Chemical Engineering Journal

Size: px
Start display at page:

Download "Chemical Engineering Journal"

Transcription

1 Chemcal Engneerng Journal Contents lsts avalable at ScenceDrect Chemcal Engneerng Journal journal homepage: Revew Insghts nto the modelng of adsorpton sotherm systems K.Y. Foo, B.H. Hameed School of Chemcal Engneerng, Engneerng Campus, Unverst Sans Malaysa, 4300 Nbong Tebal, Penang, Malaysa artcle nfo abstract Artcle hstory: Receved 2 March 2009 Receved n revsed form 6 September 2009 Accepted 7 September 2009 Keywords: Adsorpton Isotherm Lnear Nonlnear Error functon Concern about envronmental protecton has ncreased over the years from a global vewpont. To date, the prevalence of adsorpton separaton n the envronmental chemstry remans an aesthetc attenton and consderaton abroad the natons, ownng to ts low ntal cost, smplcty of desgn, ease of operaton, nsenstvty to toxc substances and complete removal of pollutants even from dlute solutons. Wth the renassance of sotherms modelng, there has been a steadly growng nterest n ths research feld. Confrmng the asserton, ths paper presents a state of art revew of adsorpton sotherms modelng, ts fundamental characterstcs and mathematcal dervatons. Moreover, the key advance of the error functons, ts utlzaton prncples together wth the comparsons of lnearzed and non-lnearzed sotherm models have been hghlghted and dscussed. Conclusvely, the expandng of the nonlnear sotherms represents a potentally vable and powerful tool, leadng to the superor mprovement n the area of adsorpton scence Elsever B.V. All rghts reserved.. Introducton Over the past several decades, the exponental populaton and socal cvlzaton expanson, change affluent lfestyles and resources use, and contnung progress of the ndustral and technologes has been accompaned by a sharp modernzaton and metropoltan growth []. Wth the rsng awareness of the occurrences of ndustral actvtes whch has ntensfed numerous deteroratons on several ecosystems and serously threatens the human health and envronment, the enforcement of strngent rules and regulatons concernng the emsson of contamnants from ndustral waste streams by varous regulatory agences has been promulgated [2]. Smultaneously, a developng research by the nventon of a wde range of treatment technologes precptaton, coagulaton flocculaton, sedmentaton, flotaton, fltraton, membrane processes, electrochemcal technques, bologcal process, chemcal reactons, adsorpton and on exchange wth varyng levels of successes has accelerated a dramatc progress n the scentfc communty [3 3]. Of major nterest, adsorpton process, a surface phenomenon by whch a mult-component flud gas or lqud mxture s attracted to the surface of a sold adsorbent and forms attachments va physcal or chemcal bonds, s recognzed as the most effcent, promsng and wdely used fundamental approach n wastewater treatment processes [4], manly hnges on ts smplc- Correspondng author. Tel.: ; fax: E-mal address: B.H. Hameed. ty, economcally vable, techncally feasble and socally acceptable [5]. A notable trend n the development of actvated carbon AC, an adsorbent wth ts large porous surface area, controllable pore structure, thermo-stablty and low acd/base reactvty has been wtnesses [6], n terms ts versatlty for removal of a broad type of organc and norganc pollutants dssolved n aqueous meda, even from gaseous envronment [7]. Despte ts prolfc use n adsorpton processes, the bggest barrer of ts applcaton by the ndustres s the cost-prohbtve adsorbent and dffcultes assocated wth regeneraton [8]. Realzng the complcaton, a growng explotaton to evaluate the feasblty and sutablty of natural, renewable and low-cost materals bamboo dust, peat, chtosan, lgnte, fung, moss, bark husk, chtn, cor pth, maze cob, pnewood sawdust, rce husk, sugar cane bagasse, tea leaves, and sago waste as alternatve adsorbents n water polluton control, remedaton and decontamnaton processes has been exerted [9,20]. In the endeavor to explore novel adsorbents n accessng an deal adsorpton system, t s essental to establsh the most approprate adsorpton equlbrum correlaton [2], whch s ndspensable for relable predcton of adsorpton parameters and quanttatve comparson of adsorbent behavor for dfferent adsorbent systems or for vared expermental condtons [22,23]. In the perspectve, equlbrum relatonshps, generally known as adsorpton sotherms, descrbe how pollutants nteract wth the adsorbent materals, and thus are crtcal for optmzaton of the adsorpton mechansm pathways, expresson of the surface propertes and capactes of adsorbents, and effectve desgn of the adsorpton systems [24,25] /$ see front matter 2009 Elsever B.V. All rghts reserved. do:0.06/j.cej

2 K.Y. Foo, B.H. Hameed / Chemcal Engneerng Journal Nomenclature a K Khan sotherm model exponent a R sotherm constant /mg a RP Radke Prausntz sotherm model constant a S Sps sotherm model constant L/mg a T Toth sotherm constant L/mg A Koble Corrgan sotherm constant L n mg n /g A T Tempkn sotherm equlbrum bndng constant L/g b Langmur sotherm constant dm 3 /mg b K Khan sotherm model constant b T Tempkn sotherm constant B Koble Corrgan sotherm constant L/mg n B DR Dubnn Radushkevch sotherm constant C e equlbrum concentraton mg/l C o adsorbate ntal concentraton mg/l C s adsorbate monolayer saturaton concentraton mg/l C BET BET adsorpton sotherm relatng to the energy of surface nteracton L/mg d Interlayer spacng m ε Dubnn Radushkevch sotherm constant E mean free energy kj/mol g Redlch Peterson sotherm exponent G Gbbs energy change kj/mol k MacMllan Teller MET sotherm constant K ad Dubnn Radushkevch sotherm constant mol 2 /kj 2 K D Hll constant K F Freundlch sotherm constant mg/g dm 3 /g n related to adsorpton capacty K FH Flory Huggns sotherm equlbrum constant L/g K L Langmur sotherm constant L/mg K R sotherm constant L/g K s Sps sotherm model constant L/g K T Toth sotherm constant mg/g n adsorpton ntensty n FH Flory Huggns sotherm model exponent n H Hll cooperatvty coeffcent of the bndng nteracton p number of parameter q e amount of adsorbate n the adsorbent at equlbrum mg/g q e,calc calculated adsorbate concentraton at equlbrum mg/g q e,meas measured adsorbate concentraton at equlbrum mg/g q s theoretcal sotherm saturaton capacty mg/g q sh Hll sotherm maxmum uptake saturaton mg/l Q o maxmum monolayer coverage capactes mg/g r nverse power of dstance from the surface r R Radke Prausntz sotherm model constant R unversal gas constant 8.34 J/mol K R 2 correlaton coeffcent R L separaton factor t Toth sotherm constant T temperature K degree of surface coverage Frenkel Halsey Hll sotherm constant J m r /mole wth r s the sgn of nverse power of dstance from the surface ˇR Radke Prausntz sotherm model exponent ˇS Sps sotherm model exponent Meanwhle, lnear least-squares method s a tradtonal lnearly transformed approach wdely adopted to determne the sotherm parameters or the most ftted model, prmarly subjected to ts goodness ft to the expermental data, wth the magntude regresson correlaton coeffcents that close to unty [26]. Nevertheless, a substantal constrcton related to the lnearzed sotherm expressons has recently been ponted out, whch produce a vast amount of dfferent outcomes, mplctly alter the error structure, volate the error varance and normalty assumptons of standard least squares, leadng to the bas of the adsorpton data [27,28]. Dependng on the way the adsorptve equaton s lnearzed, the error dstrbuton changes worse. Ths has attested the utlzaton of nonlnearzed models n conjuncton wth a number of error analyss technques [29 3]. Wth the aforementoned, ths bblographc revew attempts to postulate a platform n descrbng the dstnct propertes, development and potental applcatons of adsorpton sotherm systems. The present work s amed at evaluatng ther accuracy and consstency n parameters predcton or estmaton. The extent of the error functons together wth ts comprehensve lterature comparsons has been hghlghted and outlned, to famlarze the knowledge defcences regardng non-lnearzed adsorpton sotherms. 2. Adsorpton sotherms models In general, an adsorpton sotherm s an nvaluable curve descrbng the phenomenon governng the retenton or release or moblty of a substance from the aqueous porous meda or aquatc envronments to a sold-phase at a constant temperature and ph [32,33]. Adsorpton equlbrum the rato between the adsorbed amount wth the remanng n the soluton s establshed when an adsorbate contanng phase has been contacted wth the adsorbent for suffcent tme, wth ts adsorbate concentraton n the bulk soluton s n a dynamc balance wth the nterface concentraton [30,34]. Typcally, the mathematcal correlaton, whch consttutes an mportant role towards the modelng analyss, operatonal desgn and applcable practce of the adsorpton systems, s usually depcted by graphcally expressng the sold-phase aganst ts resdual concentraton [35]. Its physcochemcal parameters together wth the underlyng thermodynamc assumptons provde an nsght nto the adsorpton mechansm, surface propertes as well as the degree of affnty of the adsorbents [36]. Over the years, a wde varety of equlbrum sotherm models Langmur, Freundlch, Brunauer Emmett Teller, Redlch Peterson, Dubnn Radushkevch, Temkn, Toth, Koble Corrgan, Sps, Khan, Hll, Flory Huggns and Radke Prausntz sotherm, have been formulated n terms of three fundamental approaches [37]. Knetc consderaton s the frst approach to be referred. Hereby, adsorpton equlbrum s defned beng a state of dynamc equlbrum, wth both adsorpton and desorpton rates are equal [38]. Whereas, thermodynamcs, beng a base of the second approach, can provde a framework of dervng numerous forms of adsorpton sotherm models [39,40], and potental theory, as the thrd approach, usually conveys the man dea n the generaton of characterstc curve [4]. However, an nterestng trend n the sotherm modelng s the dervaton n more than one approach, thus drectng to the dfference n the physcal nterpretaton of the model parameters [42]. 2.. Two parameter sotherms 2... Langmur sotherm model Langmur adsorpton sotherm, orgnally developed to descrbe gas sold-phase adsorpton onto actvated carbon, has tradtonally

