A System ContextAware Approach for Battery Lifetime Prediction in Smart Phones


 Garey Stephens
 2 years ago
 Views:
Transcription
1 A System ContextAwre Approh for Bttery Lifetime Predition in Smrt Phones Xi Zho, Yo Guo, Qing Feng, nd Xingqun Chen Key Lbortory of High Confidene Softwre Tehnologies (Ministry of Edution) Shool of Eletronis Engineering nd Computer Siene, Peking University, Beijing, Chin ABSTRACT Energy is bottlenek in smrt phone systems, nd knowing the sttus of the bttery lifetime nd being ble to use it effiiently is n importnt requirement from users. We propose system ontextwre pproh for prediting bttery lifetime, whih llows user to know the urte bttery sttus nd to utilize the power effiiently. We refer to olletion of system omponent sttes s system ontext nd model the quntittive reltion between system ontext ttributes nd the bttery dishrge rte by multiple liner regressions. When the user hnges pplitions or opertions, we n dynmilly predit the remining bttery lifetime s well s its vritions by monitoring system ontext ttributes. We implement the CABLI system with our pproh s on n HTC G smrt phone running the Android operting system. Experiments show tht our model desribes how the hnges of system omponent sttes ffet the bttery lifetime, nd tht it improves the ury of online bttery lifetime predition. Ctegories nd Subjet Desriptors D.4. [Operting Systems]: Orgniztion nd Design Reltime systems nd embedded systems, Performne Modeling nd predition Generl Terms Mngement, Mesurement, Experimenttion, Humn Ftors Keywords Smrt Phone, bttery lifetime, energy onsumption, system ontextwre.. INTRODUCTION A smrt phone hs extended its funtionlities beyond the trditionl role of phone nd beome pervsive omputing devie. The lwyson bkground pplitions inrese the omplexity of the system environment s well s the power onsumption. For smrt phone users, bttery lifetime is one of the primry usbility onerns. Knowing the sttus of the bttery lifetime nd using it effiiently is n importnt requirement from users. Trditionl solutions tke the form of bttery inditor, informing users the remining bttery hrge level with four to seven brs. However, it is hrd for users to know how long the bttery lsts if they perform vriety of tsks, nd how their Permission to mke digitl or hrd opies of ll or prt of this work for personl or lssroom use is grnted without fee provided tht opies re not mde or distributed for profit or ommeril dvntge nd tht opies ber this notie nd the full ittion on the first pge. To opy otherwise, or republish, to post on servers or to redistribute to lists, requires prior speifi permission nd/or fee. SAC, Mrh 5,, TiChung, Tiwn. Copyright ACM //3 $.. hnges of opertions ffet the bttery lifetime. If the operting system n provide more urte nd quntittive informtion bout remining bttery energy nd lifetime, then the users n djust the opertions to extend the bttery life nd enjoy more qulity time. Prior reserhes tried to monitor the bttery energy level during the exeution of some trget pplitions nd then to predit the bttery lifetime bsed on the bttery dishrge mesurements of pst period #,[]. These pprohes work well when the trget pplition is the only running pplition in the system nd hs onstnt worklod. However, in multiproess OS environment with bkground onurrent pplitions, it is diffiult to identify whih pplition should ount for energy onsumption in ertin period. Furthermore, the ssumption tht the future energy onsumption ws the sme s the historil mesurement is in generl not vlid. In this pper, we propose system ontextwre pproh for bttery lifetime predition in smrt phone systems. We obtin the ritil system omponents tht ffet energy onsumption of smrt phone nd refer to olletion of their sttes s system ontext. We then build quntittive model for the system ontext nd the bttery dishrge rte by using multiple liner regressions. In ddition, we monitor the system ontext nd dynmilly predit the remining bttery lifetime nd its vrition. We implement this pproh on n HTC G smrt phone running the Android operting system. In our experiments, we nlyze the predition effiieny of the model nd ompre it with n existing pproh []. The results show tht our model desribes how the hnges of system omponent sttes ffet the bttery lifetime, nd it improves the ury of online bttery lifetime predition. We orgnize the rest of the pper s follows. Setion desribes the relted work. Setion 3 presents the proess of the pproh nd the system ontextwre bttery lifetime model. After presenting experimentl results in Setion 4, we onlude with Setion 5.. RELATED WORK There hs been lot of work on lptop bttery lifetime predition. Most of erly reserhers dopted eletrohemil fetures to predit bttery lifetime nd optimize the energy usge [, 3]. The bttery lifetime reserh of mobile phones reeived lot of ttention over the yers. Rhmti et l. studied humnbttery intertions nd improved the intertion between users nd bttery dishrge of smrt phones [4]. They pointed out tht users need higher resolution bttery inditors, whih enble them to hrge phones more onveniently. However, they did not disuss how to urtely predit bttery lifetime. In order to enhne user experienes of using smrt phones, some reserhers mesured nd nlyzed energy onsumption nd 64
2 bttery lifetime under different pplitions nd usge ptterns [5][6][7]. They did not onsider how the system omponents ffet the bttery lifetime nd how to use this informtion to predit the bttery lifetime. Rvi et l. proposed bttery mngement pproh for mobile phones [8]. They used bse urve nd the dishrge speedup ftor to predit the bttery life. However, their pproh n only be pplied to given set of pplitions observed in dvne. Our pproh is pplied to the entire smrt phone systems, not limited to some speil pplitions. Wen et l. proposed n online pproh for prediting bttery lifetime []. They ssumed tht the future energy onsumption is the sme s the historil mesurements. This pproh works on vrious pplitions, but it hs reltively lrge men errors for vrible worklods. In our method, the sttes of system omponents re more ruil for bttery lifetime predition. Our experiment results show tht our pproh performs with higher ury nd provides users better usge experienes thn their pproh. Shye et l. studied mobile rhitetures by logger pplition tht olleted rel user tivity nd the tres of power onsumption [9]. They dopted liner regression nlysis method nd system prmeters similr with ours. But they didn t onsider the reltionship between the bttery lifetime nd the system omponent sttes. We model the quntittive reltionship mong the bttery dishrge rte, bttery lifetime nd the system omponent sttes. One of our distinguished ontributions is tht we pplied the model to bttery lifetime predition, nd hieved muh more ury thn the existing pprohes. Their work onfirms our finding tht the system omponent sttes re the key nd strightforwrd inditors for bttery energy onsumption nd lifetime predition. 