A Network Management System for Power-Line Communications and its Verification by Simulation

Size: px
Start display at page:

Download "A Network Management System for Power-Line Communications and its Verification by Simulation"

Transcription

1 A Network Mngement System for Power-Line Communictions nd its Verifiction y Simultion Mrkus Seeck, Gerd Bumiller GmH Unterschluerscher-Huptstr. 10, D Großhersdorf, Germny Phone: , Fx: , Emil: Gerd.Bumiller@id-de.com Keywords: OFDM, TDMA, Repeters, Automtic Logon, Adptive Network Routing Astrct The network mngement system (NMS) developed y the compny GmH is used for the co-ordintion of communiction in networks where ll users shre the sme chnnel nd connection-oriented services re not required. Typicl pplictions of the NMS re remote metering, vlue-dded services for utility compnies, intelligent power mngement, security services nd home utomtion. The NMS is sed on mster-slve concept using repeters to increse the rnge of the network where every slve is possile repeter. Due to utomtic logon t ny time, the numer of slves in the network is dynmic nd hence, self-configurtion is provided. For dpttion to vrile chnnel conditions, dynmic routing is pplied. For purposes of evlution nd prmeteristion simultion model hs een developed which is sed on chnnel trnsfer mtrix nd two different models re pplied for this. Introduction For digitl dt trnsmissions over power-lines orthogonl frequency division multiplexing (OFDM) in comintion with FEC seems to e n pproprite modultion scheme, which provides optimum performnce if the whole chnnel ndwidth is llocted to only one communiction link, see e.g. [1]. Thus, if severl modems mking up network hve to communicte on the sme chnnel, only one cn trnsmit t the sme time, which requires time division multiple ccess (TDMA). Therefore, it is necessry to provide n intelligent network mngement which on the one hnd yields high communiction rte nd t the sme time tries to void collisions on the chnnel in order to mke n efficient use of chnnel cpcity. For purposes of verifiction of protocol nd testing different methods, trnsmission chnnel is required which cn e completely nlysed nd lso reproduced. In cse of field tests oth requirements cnnot e stisfied nd, moreover, lot of time nd effort is necessry, especilly if networks with lrge numer of slves re considered. Thus, it is hrdly possile to repet mesurements for different versions of protocol or different sets of prmeters. Therefore, simultion model ws designed. Furthermore, the NMS is lredy in use in our DLC-2 modem which ws introduced t ISPLC 99 in the pper Integrted PLC modem sed on OFDM [2]. The modem uses OFDM together with 64-stte convolutionl coder nd Viteri decoder on the physicl lyer. Due to differentil coding loding lgorithm is not required nd therefore it is especilly pproprite for point-to-multipoint trnsmissions. In the DLC-2 modem the lyers of the NMS s well s the ppliction lyer re implemented in micro controller unit (MCU) nd the physicl lyer is implemented in digitl signl processor (DSP). In the current version the protocol opertes with lock sizes of 48 to 168 ytes nd possile dt rtes up to 100kps.

2 Concept of the NMS The network mngement system is sed on mster-slve concept where ll modems shre the sme frequency nd nd thus TDMA scheme is pplied. The use of different frequency nds enles the coexistence of severl logicl networks on the sme physicl network. In order to expnd the physicl rnge of the network, two repeter levels re used nd every slve cn lso e repeter. There is no direct communiction etween two slves nd hence, the network structure represents virtul str topology, which is depicted in Figure 1. MASTER Power-Line Level 1 SLAVE 1 SLAVE 2 SLAVE 3 Level 2 SLAVE 4 SLAVE 5 SLAVE 6 Level 3 SLAVE 7 SLAVE 8 Figure 1: Virtul str topology of the NMS Slves re only llowed to trnsmit on demnd of the mster. As OFDM performs prllel trnsmission of its, decoding cn only strt fter the reception of complete lock. Therefore, responding is not possile within the next TDMA slot ut insted n interlef is specified fter which the slve is supposed to respond. Thus, system delys cused y run times of oth the physicl lyer nd the lyers of the network mngement re tken into ccount which is outlined in Figure 2. This figure shows n exmple of the mster s (M) communiction with slves (S) of levels 1-3 which mens tht 0, 1 or 2 repeters (R) re used, respectively. Telegrms lelled with their respective pth re depicted over the time xis which is normlised to the length of TDMA slot. As cn e seen, every slve responds its requests fter n interlef of 3 slots nd thus, the mster does not hve to wit for response of slve ut cn use the intermedite time for ddressing other slves so tht n effective use of chnnel cpcity is provided. processing NMS telegrm from mster repetition y repeter Demod Mod response from slve Figure 2: Exmple of scheduling of telegrms to slves of levels 1-3 t Dt trnsmission on the power-line tkes plce y mens of telegrms ech consisting of lock of OFDM signls. There re two types of telegrms: the user PDU (protocol dt unit) crrying dt for the ppliction lyer nd the service PDU contining informtion for network mngement purposes. Ech PDU is protected y

