, n the prevous chapters, some examples of fnte felds. For example, the resdue class rng Z/pZ (when p s a prme) forms a feld wth p elements whch may be dentfed wth the
More informationAddendum to: Importing Skill-Biased Technology
Addendum to: Importng Skll-Based Technology Arel Bursten UCLA and NBER Javer Cravno UCLA August 202 Jonathan Vogel Columba and NBER Abstract Ths Addendum derves the results dscussed n secton 3.3 of our
More informationExtending Probabilistic Dynamic Epistemic Logic
Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σ-algebra: a set
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract - Stock market s one of the most complcated systems
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationLecture Topics. 6. Sensors and instrumentation 7. Actuators and power transmission devices. (System and Signal Processing) DR.1 11.12.
Lecture Tocs 1. Introducton 2. Basc knematcs 3. Pose measurement and Measurement of Robot Accuracy 4. Trajectory lannng and control 5. Forces, moments and Euler s laws 5. Fundamentals n electroncs and
More informationPricing Model of Cloud Computing Service with Partial Multihoming
Prcng Model of Cloud Computng Servce wth Partal Multhomng Zhang Ru 1 Tang Bng-yong 1 1.Glorous Sun School of Busness and Managment Donghua Unversty Shangha 251 Chna E-mal:ru528369@mal.dhu.edu.cn Abstract
More informationAn Interest-Oriented Network Evolution Mechanism for Online Communities
An Interest-Orented Network Evoluton Mechansm for Onlne Communtes Cahong Sun and Xaopng Yang School of Informaton, Renmn Unversty of Chna, Bejng 100872, P.R. Chna {chsun,yang}@ruc.edu.cn Abstract. Onlne
More informationn + d + q = 24 and.05n +.1d +.25q = 2 { n + d + q = 24 (3) n + 2d + 5q = 40 (2)
MATH 16T Exam 1 : Part I (In-Class) Solutons 1. (0 pts) A pggy bank contans 4 cons, all of whch are nckels (5 ), dmes (10 ) or quarters (5 ). The pggy bank also contans a con of each denomnaton. The total
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationOptimal Control Approach to Production Systems. with Inventory-Level-Dependent Demand
Optmal Control Approach to Prodcton Systems wth Inventory-Level-Dependent Demand Egene Khmelntsky and Ygal Gerchak Department of Indstral Engneerng, Tel-Avv Unversty, Tel-Avv 69978, Israel Fax: 97--647669,
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationLearning User's Scheduling Criteria in a Personal Calendar Agent!
Learnng User's Schedulng Crtera n a Personal Calendar Agent! Shh-ju Ln and Jane Yung-jen Hsu Deartment of Comuter Scence and Informaton Engneerng Natonal Tawan Unversty 1 Sec 4 Roosevelt Road, Tae, 106
More informationChapter 3: Dual-bandwidth Data Path and BOCP Design
Chater 3: Dual-bandwdth Data Path and BOCP Desgn 3. Introducton The focus of ths thess s on the 4G wreless moble Internet networks to rovde data servces wthn the overlang areas of CDA2000-WLA networks.