3. SYSTEM CONTEXTAWARE BATTERY LIFETIME PREDICTION Through extensive profiling, we found tht the hnges of system omponent sttes re driven by pplitions, nd tht the system omponent sttes re good inditors for worklods in the system. The bttery lifetime is ffeted by the summtion of energy onsumption of ll system omponents. Energy onsumption of omponent depends on its power stte (whih n be mpped to the opertion stte) nd the durtion it remins in tht stte. Therefore, we n use regression nlysis to quntify the reltion between system omponent sttes nd bttery energy onsumption. 3. System Context In mobile phone, the mjor energy onsumers re the CPU, LCD bklight, nd network interfe [9, ]. However, no existing work hs onduted the quntittive nlysis on the reltion between these omponent sttes nd bttery dishrge rte. We nlyze lrge mount of profiling dt quntittively, nd find out tht there re pproximtely liner reltion between the bttery dishrge rte nd some system omponent stte ttributes (Tble ). For some omponents, we use their resoure utiliztions to desribe their sttes beuse the resoure utiliztions more urtely express the worklod intensiveness nd n be mpped to energy onsumption of the omponents. For exmple, we use verge CPU utiliztion during time intervl to desribe CPU stte, nd use dt trnsfer rte to desribe the stte of the network interfe. We refer to set of system omponent sttes s system ontext nd tret eh stte s n ttribute of the system ontext. We denote system ontext nd its ttributes s tuple C brt,pu,wifi,io,spd. Tble shows the system ontext ttributes we use in our urrent predition model. The vlues of the ontext ttributes vry ording to differently running pplitions nd user s opertions. Tble. System Context Attributes Attribute Desription & Rnge Exmple CPU Utiliztion The rtio between the idle time to the (pu) totl time of intervl, []. LCD Bklight Brightness (brt) Rnge from [3,55] in HTC G 55 Wireless Stte (wifi) Disble or Enble [, ] IO Idle Rte (io) IO idle rte during time intervl.6 Dt Trnsfer rte(spd) Volumes of dt trnsferred (KB) It is well known tht intensive usge of omponents tends to redue bttery lifetime. However, in order to urtely predit the bttery lifetime, we need to present the quntittive reltion between the system ontext nd the bttery dishrge rte. 3. The Proess of Our Approh Our pproh for bttery lifetime predition onsists of two stges: modeling nd prediting. Figure shows the proess of this pproh. Figure. Proess of dynmi bttery lifetime predition During the modeling stge, we ustom speifi senrios tht hve stble system omponent sttes for whole bttery lifetime durtion. For exmple, we run video plyer pplition tht plys movie with the mximum LCD bklight brightness vlue 55. For the whole bttery lifetime, the verge CPU utiliztion, wifi, io, nd spd re ll pproximtely stble, s listed in the third volume in Tble. Then we profile the bttery energy level vs. time under this senrio during the whole bttery lifetime by using the API provided by the Jv frmework nd the operting system. Figure () shows the bttery dishrge urves nd bttery lifetime of the VideoPlyer pplition under this senrio. The bttery energy level is in terms of perentge. The slope of the fitted line of the urve is the dishrge rte, whih mens the bttery energy level deresement per minute. In this exmple, its bsolute vlue on verge is.574. If we hnge the brightness to nother vlue (for HTC G, this vlue rnges between 3 nd 55), suh s 3, while keeping other omponent sttes fixed, we n get nother dishrge rte.347 shown in Figure (b). 64
3 remining bttery lifetime. Furthermore, by lulting the differene of the urrent nd the lst predition, we n tell the vrition of predited bttery lifetime used by the hnges of the system omponent sttes. bttery energy level (%) 55brt liner y =.564x +.98 R² = Regressions of Dishrge Rte In order to predit the remining bttery lifetime, we first need to estimte the dishrge rte by using the system ontext ttributes. As shown in Figure, the dishrge rte is the energy onsumption rte of the system. We build quntittive model of system ontext nd dishrge rte by using multiple liner regression nlysis. time(min.) () bttery energy level (%) We tke system ontext ttributes s independent vribles nd bttery dishrge rte s dependent vribles. We use the multiliner regression model shown in eqution to desribe their reltionship. 8 3brt liner3 6 4 y =.347x +.99 R² =.9936 A X time(min.) where, (b) Figure. Bttery dishrge urve nd bttery lifetime of VideoPlyer pplition with the brightness of 55 nd 3. In this mnner, we ollet series of dishrge rtes under different system ontexts. The Tble shows smple list of system ontext ttributes nd the bttery dishrge rte. Tble. A smple list of system ontext ttributes nd bttery dishrge rte (brt, pu, wifi, io, spd) () Bttery Dishrge Rte 55,.,,.8,.56 9,.,,,.8,.47 8,.,,,.8,.4 3,.,,,.8,.35 55,,,,.6 55,.9,,,.58 55,.73,,,.55 55,.63,,,.5 55,.38,,,.5 55,.3,,,.48 55,.,,,.47 55,.,,,.46 55,.6,,, ,.4,,, ,.3,,,.66 55,.,,,.65 With the olleted dt, we ondut multiple liner regressions nd hieve quntittive model to desribe how the dishrge rte of the bttery hnges long with system omponent sttes. We sve the model s oeffiient sets. The modeling work is onetime work for smrt phone bttery, nd the results built from the dt n be used gin for long period before the bttery ges. In the prediting phse, we monitor the bttery energy level nd system omponent sttes under the urrent pplition senrio. Then, we use the model oeffiients nd the monitored ttributes to ompute the dishrge rte of the bttery. With the dishrge rte nd the urrent bttery energy level, we n predit the 643 x x xk x x xk A, X,,nd ε xn xn xnk n k n A is n ( n ) dependent vrible vetor representing the bsolute bttery dishrge rte, where n is the number of dishrge rtes. X is n (n k) mtrix of ttribute vlues, where k is the number of ttributes. is ( k ) vetor of regression oeffiients. is n ( n ) vetor of rndom errors, nd they ount for derivtions of the tul dt from the predited vlues. We usully think of s sttistil error nd ssume tht it is normlly distributed with men zero nd vrine, bbrevited s N,. In order to find out how the system ontext ttributes ffet the predition ury nd identify the most proper set of system ontext ttributes, we dpt model fmily of six equtions, whih inludes different ttributes seleted from (brt, pu, wifi, io, spd). Tble 3 lists the nmes of the equtions nd their desriptions. The dr eqution only onsiders the LCD brightness, nd other system ontexts re treted s onstnts. The dr eqution only onsiders CPU utiliztion. The dr3 eqution onsiders the LCD brightness nd CPU utiliztion. The subsequent equtions inorporte more nd more system ontext ttributes in the model. Tble 3. Different System Context Attributes Eqution k brt pu wifi io spd drbrt drpu dr The experiment results presented in the next setion illustrte tht different ombintions of system ontext ttributes result in different predition ury, nd there is trdeoff between the omplexity nd the predition ury of the model.