3 32-it CRC nd hence, the proility tht wrong PDU is considered to e correct is only By use of sequence counter of the respective modems, every modem cn detect multiple receptions of the sme PDU or missing PDU. In cse of point-to-point PDUs confirmtion nd retrnsmissions re supported. In cse of rodcsts, severl repetitions of the sme telegrm y the mster s well s y selected repeters shll provide high coverge of slves. The numer of slves in the network is dynmic nd logon s well s logoff of the slves is performed utomticlly y the mster modem. Every modem in the network cn e identified y its unique seril numer nd during logon it is dditionlly ssigned unique network ddress y the mster which is vlid for the period of its logon. If no ppliction requires dt trnsmissions, the mster constntly updtes its network sttistics (logged-on modems, routing tles) y cyclic poll of ll slves. In the response PDU to those sttus polls the slve provides the mster with informtion out its current sttus, possile ville dt nd sttisticl informtion for routing purposes. The sttus poll period, i.e. the numer of cycles for polling ll slves, depends on the numer of slves in the network nd is used s reference for the computtion of network sttistics. Automtic Routing The use of repeters requires the determintion of the est routing pths, which is done y the network mngement protocol in the mster modem. For this purpose, every slve keeps tle with its fvourite repeter slves nd in response to sttus polls forwrds the est five entries to the mster. Bsed on the sttus poll period nd the counting of sent nd received telegrms, every slve cn compute its own frequency of trnsmission - tht it includes in its service PDUs - s well s the frequency of reception y ny other slve. In order to prefer short routing pths, weighting fctors re pplied to the counting depending on the numer of repeters used. In ddition to those reltive numers, the solute numer of received telegrms is lso tken into ccount wherey slves re preferred tht lredy work s repeters. This leds to the forming of repeter nodes which is fvourle in cse of rodcsts where s mny slves s possile shll e reched y using the smllest numer of repeters possile. By use of these vlues the repeter qulity of slve is determined s the reception proility from tht slve. Furthermore, the mster keeps two response quots for every slve representing the success of the mster s lst ttempts to ddress this slve directly nd over one repeter, respectively. As the second vlue does not tke into ccount which repeters were used, it my temporrily devite from the current sitution. In contrst to the reception proilities, the response quots do not ssume symmetric communiction chnnels, nd hence re closer to relity. In cse of telegrms to single slve, the mster hs to compre nd test eleven different pths including the direct pth, 5 pths using one repeter ech nd nother 5 pths using two repeters. For this purpose, every pth is judged y n evlution figure, computed y mens of the respective response quot, the reception proility of possily pplied repeter nd n dditionl weighting fctor used to prefer short pths. In cse of two repeters R1 nd R2, the first repeter R1 is still unknown nd hs to e determined nlogously to finding the est repeter for single-repeter-pth to trget slve R2. The d Hondt lgorithm is then pplied for the sequentil determintion of the currently est pth which chnges with the sttistics, which re updted y the mster in every cycle. This lgorithm is stopped in cse of success or if the mximum numer of ttempts is exceeded. Depending on rndom numer, the direct pth is chosen sometimes in the first ttempt, even if it is not the est one, to provide the chnce tht chnges in network conditions cn e noticed t ll. In cse of rodcsts multiple repetitions of the sme telegrm y the mster s well s y certin repeter slves re supposed to provide good coverge of slves. In this context, the question rises which repeters shll e used in order to mke do with low numer of repetitions. Using the sttisticl informtion in its routing tle the mster is le to estimte the proility of every slve tht it hs not yet received the rodcst. This proility is updted fter every telegrm sent. Thus, the mster chooses the respective pth such tht the proility of the slve with the currently highest proility is minimised wherey the proilities of the other slves re lso decresed. A few telegrms re lso trnsmitted using the direct pth. This procedure is repeted until either the proilities of ll slves hve reched minimum vlue or mximum numer of repetitions is exceeded.