3 4 K.Y. Foo, B.H. Hameed / Chemcal Engneerng Journal been used to quantfy and contrast the performance of dfferent bo-sorbents [38]. In ts formulaton, ths emprcal model assumes monolayer adsorpton the adsorbed layer s one molecule n thckness, wth adsorpton can only occur at a fnte fxed number of defnte localzed stes, that are dentcal and equvalent, wth no lateral nteracton and sterc hndrance between the adsorbed molecules, even on adjacent stes [43]. In ts dervaton, Langmur sotherm refers to homogeneous adsorpton, whch each molecule possess constant enthalpes and sorpton actvaton energy all stes possess equal affnty for the adsorbate [44], wth no transmgraton of the adsorbate n the plane of the surface [45]. Graphcally, t s characterzed by a plateau, an equlbrum saturaton pont where once a molecule occupes a ste, no further adsorpton can take place [33,46]. Moreover, Langmur theory has related rapd decrease of the ntermolecular attractve forces to the rse of dstance. The mathematcal expresson of Langmur sotherm models are llustrated n Table. Hereby, a dmensonless constant, commonly known as separaton factor R L defned by Webber and Chakkravort [47] can be represented as: R L = + K L C o where K L L/mg refers to the Langmur constant and C o s denoted to the adsorbate ntal concentraton mg/l. In ths context, lower R L value reflects that adsorpton s more favourable. In a deeper explanaton, R L value ndcates the adsorpton nature to be ether unfavourable R L >, lnear R L =, favourable 0 < R L < or rreversble R L = Freundlch sotherm model Freundlch sotherm [48] s the earlest known relatonshp descrbng the non-deal and reversble adsorpton, not restrcted to the formaton of monolayer. Ths emprcal model can be appled to multlayer adsorpton, wth non-unform dstrbuton of adsorpton heat and affntes over the heterogeneous surface [49]. Hstorcally, t s developed for the adsorpton of anmal charcoal, demonstratng that the rato of the adsorbate onto a gven mass of adsorbent to the solute was not a constant at dfferent soluton concentratons [9]. In ths perspectve, the amount adsorbed s the summaton of adsorpton on all stes each havng bond energy, wth the stronger bndng stes are occuped frst, untl adsorpton energy are exponentally decreased upon the completon of adsorpton process [50]. At present, Freundlch sotherm s wdely appled n heterogeneous systems especally for organc compounds or hghly nteractve speces on actvated carbon and molecular seves. The slope ranges between 0 and s a measure of adsorpton ntensty or surface heterogenety, becomng more heterogeneous as ts value gets closer to zero. Whereas, a value below unty mples chemsorptons process where /n above one s an ndcatve of cooperatve adsorpton [5]. Its lnearzed and non-lnearzed equatons are lsted n Table. Recently, Freundlch sotherm s crtczed for ts lmtaton of lackng a fundamental thermodynamc bass, not approachng the Henry s law at vanshng concentratons [23] Dubnn Radushkevch sotherm model Dubnn Radushkevch sotherm [52], s an emprcal model ntally conceved for the adsorpton of subcrtcal vapors onto mcropore solds followng a pore fllng mechansm. It s generally appled to express the adsorpton mechansm [53] wth a Gaussan energy dstrbuton onto a heterogeneous surface [54]. The model has often successfully ftted hgh solute actvtes and the ntermedate range of concentratons data well, but has unsatsfactory asymptotc propertes and does not predct the Henry s law at low pressure [55]. The approach was usually appled to dstngush the physcal and chemcal adsorpton of metal ons [4], wth ts mean free energy, E per molecule of adsorbate for removng a molecule from ts locaton n the sorpton space to the nfnty can be computed by the relatonshp [56]: [ ] E = 2B DR 2 where B DR s denoted as the sotherm constant. Meanwhle, the parameter ε can be correlated as: ] ε = RT ln [ + 3 where R, T and C e represent the gas constant 8.34 J/mol K, absolute temperature K and adsorbate equlbrum concentraton mg/l, respectvely. One of the unque features of the Dubnn Radushkevch sotherm model les on the fact that t s temperature-dependent, whch when adsorpton data at dfferent temperatures are plotted as a functon of logarthm of amount adsorbed vs the square of potental energy, all sutable data wll le on the same curve, named as the characterstc curve Temkn sotherm model Temkn sotherm s the early model descrbng the adsorpton of hydrogen onto platnum electrodes wthn the acdc solutons. The sotherm [57] contans a factor that explctly takng nto the account of adsorbent adsorbate nteractons. By gnorng the extremely low and large value of concentratons, the model assumes that heat of adsorpton functon of temperature of all molecules n the layer would decrease lnearly rather than logarthmc wth coverage [58]. As mpled n the equaton, ts dervaton s characterzed by a unform dstrbuton of bndng energes up to some maxmum bndng energy. Temkn equaton s excellent for predctng the gas phase equlbrum when organzaton n a tghtly packed structure wth dentcal orentaton s not necessary, conversely complex adsorpton systems ncludng the lqud-phase adsorpton sotherms are usually not approprate to be represented [59] Flory Huggns sotherm model Flory Huggns sotherm model [60], whch occasonally dervng the degree of surface coverage characterstcs of adsorbate onto adsorbent, can express the feasblty and spontaneous nature of an adsorpton process. In ths respect, s the degree of surface coverage, where K FH and n FH are the ndcaton of ts equlbrum constant and model exponent. Its equlbrum constant, K FH that used for the calculaton of spontanety free Gbbs energy, s related to the equaton [43]: G = RT ln K FH Hll sotherm model Hll equaton [6], that orgnated from the NICA [62] model, was postulated to descrbe the bndng of dfferent speces onto homogeneous substrates. The model assumes that adsorpton s a cooperatve phenomenon, wth the lgand bndng ablty at one ste on the macromolecule, may nfluence dfferent bndng stes on the same macromolecule [63] Three parameter sotherms sotherm model sotherm [64] s a hybrd sotherm featurng both Langmur and Freundlch sotherms, whch ncorporate three parameters nto an emprcal equaton [65]. The model has a lnear dependence on concentraton n the numerator and an exponental functon n the denomnator [66] to represent adsorpton equlbra over a wde concentraton range, that can be appled ether

4 K.Y. Foo, B.H. Hameed / Chemcal Engneerng Journal Table Lsts of adsorpton sotherms models. Isotherm Nonlnear form Lnear form Plot Reference Langmur q e = Qob +b = + bqo Qo vs C e [38] = Qo + bqo vs q e = Q o b q e vs b = bqo b vs q e Freundlch q e = K F C /n e log q e = log K F + log log vs log [48] n Dubnn Radushkevch q e =q s exp k ad ε 2 lnq e=lnq s k ad ε 2 Inq evsε 2 [52] Tempkn Flory Huggns Hll q e = RT b T ln A T C e q e = RT b T ln A T + Co = KFH n FH log q e = qs H Cn H e K D +C n H e q e = K R +a R C g e Sps q e = KsCˇS e +a S CˇS e Toth q e = K T log ln a T + /t ln Co RT ln C b e q e vs ln C e [57] T = log K FH + n FH log log qs H Co = n H log C e log K D log vs log [60] qs H K R = g lnc e + lna R ln K R ˇS lnc e = ln Ks K T + lna S ln Ks vs logc e [6] vs lnc e [64] vs lnc e [68] = lnc e t lnat + ln K T vs lnc e [69] Koble Corrgan q e = ACn e +BC n e = AC e n + B [70] A Khan q e = qsb K +b K a K [7] Radke Prausntz q e = a RP r R CˇR e a RP +r R CˇR e [43] BET q e = FHH ln qsc BET Cs [+C BET /Cs] Cs = RT Cs = + C BET qsc BET qsc BET Cs vs Cs Cs qs d r [74] /3 k MET q e = q s lncs/ [75] [73] n homogeneous or heterogeneous systems due to ts versatlty [22]. Typcally, a mnmzaton procedure s adopted n solvng the equatons by maxmzng the correlaton coeffcent between the expermental data ponts and theoretcal model predctons wth solver add-n functon of the Mcrosoft excel [26]. In the lmt, t approaches Freundlch sotherm model at hgh concentraton as the exponent ˇ tends to zero and s n accordance wth the low concentraton lmt of the deal Langmur condton as the ˇ values are all close to one [67] Sps sotherm model Sps sotherm [68] s a combned form of Langmur and Freundlch expressons deduced for predctng the heterogeneous adsorpton systems [53] and crcumventng the lmtaton of the rsng adsorbate concentraton assocated wth Freundlch sotherm model. At low adsorbate concentratons, t reduces to Freundlch sotherm; whle at hgh concentratons, t predcts a monolayer adsorpton capacty characterstc of the Langmur sotherm. As a general rule, the equaton parameters are governed manly by the operatng condtons such as the alteraton of ph, temperature and concentraton [45] Toth sotherm model Toth sotherm model [69], s another emprcal equaton developed to mprove Langmur sotherm fttngs expermental data, and useful n descrbng heterogeneous adsorpton systems, whch satsfyng both low and hgh-end boundary of the concentraton [43]. Its correlaton presupposes an asymmetrcal quas-gaussan energy dstrbuton, wth most of ts stes has an adsorpton energy lower than the peak maxmum or mean value [23] Koble Corrgan sotherm model Smlar to the Sps sotherm model, Koble Corrgan sotherm [70] s a three-parameter equaton, whch ncorporated both Langmur and Freundlch sotherm models for representng the equlbrum adsorpton data. The sotherm constants, A, B and n are evaluated from the lnear plot usng a tral and error optmzaton Khan sotherm model Khan sotherm [7] s a generalzed model suggested for the pure solutons, wth b K and a K are devoted to the model constant and model exponent. At relatvely hgh correlaton coeffcents and mnmum ERRSQ or ch-square values, ts maxmum uptake values can be well determned [72] Radke Prausntz sotherm model The correlaton of Radke Prausntz sotherm s usually predcted well by the hgh RMSE and ch-square values. Its model exponent s represented by ˇR, where a R and r R are referred to the model constants [43] Multlayer physsorpton sotherms Brunauer Emmett Teller BET [73] sotherm s a theoretcal equaton, most wdely appled n the gas sold equlbrum systems. It was developed to derve multlayer adsorpton systems