4 We put the bsolute vlues of bttery dishrge rte nd system ontext ttributes in the mtrix nd use the method of lest squres to ompute the oeffiients. With different ombintions of ontext ttributes, we get different equtions by the regression model. They re shown s set of equtions in formul. = brt = pu 3 = brt 5. pu 4 = brt 5. pu 8. wifi 5 = brt 8. pu. wifi 79. *io = brt 8. pu 5. 9wifi 79. *io.7*spd 6 The bove equtions desribe how the hnges of system ontext ttributes ffet the vritions of bttery dishrge rte nd the bttery lifetime. For exmple, suppose tht the urrent bttery energy level is 86. If user hnges the LCD bklight brightness vlue from 8 to 9 while keeping other ontexts fixed, then with the eqution we lulte tht the bsolute dishrge rte hnges from.43 to.49. In ddition, we n predit tht the bttery lifetime will shrink from minutes to 75 minutes. This gives the user quntittive informtion bout the hnge of the bttery lifetime nd the impts of his opertions on the bttery lifetime. 3.4 Dishrge RteBsed Bttery Lifetime Predition In this prt, we will present how to predit the bttery lifetime by using the estimted dishrge rte. Refer to the bttery dishrge urve in Figure, we use formul 3 to desribe the reltionship between the bttery energy level nd the remining time: v=f t where, v is the bttery energy level in terms of perentge, represents the ontext tuple, nd t is the time in minutes. We write the liner regression funtion of the bttery dishrge urve under the ontext tuple s in formul 4: v t where, nd ( ) re the interept nd slope of the trend line, respetively. In order to illustrte the predition model more lerly, we plot the line with vrible nmes in Figure 3. ( ) mesures the hnge in the men of v for unit hnge in t, whih is the dishrge rte of the bttery. Figure 3. A trend line of bttery dishrge urve Suppose t the time t, the bttery energy level is v ur, nd the trget bttery energy level is v tr t t. Then, we lulte the bttery lifetime from t to t by the formul 5. () (3) (4) 4. EXPERIMENTS AND EVALUATION We implement the CABLI system using our pproh in n HTC G smrt phone running the Android operting system (Linux kernel.6.7). The phone hs 58MHZ Qulomm MSM7A ARM proessor nd 56MB flsh memory. It is equipped with n 5mAh/3.7V lithiumion bttery, nd the pity of the bttery is 538mJ in terms of energy. We develop set of tools in the CABLI system. A system ontext monitor servie tool ollets the profiling dt in the running system. A modeling tool nlyzes the dt nd hieves the oeffiients of the model. A bttery lifetime inditor monitors the system ontexts nd predits the bttery lifetime online by using the prepred model oeffiients. In order to hieve good results for the regression model, we ollet lrge mount of dt from more thn 4 different test senrios. We selet 6 group smples to build the model nd use other dt to evlute the model. These smples re olleted under the senrios with stble system omponent sttes, whih re CPU utiliztion, LCD bklight brightness, WiFi stte, I/O idle rte, nd network dt trnsfer rte. We use the benhmrks listed in Tble 4 to test the predition ury. For exmple, VideoPlyer provided by HTC G produes pproximtely onstnt worklod; Simulte written by ourselves produes vrible CPU utiliztion whih we n ontrol. Furthermore, we rndomly run pplitions, suh s settings, ontts, notes, et., to produe vrible worklod, nd nme these senrios s MisOper. Benhmrk Worklod T(v,v ) t t ur tr Tble 4. Benhmrk Desriptions Desription VideoPlyer Constnt An video plyer Jv progrm Ping Vrible An operting system ntive utility, sends dt to the server by WiFi QuikSort Constnt A sorting Jv progrm with quik sort lgorithm Dijkstr Constnt A grph serh Jv progrm tht solves the singlesoure shortest pth BubbleSort Constnt A sorting Jv progrm with bubble sort lgorithm MisOper Vrible Misellneous nd pplitions, suh s settings, ontts, notes Simulte Constnt A CPUintensive Jv progrm with onstnt CPU utiliztion Simulte Vrible A CPUintensive Jv progrm with vrible CPU utiliztion In the following setions, we first show n nlysis on the energy onsumption distributions of the smrt phone. Then we evlute the fitness of the regression model. Lst, we present the omprison of our pproh with previous pproh on effiieny nd performne. 4. Energy onsumption distributions As desribed bove, the bttery dishrge rte expresses the bttery energy dissiption by the smrt phone in the unit time. Bsed on the regressive model of the bttery dishrge rte, we vur v tr (5) 644
5 .35 Tble 5. System omponent sttes.6 9. spd 4 io..8.8 No No No. No.3 dr3 drpu dr brt First, we ompre Wen s pproh [] (denoted s HBI) with ours (denoted s CABLI). We exeute the bove benhmrks nd monitor the bttery energy level vs. time. We predit the bttery lifetime with two different pprohes t every bttery energy level nd get the predition errors. Beuse of the limited spe, we tke VideoPlyer senrio nd ping wireless dt trnsfer senrio s exmples to illustrte the effiieny of the pprohes. From the results in Figure 6, we find tht the predition error of HBI is bout 35%~55%, while tht of CABLI is only bout % ~%. The reson is tht HBI ssumes tht the future bttery power dringe tends to be the sme with the history. In ontrst, CABLI thinks tht the system omponents re the mjor power onsumers nd predits the bttery power dringe bsed on the urrent vlues of their sttes. Therefore, it n reflet the vrition of the remining bttery lifetime more urtely BtteryLevel Contextbsed Historybsed 7 No.4 Ping with 3KB Dt Trnsferred VideoPlyer with Brightness No. Eqution A Comprison with Wen s Approh BtteryLevel Energy Distribution.3. Figure 5. Predition errors nd residuls of dishrge rte other io spd wifi pu brt Our model lso n be used to support the online dynmi power mngement. For exmple, during the system exeution, we monitor the system omponent sttes nd estimte energy onsumption distributions of system omponents, nd then we n djust the worklods or sttes of the system omponents online to mke trdeoff between the performne nd energy onsumption As shown in Figure 4, the energy onsumption distributions of the system omponents re diret proportionl to their sttes nd resoure utiliztions, whih