4 Auto Configurtion of the Network The numer of slves in the network s well s the network topology re dynmic, nd for this reson the network cnnot e configured from the eginning, ut insted, uto-configurtion is required. There re three sttes for slves which re depicted in Figure 3. When new slve modem is plugged to the physicl network, it is in stte frequency scn. In this stte it scns ll frequency nds nd tries to find n pproprite mster y listening to ll telegrms in the respective nd nd evluting them to get informtion out the respective network. Bsed on different criteri, like network qulity nd equl ssignment of slves to the different networks, it finlly mkes decision for certin frequency nd enters stte logon. In this stte it tries to log on to the network. If this is not possile within fixed timeout it returns to stte frequency scn. In cse of success it is ssigned unique network ddress y the mster which is vlid s long s the slve is logged in, nd proceeds to stte logged on. For purposes of uto logon the mster regulrly sends uto logon requests. These re sent s rodcst PDUs using selected repeters. In order to void collisions on the chnnel s fr s possile, the slves which wnt to log on ech respond fter rndom dely within fixed timeout. If the mster detects collisions on the chnnel, nywy, he cn reduce the numer of slves which re llowed to nswer the request y specifying few its in their seril numer nd thus reduce the proility of collisions. As the rndom delys cn only e multiples of the slot intervl the system cn e considered s slotted ALOHA system during periods of uto logon. frequency scn loginprocedure logintimeout found frequency logged- on logoutprocedure logon Figure 3: Stte digrm of slve modem Simultion For purposes of evlution nd prmeteristion of the NMS, simultion model hs een developed s shown in Figure 4. Every modem in the network is represented y dt genertor mking up the ppliction lyer, NMS nd two physicl lyer simultors for oth the trnsmitting nd the receiving prt. All prts of the simultion which my vry for the different modems, e.g. dt genertors nd physicl lyer reception simultors, re implemented such tht they cn e specified differently. The dt genertors representing the ppliction lyer hve to e dpted ccording to the suject of the current simultion. The NMS is designed for use in TDMA system where trnsmission is only llowed within fixed time slots. Therefore, the simultion does not need to replicte the physicl lyer ut cn e sed on the ssumption of slotted system with slot intervl which corresponds to the durtion of n OFDM symol. This is lso justified in cse of uto logon periods where the system cn e considered s slotted ALOHA system.

5 The network mngement protocol uses 32-it CRC for error detection nd throws wy erroneous telegrms. This is simulted y throwing wy telegrms rndomly with proility depending on the chnnel properties etween trnsmitter nd receiver. Since the proility tht n erroneous telegrm is considered to e correct is only this cse does not hve to e considered in simultion. In network of N modems, these chnnel properties, which re not necessrily reciprocl, re descried y chnnel trnsfer mtrix of formt N N. As system vlues were not ville, chnnel model hd to e designed which will e descried lter. control flow dt flow simultion time dt genertor properties simultion control chnnel trnsfer mtrix dt genertor evlution physicl lyer receiving simultor NMS physicl lyer trnsmission simultor NMS memory chnnel memory Figure 4: Simultion model (grey: glol elements; white: elements existing once for every user) The line of ctions during one system period cn e descried s follows. First, the simultion control sequentilly clls the dt genertors of ll modems. If nyone wnts to send, the NMS is ctivted to process the dt nd forwrd them to the physicl lyer trnsmission simultor. Afterwrds, the physicl lyer receiving simultors of ll modems re clled sequentilly. Due to this modulr structure of the simultion nd the use of the sme interfces s in system implementtion the NMS will not recognise ny difference etween working in simultion nd working in rel system. The physicl lyer receiving simultor is clled in every cycle for every modem. It checks if collision hs occurred on the chnnel. Besides, it determines if premle ws detected ccording to the respective proility, nd sed on the length of the PDU, the it error rte nd rndom process it decides whether the PDU ws received correctly or not. Chnnel Model For the simultion chnnel trnsfer mtrix is required nd for this purpose two different models re pplied. The first one is line model where ll slves re connected to the min t equl distnces using rnch lines of equl lengths, s depicted in Figure 5. This model cn e considered s specil cse of n rrngement s it my pper in relity in cse of row of terrced houses. As it is deterministic nd regulr the respective results cn esily e checked nd therefore it is pproprite for the verifiction of the protocol.

6 Slve 1 Slve 2 Slve 3 Slve 4 Slve 5 Slve 6 Slve 7 Slve N-1 + Mster Figure 5: deterministic line model The second one is stochstic plne model where ll slves re distriuted eqully within plne t limited distnce to the mster, s shown in Figure 6. The network consists of 4 mins originting from the mster on the specified xes nd slves re locted t the end of rnch lines which re orthogonl to the mins. This model is more relistic nd therefore pproprite for the optimistion of prmeters. Arrngements s they normlly pper in relity cn e expected to e less regulr thn in Figure 5 ut more structured thn in Figure 6 nd therefore comintion of oth models cn e ssumed. Hence, if the NMS works well for oth models it is supposed to work in rel systems, too. Im Slve 3 Slve 2 Slve 1 Slve 4 Slve 5 Mster Re Slve 8 Slve N-1 Slve 6 Slve 7 Slve 9 Figure 6: stochstic plne model The chnnel is descried y word error rte (WER) nd synchronistion error rte (SER) which mke up the prmeters of the chnnel trnsfer mtrix nd which re derived s follows. If we ssume equl trnsmit power S s well s equl power of ckground noise N for ll modems nd constnt ttenution incresing only with the distnce d, the SNR etween ny two modems S n nd S n is only function of distnce:

7 SNR S d Sn, S n' = 10 log = S N 100m N Sn, Sn' d Sn, Sn' 100m The SNR hs to e trnsformed to the E /N 0 vlue which is done y pplying correction fctor Cor which depends on the current trnsfer mode nd thus lso on ndwidth efficiency. This E /N 0 vlue is further used to determine the it error rte (BER). For this purpose, simultion results were used to derive functionl dependency etween BER nd E /N 0. Bsed on the formul for uncoded trnsmission this led to the use of the error function, such tht E BER N 0 = BER ( SNR + Cor ) = ( SNR Cor ) + erf 2β where the dditionl prmeters α nd β re used for pproximtion to existing results of physicl lyer simultions. If we ssume sttisticl independence of it errors, the WER for words of length N W cn e expressed s N ( ) W 1. WER = 1 BER This ssumption, of course, represents the worst cse, ecuse using Viteri decoder in the physicl lyer leds to urst errors nd thus to etter WER. Since pproprite simultion results re not ville for the determintion of the SER, model is pplied which is lso sed on the use of the error function. In comprison to the OFDM lock the trnsmit power of the synchronistion sequence is higher. This is due to the Crest fctor which is smller in cse of the synchronistion sequence (see [2]) nd cn e tken into ccount y dding respective gin Crest to the SNR. Furthermore, urst losses cused y impulse noise re simulted y specifying vlue SER min. Thus, the SER is pproximted y use of the error function s α SNR + Crest 1 erf + δ SER = ε SERmin if else > SER min with prmeters δ nd ε for pproximtion to results of field tests. Simultion Results As n exmple of simultion results the evlution of the uto logon procedure shll e presented. For this purpose, the plne model ws considered during simultion period of cycles where 499 slves simultneously strted in stte logon nd tried to log on. This sitution, of course, is not the norml cse ut my pper if the mster hs suffered temporry power supply interrupt. After out cycles 473 slves were in stte logged-on, 90 of which were directly reched y the mster, 127 y using one repeter nd 256 y using two repeters ech. The remining 26 slves were outside the receiving rnge nd therefore no logon ws possile. Tht mens, if we ssume n OFDM symol durtion of 13ms, it would hve tken only out 26 minutes to log on those 473 slves lthough most of them t lest needed one repeter nd hence, uto logon s well s utomtic routing ws required. In comprison to this, mnul configurtion of the sme network including determintion of repeters nd respective optimistion would hve required few weeks of work, we guess.

8 Conclusion In this contriution we hve presented network mngement system (NMS) which is sed on mster-slve concept using repeters to increse the rnge of the network where every slve cn lso e repeter. As slves re logged on utomticlly y the mster, the numer of slves in the network is dynmic nd therefore, selfconfigurtion of the network is pplied. Besides, the NMS is le to cope with chnging conditions on the communiction chnnel y use of dynmic routing. Furthermore, simultion model hs een developed where chnnel properties re descried y chnnel trnsfer mtrix nd for this purpose two different chnnel models were pplied. The simultion hs een used to verify the functionlity of the protocol nd to optimise prmeters. Severl simultion runs concerning uto logon procedure s well s utomtic routing, stility of the NMS nd other fetures hve shown promising results nd thus confirm the concept of the NMS nd demonstrte its suitility even for lrge networks. Moreover, the NMS is lredy implemented in our DLC-2 modem nd currently field tests re eing prepred. Besides, we re currently working on further implementtions on more powerful chips for 300kit/s solution for oth the CENELEC nd nd the USA-Asi mrket. References [ 1 ] Comprison nd Optimistion of Differentil Encoded Trnsmission on Fding Chnnels, L. Lmpe nd R. Fischer, University Erlngen-Nürnerg, Germny [ 2 ] Integrted PLC-Modem sed on OFDM, M. Deinzer nd M. Stöger, iad GmH, Germny, Pper presented on ISPLC 99

T H E S E C U R E T R A N S M I S S I O N P R O T O C O L O F S E N S O R A D H O C N E T W O R K

T H E S E C U R E T R A N S M I S S I O N P R O T O C O L O F S E N S O R A D H O C N E T W O R K Z E S Z Y T Y N A U K O W E A K A D E M I I M A R Y N A R K I W O J E N N E J S C I E N T I F I C J O U R N A L O F P O L I S H N A V A L A C A D E M Y 2015 (LVI) 4 (203) A n d r z e j M r c z k DOI: 10.5604/0860889X.1187607

More information

Reasoning to Solve Equations and Inequalities

Reasoning 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 information

AntiSpyware Enterprise Module 8.5

AntiSpyware Enterprise Module 8.5 AntiSpywre Enterprise Module 8.5 Product Guide Aout the AntiSpywre Enterprise Module The McAfee AntiSpywre Enterprise Module 8.5 is n dd-on to the VirusScn Enterprise 8.5i product tht extends its ility

More information

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

Polynomial 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 information

5 a LAN 6 a gateway 7 a modem

5 a LAN 6 a gateway 7 a modem STARTER With the help of this digrm, try to descrie the function of these components of typicl network system: 1 file server 2 ridge 3 router 4 ckone 5 LAN 6 gtewy 7 modem Another Novell LAN Router Internet

More information

EQUATIONS OF LINES AND PLANES

EQUATIONS OF LINES AND PLANES EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint

More information

Section 5.2, Commands for Configuring ISDN Protocols. Section 5.3, Configuring ISDN Signaling. Section 5.4, Configuring ISDN LAPD and Call Control

Section 5.2, Commands for Configuring ISDN Protocols. Section 5.3, Configuring ISDN Signaling. Section 5.4, Configuring ISDN LAPD and Call Control Chpter 5 Configurtion of ISDN Protocols This chpter provides instructions for configuring the ISDN protocols in the SP201 for signling conversion. Use the sections tht reflect the softwre you re configuring.