5 6 K.Y. Foo, B.H. Hameed / Chemcal Engneerng Journal Table 2 Lsts of error functons. Error functon Abbrevaton Defnton/expresson Reference Sum squares errors ERRSQ/SSE q e,calc q e,meas 2 [80] Hybrd fractonal error functon HYBRID 00 n p [,meas q e,calc,meas ] [66] Average relatve error ARE 00 n,meas q e,calc,meas [82] Sum of absolute error EABS q e,meas q e,calc Marquardt s percent standard devaton MPSD 00 n p,meas,calc 2,meas [83] [84] The coeffcent of determnaton R 2 r 2 =,meas q e,calc 2,meas q e,calc 2 +,meas q e,calc 2 [78] n Spearman s correlaton coeffcent r s 6,meas q e,calc 2 [78] nn 2 Standard devaton of relatve errors s RE n Nonlnear ch-square test 2 2 [,meas q e,calc ARE] [78] n q e,calc,meas 2 Coeffcent of non-determnaton K 2 [80],meas [78] Sum of normalzed errors SNE [88] wth relatve pressure ranges from 0.05 to 0.30 correspondng to a monolayer coverage lyng between 0.50 and.50. Its extncton model related to lqud sold nterface s exhbted as: q s C BET C e q e = 5 C s C e [ + C BET C e /C s ] where C BET, C s, q s and q e are the BET adsorpton sotherm L/mg, adsorbate monolayer saturaton concentraton mg/l, theoretcal sotherm saturaton capacty mg/g and equlbrum adsorpton capacty mg/g, respectvely. As C BET and C BET C e /C s are much greater than, the equaton s smplfed as: q s q e = 6 C e /C s Meanwhle, Frenkel Halsey Hll FHH sotherm [74], another multlayer adsorpton dervaton from the potental theory may be wrtten as: ln = qs r 7 C s RT q e d where d, and r are the sgn of the nterlayer spacng m, sotherm constant J m r /mole and nverse power of dstance from the surface about 3, respectvely. Smlarly, MacMllan Teller MET sotherm [75], an adsorpton model nterpreted from the ncluson of surface tenson effects n the BET sotherm s termed as: /3 k q e = q s 8 lnc s /C e where k s an sotherm constant. When C s /C e s approachng unty, the logarthmc term can be approxmated as: k /3 q e = q s 9 C s C e As a note, the emprcal sotherm s reasonable ft to Frenkel Halsey Hll FHH or MacMllan Teller MET sotherms for relatve pressures hgher than 0.8 and approxmately Brunauer Emmett Teller BET sotherm for relatve pressures lower than Error functons Wthn recent decades, lnear regresson has been one of the most vable tool defnng the best-fttng relatonshp [76] quantfyng the dstrbuton of adsorbates, mathematcally analyzng the adsorpton systems [77] and verfyng the consstency and theoretcal assumptons of an sotherm model [78]. Due to the nherent bas resultng from the transformaton whch rdng towards a dverse form of parameters estmaton errors and fts dstorton, several mathematcally rgorous error functons sum square error, Hybrd fractonal error functon, sum of absolute errors, average relatve error, Marquardt s percent standard devaton, coeffcent of determnaton, Spearman s correlaton coeffcent, standard devaton of relatve errors, nonlnear ch-square test, coeffcent of nondetermnaton and sum of normalzed errors Table 2 have lately drastcally been addressed and confronted [79]. Concomtant wth the development of computer technology n the 980s, the progresson of the nonlnear sotherm modelng has extensvely been facltated and motvated [78]. Contrary to the lnearzaton models, nonlnear regresson usually nvolves the mnmzaton or maxmzaton of error dstrbuton between the expermental data and the predcted sotherm based on ts convergence crtera [79]. 3.. Sum square error ERRSQ Despte ERRSQ s the most wdely used error functon [80], at hgher end of the lqud-phase concentraton ranges, the magntude

6 K.Y. Foo, B.H. Hameed / Chemcal Engneerng Journal and squares of the errors tend to ncrease, llustratng a better ft for the sotherm parameters dervaton [8] Hybrd fractonal error functon HYBRID The error functon was developed to mprove ERRSQ ft at low concentratons. Hereby, each ERRSQ value s dvded by the expermental sold-phase concentraton wth a dvsor ncluded n the system as a term for the number of degrees of freedom the number of data ponts mnus the number of parameters wthn the sotherm equaton [66] Average relatve error ARE ARE model [82] whch ndcates a tendency to under or overestmate the expermental data, attempts to mnmze the fractonal error dstrbuton across the entre studed concentraton range Sum of absolute errors EABS The approach s smlar to the ERRSQ functon, wth an ncrease n the errors wll provde a better ft, leadng to the bas towards the hgh concentraton data [83] Marquardt s percent standard devaton MPSD Marquardt s percent standard devaton MPSD error functon [84] has prevously practced by a number of researchers n the sotherm studes [26,83,85,86]. Accordng to the number of degrees of freedom n the system, t s smlar to some respects of a modfed geometrc mean error dstrbuton [87] Coeffcent of determnaton R 2, Spearman s correlaton coeffcent r s and standard devaton of relatve errors s RE Coeffcent of determnaton, whch represents the percentage of varablty n the dependent varable the varance about the mean s employed to analyze the fttng degree of sotherm and knetc models wth the expermental data [88]. Its value may vary from 0 to [89] where Spearman s correlaton coeffcent and standard devaton of relatve errors are ndvdually determned to evaluate the global correlaton and the dsperson of ts relatve errors [78] Nonlnear ch-square test 2 Nonlnear ch-square test s a statstcal tool necessary for the best ft of an adsorpton system, obtaned by judgng the sum squares dfferences between the expermental and the calculated data, wth each squared dfference s dvded by ts correspondng value calculated from the models. Small 2 value ndcates ts smlartes whle a larger number represents the varaton of the expermental data [78] Coeffcent of non-determnaton K 2 Another statstcal term, coeffcent of non-determnaton, s much useful n descrbng the extent relatonshp between the transformed expermental data and the predcted sotherms, and mnmzaton of the error dstrbuton [90] Sum of normalzed errors SNE Consequence of dfferent error crtera s lkely to produce dfferent sets of sotherm parameters, a standard procedure normalzng and combnng varous errors for better and meanngful comparson between the parameter sets for the sngle sotherm model s adopted [44,78,83,9]. The calculaton orentaton s revealed as follows: a Selecton of an sotherm model and error functon, and determnaton of the adjustable parameters whch mnmze the error functon. b Determnaton of all other error functons by referrng to the parameter set. c Computaton of other parameter sets assocated wth ther error functon values ntaton of the procedure by mnmzng the error functon. d Normalzaton and selecton of the maxmum parameter sets wth respect to the largest error measurement. e Summaton of each parameter set whch generates the mnmum normalzaton error. 4. Lterature revew on applcatons of lnear and nonlnear forms of sotherm models An accuracy of an sotherm model s generally a functon of the number of ndependent parameters, whle ts popularty n relaton to the process applcaton s an ndcatve of ts mathematcal smplcty [37]. Undoubtedly, lnear regresson analyss has frequently been employed n accessng the qualty of fts and adsorpton performance [44], prmarly owng to ts wde usefulness n a varety of adsorpton data [9] and partly reflectng the appealng smplcty of ts equatons [92]. However, durng the last few years, a development nterest n the utlzaton of nonlnear optmzaton modelng has been noted [65]. A number of researches have been advocated to nvestgate the applcablty of lnear or nonlnear sotherm models n descrbng the adsorpton of dyes, heavy metals and organc pollutants onto actvated carbons, zeoltes, chtosans, bentontes, montmorllontes, kaolntes and a lst of low-cost adsorbents Table 3. In 984, Harter [03] had frstly examned Langmur sotherm model n an ons adsorpton system adsorpton of on phosphate, znc, and copper by sol. Wthout suffcent ranges of adsorbate concentraton, he emphaszed that the estmaton of maxmum adsorpton capacty could be qute msleadng n error by 50% or more, reducng the varablty of ts lnearty. In 988, Persoff and Thomas [04] had proposed the use of nonlnear least-squares NLLS curve-fttng method for determnaton of the Mchaels Menten and Langmur adsorpton sotherm constants from the expermental data. From the applcaton, they concluded that weghted NLLS yelded a more precse and accurate estmaton. More recently, smlar observatons have been reported by several researchers [24,63,78,79,96,0]. The authors suggested that the lnearzed equatons apparently generate real problems and errors arsng from the complextes and complcatons for smultaneous transformaton of data, leadng to the volaton of theores behnd the sotherms. In certan cases, t has been llustrated that a dfferent axs settng dfferent lnearzed models would alter the regresson results, nfluencng ts consstency and accuracy [97]. Such tendency more statstcal functons are vald for nonlnear than lnear analyss could be drectly proportonal to the dstorton of the expermental errors, creatng an nherent errors estmaton problem whch lmts the valdty of the studed tools [35]. Moreover, lnear analyss method assumes that the scatter vertcal ponts around the lne follows a Gaussan dstrbuton, and the error dstrbuton s unform at every value of the lqud-phase resdual concentraton X-axs [89]. Nonetheless, such behavor s practcally mpossble wth the equlbrum relatonshps snce sotherm models had nonlnear shape,