is in onformity with our ommon sense. For exmple, the ontext No. hs the sme brt, wifi, io nd spd ttribute vlues with ontext No.3, but its pu utiliztion is.6, whih in less thn tht of No.3. Then, the CPU energy onsumption of No. is less thn tht of No.3 by bout 4%. This demonstrtes tht our model n be used to evlute how the omponent sttes ffet energy onsumption of the smrt phone system BtteryLevel wifi.5 9 BtteryLevel Contextbsed Historybsed System Context Time () 4 Time 6 8 (b) Figure 6. Predition errors of the pprohes. Figure 4. Energy onsumption distributions of the system omponents 4.4 Predition Errors of the Equtions We evlute the fitness of the predition model by using residuls nd predition errors of the bttery dishrge rte. The differene between the smpled vlue whih is used to build model nd the estimted vlue is lled residul. The predition error is the differene between the observed vlue nd the estimted vlue. The residuls nd predition errors of the dishrge rte re shown in Figure 5. From the results, we n find tht, the men residul of is less thn.%, nd the men predition error is less thn %. The drbrt model hs the worst bsolute residul of not more thn % nd the drpu hs the worst bsolute error of not more thn 3%. This mens tht the model with ontext ttributes inluding LCD 645 Vrible Worklod with Mis Opertions Simulte with Vrible CPU Utiliztion 6 4 Men Errors (%) 4. Model Evlution  HBI dr3 drpu drbrt () pu_3 pu_38 pu_63 pu_78 pu_ Men Errors (%) 55 pu.3 Men Errors Men Residuls Men Error (%) No. brt Men Errors Context Number No. Men Errors nd Residuls of Dishrge Rte.4 Men Error (%) We selet four exmples tht re listed in Tble 5, nd nlyze energy onsumption distributions of the system omponents under these system ontexts. bklight, CPU utiliztion, WiFi stte, I/O idle rte nd network dt trnsfer rte performs the best, nd tht the too few system ontext ttributes ffet the performne of the regression model. Men Residuls n understnd the ontribution of eh system omponent to the dishrge rte under given ertin system ontext. HBI dr3 drpudrbrt  pu_rm_ pu_rm_3 rndom rndom (d) 8 Figure 7. Men predition errors of different equtions In CABLI, different model equtions represent different omplexity levels of the model. We ompre the predition results
6 of bttery lifetime obtined by different equtions. In Figure 7, we tke Simulte nd MisOper s the exmples. The results show tht, the men error of is the smllest nd is within % ~ %, nd performs best mong the six equtions. 4.5 Predition Errors of Vritions of the Bttery Lifetime for Chnged Worklods When user hnges the worklod, whih pproh n urtely notify the user the vritions of the bttery lifetime used by the hnges? In order to nswer this question, we ompre the predition errors of vritions of the bttery lifetime given by the two pprohes. In Figure 8, we present the errors nd the perentge errors of the predited hnges under five senrios. The lbels 55>8, 55>3, 3>55 represent three senrios of the VideoPlyer pplition. Under these senrios, the user hnges bklight brightness from 55 to 8, 55 to 3, nd 3 to 55, respetively. The lbel Video>sort represents senrio, under whih, the user hnges VideoPlyer to Quiksort. The lbel pu.8>.5 represents senrio of the simulte progrm, under whih, the user hnges CPU utiliztion from.8 to.5. From the Figure 8, we n find tht the mximum perentge error of CABLI is less thn 6%, while tht of HBI is lose to 4%. CABLI predits the bttery lifetime hnges more urtely thn HBI, nd performs better thn HBI. Predition Errors nd Perentge Errors Errors Perentge Errors (%) CABLI_Err CABLI_Err% HBI_Err HBI_Err%  55>8 55>34 3>55 Video>Sort pu.8>.54 Figure 8. Predition Errors nd Perentge Errors under hnged worklods 5. CONCLUSION We propose system ontextwre pproh for online bttery lifetime predition. We uses multiple liner regressions to build quntittive bttery lifetime predition model for smrt phones. The model desribes how the hnges of system ontext ttributes ffet the vritions of energy onsumption nd bttery lifetime. Using this pproh, we dynmilly predit the remining bttery lifetime bsed on monitored system ontext ttributes. We implement our pproh in the HTC G smrt phone running the Android operting system. Experiments show tht our pproh predits bttery lifetime with higher ury thn prior works. The urte predition of remining bttery lifetime n provides smrt phone users with better usge experienes ACKNOWLEDGEMENT This work ws supported by the Ntionl High Tehnology Development Progrm of Chin (863) under Grnt No. 8AAZ33, the Ntionl Bsi Reserh Progrm of Chin (973) under Grnt No. 9CB373, the Siene Fund for Cretive Reserh Groups of Chin under Grnt No. 683, nd the Chin Postdotorl Siene Foundtion under Grnt No REFERENCES []Y. Wen, R. Wolski, C. Krintz, nd R. Krintz, "Online Predition of Bttery Lifetime for Embedded nd Mobile Devies," in Issue on Embedded Systems: SpringerVerlg Heidelberg Leture Notes in Computer Siene, 4, p. 4. []D. U. Suer nd H. Wenzl, "Comprison of different pprohes for lifetime predition of eletrohemil systemsusing ledid btteries s exmple," Journl of Power Soures, vol. 76, pp , 8. [3]L. Benini, G. Cstelli, A. Mii, E. Mii, M. Ponino, nd R. Srsi, "Disretetime bttery models for systemlevel lowpower design," IEEE Trns. Very Lrge Sle Integr. Syst., vol. 9, pp ,. [4]A. Rhmti, A. Qin nd L. Zhong, "Understnding humnbttery intertion on mobile phones," in MobileHCI '7: Proeedings of the 9th interntionl onferene on Humn omputer intertion with mobile devies nd servies, New York, NY, USA, 7, pp [5]A. Crroll nd G. Heiser, "An nlysis of power onsumption in smrtphone," in Proeedings of the USENIX Annul Tehnil Conferene, Boston, MA, USA,. [6]J. Kng, C. Prk, S. Seo, M. Choi, nd J. W. Hong, "UserCentri Predition for Bttery Lifetime of Mobile Devies," in APNOMS '8: Proeedings of the th AsiPifi Symposium on Network Opertions nd Mngement, Berlin, Heidelberg, 8, pp [7]N. Blsubrmnin, A. Blsubrmnin nd A. Venktrmni, "Energy onsumption in mobile phones: mesurement study nd implitions for network pplitions," in IMC '9: Proeedings of the 9th ACM SIGCOMM onferene on Internet mesurement onferene, New York, NY, USA, 9, pp [8]N. Rvi, J. Sott, L. Hn, nd L. Iftode, "Contextwre Bttery Mngement for Mobile Phones," in PERCOM '8: Proeedings of the 8 Sixth Annul IEEE Interntionl Conferene on Pervsive Computing nd Communitions, Wshington, DC, USA, 8, pp [9]A. Shye, B. Sholbrok nd G. Memik, "Into the wild: Studying rel user tivity ptterns to guide power optimiztion for mobile rhitetures," in Proeedings of the Interntionl Symposium on Mirorhiteture (MICRO 9), 9. []H. Flki, R. Mhjn, S. Kndul, D. Lymberopoulos, R. Govindn, nd D. Estrin, "Diversity in smrtphone usge," in MobiSys ': Proeedings of the 8th interntionl onferene on Mobile systems, pplitions, nd servies, New York, NY, USA,, pp