More information

How To Network A Smll Business

How To Network A Smll Business Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

New Internet Radio Feature

New Internet Radio Feature XXXXX XXXXX XXXXX /XW-SMA3/XW-SMA4 New Internet Rdio Feture EN This wireless speker hs een designed to llow you to enjoy Pndor*/Internet Rdio. In order to ply Pndor/Internet Rdio, however, it my e necessry

More information

Helicopter Theme and Variations

Helicopter 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 information

Dynamic TDMA Slot Assignment in Ad Hoc Networks

Dynamic TDMA Slot Assignment in Ad Hoc Networks Dynmic TDMA Slot Assignment in Ad Hoc Networks Akimitsu KANZAKI, Toshiki UEMUKAI, Tkhiro HARA, Shojiro NISHIO Dept. of Multimedi Eng., Grd. Sch. of Informtion Science nd Technology, Osk Univ. Dept. of

More information

FAULT TREES AND RELIABILITY BLOCK DIAGRAMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University

FAULT TREES AND RELIABILITY BLOCK DIAGRAMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University SYSTEM FAULT AND Hrry G. Kwtny Deprtment of Mechnicl Engineering & Mechnics Drexel University OUTLINE SYSTEM RBD Definition RBDs nd Fult Trees System Structure Structure Functions Pths nd Cutsets Reliility

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00

Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00 COMP20212 Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE Digitl Design Techniques Dte: Fridy 16 th My 2008 Time: 14:00 16:00 Plese nswer ny THREE Questions from the FOUR questions provided

More information

How To Set Up A Network For Your Business

How To Set Up A Network For Your Business 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

ClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment

ClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment ClerPeks Customer Cre Guide Business s Usul (BU) Services Pece of mind for your BI Investment ClerPeks Customer Cre Business s Usul Services Tble of Contents 1. Overview...3 Benefits of Choosing ClerPeks

More information

QoS Mechanisms C HAPTER 3. 3.1 Introduction. 3.2 Classification

QoS Mechanisms C HAPTER 3. 3.1 Introduction. 3.2 Classification C HAPTER 3 QoS Mechnisms 3.1 Introduction In the previous chpter, we introduced the fundmentl QoS concepts. In this chpter we introduce number of key QoS mechnisms tht enble QoS services. At the end of

More information

Or more simply put, when adding or subtracting quantities, their uncertainties add.

Or more simply put, when adding or subtracting quantities, their uncertainties add. Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re

More information

JaERM Software-as-a-Solution Package

JaERM Software-as-a-Solution Package JERM Softwre-s--Solution Pckge Enterprise Risk Mngement ( ERM ) Public listed compnies nd orgnistions providing finncil services re required by Monetry Authority of Singpore ( MAS ) nd/or Singpore Stock

More information

Engineer-to-Engineer Note

Engineer-to-Engineer Note Engineer-to-Engineer Note EE-265 Technicl notes on using Anlog Devices DSPs, processors nd development tools Contct our technicl support t dsp.support@nlog.com nd t dsptools.support@nlog.com Or visit our

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

Network Configuration Independence Mechanism

Network Configuration Independence Mechanism 3GPP TSG SA WG3 Security S3#19 S3-010323 3-6 July, 2001 Newbury, UK Source: Title: Document for: AT&T Wireless Network Configurtion Independence Mechnism Approvl 1 Introduction During the lst S3 meeting

More information

Technical manual for Multi Apartment Gateway 1456B Passion.Technology.Design.

Technical manual for Multi Apartment Gateway 1456B Passion.Technology.Design. E TECHICAL MAUAL Art 456B B + - 40-56 Vdc SOLO CO CAVO ROSSO COMELIT 2E7T000500 OLY WITH COMELIT RED CABLE 2E7T000500 FIXED POE SETTABLE POE 0 POE A A2 A3 A4 Technicl mnul for Multi Aprtment Gtewy 456B

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

2 DIODE CLIPPING and CLAMPING CIRCUITS

2 DIODE CLIPPING and CLAMPING CIRCUITS 2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of

More information

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the

More information

Graphs on Logarithmic and Semilogarithmic Paper

Graphs 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 information

Econ 4721 Money and Banking Problem Set 2 Answer Key

Econ 4721 Money and Banking Problem Set 2 Answer Key Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in

More information

Small Businesses Decisions to Offer Health Insurance to Employees

Small Businesses Decisions to Offer Health Insurance to Employees Smll Businesses Decisions to Offer Helth Insurnce to Employees Ctherine McLughlin nd Adm Swinurn, June 2014 Employer-sponsored helth insurnce (ESI) is the dominnt source of coverge for nonelderly dults

More information

A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324

A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324 A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................