7 8 K.Y. Foo, B.H. Hameed / Chemcal Engneerng Journal Table 3 Prevous researches of the lnear and nonlnear sotherm studes. Adsorbent Adsorbate Isotherm models Determnaton Preference types Reference Wheat bran Cadmum ons Freundlch, Langmur R 2 Nonlnear [5] Babasse fly ash Orange-G dyemethyl Volet dye Freundlch, Langmur, R 2 Nonlnear [9], Temkn, Dubnn Radushkevch, Elovch Peat Dvalent metal ons Freundlch, Langmur, R 2, ERRSQ, ARE, HYBRID, Both [23], Temkn, Dubnn Radushkevch, Toth MPSD, SAE, SNE Water hyacnth Methylene blue dye Freundlch, Langmur R 2 Nonlnear [24] Rce husk Safrann Freundlch, Langmur, R 2 Nonlnear [30] Fbrous bomass Drect Solophenyl Brown dye Langmur,, Temkn, ARED, EABS, MPSD, Nonlnear [35] Dubnn Radushkevch, Elovch HYBRID, R 2, RESID Iron oxde-coated cement Arsenc Freundlch, Langmur, SAE, ARE, HYBRID, MPSD, Both [44], Temkn EABS Montmorllonte, kaolnte Heavy metals Freundlch, Langmur R 2 Both [55] Yeast bomass Ochratoxn A Freundlch, Langmur, BET, R 2, EABS, HYBRID, ARE, Nonlnear [63] SAE, MPSD Actvated carbon Malachte green dye Freundlch, Langmur, R 2 Nonlnear [76] Actvated carbon Tetrahydrothophene Langmur R 2, r s, EABS, RSS, ARE, s RE, Nonlnear [78] HYBRID Actvated carbon Methylene blue Freundlch, Langmur, R 2, ERRSQ, ARE, HYBRID, Nonlnear [79] MPSD, EABS Actvated carbon Malachte green dye Freundlch, Langmur, R 2 Nonlnear [80] Rce husk ash Brllant green dye Freundlch, Langmur,, Temkn, Dubnn Radushkevch Chtosan Lead Freundlch, Langmur, SSE, SAE, ARE, HYBRID, MPSD Both [8] ERRSQ, ARE, HYBRID, Nonlnear [83] MPSD, EABS Zeolte Ammonum Freundlch, Langmur R 2 Nonlnear [88] Actvated carbon Basc dyes Freundlch, Langmur, R 2 Nonlnear [89] Actvated carbon Basc red 9 Freundlch, Langmur, R 2, EABS HYBRID, ARE, Nonlnear [90] SAE, MPSD Alumna cement granules Fluorde Freundlch, Langmur, R 2, SNE, EABS HYBRID, Both [92] Dubnn Radushkevch ARE, SAE, MPSD Eucalyptus bark Cadmum ons Freundlch, Langmur R 2 Nonlnear [93] Zeolte Methylene blue Freundlch, Koble Corrgan, Langmur, SAE, ARE, ARS, EABS Both [94], Temkn Bagasse fly ash Brllant green dye Freundlch, Langmur,, Temkn, Dubnn Radushkevch SSE, SAE, ARE, HYBRID, MPSD Both [95] Actvated carbon Basc blue 9 dye Freundlch, Langmur, R 2, ERRSQ, 2 Nonlnear [96] Sugarcane dust Basc dyes Freundlch, Langmur, R 2 Nonlnear [97] 2 Fly ash Dyes Freundlch, Langmur R 2 Nonlnear [98] Rce husk Bsmarck brown dye Freundlch, Langmur, R 2 Nonlnear [99] Bentonte Strontum Freundlch, Langmur RMSE Nonlnear [00] Ca-algnate beads Znc II ons Freundlch, Langmur R 2 Nonlnear [0] Mansona wood sawdust Methyl volet Freundlch, Langmur, R 2 Both [02] as the error dstrbuton tends to get altered after transformng nto a lnearzed order [26]. In another study, lnearzaton sotherms models Langmur and Freundlch sotherm models have been demonstrated napproprate n predctng the goodness of ft for a partcular set of condtons [95], and unable for provdng a fundamental understandng of the ons adsorpton systems, resultng n an mproper concluson. On the contrary, the nonlnear sotherm models are conducted on the same abscssa and ordnate, thus avodng such drawbacks of lnearzaton [92]. Nevertheless, a few researchers [23,44,94,95,02] also ndcated the smlartes and consstency of both lnear and nonlnear sotherms, lyng nto the same error dstrbutons and structures. Under such condtons, t would be more ratonal and relable to nterpret adsorpton data through a process of lnear and nonlnear regresson [92]. Irrespectve of ts technque ether the lnear or the nonlnear method, the avalablty and usefulness of the equlbrum data should be suffcent enough to effectvely represent an effcent and complete sotherm model [76]. 5. Concluson The past 0 years has seen a developng nterest n the preparaton of low-cost adsorbents as alternatves to actvated carbons n water and wastewater treatment processes. To date, lmted success of adsorbents n the feld applcatons has rased apprehensons over the use of adsorpton capacty generated from equlbrum data as a measure of ther effectveness n drnkng water treatment. Over the past few decades, lnear regresson has been developed as a major opton n desgnng the adsorpton systems. However, recent nvestgatons have ndcated the growng dscrepancy between the predctons and expermental data and dsablty of the model, propagatng towards a dfferent out-