UNIVERSITY AND WORKSTUDY EMPLOYERS WEBSITE USER S GUIDE
UNIVERSITY AND WORKSTUDY EMPLOYERS WEBSITE USER S GUIDE Tble of Contents 1 Home Pge 1 2 Pge 2 3 Your Control Pnel 3 4 Add New Job (ThreeStep Form) 46 5 Mnging Job Postings (Mnge Job Pge) 78 6 Additionl
More informationActive Directory Service
In order to lern whih questions hve een nswered orretly: 1. Print these pges. 2. Answer the questions. 3. Send this ssessment with the nswers vi:. FAX to (212) 9673498. Or. Mil the nswers to the following
More informationSimple Electric Circuits
Simple Eletri Ciruits Gol: To uild nd oserve the opertion of simple eletri iruits nd to lern mesurement methods for eletri urrent nd voltge using mmeters nd voltmeters. L Preprtion Eletri hrges move through
More informationIt may be helpful to review some right triangle trigonometry. Given the right triangle: C = 90º
Ryn Lenet Pge 1 Chemistry 511 Experiment: The Hydrogen Emission Spetrum Introdution When we view white light through diffrtion grting, we n see ll of the omponents of the visible spetr. (ROYGBIV) The diffrtion
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationOUTLINE SYSTEMONCHIP DESIGN. GETTING STARTED WITH VHDL August 31, 2015 GAJSKI S YCHART (1983) TOPDOWN DESIGN (1)
August 31, 2015 GETTING STARTED WITH VHDL 2 Topdown design VHDL history Min elements of VHDL Entities nd rhitetures Signls nd proesses Dt types Configurtions Simultor sis The testenh onept OUTLINE 3 GAJSKI
More informationREMO: ResourceAware Application State Monitoring for LargeScale Distributed Systems
: ResoureAwre Applition Stte Monitoring for LrgeSle Distriuted Systems Shiong Meng Srinivs R. Kshyp Chitr Venktrmni Ling Liu College of Computing, Georgi Institute of Tehnology, Atlnt, GA 332, USA {smeng,
More informationPROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * challenge questions
PROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * hllenge questions e The ll will strike the ground 1.0 s fter it is struk. Then v x = 20 m s 1 nd v y = 0 + (9.8 m s 2 )(1.0 s) = 9.8 m s 1 The speed
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More informationThe following information must be known for the correct selection of current measurement transformer (measurement or protection):
P 5 Protetion trnsformers P.5.01 GB Protetion trnsformers The following informtion must e known for the orret seletion of urrent mesurement trnsformer (mesurement or protetion): The pplition for whih it
More informationEnterprise Digital Signage Create a New Sign
Enterprise Digitl Signge Crete New Sign Intended Audiene: Content dministrtors of Enterprise Digitl Signge inluding stff with remote ess to sign.pitt.edu nd the Content Mnger softwre pplition for their
More information1. Definition, Basic concepts, Types 2. Addition and Subtraction of Matrices 3. Scalar Multiplication 4. Assignment and answer key 5.
. Definition, Bsi onepts, Types. Addition nd Sutrtion of Mtries. Slr Multiplition. Assignment nd nswer key. Mtrix Multiplition. Assignment nd nswer key. Determinnt x x (digonl, minors, properties) summry
More informationThe AVL Tree Rotations Tutorial
The AVL Tree Rottions Tutoril By John Hrgrove Version 1.0.1, Updted Mr222007 Astrt I wrote this doument in n effort to over wht I onsider to e drk re of the AVL Tree onept. When presented with the tsk
More informationGAO POSTSECONDARY EDUCATION. Student Outcomes Vary at ForProfit, Nonprofit, and Public Schools. Report to Congressional Requesters
GAO United Sttes Government Aountbility Offie Report to Congressionl Requesters Deember 2011 POSTSECONDARY EDUCATION Outomes Vry t ForProfit, Nonprofit, nd Publi Shools GAO12143 Contents Letter 1 Limited
More informationRatio and Proportion
Rtio nd Proportion Rtio: The onept of rtio ours frequently nd in wide vriety of wys For exmple: A newspper reports tht the rtio of Repulins to Demorts on ertin Congressionl ommittee is 3 to The student/fulty
More informationTreatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the ttest is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the ttest cn be used to compre the mens of only
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationIntegration by Substitution
Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is
More informationWEB DELAY ANALYSIS AND REDUCTION BY USING LOAD BALANCING OF A DNSBASED WEB SERVER CLUSTER
Interntionl Journl of Computers nd Applictions, Vol. 9, No., 007 WEB DELAY ANALYSIS AND REDUCTION BY USING LOAD BALANCING OF A DNSBASED WEB SERVER CLUSTER Y.W. Bi nd Y.C. Wu Abstrct Bsed on our survey
More informationTHE LONGITUDINAL FIELD IN THE GTEM 1750 AND THE NATURE OF THE TERMINATION.
THE LONGITUDINAL FIELD IN THE GTEM 175 AND THE NATURE OF THE TERMINATION. Benjmin Guy Loder Ntionl Physil Lbortory, Queens Rod, Teddington, Middlesex, Englnd. TW11 LW Mrtin Alexnder Ntionl Physil Lbortory,
More informationPlotting and Graphing
Plotting nd Grphing Much of the dt nd informtion used by engineers is presented in the form of grphs. The vlues to be plotted cn come from theoreticl or empiricl (observed) reltionships, or from mesured
More informationSimulation of a large electric distribution system having intensive harmonics in the industrial zone of Konya
Turkish Journl of Eletril Engineering & omputer Sienes http:// journls. tuitk. gov. tr/ elektrik/ Reserh rtile Turk J Ele Eng & omp Si (2013) 21: 934 944 TÜİTK doi:10.3906/elk120155 Simultion of lrge
More informationD e c i m a l s DECIMALS.