More information

Quick Reference Guide: One-time Account Update

Quick Reference Guide: One-time Account Update Quick Reference Guide: One-time Account Updte How to complete The Quick Reference Guide shows wht existing SingPss users need to do when logging in to the enhnced SingPss service for the first time. 1)

More information

IaaS Configuration for Virtual Platforms

IaaS Configuration for Virtual Platforms IS Configurtion for Virtul Pltforms vcloud Automtion Center 6.0 This document supports the version of ech product listed nd supports ll susequent versions until the document is replced y new edition. To

More information

Experiment 6: Friction

Experiment 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 information

Section 5-4 Trigonometric Functions

Section 5-4 Trigonometric Functions 5- Trigonometric Functions Section 5- Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form

More information

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001 CS99S Lortory 2 Preprtion Copyright W. J. Dlly 2 Octoer, 2 Ojectives:. Understnd the principle of sttic CMOS gte circuits 2. Build simple logic gtes from MOS trnsistors 3. Evlute these gtes to oserve logic

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs VoIP (Voice over Internet Protocol) offers low cost lterntive to expensive trditionl phone services nd is rpidly becoming the communictions system of choice for smll

More information

EasyMP Network Projection Operation Guide

EasyMP Network Projection Operation Guide EsyMP Network Projection Opertion Guide Contents 2 About EsyMP Network Projection Functions of EsyMP Network Projection... 5 Vrious Screen Trnsfer Functions... 5 Instlling the Softwre... 6 Softwre Requirements...6

More information

Traffic Rank Based QoS Routing in Wireless Mesh Network

Traffic Rank Based QoS Routing in Wireless Mesh Network Trffic Rnk Bsed QoS Routing in Wireless Mesh Network Deep P Kmble #1, Sujth P Terdl *2 #1 Deprtment of Computer Science nd Engineering, Poojy Doddp App College of Engineering, Gulbrg, Krntk, Indi. *2 Deprtment

More information

Regular Sets and Expressions

Regular Sets and Expressions Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite

More information

WEB DELAY ANALYSIS AND REDUCTION BY USING LOAD BALANCING OF A DNS-BASED WEB SERVER CLUSTER

WEB DELAY ANALYSIS AND REDUCTION BY USING LOAD BALANCING OF A DNS-BASED WEB SERVER CLUSTER Interntionl Journl of Computers nd Applictions, Vol. 9, No., 007 WEB DELAY ANALYSIS AND REDUCTION BY USING LOAD BALANCING OF A DNS-BASED WEB SERVER CLUSTER Y.W. Bi nd Y.C. Wu Abstrct Bsed on our survey

More information

Vendor Rating for Service Desk Selection

Vendor Rating for Service Desk Selection Vendor Presented By DATE Using the scores of 0, 1, 2, or 3, plese rte the vendor's presenttion on how well they demonstrted the functionl requirements in the res below. Also consider how efficient nd functionl

More information

Data replication in mobile computing

Data replication in mobile computing Technicl Report, My 2010 Dt repliction in mobile computing Bchelor s Thesis in Electricl Engineering Rodrigo Christovm Pmplon HALMSTAD UNIVERSITY, IDE SCHOOL OF INFORMATION SCIENCE, COMPUTER AND ELECTRICAL

More information

Health insurance marketplace What to expect in 2014

Health 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 information

Health insurance exchanges What to expect in 2014

Health 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 information

Engineer-to-Engineer Note

Engineer-to-Engineer Note Engineer-to-Engineer Note EE-280 Technicl notes on using Anlog Devices DSPs, processors nd development tools Visit our Web resources http://www.nlog.com/ee-notes nd http://www.nlog.com/processors or e-mil

More information

9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes

9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes The Sclr Product 9.3 Introduction There re two kinds of multipliction involving vectors. The first is known s the sclr product or dot product. This is so-clled becuse when the sclr product of two vectors

More information

Operations with Polynomials

Operations 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

Lecture 3 Gaussian Probability Distribution

Lecture 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 information

Homework 3 Solutions

Homework 3 Solutions CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.

More information

Small Business Cloud Services

Small Business Cloud Services Smll Business Cloud Services Summry. We re thick in the midst of historic se-chnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

Project 6 Aircraft static stability and control

Project 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 information

Outline of the Lecture. Software Testing. Unit & Integration Testing. Components. Lecture Notes 3 (of 4)

Outline of the Lecture. Software Testing. Unit & Integration Testing. Components. Lecture Notes 3 (of 4) Outline of the Lecture Softwre Testing Lecture Notes 3 (of 4) Integrtion Testing Top-down ottom-up ig-ng Sndwich System Testing cceptnce Testing istriution of ults in lrge Industril Softwre System (ISST

More information

How To Reduce Telecommunictions Costs

How To Reduce Telecommunictions Costs Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

VMware Horizon Mirage Web Manager Guide

VMware Horizon Mirage Web Manager Guide VMwre Horizon Mirge We Mnger Guide Horizon Mirge 4.3 This document supports the version of ech product listed nd supports ll susequent versions until the document is replced y new edition. To check for