8 K.Y. Foo, B.H. Hameed / Chemcal Engneerng Journal come. Despte ths obvous nherent bas of the model, lnearzaton remans a confdent opton n the lterature, appled n over 95% of the lqud-phase adsorpton systems. Hence, the next real challenge n the adsorpton feld s the dentfcaton and clarfcaton of both sotherm models n varous adsorpton systems. Further exploratons on developng n ths area are recommended. Acknowledgement The authors acknowledge the research grant provded by the Unverst Sans Malaysa under the Research Unversty RU Scheme Project No. 00/PJKIMIA/ References [] K.Y. Foo, B.H. Hameed, Utlzaton of bodesel waste as a renewable resource for actvated carbon: applcaton to envronmental problems, Renew. Sust. Energy Rev [2] K.Y. Foo, B.H. Hameed, Value-added utlzaton of ol palm ash: a superor recyclng of the ndustral agrcultural waste, J. Hazard. Mater. 2009, do:0.06/j.jhazmat [3] N. Mart, A. Bouzas, A. Seco, J. Ferrer, Struvte precptaton assessment n anaerobc dgeston processes, Chem. Eng. J [4] Z. Lang, Y.X. Wang, Y. Zhou, H. Lu, Coagulaton removal of melanodns from bologcally treated molasses wastewater usng ferrc chlorde, Chem. Eng. J [5] R. Bürger, F. Concha, F.M. Tller, Applcatons of the phenomenologcal theory to several publshed expermental cases of sedmentaton processes, Chem. Eng. J [6] A.L. Macfarlane, R. Prestdge, M.M. Fard, J.J.J. Chen, Dssolved ar flotaton: a novel approach to recovery of organosolv lgnn, Chem. Eng. J [7] T. Deuschle, U. Janoske, M. Pesche, A CFD-model descrbng fltraton, regeneraton and depost rearrangement effects n gas flter systems, Chem. Eng. J [8] H. Valdés, J. Romero, J. Sanchez, S. Bocquet, G.M. Ros, F. Valenzuela, Characterzaton of chemcal knetcs n membrane-based lqud lqud extracton of molybdenumvi from aqueous solutons, Chem. Eng. J [9] K.Y. Foo, B.H. Hameed, A short revew of actvated carbon asssted electrosorpton process: An overvew, current stage and future prospects, J. Hazard. Mater [0] G.B. Zhu, Y.Z. Peng, B. Ma, Y. Wang, C.Q. Yn, Optmzaton of anoxc/oxc step feedng actvated sludge process wth fuzzy control model for mprovng ntrogen removal, Chem. Eng. J [] H. Delmas, C. Creanga, C. Julcour-Lebgue, A.M. Wlhelm, AD OX: a sequental oxdatve process for water treatment adsorpton and batch CWAO regeneraton of actvated carbon, Chem. Eng. J [2] M.A. Abdullah, L. Chang, M. Nadeem, Comparatve evaluaton of adsorpton knetcs and sotherms of a natural product removal by Amberlte polymerc adsorbents, Chem. Eng. J [3] N. Mladnovc, L.R. Weatherley, Intensfcaton of ammona removal n a combned on-exchange and ntrfcaton column, Chem. Eng. J [4] K.Y. Foo, B.H. Hameed, An overvew of landfll leachate treatment va actvated carbon adsorpton process, J. Hazard. Mater. 2009, do:0.06/j.jhazmat [5] L. Nour, I. Ghodbane, O. Hamdaou, M. Chha, Batch sorpton dynamcs and equlbrum for the removal of cadmum ons from aqueous phase usng wheat bran, J. Hazard. Mater [6] D. Mohan, C.U. Pttman Jr., Actvated carbons and low cost adsorbents for remedaton of tr- and hexavalent chromum from water, J. Hazard. Mater [7] E.N. El Qada, S.J. Allen, G.M. Walker, Influence of preparaton condtons on the characterstcs of actvated carbons produced n laboratory and plot scale systems, Chem. Eng. J [8] K.Y. Foo, B.H. Hameed, Recent developments n the preparaton and regeneraton of actvated carbons by mcrowaves, Adv. Collod Interface Sc [9] Md. Ahmaruzzaman, Adsorpton of phenolc compounds on low-cost adsorbents: a revew, Adv. Collod Interface Sc [20] D. Kalders, D. Koutoulaks, P. Paraskeva, E. Damadopoulos, E. Otal, J.O. del Valle, C. Fernández-Perera, Adsorpton of pollutng substances on actvated carbons prepared from rce husk and sugarcane bagasse, Chem. Eng. J [2] V.V. Srvastava, M.M. Swamy, I.D. Mall, B. Prasad, I.M. Mshra, Adsorptve removal of phenol by bagasse fly ash and actvated carbon: equlbrum, knetcs and thermodynamcs, Collods Surf. A [22] F. Gmbert, N. Morn-Crn, F. Renault, P.M. Badot, G. Crn, Adsorpton sotherm models for dye removal by catonzed starch-based materal n a sngle component system: error analyss, J. Hazard. Mater [23] Y.S. Ho, J.F. Porter, G. Mckay, Equlbrum sotherm studes for the sorpton of dvalent metal ons onto peat: copper, nckel and lead sngle component systems, Water Ar Sol Pollut [24] M.I. El-Khaary, Least-squares regresson of adsorpton equlbrum data: comparng the optons, J. Hazard. Mater [25] G. Thompson, J. Swan, M. Kay, C.F. Forster, The treatment of pulp and paper mll effluent: a revew, Boresour. Technol [26] Y.C. Wong, Y.S. Szeto, W.H. Cheung, G. McKay, Adsorpton of acd dyes on chtosan-equlbrum sotherm analyses, Process Bochem [27] S. Hong, C. Wen, J. He, F.X. Gan, Y.S. Ho, Adsorpton thermodynamcs of Methylene Blue onto bentonte, J. Hazard. Mater. 2009, do:0.06/j.jhazmat [28] Y.S. Ho, Selecton of optmum sorpton sotherm, Carbon [29] R.P. Han, Y. Wang, W.H. Zou, Y.F. Wang, J. Sh, Comparson of lnear and nonlnear analyss n estmatng the Thomas model parameters for methylene blue adsorpton onto natural zeolte n fxed-bed column, J. Hazard. Mater [30] K.V. Kumar, S. Svanesan, Sorpton sotherm for safrann onto rce husk: comparson of lnear and non-lnear methods, Dyes Pgments [3] Y.S. Ho, Second-order knetc model for the sorpton of cadmum onto tree fern: a comparson of lnear and non-lnear methods, Water Res [32] G. Lmousn, J.P. Gaudet, L. Charlet, S. Szenknect, V. Barthes, M. Krmssa, Sorpton sotherms: a revew on physcal bases, modelng and measurement, Appl. Geochem [33] S.J. Allen, G. Mckay, J.F. Porter, Adsorpton sotherm models for basc dye adsorpton by peat n sngle and bnary component systems, J. Collod Interface Sc [34] M. Ghac, A. Abbaspur, R. Ka, F. Seyedeyn-Azad, Equlbrum sotherm studes for the sorpton of benzene, toluene, and phenol onto organo-zeoltes and as-syntheszed MCM-4, Sep. Purf. Technol [35] M.C. Ncb, Applcablty of some statstcal tools to predct optmum adsorpton sotherm after lnear and non-lnear regresson analyss, J. Hazard. Mater [36] E. Bulut, M. Ozacar, I.A. Sengl, Adsorpton of malachte green onto bentonte: equlbrum and knetc studes and process desgn, Mcropor. Mesopor. Mater [37] A. Malek, S. Farooq, Comparson of sotherm models for hydrocarbon adsorpton on actvated carbon, AIChE J [38] I. Langmur, The consttuton and fundamental propertes of solds and lquds, J. Am. Chem. Soc [39] J.H. De Boer, The Dynamcal Character of Adsorpton, second ed., Oxford Unversty Press, London, 968. [40] A.L. Myers, J.M. Prausntz, Thermodynamcs of mxed gas adsorpton, AIChE J [4] M.M. Dubnn, The potental theory of adsorpton of gases and vapors for adsorbents wth energetcally non-unform surface, Chem. Rev [42] D.M. Ruthven, Prncples of Adsorpton and Adsorpton Processes, Wley, New York, 984. [43] K. Vjayaraghavan, T.V.N. Padmesh, K. Palanvelu, M. Velan, Bosorpton of nckelii ons onto Sargassum wght: applcaton of two-parameter and three parameter sotherm models, J. Hazard. Mater. B [44] S. Kundu, A.K. Gupta, Arsenc adsorpton onto ron oxde-coated cement IOCC: regresson analyss of equlbrum data wth several sotherm models and ther optmzaton, Chem. Eng. J [45] A.B. Pérez-Marín, V. Meseguer Zapata, J.F. Ortuno, M. Agular, J. Sáez, M. Llorens, Removal of cadmum from aqueous solutons by adsorpton onto orange waste, J. Hazard. Mater. B [46] E. Demrbas, M. Kobya, A.E.S. Konukman, Error analyss of equlbrum studes for the almond shell actvated carbon adsorpton of CrVI from aqueous solutons, J. Hazard. Mater [47] T.W. Webber, R.K. Chakkravort, Pore and sold dffuson models for fxed-bed adsorbers, AlChE J [48] H.M.F. Freundlch, Over the adsorpton n soluton, J. Phys. Chem [49] A.W. Adamson, A.P. Gast, Physcal Chemstry of Surfaces, sxth ed., Wley- Interscence, New York, 997. [50] J. Zeldowtsch, Adsorpton ste energy dstrbuton, Acta Phys. Chm. URSS [5] F. Haghseresht, G. Lu, Adsorpton characterstcs of phenolc compounds onto coal-reject-derved adsorbents, Energy Fuels [52] M.M. Dubnn, L.V. Radushkevch, The equaton of the characterstc curve of the actvated charcoal, Proc. Acad. Sc. USSR Phys. Chem. Sect [53] A. Gunay, E. Arslankaya, I. Tosun, Lead removal from aqueous soluton by natural and pretreated clnoptlolte: adsorpton equlbrum and knetcs, J. Hazard. Mater [54] A. Dabrowsk, Adsorpton from theory to practce, Adv. Collod Interface Sc [55] O. Altn, H.O. Ozbelge, T. Dogu, Use of general purpose adsorpton sotherms for heavy metal clay mneral nteractons, J. Collod Interface Sc