More informationGeneralizing the degree sequence problem
Mddlebury College March 2009 Arzona State Unversty Dscrete Mathematcs Semnar The degree sequence problem Problem: Gven an nteger sequence d = (d 1,...,d n ) determne f there exsts a graph G wth d as ts
More information1 Example 1: Axis-aligned rectangles
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton
More informationData Broadcast on a Multi-System Heterogeneous Overlayed Wireless Network *
JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 24, 819-840 (2008) Data Broadcast on a Mult-System Heterogeneous Overlayed Wreless Network * Department of Computer Scence Natonal Chao Tung Unversty Hsnchu,
More informationAnalysis and Modeling of Buck Converter in Discontinuous-Output-Inductor-Current Mode Operation *
Energy and Power Engneerng, 3, 5, 85-856 do:.436/ee.3.54b63 Publshed Onlne July 3 (htt://www.scr.org/journal/ee) Analyss and Modelng of Buck Converter n Dscontnuous-Outut-Inductor-Current Mode Oeraton
More informationA Performance Analysis of View Maintenance Techniques for Data Warehouses
A Performance Analyss of Vew Mantenance Technques for Data Warehouses Xng Wang Dell Computer Corporaton Round Roc, Texas Le Gruenwald The nversty of Olahoma School of Computer Scence orman, OK 739 Guangtao
More informationADOPTION OF BIG DATA ANALYTICS IN HEALTHCARE: THE EFFICIENCY AND PRIVACY
ADOPTION OF BIG DATA ANALYTICS IN HEALTHCARE: THE EFFICIENCY AND PRIVACY He L, School of Economc Informaton Engneerng, Southwestern Unversty of Fnance and Economcs, Chengdu, Chna, olverlhe@gmalcom Jng
More information+ + + - - This circuit than can be reduced to a planar circuit
MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to
More informationJCM_VN_AM003_ver01.0 Sectoral scope: 03
Sectoral scoe: 03 Jont Credtng Mechansm Aroved Methodology VN_AM003 Imrovng the energy effcency of commercal buldngs by utlzaton of hgh effcency equment A. Ttle of the methodology Imrovng the energy effcency
More informationTwo-Phase Traceback of DDoS Attacks with Overlay Network
4th Internatonal Conference on Sensors, Measureent and Intellgent Materals (ICSMIM 205) Two-Phase Traceback of DDoS Attacks wth Overlay Network Zahong Zhou, a, Jang Wang2, b and X Chen3, c -2 School of
More informationPERRON FROBENIUS THEOREM
PERRON FROBENIUS THEOREM R. CLARK ROBINSON Defnton. A n n matrx M wth real entres m, s called a stochastc matrx provded () all the entres m satsfy 0 m, () each of the columns sum to one, m = for all, ()
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationEnergies of Network Nastsemble
Supplementary materal: Assessng the relevance of node features for network structure Gnestra Bancon, 1 Paolo Pn,, 3 and Matteo Marsl 1 1 The Abdus Salam Internatonal Center for Theoretcal Physcs, Strada
More informationPortfolio Loss Distribution
Portfolo Loss Dstrbuton Rsky assets n loan ortfolo hghly llqud assets hold-to-maturty n the bank s balance sheet Outstandngs The orton of the bank asset that has already been extended to borrowers. Commtment
More informationwhere the coordinates are related to those in the old frame as follows.
Chapter 2 - Cartesan Vectors and Tensors: Ther Algebra Defnton of a vector Examples of vectors Scalar multplcaton Addton of vectors coplanar vectors Unt vectors A bass of non-coplanar vectors Scalar product
More informationThe difference between voltage and potential difference
Slavko Vjevć 1, Tonć Modrć 1 and Dno Lovrć 1 1 Unversty of Splt, Faclty of electrcal engneerng, mechancal engneerng and naval archtectre Splt, Croata The dfference between voltage and potental dfference
More informationStochastic Models of Load Balancing and Scheduling in Cloud Computing Clusters
Stochastc Models of Load Balancng and Schedulng n Cloud Coputng Clusters Sva Theja Magulur and R. Srkant Departent of ECE and CSL Unversty of Illnos at Urbana-Chapagn sva.theja@gal.co; rsrkant@llnos.edu
More informationIMPACT ANALYSIS OF A CELLULAR PHONE
4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng
More informationthe Manual on the global data processing and forecasting system (GDPFS) (WMO-No.485; available at http://www.wmo.int/pages/prog/www/manuals.