More information

Enterprise Risk Management Software Buyer s Guide

Enterprise Risk Management Software Buyer s Guide Enterprise Risk Mngement Softwre Buyer s Guide 1. Wht is Enterprise Risk Mngement? 2. Gols of n ERM Progrm 3. Why Implement ERM 4. Steps to Implementing Successful ERM Progrm 5. Key Performnce Indictors

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

Economics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999

Economics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999 Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,

More information

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY

PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive

More information

How To Get A Free Phone Line From A Cell Phone To A Landline For A Business

How To Get A Free Phone Line From A Cell Phone To A Landline For A Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

Factoring Polynomials

Factoring 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 information

Basic Analysis of Autarky and Free Trade Models

Basic Analysis of Autarky and Free Trade Models Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently

More information

Kofax Reporting. Administrator's Guide 2.0.0 2013-09-19

Kofax Reporting. Administrator's Guide 2.0.0 2013-09-19 Kofx Reporting 2.0.0 Administrtor's Guide 2013-09-19 2013 Kofx, Inc. All rights reserved. Use is subject to license terms. Third-prty softwre is copyrighted nd licensed from Kofx s suppliers. THIS SOFTWARE

More information

. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2

. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2 7 CHAPTER THREE. Cross Product Given two vectors = (,, nd = (,, in R, the cross product of nd written! is defined to e: " = (!,!,! Note! clled cross is VECTOR (unlike which is sclr. Exmple (,, " (4,5,6

More information

Utilization of Smoking Cessation Benefits in Medicaid Managed Care, 2009-2013

Utilization of Smoking Cessation Benefits in Medicaid Managed Care, 2009-2013 Utiliztion of Smoking Cesstion Benefits in Medicid Mnged Cre, 2009-2013 Office of Qulity nd Ptient Sfety New York Stte Deprtment of Helth Jnury 2015 Introduction According to the New York Stte Tocco Control

More information

How To Make A Network More Efficient

How To Make A Network More Efficient Rethinking Virtul Network Emedding: Sustrte Support for Pth Splitting nd Migrtion Minln Yu, Yung Yi, Jennifer Rexford, Mung Ching Princeton University Princeton, NJ {minlnyu,yyi,jrex,chingm}@princeton.edu

More information

Distributions. (corresponding to the cumulative distribution function for the discrete case).

Distributions. (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 information

Techniques for Requirements Gathering and Definition. Kristian Persson Principal Product Specialist

Techniques for Requirements Gathering and Definition. Kristian Persson Principal Product Specialist Techniques for Requirements Gthering nd Definition Kristin Persson Principl Product Specilist Requirements Lifecycle Mngement Elicit nd define business/user requirements Vlidte requirements Anlyze requirements

More information

VoIP for the Small Business

VoIP for the Small Business VoIP for the Smll Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become

More information

Architecture and Data Flows Reference Guide

Architecture and Data Flows Reference Guide Architecture nd Dt Flows Reference Guide BlckBerry Enterprise Service 12 Version 12.0 Pulished: 2014-11-10 SWD-20141110103011848 Contents Components used in the BES12 solution... 5 Components used to mnge

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

VoIP for the Small Business

VoIP for the Small Business VoIP for the Smll Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become

More information

STATUS OF LAND-BASED WIND ENERGY DEVELOPMENT IN GERMANY

STATUS OF LAND-BASED WIND ENERGY DEVELOPMENT IN GERMANY Yer STATUS OF LAND-BASED WIND ENERGY Deutsche WindGurd GmbH - Oldenburger Strße 65-26316 Vrel - Germny +49 (4451)/9515 - info@windgurd.de - www.windgurd.com Annul Added Cpcity [MW] Cumultive Cpcity [MW]

More information

DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report

DlNBVRGH + 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 information

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives

More information

GFI MilArchiver 6 vs C2C Archive One Policy Mnger GFI Softwre www.gfi.com GFI MilArchiver 6 vs C2C Archive One Policy Mnger GFI MilArchiver 6 C2C Archive One Policy Mnger Who we re Generl fetures Supports

More information

GFI MilArchiver 6 vs Quest Softwre Archive Mnger GFI Softwre www.gfi.com GFI MilArchiver 6 vs Quest Softwre Archive Mnger GFI MilArchiver 6 Quest Softwre Archive Mnger Who we re Generl fetures Supports

More information

Lectures 8 and 9 1 Rectangular waveguides

Lectures 8 and 9 1 Rectangular waveguides 1 Lectures 8 nd 9 1 Rectngulr wveguides y b x z Consider rectngulr wveguide with 0 < x b. There re two types of wves in hollow wveguide with only one conductor; Trnsverse electric wves

More information

Efficient load-balancing routing for wireless mesh networks

Efficient load-balancing routing for wireless mesh networks Computer Networks 51 (007) 50 66 www.elsevier.com/locte/comnet Efficient lod-blncing routing for wireless mesh networks Yigl Bejerno, Seung-Je Hn b, *,1, Amit Kumr c Bell Lbortories, Lucent Technologies,