9 0 K.Y. Foo, B.H. Hameed / Chemcal Engneerng Journal [56] J.P. Hobson, Physcal adsorpton sotherms extendng from ultra hgh vacuum to vapor pressure, J. Phys. Chem [57] M.I. Tempkn, V. Pyzhev, Knetcs of ammona synthess on promoted ron catalyst, Acta Phys. Chm. USSR [58] C. Aharon, M. Ungarsh, Knetcs of actvated chemsorpton. Part 2. Theoretcal models, J. Chem. Soc. Faraday Trans [59] Y. Km, C. Km, I. Cho, S. Rengraj, J. Y, Arsenc removal usng mesoporous alumna prepared va a templatng method, Envron. Sc. Technol [60] M. Horsfall, A.I. Spff, Equlbrum sorpton study of Al 3+,Co 2+ and Ag 2+ n aqueous solutons by fluted pumpkn Telfara occdentals HOOK waste bomass, Acta Chm. Slov [6] A.V. Hll, The possble effects of the aggregaton of the molecules of haemoglobn on ts dssocaton curves, J. Physol. London v v. [62] L.K. Koopal, W.H. Van Remsdjk, J.C.M. de Wt, M.F. Benedett, Analytcal sotherm equaton for multcomponent adsorpton to heterogeneous surfaces, J. Collod Interface Sc [63] D. Rngot, B. Lerzy, K. Chaplan, J.P. Bonhoure, E. Auclar, Y. Larondelle, In vtro bosorpton of ochratoxn A on the yeast ndustry by-products: comparson of sotherm models, Boresour. Technol [64] O. Redlch, D.L. Peterson, A useful adsorpton sotherm, J. Phys. Chem [65] R.K. Prasad, S.N. Srvastava, Sorpton of dstllery spent wash onto fly ash: knetcs and mass transfer studes, Chem. Eng. J [66] J.C.Y. Ng, W.H. Cheung, G. McKay, Equlbrum studes of the sorpton of CuII ons onto chtosan, J. Collod Interface Sc [67] L. Jossens, J.M. Prausntz, W. Frtz, E.U. Schlünder, A.L. Myers, Thermodynamcs of mult-solute adsorpton from dlute aqueous solutons, Chem. Eng. Sc [68] R. Sps, Combned form of Langmur and Freundlch equatons, J. Chem. Phys [69] J. Toth, State equatons of the sold gas nterface layer, Acta Chem. Acad. Hung [70] R.A. Koble, T.E. Corrgan, Adsorpton sotherms for pure hydrocarbons, Ind. Eng. Chem [7] A.R. Khan, R. Ataullah, A. Al-Haddad, Equlbrum adsorpton studes of some aromatc pollutants from dlute aqueous solutons on actvated carbon at dfferent temperatures, J. Collod Interface Sc [72] A.R. Khan, I.R. Al Waheab, A.A. Al-Haddad, Generalzed equaton for adsorpton sotherms for multcomponent organc pollutants n dlute aqueous soluton, Envron. Technol [73] S. Bruanuer, P.H. Emmett, E. Teller, Adsorpton of gases n multmolecular layers, J. Am. Chem. Soc [74] T.L. Hll, Theory of physcal adsorpton, Adv. Catal [75] W.G. McMllan, E. Teller, The assumptons of the B.E.T. theory, J. Phys. Collod Chem [76] K.V. Kumar, Comparatve analyss of lnear and non-lnear method of estmatng the sorpton sotherm parameters for malachte green onto actvated carbon, J. Hazard. Mater. B [77] D.H. Lataye, I.M. Mshra, I.D. Mall, Adsorpton of 2-pcolne onto bagasse fly ash from aqueous soluton, Chem. Eng. J [78] B. Boulnguez, P. Le Clorec, D. Wolbert, Revstng the determnaton of Langmur parameters applcaton to tetrahydrothophene adsorpton onto actvated carbon, Langmur [79] K.V. Kumar, K. Porkod, F. Rocha, Isotherms and thermodynamcs by lnear and non-lnear regresson analyss for the sorpton of methylene blue onto actvated carbon: comparson of varous error functons, J. Hazard. Mater [80] K.V. Kumar, S. Svanesan, Pseudo second order knetcs and pseudo sotherms for malachte green onto actvated carbon: comparson of lnear and nonlnear regresson methods, J. Hazard. Mater. B [8] V.S. Mane, I.D. Mall, V.C. Srvastava, Knetc and equlbrum sotherm studes for the adsorptve removal of Brllant Green dye from aqueous soluton by rce husk ash, J. Envron. Manage [82] A. Kapoor, R.T. Yang, Correlaton of equlbrum adsorpton data of condensable vapours on porous adsorbents, Gas Sep. Purf [83] J.C.Y. Ng, W.H. Cheung, G. McKay, Equlbrum studes for the sorpton of lead from effluents usng chtosan, Chemosphere [84] D.W. Marquardt, An algorthm for least-squares estmaton of nonlnear parameters, J. Soc. Ind. Appl. Math [85] I.D. Mall, V.C. Srvastava, N.K. Agarwal, I.M. Mshra, Adsorptve removal of malachte green dye from aqueous soluton by bagasse fly ash and actvated carbon-knetc study and equlbrum sotherm analyses, Collod Surf. A [86] I.D. Mall, V.C. Srvastava, N.K. Agarwal, I.M. Mshra, Removal of Congo red from aqueous soluton by bagasse fly ash and actvated carbon: knetc study and equlbrum sotherm analyses, Chemosphere [87] A. Sedel, D. Gelbn, On applyng the deal adsorbed soluton theory to multcomponent adsorpton equlbra of dssolved organc components on actvated carbon, Chem. Eng. Sc [88] D. Karadag, Y. Koc, M. Turan, M. Ozturk, A comparatve study of lnear and nonlnear regresson analyss for ammonum exchange by clnoptlolte zeolte, J. Hazard. Mater [89] K.V. Kumar, S. Svanesan, Isotherm parameters for basc dyes onto actvated carbon: comparson of lnear and non-lnear method, J. Hazard. Mater. B [90] K.V. Kumar, K. Porkod, F. Rocha, Comparson of varous error functons n predctng the optmum sotherm by lnear and non-lnear regresson analyss for the sorpton of basc red 9 by actvated carbon, J. Hazard. Mater [9] F.J. Rvas, F.J. Beltran, O. Gmeno, J. Frades, F. Carvalho, Adsorpton of landfll leachates onto actvated carbon equlbrum and knetcs, J. Hazard. Mater. B [92] S. Ayoob, A.K. Gupta, Insghts nto sotherm makng n the sorptve removal of fluorde from drnkng water, J. Hazard. Mater [93] I. Ghodbane, L. Nour, O. Hamdaou, M. Chha, Knetc and equlbrum study for the sorpton of cadmumii ons from aqueous phase by eucalyptus bark, J. Hazard. Mater [94] R.P. Han, J.J. Zhang, P. Han, Y.F. Wang, Z.H. Zhao, M.S. Tang, Study of equlbrum, knetc and thermodynamc parameters about methylene blue adsorpton onto natural zeolte, Chem. Eng. J [95] V.S. Mane, I.D. Mall, V.C. Srvastava, Use of bagasse fly ash as an adsorbent for the removal of brllant green dye from aqueous soluton, Dyes Pgments [96] A. Jumasah, T.G. Chuah, J. Gmbon, T.S.Y. Choong, I. Azn, Adsorpton of basc dye onto palm kernel shell actvated carbon: sorpton equlbrum and knetcs studes, Desalnaton [97] Y.S. Ho, W.T. Chu, C.C. Wang, Regresson analyss for the sorpton sotherms of basc dyes on sugarcane dust, Boresour. Technol [98] D. Mohan, K.P. Sngh, G. Sngh, K. Kumar, Removal of dyes from wastewater usng fly ash, a low-cost adsorbent, Ind. Eng. Chem. Res [99] K.V. Kumar, S. Svanesan, Predcton of optmum sorpton sotherm: comparson of lnear and non-lnear method, J. Hazard. Mater. B [00] S.C. Tsa, K.W. Juang, Comparson of lnear and nonlnear forms of sotherm models for strontum sorpton on a sodum bentonte, J. Radoanal. Nucl. Chem [0] Y.L. La, G. Annadura, F.C. Huang, J.F. Lee, Bosorpton of ZnII on the dfferent Ca-algnate beads from aqueous soluton, Boresour. Technol [02] A.E. Ofomaja, Y.S. Ho, Effect of temperatures and ph on methyl volet bosorpton by Mansona wood sawdust, Boresour. Technol [03] R.D. Harter, Curve-ft errors n Langmur adsorpton maxma, Sol Sc. Soc. Am. J [04] P. Persoff, J.F. Thomas, Estmatng Mchaels Menten or Langmur sotherm constants by weghted nonlnear least squares, Sol Sc. Soc. Am. J

Topical Workshop for PhD students Adsorption and Diffusion in MOFs Institut für Nichtklassische Chemie, Germany, www.uni-leipzig.

Topical Workshop for PhD students Adsorption and Diffusion in MOFs Institut für Nichtklassische Chemie, Germany, www.uni-leipzig. Gas Separaton and Purfcaton Measurement of Breakthrough Curves Topcal Workshop for PhD students Adsorpton and Dffuson n MOFs Adsorpton on Surfaces / Separaton effects Useful features Thermodynamc effect

More information

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis The Development of Web Log Mnng Based on Improve-K-Means Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.

More information

An Alternative Way to Measure Private Equity Performance

An 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 information

Causal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting

Causal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting Causal, Explanatory Forecastng Assumes cause-and-effect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of

More information

An Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services

An Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces Charles V. Trappey a,1, Hsn-yng Wu b a Professor (Management Scence), Natonal Chao

More information

Can Auto Liability Insurance Purchases Signal Risk Attitude?

Can 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 information

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).

benefit 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 information

Damage detection in composite laminates using coin-tap method

Damage 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 information

Feature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College

Feature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College Feature selecton for ntruson detecton Slobodan Petrovć NISlab, Gjøvk Unversty College Contents The feature selecton problem Intruson detecton Traffc features relevant for IDS The CFS measure The mrmr measure

More information

An Interest-Oriented Network Evolution Mechanism for Online Communities

An 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 information

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by

8.5 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 information

Viscosity of Solutions of Macromolecules

Viscosity of Solutions of Macromolecules Vscosty of Solutons of Macromolecules When a lqud flows, whether through a tube or as the result of pourng from a vessel, layers of lqud slde over each other. The force f requred s drectly proportonal

More information

Calculating the high frequency transmission line parameters of power cables

Calculating the high frequency transmission line parameters of power cables < ' Calculatng the hgh frequency transmsson lne parameters of power cables Authors: Dr. John Dcknson, Laboratory Servces Manager, N 0 RW E B Communcatons Mr. Peter J. Ncholson, Project Assgnment Manager,

More information

Gibbs Free Energy and Chemical Equilibrium (or how to predict chemical reactions without doing experiments)

Gibbs Free Energy and Chemical Equilibrium (or how to predict chemical reactions without doing experiments) Gbbs Free Energy and Chemcal Equlbrum (or how to predct chemcal reactons wthout dong experments) OCN 623 Chemcal Oceanography Readng: Frst half of Chapter 3, Snoeynk and Jenkns (1980) Introducton We want

More information

Inequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.

Inequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001. Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.

More information

IMPACT ANALYSIS OF A CELLULAR PHONE

IMPACT 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 information

MAPP. MERIS level 3 cloud and water vapour products. Issue: 1. Revision: 0. Date: 9.12.1998. Function Name Organisation Signature Date

MAPP. MERIS level 3 cloud and water vapour products. Issue: 1. Revision: 0. Date: 9.12.1998. Function Name Organisation Signature Date 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 information

"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *

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 information

The issue of June, 1925 of Industrial and Engineering Chemistry published a famous paper entitled

The issue of June, 1925 of Industrial and Engineering Chemistry published a famous paper entitled Revsta Cêncas & Tecnologa Reflectons on the use of the Mccabe and Thele method GOMES, João Fernando Perera Chemcal Engneerng Department, IST - Insttuto Superor Técnco, Torre Sul, Av. Rovsco Pas, 1, 1049-001

More information

Forecasting the Demand of Emergency Supplies: Based on the CBR Theory and BP Neural Network

Forecasting the Demand of Emergency Supplies: Based on the CBR Theory and BP Neural Network 700 Proceedngs of the 8th Internatonal Conference on Innovaton & Management Forecastng the Demand of Emergency Supples: Based on the CBR Theory and BP Neural Network Fu Deqang, Lu Yun, L Changbng School

More information

Analysis of Premium Liabilities for Australian Lines of Business

Analysis of Premium Liabilities for Australian Lines of Business Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton

More information

ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING

ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 610-519-4390,

More information

The Analysis of Outliers in Statistical Data

The Analysis of Outliers in Statistical Data THALES Project No. xxxx The Analyss of Outlers n Statstcal Data Research Team Chrysses Caron, Assocate Professor (P.I.) Vaslk Karot, Doctoral canddate Polychrons Economou, Chrstna Perrakou, Postgraduate

More information

Calculation of Sampling Weights

Calculation 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 information

FLASH POINT DETERMINATION OF BINARY MIXTURES OF ALCOHOLS, KETONES AND WATER. P.J. Martínez, E. Rus and J.M. Compaña

FLASH POINT DETERMINATION OF BINARY MIXTURES OF ALCOHOLS, KETONES AND WATER. P.J. Martínez, E. Rus and J.M. Compaña FLASH POINT DETERMINATION OF BINARY MIXTURES OF ALCOHOLS, KETONES AND WATER Abstract P.J. Martínez, E. Rus and J.M. Compaña Departamento de Ingenería Químca. Facultad de Cencas. Unversdad de Málaga. 29071