Gudelne on the exchange and use of EPS verfcaton results Update date: 30 November 202. Introducton World Meteorologcal Organzaton (WMO) CBS-XIII (2005) recommended that the general responsbltes for a Lead
More informationSmall pots lump sum payment instruction
For customers Small pots lump sum payment nstructon Please read these notes before completng ths nstructon About ths nstructon Use ths nstructon f you re an ndvdual wth Aegon Retrement Choces Self Invested
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More informationPower-of-Two Policies for Single- Warehouse Multi-Retailer Inventory Systems with Order Frequency Discounts
Power-of-wo Polces for Sngle- Warehouse Mult-Retaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)
More informationNMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING. Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582
NMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582 7. Root Dynamcs 7.2 Intro to Root Dynamcs We now look at the forces requred to cause moton of the root.e. dynamcs!!
More informationPeriod and Deadline Selection for Schedulability in Real-Time Systems
Perod and Deadlne Selecton for Schedulablty n Real-Tme Systems Thdapat Chantem, Xaofeng Wang, M.D. Lemmon, and X. Sharon Hu Department of Computer Scence and Engneerng, Department of Electrcal Engneerng
More informationTime Domain simulation of PD Propagation in XLPE Cables Considering Frequency Dependent Parameters
Internatonal Journal of Smart Grd and Clean Energy Tme Doman smulaton of PD Propagaton n XLPE Cables Consderng Frequency Dependent Parameters We Zhang a, Jan He b, Ln Tan b, Xuejun Lv b, Hong-Je L a *
More informationResearch Article Load Balancing for Future Internet: An Approach Based on Game Theory
Appled Matheatcs, Artcle ID 959782, 11 pages http://dx.do.org/10.1155/2014/959782 Research Artcle Load Balancng for Future Internet: An Approach Based on Gae Theory Shaoy Song, Tngje Lv, and Xa Chen School
More informationBasic Queueing Theory M/M/* Queues. Introduction
Basc Queueng Theory M/M/* Queues These sldes are created by Dr. Yh Huang of George Mason Unversty. Students regstered n Dr. Huang's courses at GMU can ake a sngle achne-readable copy and prnt a sngle copy
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annuty-mmedate, and ts present value Study annuty-due, and
More informationChosen Public Key and Ciphertext Secure Proxy Re-encryption Schemes
Internatonal Journal of Dgtal ontent Technology and ts Alcatons Volume 4 Number 9 December 00 hosen Publc Key and hertext Secure Proxy Re-encryton Schemes Lmng Fang Wlly Suslo Yongun Ren huneng Ge and
More informationHow Much to Bet on Video Poker
How Much to Bet on Vdeo Poker Trstan Barnett A queston that arses whenever a gae s favorable to the player s how uch to wager on each event? Whle conservatve play (or nu bet nzes large fluctuatons, t lacks
More informationSimulating injection moulding of microfeatured components
Smulatng njecton mouldng of mcrofeatured components T. Tofteberg 1 * and E. Andreassen 1 1 SINTEF Materals and Chemstry, Oslo, Norway terje.tofteberg@sntef.no; erk.andreassen@sntef.no Numercal smulaton
More informationThe Application of Fractional Brownian Motion in Option Pricing
Vol. 0, No. (05), pp. 73-8 http://dx.do.org/0.457/jmue.05.0..6 The Applcaton of Fractonal Brownan Moton n Opton Prcng Qng-xn Zhou School of Basc Scence,arbn Unversty of Commerce,arbn zhouqngxn98@6.com
More informationResearch Article Enhanced Two-Step Method via Relaxed Order of α-satisfactory Degrees for Fuzzy Multiobjective Optimization
Hndaw Publshng Corporaton Mathematcal Problems n Engneerng Artcle ID 867836 pages http://dxdoorg/055/204/867836 Research Artcle Enhanced Two-Step Method va Relaxed Order of α-satsfactory Degrees for Fuzzy
More informationA Cryptographic Key Binding Method Based on Fingerprint Features and the Threshold Scheme
A Cryptographc Key ndng Method Based on Fngerprnt Features and the Threshold Schee 1 Ln You, 2 Guowe Zhang, 3 Fan Zhang 1,3 College of Councaton Engneerng, Hangzhou Danz Unv., Hangzhou 310018, Chna, ryouln@gal.co
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More information