D e i m l s DECIMALS www.mthletis.om.u Deimls DECIMALS A deiml numer is sed on ple vlue. 214.84 hs 2 hundreds, 1 ten, 4 units, 8 tenths nd 4 hundredths. Sometimes different 'levels' of ple vlue re needed
More information1 Numerical Solution to Quadratic Equations
cs42: introduction to numericl nlysis 09/4/0 Lecture 2: Introduction Prt II nd Solving Equtions Instructor: Professor Amos Ron Scribes: Yunpeng Li, Mrk Cowlishw Numericl Solution to Qudrtic Equtions Recll
More informationSParameters for Three and Four Two Port Networks
the ehnology Interfe/pring 2007 Mus, diku, nd Akujuoi Prmeters for hree nd Four wo Port Networks rhn M. Mus, Mtthew N.O. diku, nd Cjetn M. Akujuoi Center of Exellene for Communition ystems ehnology Reserh
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More information DAY 1  Website Design and Project Planning
Wesite Design nd Projet Plnning Ojetive This module provides n overview of the onepts of wesite design nd liner workflow for produing wesite. Prtiipnts will outline the sope of wesite projet, inluding
More informationOxCORT v4 Quick Guide Revision Class Reports
OxCORT v4 Quik Guie Revision Clss Reports This quik guie is suitble for the following roles: Tutor This quik guie reltes to the following menu options: Crete Revision Clss Reports pg 1 Crete Revision Clss
More informationTests for One Poisson Mean
Chpter 412 Tests for One Poisson Men Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson distribution
More informationOn the Meaning of Regression Coefficients for Categorical and Continuous Variables: Model I and Model II; Effect Coding and Dummy Coding
Dt_nlysisclm On the Mening of Regression for tegoricl nd ontinuous Vribles: I nd II; Effect oding nd Dummy oding R Grdner Deprtment of Psychology This describes the simple cse where there is one ctegoricl
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More informationFundamentals of Cellular Networks
Fundmentls of ellulr Networks Dvid Tipper Assoite Professor Grdute Progrm in Teleommunitions nd Networking University of Pittsburgh Slides 4 Telom 2720 ellulr onept Proposed by ell Lbs 97 Geogrphi Servie
More informationA dynamically SVC based compact control algorithm for load balancing in distribution systems
NTERNATONA JOURNA OF ENERG, ssue 3, ol., 7 A dynmilly S bsed ompt ontrol lgorithm for lod blning in distribution systems A. Kzemi, A. Mordi Koohi nd R. Rezeipour Abstrt An lgorithm for pplying fixed pitorthyristorontrolled
More informationpq Theory Power Components Calculations
ISIE 23  IEEE Interntionl Symposium on Industril Eletronis Rio de Jneiro, Brsil, 911 Junho de 23, ISBN: 78379128 pq Theory Power Components Clultions João L. Afonso, Memer, IEEE, M. J. Sepúlved Freits,
More informationFactoring Polynomials
Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles
More informationMath Review 1. , where α (alpha) is a constant between 0 and 1, is one specific functional form for the general production function.
Mth Review Vribles, Constnts nd Functions A vrible is mthemticl bbrevition for concept For emple in economics, the vrible Y usully represents the level of output of firm or the GDP of n economy, while
More informationNOTES AND CORRESPONDENCE. Uncertainties of Derived Dewpoint Temperature and Relative Humidity
MAY 4 NOTES AND CORRESPONDENCE 81 NOTES AND CORRESPONDENCE Uncertinties of Derived Dewpoint Temperture nd Reltive Humidity X. LIN AND K. G. HUBBARD High Plins Regionl Climte Center, School of Nturl Resource
More informationThe Pythagorean Theorem Tile Set
The Pythgoren Theorem Tile Set Guide & Ativities Creted y Drin Beigie Didx Edution 395 Min Street Rowley, MA 01969 www.didx.om DIDAX 201 #211503 1. Introdution The Pythgoren Theorem sttes tht in right
More informationPerformance analysis model for big data applications in cloud computing
Butist Villlpndo et l. Journl of Cloud Computing: Advnces, Systems nd Applictions 2014, 3:19 RESEARCH Performnce nlysis model for big dt pplictions in cloud computing Luis Edurdo Butist Villlpndo 1,2,
More informationDlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report
DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of
More informationInterpreting the Mean Comparisons Report
Interpreting the Men Comprisons Report Smple The Men Comprisons report is bsed on informtion from ll rndomly seleted students for both your institution nd your omprison institutions. 1 Trgeted oversmples
More informationexcenters and excircles
21 onurrene IIi 2 lesson 21 exenters nd exirles In the first lesson on onurrene, we sw tht the isetors of the interior ngles of tringle onur t the inenter. If you did the exerise in the lst lesson deling
More informationStudent Access to Virtual Desktops from personally owned Windows computers
Student Aess to Virtul Desktops from personlly owned Windows omputers Mdison College is plesed to nnoune the ility for students to ess nd use virtul desktops, vi Mdison College wireless, from personlly
More informationNet Change and Displacement
mth 11, pplictions motion: velocity nd net chnge 1 Net Chnge nd Displcement We hve seen tht the definite integrl f (x) dx mesures the net re under the curve y f (x) on the intervl [, b] Any prt of the
More information14.2. The Mean Value and the RootMeanSquare Value. Introduction. Prerequisites. Learning Outcomes
he Men Vlue nd the RootMenSqure Vlue 4. Introduction Currents nd voltges often vry with time nd engineers my wish to know the men vlue of such current or voltge over some prticulr time intervl. he men
More informationPLWAP Sequential Mining: Open Source Code
PL Sequentil Mining: Open Soure Code C.I. Ezeife Shool of Computer Siene University of Windsor Windsor, Ontrio N9B 3P4 ezeife@uwindsor. Yi Lu Deprtment of Computer Siene Wyne Stte University Detroit, Mihign
More informationMonopolistic competition Market in which firms can enter freely, each producing its own brand or version of a differentiated product
EON9 ring 0 & 6.5.0 Tutoril 0 hter onoolisti ometition nd Oligooly onoolisti ometition rket in whih firms n enter freely, eh roduing its own brnd or version of differentited rodut Key hrteristis: Firms
More informationPRIVATE HEALTH INSURANCE. Geographic Variation in Spending for Certain HighCost Procedures Driven by Inpatient Prices
United Sttes Government Aountility Offie Report to the Rnking Memer, Committee on Energy nd Commere, House of Representtives Deemer 2014 PRIVATE HEALTH INSURANCE Geogrphi Vrition in Spending for Certin
More informationSScrum: a Secure Methodology for Agile Development of Web Services
Worl of Computer Siene n Informtion Tehnology Journl (WCSIT) ISSN: 22210741 Vol. 3, No. 1, 1519, 2013 SSrum: Seure Methoology for Agile Development of We Servies Dvou Mougouei, Nor Fzli Moh Sni, Mohmm
More informationValue Function Approximation using Multiple Aggregation for Multiattribute Resource Management
Journl of Mchine Lerning Reserch 9 (2008) 20792 Submitted 8/08; Published 0/08 Vlue Function Approximtion using Multiple Aggregtion for Multittribute Resource Mngement Abrhm George Wrren B. Powell Deprtment
More informationEquivalence Checking. Sean Weaver
Equivlene Cheking Sen Wever Equivlene Cheking Given two Boolen funtions, prove whether or not two they re funtionlly equivlent This tlk fouses speifilly on the mehnis of heking the equivlene of pirs of
More information2. Use of Internet attacks in terrorist activities is termed as a. Internetattack b. National attack c. Cyberterrorism d.