More information

The Application of Fractional Brownian Motion in Option Pricing

The 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 information

What is Candidate Sampling

What 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 information

Abstract. 260 Business Intelligence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING

Abstract. 260 Business Intelligence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING 260 Busness Intellgence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING Murphy Choy Mchelle L.F. Cheong School of Informaton Systems, Sngapore

More information

Modern Problem Solving Techniques in Engineering with POLYMATH, Excel and MATLAB. Introduction

Modern Problem Solving Techniques in Engineering with POLYMATH, Excel and MATLAB. Introduction Modern Problem Solvng Tehnques n Engneerng wth POLYMATH, Exel and MATLAB. Introduton Engneers are fundamentally problem solvers, seekng to aheve some objetve or desgn among tehnal, soal eonom, regulatory

More information

The Analysis of Covariance. ERSH 8310 Keppel and Wickens Chapter 15

The Analysis of Covariance. ERSH 8310 Keppel and Wickens Chapter 15 The Analyss of Covarance ERSH 830 Keppel and Wckens Chapter 5 Today s Class Intal Consderatons Covarance and Lnear Regresson The Lnear Regresson Equaton TheAnalyss of Covarance Assumptons Underlyng the

More information

The Effect of Mean Stress on Damage Predictions for Spectral Loading of Fiberglass Composite Coupons 1

The Effect of Mean Stress on Damage Predictions for Spectral Loading of Fiberglass Composite Coupons 1 EWEA, Specal Topc Conference 24: The Scence of Makng Torque from the Wnd, Delft, Aprl 9-2, 24, pp. 546-555. The Effect of Mean Stress on Damage Predctons for Spectral Loadng of Fberglass Composte Coupons

More information

Risk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008

Risk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008 Rsk-based Fatgue Estmate of Deep Water Rsers -- Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn

More information

The OC Curve of Attribute Acceptance Plans

The OC Curve of Attribute Acceptance Plans The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4

More information

THE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek

THE 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 information

A Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy S-curve Regression

A Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy S-curve Regression Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy S-curve Regresson Cheng-Wu Chen, Morrs H. L. Wang and Tng-Ya Hseh Department of Cvl Engneerng, Natonal Central Unversty,

More information

Numerical Analysis of the Natural Gas Combustion Products

Numerical Analysis of the Natural Gas Combustion Products Energy and Power Engneerng, 2012, 4, 353-357 http://dxdoorg/104236/epe201245046 Publshed Onlne September 2012 (http://wwwscrporg/journal/epe) Numercal Analyss of the Natural Gas Combuston Products Fernando

More information

CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES

CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable

More information

A hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm

A 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 information

CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol

CHOLESTEROL 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 information

Credit Limit Optimization (CLO) for Credit Cards

Credit Limit Optimization (CLO) for Credit Cards Credt Lmt Optmzaton (CLO) for Credt Cards Vay S. Desa CSCC IX, Ednburgh September 8, 2005 Copyrght 2003, SAS Insttute Inc. All rghts reserved. SAS Propretary Agenda Background Tradtonal approaches to credt

More information

Risk Model of Long-Term Production Scheduling in Open Pit Gold Mining

Risk Model of Long-Term Production Scheduling in Open Pit Gold Mining Rsk Model of Long-Term Producton Schedulng n Open Pt Gold Mnng R Halatchev 1 and P Lever 2 ABSTRACT Open pt gold mnng s an mportant sector of the Australan mnng ndustry. It uses large amounts of nvestments,

More information

NEURO-FUZZY INFERENCE SYSTEM FOR E-COMMERCE WEBSITE EVALUATION

NEURO-FUZZY INFERENCE SYSTEM FOR E-COMMERCE WEBSITE EVALUATION NEURO-FUZZY INFERENE SYSTEM FOR E-OMMERE WEBSITE EVALUATION Huan Lu, School of Software, Harbn Unversty of Scence and Technology, Harbn, hna Faculty of Appled Mathematcs and omputer Scence, Belarusan State

More information

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic

Institute 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 information

The Current Employment Statistics (CES) survey,

The Current Employment Statistics (CES) survey, Busness Brths and Deaths Impact of busness brths and deaths n the payroll survey The CES probablty-based sample redesgn accounts for most busness brth employment through the mputaton of busness deaths,

More information

APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT

APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT Toshhko Oda (1), Kochro Iwaoka (2) (1), (2) Infrastructure Systems Busness Unt, Panasonc System Networks Co., Ltd. Saedo-cho

More information

Time Series Analysis in Studies of AGN Variability. Bradley M. Peterson The Ohio State University

Time Series Analysis in Studies of AGN Variability. Bradley M. Peterson The Ohio State University Tme Seres Analyss n Studes of AGN Varablty Bradley M. Peterson The Oho State Unversty 1 Lnear Correlaton Degree to whch two parameters are lnearly correlated can be expressed n terms of the lnear correlaton

More information

Project Networks With Mixed-Time Constraints

Project Networks With Mixed-Time Constraints Project Networs Wth Mxed-Tme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa

More information

SPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:

SPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background: SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and

More information

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP) 6.3 / -- Communcaton Networks II (Görg) SS20 -- www.comnets.un-bremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes

More information

CHAPTER 14 MORE ABOUT REGRESSION

CHAPTER 14 MORE ABOUT REGRESSION CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp

More information

SIMPLE LINEAR CORRELATION

SIMPLE LINEAR CORRELATION SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.

More information

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 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 information

1. Measuring association using correlation and regression

1. 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

Traffic-light a stress test for life insurance provisions

Traffic-light a stress test for life insurance provisions MEMORANDUM Date 006-09-7 Authors Bengt von Bahr, Göran Ronge Traffc-lght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE-113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax

More information

Research on Evaluation of Customer Experience of B2C Ecommerce Logistics Enterprises

Research on Evaluation of Customer Experience of B2C Ecommerce Logistics Enterprises 3rd Internatonal Conference on Educaton, Management, Arts, Economcs and Socal Scence (ICEMAESS 2015) Research on Evaluaton of Customer Experence of B2C Ecommerce Logstcs Enterprses Yle Pe1, a, Wanxn Xue1,

More information

FREQUENCY OF OCCURRENCE OF CERTAIN CHEMICAL CLASSES OF GSR FROM VARIOUS AMMUNITION TYPES

FREQUENCY OF OCCURRENCE OF CERTAIN CHEMICAL CLASSES OF GSR FROM VARIOUS AMMUNITION TYPES FREQUENCY OF OCCURRENCE OF CERTAIN CHEMICAL CLASSES OF GSR FROM VARIOUS AMMUNITION TYPES Zuzanna BRO EK-MUCHA, Grzegorz ZADORA, 2 Insttute of Forensc Research, Cracow, Poland 2 Faculty of Chemstry, Jagellonan

More information

An Empirical Study of Search Engine Advertising Effectiveness

An Empirical Study of Search Engine Advertising Effectiveness An Emprcal Study of Search Engne Advertsng Effectveness Sanjog Msra, Smon School of Busness Unversty of Rochester Edeal Pnker, Smon School of Busness Unversty of Rochester Alan Rmm-Kaufman, Rmm-Kaufman

More information

DEFINING %COMPLETE IN MICROSOFT PROJECT

DEFINING %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 information

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12

PSYCHOLOGICAL 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 information

On the Optimal Control of a Cascade of Hydro-Electric Power Stations

On the Optimal Control of a Cascade of Hydro-Electric Power Stations On the Optmal Control of a Cascade of Hydro-Electrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;

More information

Moving Beyond Open Markets for Water Quality Trading: The Gains from Structured Bilateral Trades

Moving Beyond Open Markets for Water Quality Trading: The Gains from Structured Bilateral Trades Movng Beyond Open Markets for Water Qualty Tradng: The Gans from Structured Blateral Trades Tanl Zhao Yukako Sado Rchard N. Bosvert Gregory L. Poe Cornell Unversty EAERE Preconference on Water Economcs

More information

Study on Model of Risks Assessment of Standard Operation in Rural Power Network

Study on Model of Risks Assessment of Standard Operation in Rural Power Network Study on Model of Rsks Assessment of Standard Operaton n Rural Power Network Qngj L 1, Tao Yang 2 1 Qngj L, College of Informaton and Electrcal Engneerng, Shenyang Agrculture Unversty, Shenyang 110866,

More information

BERNSTEIN POLYNOMIALS

BERNSTEIN 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 information

Characterization of Assembly. Variation Analysis Methods. A Thesis. Presented to the. Department of Mechanical Engineering. Brigham Young University

Characterization of Assembly. Variation Analysis Methods. A Thesis. Presented to the. Department of Mechanical Engineering. Brigham Young University Characterzaton of Assembly Varaton Analyss Methods A Thess Presented to the Department of Mechancal Engneerng Brgham Young Unversty In Partal Fulfllment of the Requrements for the Degree Master of Scence

More information

A Secure Password-Authenticated Key Agreement Using Smart Cards

A 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 information

Published: 2003-01-01. Link to publication

Published: 2003-01-01. Link to publication A Thermodesorber for Onlne studes of Combuston Aerosols - Influence of partcle dameter, resdence tme and mass concentraton Dahl, Andreas; Pagels, Joakm Publshed: 2003-01-01 Lnk to publcaton Ctaton for

More information

Optimization of High-Pressure Vapor-Liquid Equilibrium Modelling of Binary Mixtures (Supercritical Fluid + Ionic Liquid) by Particle Swarm Algorithm

Optimization of High-Pressure Vapor-Liquid Equilibrium Modelling of Binary Mixtures (Supercritical Fluid + Ionic Liquid) by Particle Swarm Algorithm MATCH Communcatons n Mathematcal and n Computer Chemstry MATCH Commun. Math. Comput. Chem. 73 (215) 663-688 ISSN 34-6253 Optmzaton of Hgh-Pressure Vapor-Lqud Equlbrum Modellng of Bnary Mxtures (Supercrtcal