More information

STRM Log Manager Installation Guide

STRM Log Manager Installation Guide Security Thret Response Mnger Relese 2012.0 Juniper Networks, Inc. 1194 North Mthild Avenue Sunnyvle, CA 94089 USA 408-745-2000 www.juniper.net Pulished: 2012-09-12 Copyright Notice Copyright 2012 Juniper

More information

Space Vector Pulse Width Modulation Based Induction Motor with V/F Control

Space Vector Pulse Width Modulation Based Induction Motor with V/F Control Interntionl Journl of Science nd Reserch (IJSR) Spce Vector Pulse Width Modultion Bsed Induction Motor with V/F Control Vikrmrjn Jmbulingm Electricl nd Electronics Engineering, VIT University, Indi Abstrct:

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

Welch Allyn CardioPerfect Workstation Installation Guide

Welch Allyn CardioPerfect Workstation Installation Guide Welch Allyn CrdioPerfect Worksttion Instlltion Guide INSTALLING CARDIOPERFECT WORKSTATION SOFTWARE & ACCESSORIES ON A SINGLE PC For softwre version 1.6.5 or lter For network instlltion, plese refer to

More information

Protocol Analysis. 17-654/17-764 Analysis of Software Artifacts Kevin Bierhoff

Protocol Analysis. 17-654/17-764 Analysis of Software Artifacts Kevin Bierhoff Protocol Anlysis 17-654/17-764 Anlysis of Softwre Artifcts Kevin Bierhoff Tke-Awys Protocols define temporl ordering of events Cn often be cptured with stte mchines Protocol nlysis needs to py ttention

More information

VoIP for the Small Business

VoIP for the Small Business VoIP for the Smll Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become

More information

All pay auctions with certain and uncertain prizes a comment

All pay auctions with certain and uncertain prizes a comment CENTER FOR RESEARC IN ECONOMICS AND MANAGEMENT CREAM Publiction No. 1-2015 All py uctions with certin nd uncertin prizes comment Christin Riis All py uctions with certin nd uncertin prizes comment Christin

More information

RTL Power Optimization with Gate-level Accuracy

RTL Power Optimization with Gate-level Accuracy RTL Power Optimiztion with Gte-level Accurcy Qi Wng Cdence Design Systems, Inc Sumit Roy Clypto Design Systems, Inc 555 River Oks Prkwy, Sn Jose 95125 2903 Bunker Hill Lne, Suite 208, SntClr 95054 qwng@cdence.com

More information

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.

Use 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 information

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered: Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you

More information

VoIP for the Small Business

VoIP for the Small Business VoIP for the Smll Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become

More information

Math 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1.

Math 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1. Mth 4, Homework Assignment. Prove tht two nonverticl lines re perpendiculr if nd only if the product of their slopes is. Proof. Let l nd l e nonverticl lines in R of slopes m nd m, respectively. Suppose

More information

g(y(a), y(b)) = o, B a y(a)+b b y(b)=c, Boundary Value Problems Lecture Notes to Accompany

g(y(a), y(b)) = o, B a y(a)+b b y(b)=c, Boundary Value Problems Lecture Notes to Accompany Lecture Notes to Accompny Scientific Computing An Introductory Survey Second Edition by Michel T Heth Boundry Vlue Problems Side conditions prescribing solution or derivtive vlues t specified points required

More information

Unleashing the Power of Cloud

Unleashing the Power of Cloud Unleshing the Power of Cloud A Joint White Pper by FusionLyer nd NetIQ Copyright 2015 FusionLyer, Inc. All rights reserved. No prt of this publiction my be reproduced, stored in retrievl system, or trnsmitted,

More information

Vector differentiation. Chapters 6, 7

Vector differentiation. Chapters 6, 7 Chpter 2 Vectors Courtesy NASA/JPL-Cltech Summry (see exmples in Hw 1, 2, 3) Circ 1900 A.D., J. Willird Gis invented useful comintion of mgnitude nd direction clled vectors nd their higher-dimensionl counterprts

More information

** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand

** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand Modelling nd Simultion of hemicl Processes in Multi Pulse TP Experiment P. Phnwdee* S.O. Shekhtmn +. Jrungmnorom** J.T. Gleves ++ * Dpt. hemicl Engineering, Ksetsrt University, Bngkok 10900, Thilnd + Dpt.hemicl

More information

Source Code verification Using Logiscope and CodeReducer. Christophe Peron Principal Consultant Kalimetrix

Source Code verification Using Logiscope and CodeReducer. Christophe Peron Principal Consultant Kalimetrix Source Code verifiction Using Logiscope nd CodeReducer Christophe Peron Principl Consultnt Klimetrix Agend Introducing Logiscope: Improving confidence nd developer s productivity Bsed on stte-of-the-rt

More information

5.2. 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. 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 rel-vlued

More information