Moule2.txt 1. Choose the right ourse of tion one you feel your mil ount is ompromise?. Delete the ount b. Logout n never open gin. Do nothing, sine no importnt messge is there. Chnge psswor immeitely n
More informationORGANIZER QUICK REFERENCE GUIDE
NOTES ON ORGANIZING AND SCHEDULING MEETINGS Individul GoToMeeting orgnizers my hold meetings for up to 15 ttendees. GoToMeeting Corporte orgnizers my hold meetings for up to 25 ttendees. GoToMeeting orgnizers
More informationLecture 3 Gaussian Probability Distribution
Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike
More informationISTM206: Lecture 3 Class Notes
IST06: Leture 3 Clss otes ikhil Bo nd John Frik 9905 Simple ethod. Outline Liner Progrmming so fr Stndrd Form Equlity Constrints Solutions, Etreme Points, nd Bses The Representtion Theorem Proof of the
More informationEuropean Convention on Products Liability in regard to Personal Injury and Death
Europen Trety Series  No. 91 Europen Convention on Produts Liility in regrd to Personl Injury nd Deth Strsourg, 27.I.1977 The memer Sttes of the Counil of Europe, signtory hereto, Considering tht the
More informationORGANIZER QUICK REFERENCE GUIDE
NOTES ON ORGANIZING AND SCHEDULING MEETINGS Individul GoToMeeting orgnizers my hold meetings for up to 15 ttendees. GoToMeeting Corporte orgnizers my hold meetings for up to 25 ttendees. GoToMeeting orgnizers
More informationCalculating Principal Strains using a Rectangular Strain Gage Rosette
Clulting Prinipl Strins using Retngulr Strin Gge Rosette Strin gge rosettes re used often in engineering prtie to determine strin sttes t speifi points on struture. Figure illustrtes three ommonly used
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More informationThe area of the larger square is: IF it s a right triangle, THEN + =
8.1 Pythgoren Theorem nd 2D Applitions The Pythgoren Theorem sttes tht IF tringle is right tringle, THEN the sum of the squres of the lengths of the legs equls the squre of the hypotenuse lengths. Tht
More informationHomework #6: Answers. a. If both goods are produced, what must be their prices?
Text questions, hpter 7, problems 12. Homework #6: Answers 1. Suppose there is only one technique tht cn be used in clothing production. To produce one unit of clothing requires four lborhours nd one
More informationAgricultural Economics Working Paper Series Hohenheimer Agrarökonomische Arbeitsberichte
Agriulturl Eonomis Working Pper Series Hohenheimer Agrrökonomishe Arbeitsberihte der Generl Arbeit Equilibrium STAGE_W: An Titel Applied zweizeilig Model With Multiple Types of Wter Autor 1 nd Jons Lukmnn
More informationHealth insurance exchanges What to expect in 2014
Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 02/13 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount
More informationThe LENA TM Language Environment Analysis System:
FOUNDATION The LENA TM Lnguge Environment Anlysis System: Audio Specifictions of the DLP0121 Michel Ford, Chrles T. Ber, Dongxin Xu, Umit Ypnel, Shrmi Gry LENA Foundtion, Boulder, CO LTR032 September
More informationChap.6 Surface Energy
Chp.6 urfe Energy (1) Bkground: Consider the toms in the bulk nd surfe regions of rystl: urfe: toms possess higher energy sine they re less tightly bound. Bulk: toms possess lower energy sine they re muh
More informationUsing Maximum Power Capability of Fuel Cell in Direct Methanol Fuel Cell / Battery Hybrid Power System
Modern Applied Siene August, 2009 Using Mximum Power Cpbility of Fuel Cell in Diret Methnol Fuel Cell / Bttery Hybrid Power System Mehdi Drghi (Corresponding uthor) Islmi Azd University  Jouybr Brnh Jouybr,
More informationHealth insurance marketplace What to expect in 2014
Helth insurnce mrketplce Wht to expect in 2014 33096VAEENBVA 06/13 The bsics of the mrketplce As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum
More informationInnovation in Software Development Process by Introducing Toyota Production System
Innovtion in Softwre Development Proess y Introduing Toyot Prodution System V Koihi Furugki V Tooru Tkgi V Akinori Skt V Disuke Okym (Mnusript reeived June 1, 2006) Fujitsu Softwre Tehnologies (formerly
More informationThank you for participating in Teach It First!
Thnk you for prtiipting in Teh It First! This Teh It First Kit ontins Common Core Coh, Mthemtis teher lesson followed y the orresponding student lesson. We re onfident tht using this lesson will help you
More informationScan Tool Software Applications Installation and Updates
Sn Tool Softwre Applitions Instlltion nd Updtes Use this doument to: Unlok softwre pplitions on Sn Tool Instll new softwre pplitions on Sn Tool Instll the NGIS Softwre Suite pplitions on Personl Computer
More informationENHANCING CUSTOMER EXPERIENCE THROUGH BUSINESS PROCESS IMPROVEMENT: AN APPLICATION OF THE ENHANCED CUSTOMER EXPERIENCE FRAMEWORK (ECEF)
ENHNCING CUSTOMER EXPERIENCE THROUGH BUSINESS PROCESS IMPROVEMENT: N PPLICTION OF THE ENHNCED CUSTOMER EXPERIENCE FRMEWORK (ECEF) G.J. Both 1, P.S. Kruger 2 & M. de Vries 3 Deprtment of Industril nd Systems
More informationSOLVING EQUATIONS BY FACTORING
316 (560) Chpter 5 Exponents nd Polynomils 5.9 SOLVING EQUATIONS BY FACTORING In this setion The Zero Ftor Property Applitions helpful hint Note tht the zero ftor property is our seond exmple of getting
More informationDistributions. (corresponding to the cumulative distribution function for the discrete case).
Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive
More informationDerivatives and Rates of Change
Section 2.1 Derivtives nd Rtes of Cnge 2010 Kiryl Tsiscnk Derivtives nd Rtes of Cnge Te Tngent Problem EXAMPLE: Grp te prbol y = x 2 nd te tngent line t te point P(1,1). Solution: We ve: DEFINITION: Te
More informationVMware Horizon FLEX Administration Guide
VMwre Horizon FLEX Administrtion Guide Horizon FLEX 1.0 This doument supports the version of eh produt listed nd supports ll susequent versions until the doument is repled y new edition. To hek for more
More informationLet us recall some facts you have learnt in previous grades under the topic Area.
6 Are By studying this lesson you will be ble to find the res of sectors of circles, solve problems relted to the res of compound plne figures contining sectors of circles. Ares of plne figures Let us
More information5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.
5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous relvlued
More informationIn this section make precise the idea of a matrix inverse and develop a method to find the inverse of a given square matrix when it exists.
Mth 52 Sec S060/S0602 Notes Mtrices IV 5 Inverse Mtrices 5 Introduction In our erlier work on mtrix multipliction, we sw the ide of the inverse of mtrix Tht is, for squre mtrix A, there my exist mtrix
More informationLearneroriented distance education supporting service system model and applied research
SHS Web of Conferences 24, 02001 (2016) DOI: 10.1051/ shsconf/20162402001 C Owned by the uthors, published by EDP Sciences, 2016 Lerneroriented distnce eduction supporting service system model nd pplied
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationORBITAL MANEUVERS USING LOWTHRUST
Proceedings of the 8th WSEAS Interntionl Conference on SIGNAL PROCESSING, ROBOICS nd AUOMAION ORBIAL MANEUVERS USING LOWHRUS VIVIAN MARINS GOMES, ANONIO F. B. A. PRADO, HÉLIO KOII KUGA Ntionl Institute
More informationSolutions to Section 1
Solutions to Section Exercise. Show tht nd. This follows from the fct tht mx{, } nd mx{, } Exercise. Show tht = { if 0 if < 0 Tht is, the bsolute vlue function is piecewise defined function. Grph this
More information7 mm Diameter Miniature Cermet Trimmer
7 mm Dimeter Miniture Cermet Trimmer A dust seled plsti se proteting qulity ermet trk gurntees high performne nd proven reliility. Adjustments re mde esier y the ler sle redings. is idelly suited to ll
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse rel number to its binry representtion,. convert binry number to n equivlent bse number. In everydy
More informationEnergy Saving Analysis of Variable Primary Flow System with Screw Chiller
Energy Sving Anlysis of Vrible Primry Flow System with Screw Chiller YungChung Chng [1], PinCheng Chieng [2], JyunTing Lu [3], TienShun Chn [4], ChingLing Chen [5], ChengWen Lee [6] [1] Professor,
More informationpersons withdrawing from addiction is given by summarizing over individuals with different ages and numbers of years of addiction remaining:
COST BENEFIT ANALYSIS OF NARCOTIC ADDICTION TREATMENT PROGRAMS with Specil Reference to Age Irving Leveson,l New York City Plnning Commission Introduction Efforts to del with consequences of poverty,
More informationInterdomain Routing
COMP 631: COMPUTER NETWORKS Interdomin Routing Jsleen Kur Fll 2014 1 Internetsle Routing: Approhes DV nd linkstte protools do not sle to glol Internet How to mke routing slle? Exploit the notion of
More informationOrthodontic marketing through social media networks: The patient and practitioner s perspective
Originl rtile Orthodonti mrketing through soil medi networks: The ptient nd prtitioner s perspetive Kristin L. Nelson ; Bhvn Shroff ; l M. Best ; Steven J. Linduer d BSTRCT Ojetive: To (1) ssess orthodonti
More informationSmall Business Cloud Services
Smll Business Cloud Services Summry. We re thick in the midst of historic sechnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly
More informationArc Length. P i 1 P i (1) L = lim. i=1
Arc Length Suppose tht curve C is defined by the eqution y = f(x), where f is continuous nd x b. We obtin polygonl pproximtion to C by dividing the intervl [, b] into n subintervls with endpoints x, x,...,x
More informationJ. Q. Mou, Fukun Lai, I. B. L. See, and W. Z. Lin Data Storage Institute, 5 Engineering Drive 1, Singapore 117608
Anlysis of Noteook Computer Cssis Design for rd Disk Drive nd Speker Mounting J. Q. Mou, Fukun Li, I. B. L. See, nd W. Z. Lin Dt Storge Institute, 5 Engineering Drive 1, Singpore 117608 Astrt  Cssis design
More informationHigh School Chemistry Content Background of Introductory College Chemistry Students and Its Association with College Chemistry Grades
Reserh: Siene nd Edution Chemil Edution Reserh edited y Dine M. Bune The Ctholi University of Ameri Wshington, D.C. 20064 High Shool Chemistry Content Bkground of Introdutory College Chemistry Students
More informationSmall Business Networking
Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer
More information*These academic programs have no specific Academic Program Rules and therefore are bound entirely by the General Academic Program Rules
Msters Degrees by Reserh (exluding Mster of Philosophy) These progrms re only vilble to Interntionl Students in 2012. Interntionl students seeking to enrol in Msters Degree in Eonomis or Publi Helth must
More informationProject 6 Aircraft static stability and control
Project 6 Aircrft sttic stbility nd control The min objective of the project No. 6 is to compute the chrcteristics of the ircrft sttic stbility nd control chrcteristics in the pitch nd roll chnnel. The
More informationFDIC Study of Bank Overdraft Programs
FDIC Study of Bnk Overdrft Progrms Federl Deposit Insurnce Corportion November 2008 Executive Summry In 2006, the Federl Deposit Insurnce Corportion (FDIC) initited twoprt study to gther empiricl dt on
More informationRight Triangle Trigonometry 8.7
304470_Bello_h08_se7_we 11/8/06 7:08 PM Pge R1 8.7 Right Tringle Trigonometry R1 8.7 Right Tringle Trigonometry T E G T I N G S T R T E D The origins of trigonometry, from the Greek trigonon (ngle) nd
More informationWords Symbols Diagram. abcde. a + b + c + d + e
Logi Gtes nd Properties We will e using logil opertions to uild mhines tht n do rithmeti lultions. It s useful to think of these opertions s si omponents tht n e hooked together into omplex networks. To
More informationAccording to Webster s, the
dt modeling Universl Dt Models nd P tterns By Len Silversn According Webster s, term universl cn be defined s generlly pplicble s well s pplying whole. There re some very common ptterns tht cn be generlly
More informationRight Triangle Trigonometry
CONDENSED LESSON 1.1 Right Tringle Trigonometr In this lesson ou will lern out the trigonometri rtios ssoited with right tringle use trigonometri rtios to find unknown side lengths in right tringle use
More information