More information

L10: Linear discriminants analysis

L10: Linear discriminants analysis L0: Lnear dscrmnants analyss Lnear dscrmnant analyss, two classes Lnear dscrmnant analyss, C classes LDA vs. PCA Lmtatons of LDA Varants of LDA Other dmensonalty reducton methods CSCE 666 Pattern Analyss

More information

NPAR TESTS. One-Sample Chi-Square Test. Cell Specification. Observed Frequencies 1O i 6. Expected Frequencies 1EXP i 6

NPAR TESTS. One-Sample Chi-Square Test. Cell Specification. Observed Frequencies 1O i 6. Expected Frequencies 1EXP i 6 PAR TESTS If a WEIGHT varable s specfed, t s used to replcate a case as many tmes as ndcated by the weght value rounded to the nearest nteger. If the workspace requrements are exceeded and samplng has

More information

Binomial Link Functions. Lori Murray, Phil Munz

Binomial Link Functions. Lori Murray, Phil Munz Bnomal Lnk Functons Lor Murray, Phl Munz Bnomal Lnk Functons Logt Lnk functon: ( p) p ln 1 p Probt Lnk functon: ( p) 1 ( p) Complentary Log Log functon: ( p) ln( ln(1 p)) Motvatng Example A researcher

More information

Multiple-Period Attribution: Residuals and Compounding

Multiple-Period Attribution: Residuals and Compounding Multple-Perod Attrbuton: Resduals and Compoundng Our revewer gave these authors full marks for dealng wth an ssue that performance measurers and vendors often regard as propretary nformaton. In 1994, Dens

More information

Statistical Methods to Develop Rating Models

Statistical Methods to Develop Rating Models Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, and

More information

Number of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000

Number of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000 Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from

More information

Fuzzy Regression and the Term Structure of Interest Rates Revisited

Fuzzy Regression and the Term Structure of Interest Rates Revisited Fuzzy Regresson and the Term Structure of Interest Rates Revsted Arnold F. Shapro Penn State Unversty Smeal College of Busness, Unversty Park, PA 68, USA Phone: -84-865-396, Fax: -84-865-684, E-mal: afs@psu.edu

More information

Statistical algorithms in Review Manager 5

Statistical algorithms in Review Manager 5 Statstcal algorthms n Reve Manager 5 Jonathan J Deeks and Julan PT Hggns on behalf of the Statstcal Methods Group of The Cochrane Collaboraton August 00 Data structure Consder a meta-analyss of k studes

More information

ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C White Emerson Process Management

ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C White Emerson Process Management ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C Whte Emerson Process Management Abstract Energy prces have exhbted sgnfcant volatlty n recent years. For example, natural gas prces

More information

Passive Filters. References: Barbow (pp 265-275), Hayes & Horowitz (pp 32-60), Rizzoni (Chap. 6)

Passive Filters. References: Barbow (pp 265-275), Hayes & Horowitz (pp 32-60), Rizzoni (Chap. 6) Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called

More information

) of the Cell class is created containing information about events associated with the cell. Events are added to the Cell instance

) of the Cell class is created containing information about events associated with the cell. Events are added to the Cell instance Calbraton Method Instances of the Cell class (one nstance for each FMS cell) contan ADC raw data and methods assocated wth each partcular FMS cell. The calbraton method ncludes event selecton (Class Cell

More information

Calibration and Linear Regression Analysis: A Self-Guided Tutorial

Calibration and Linear Regression Analysis: A Self-Guided Tutorial Calbraton and Lnear Regresson Analyss: A Self-Guded Tutoral Part The Calbraton Curve, Correlaton Coeffcent and Confdence Lmts CHM314 Instrumental Analyss Department of Chemstry, Unversty of Toronto Dr.

More information

Product-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks

Product-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks Bulletn of Mathematcal Bology (21 DOI 1.17/s11538-1-9517-4 ORIGINAL ARTICLE Product-Form Statonary Dstrbutons for Defcency Zero Chemcal Reacton Networks Davd F. Anderson, Gheorghe Cracun, Thomas G. Kurtz

More information

Portfolio Loss Distribution

Portfolio 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 information

Fault tolerance in cloud technologies presented as a service

Fault tolerance in cloud technologies presented as a service Internatonal Scentfc Conference Computer Scence 2015 Pavel Dzhunev, PhD student Fault tolerance n cloud technologes presented as a servce INTRODUCTION Improvements n technques for vrtualzaton and performance

More information

The covariance is the two variable analog to the variance. The formula for the covariance between two variables is

The covariance is the two variable analog to the variance. The formula for the covariance between two variables is Regresson Lectures So far we have talked only about statstcs that descrbe one varable. What we are gong to be dscussng for much of the remander of the course s relatonshps between two or more varables.

More information

THE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES

THE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered

More information

Waste to Energy System in Shanghai City

Waste to Energy System in Shanghai City Waste to Energy System n Shangha Cty Group of Envronmental Systems, Department of Envronmental Studes M2 46876 Ya-Y Zhang 1. Introducton In the past ffteen years, the economcs of Chna has mantaned contnuously

More information

Performance Analysis of Energy Consumption of Smartphone Running Mobile Hotspot Application

Performance Analysis of Energy Consumption of Smartphone Running Mobile Hotspot Application Internatonal Journal of mart Grd and lean Energy Performance Analyss of Energy onsumpton of martphone Runnng Moble Hotspot Applcaton Yun on hung a chool of Electronc Engneerng, oongsl Unversty, 511 angdo-dong,

More information

Extending Probabilistic Dynamic Epistemic Logic

Extending 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 information

+ + + - - This circuit than can be reduced to a planar circuit

+ + + - - 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 information

INVESTIGATION OF VEHICULAR USERS FAIRNESS IN CDMA-HDR NETWORKS

INVESTIGATION OF VEHICULAR USERS FAIRNESS IN CDMA-HDR NETWORKS 21 22 September 2007, BULGARIA 119 Proceedngs of the Internatonal Conference on Informaton Technologes (InfoTech-2007) 21 st 22 nd September 2007, Bulgara vol. 2 INVESTIGATION OF VEHICULAR USERS FAIRNESS

More information

Exhaustive Regression. An Exploration of Regression-Based Data Mining Techniques Using Super Computation

Exhaustive Regression. An Exploration of Regression-Based Data Mining Techniques Using Super Computation Exhaustve Regresson An Exploraton of Regresson-Based Data Mnng Technques Usng Super Computaton Antony Daves, Ph.D. Assocate Professor of Economcs Duquesne Unversty Pttsburgh, PA 58 Research Fellow The

More information

Answer: 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

Answer: 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 information

A DATA MINING APPLICATION IN A STUDENT DATABASE

A DATA MINING APPLICATION IN A STUDENT DATABASE JOURNAL OF AERONAUTICS AND SPACE TECHNOLOGIES JULY 005 VOLUME NUMBER (53-57) A DATA MINING APPLICATION IN A STUDENT DATABASE Şenol Zafer ERDOĞAN Maltepe Ünversty Faculty of Engneerng Büyükbakkalköy-Istanbul

More information

Intra-year Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error

Intra-year Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error Intra-year Cash Flow Patterns: A Smple Soluton for an Unnecessary Apprasal Error By C. Donald Wggns (Professor of Accountng and Fnance, the Unversty of North Florda), B. Perry Woodsde (Assocate Professor

More information

A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION. Michael E. Kuhl Radhamés A. Tolentino-Peña

A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION. Michael E. Kuhl Radhamés A. Tolentino-Peña Proceedngs of the 2008 Wnter Smulaton Conference S. J. Mason, R. R. Hll, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds. A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION

More information

Mathematical modeling of water quality in river systems. Case study: Jajrood river in Tehran - Iran

Mathematical modeling of water quality in river systems. Case study: Jajrood river in Tehran - Iran European Water 7/8: 3-, 009. 009 E.W. Publcatons Mathematcal modelng of water qualty n rver systems. Case study: Jajrood rver n Tehran - Iran S.A. Mrbagher, M. Abaspour and K.H. Zaman 3 Department of Cvl

More information

Descriptive Models. Cluster Analysis. Example. General Applications of Clustering. Examples of Clustering Applications

Descriptive Models. Cluster Analysis. Example. General Applications of Clustering. Examples of Clustering Applications CMSC828G Prncples of Data Mnng Lecture #9 Today s Readng: HMS, chapter 9 Today s Lecture: Descrptve Modelng Clusterng Algorthms Descrptve Models model presents the man features of the data, a global summary

More information

substances (among other variables as well). ( ) Thus the change in volume of a mixture can be written as

substances (among other variables as well). ( ) Thus the change in volume of a mixture can be written as Mxtures and Solutons Partal Molar Quanttes Partal molar volume he total volume of a mxture of substances s a functon of the amounts of both V V n,n substances (among other varables as well). hus the change

More information

Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid

Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid J. Non-Newtonan Flud Mech., 72 (1997) 31 53 Effect of a spectrum of relaxaton tmes on the capllary thnnng of a flament of elastc lqud V.M. Entov a, E.J. Hnch b, * a Laboratory of Appled Contnuum Mechancs,

More information

Detecting Leaks from Waste Storage Ponds using Electrical Tomographic Methods

Detecting Leaks from Waste Storage Ponds using Electrical Tomographic Methods Detectng Leas from Waste Storage Ponds usng Electrcal Tomographc Methods Andrew Bnley #, Wllam Daly ## & Abelardo Ramrez ## # Lancaster Unversty, Lancaster, LA1 4YQ, UK ## Lawrence Lvermore Natonal Laboratory,

More information

Efficient Project Portfolio as a tool for Enterprise Risk Management

Efficient Project Portfolio as a tool for Enterprise Risk Management Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse

More information