DiaGen: A Generator for Diagram Editors Based on a Hypergraph Model

Size: px
Start display at page:

Download "DiaGen: A Generator for Diagram Editors Based on a Hypergraph Model"

Transcription

1 DiGen: A Genertor for Digrm Eitors Bse on Hypergrph Moel G. Viehstet M. Mins Lehrstuhl für Progrmmiersprhen Universität Erlngen-Nürnerg Mrtensstr. 3, Erlngen, Germny Emil: Astrt Digrms (e.g., trees for hierrhil strutures, or grphs for finite stte mhines) re often neee s prt of vne user interfes, n re frequently speifi to user s pplition. The implementtion of eitors for igrms shoul e supporte y tool n se on forml moel. This pper gives n overview of DiGen, our genertor for igrm eitors. An eitor for ertin kin of igrms is generte from speifition, whih inlues hypergrph grmmr to esrie the struture of igrms. The user of igrm eitor oes not hve to e onerne with the grmmr, ut n mnipulte igrms very onveniently y iret mnipultion. 1 Introution An esily omprehensile representtion of omplex strutures is gining importne for the users of informtion systems or CASE tools. A signifint n inresing shre of the effort for implementing these systems goes into the user interfe. Common interfe uilers for Grphil User Interfes (GUIs) minly fous on wigets like uttons, menus, et., whih oes not mke interfes very grphil. This ssessment ws lso me in reent CACM issue on GUIs [1]: Wht the mrket onsiers GUI is little more thn glorifie menu system, hving no grphis. This leves the grphil representtion of the pplition omin s n exerise for the eveloper ::: More omplex strutures in the pplition n often e grphilly represente y some kin of igrm. It is esirle to mke igrms prt of the user interfe n let user intertively eit them. Digrms usully hve semntil mening for the pplition. Thus, hnges to igrm hve to e trnsformtions from one onsistent stte into nother. The set of vli igrms, e.g., the set of Nssi-Shneiermn igrms (NSDs) [2, 3], is terme igrm lss n shoul e esrie y forml moel. A syntx-irete eitor tilore to some igrm lss is lle igrm eitor. A igrm eitor ensures tht igrm onstrute y the user lwys hs vli struture, n n support omplex eiting opertions n lyout. Some tools, e.g., Grnet [4], support simple kins of igrms. The struture of vli igrms, however, hs to e mintine y the progrmmer using Grnet n is more or less hien in the oe. There re only very few systems for generting igrm eitor tht re se on forml moel. A onept is presente in [5], ut not genertor. In the PAGG system [6] lyout of igrms is troulesome n eiting inonvenient. The Constrint system [7] uses grmmr moel se on on-free grmmrs n onstrints for utomti lyout of igrms. Con-free grmmrs, however, o not permit iret representtion of multiimensionl reltionships, s neee for the lyout of igrms. Furthermore, the eiting pilities re very restrite. Hypereges n hypergrphs [8], whih hve, e.g., een use y Hrel for tehrts [9], re n intuitive n vntgeous moel for representtion of igrms. DiGen, our genertor for igrm eitors, is se on hypergrph grmmr moel for speifying igrm lss. Setion 2 gives rief overview of the system. The grmmr moel is the topi of Setion 3. Setion 4 resses user intertion y iret mnipultion. Trnsformtions triggere y user intertions re esrie in Setion 5. In Setion 6 results from se stuies re presente. 2 The Genertor DiGen DiGen genertes igrm eitor, e.g., n NSD eitor s epite in Fig. 1, from speifition, whih onsists of the prts shown in Fig. 3. A mjor prt is the grmmr for the igrm lss. Some prtiulr igrm shown on the sreen is internlly represente in the igrm eitor y hypergrph, whih is erivle in the grmmr. This hy-

2 y on on n Figure 2: Hypergrph orresponing to the upper NSD in Fig. 1. Noes re shown s lk irles, n ft lines s well s the she res lele with, on, y, n n re terminl hypereges. Figure 1: Snpshot of session with n NSD eitor generte y DiGen. An eiting stte with two NSDs is shown. A group of two susequent sttements (onsisting of simple sttement n n if) is selete in the lower NSD, s inite y the hnles. pergrph is referre to s erivtion grph in Fig. 3 n is the min t struture. Lyout onitions re tthe to grmmr proutions in the speifition. Terminl symols in erivtion grph re mppe on the sreen. Their imge is ompose of primitive elements (lines,, et.) n lso prt of the speifition. The remining prts in Fig. 3 re for user intertion. 3 Digrm struture n lyout Beuse of their one-imensionl struture strings s use in [7] nnot represent multiimensionl reltionships iretly. We use hypergrphs inste s internl moels of igrms eing eite. A hypergrph is generliztion of grph, in whih eges re hypereges, i.e., they n e onnete to ny (fixe) numer of noes. Eh hyperege hs type n numer of onnetion points tht etermine how mny noes the hyperege is onnete to. We sy the hyperege visits these noes. 1 The fmilir irete grph n e seen s hypergrph in whih ll hypereges visit extly two noes. Noes in hypergrph moeling igrm stn for points (e.g., in the plne), hypereges re igrm elements whose position is given y the noes eing visite 1 Atully, we onsier irete hypergrphs. A irete hypergrph is triple (N;E; ) where N is finite set of noes, E finite set of hypereges, n funtion : E! N +, whih ssigns sorte sequene (e) =(n 1 ;n 2 ;:::;n k )of visite noes to eh hyperege e 2 E. The length of (e) is the rity of e. y the hyperege. This very intuitive representtion is illustrte in Fig. 2. A representtion in systems whih o not use hypergrphs [6, 7] woul e signifintly more omplite. A igrm lss, i.e., the syntti struture of igrms, is speifie in terms of its hypergrph moels using hypergrph grmmr. Con-free hypergrph grmmrs re nlogously efine to on-free (string) grmmrs n hve similr properties [10]. Terminl n nonterminl hypereges re use in hypergrph grmmrs inste of lphet symols in string grmmrs. Eh proution in on-free hypergrph grmmr onsists on its left hn sie (lhs) of single nonterminl hyperege n the noes visite, see Fig. 4. The lhs of proution P 1 is the strting grph of the grmmr. A proution s rhs is n ritrry hypergrph, whih my ontin terminl s well s nonterminl hypereges. Applition of proution to hypergrph is similr to string grmmrs, too: if the lhs is sugrph of the hypergrph, this sugrph is remove n reple y the rhs. The resulting hypergrph is si to e erive from the first. In orer to speify whih rhs noe reples whih lhs noe, orresponing noes of the lhs n rhs re lele with the sme letters. A smple erivtion sequene is shown in Fig. 5. The igrm lss given y (on-free) hypergrph grmmr is the set of erivtion grphs tht re erivle from the strting grph n onsist of terminl hypereges only. 2 The erivtion grph is the igrm s internl hypergrph moel, whih is mppe on the sreen. Sine the hypergrph grmmr esries the set of vli hypergrph moels, the user of igrm eitor only sees vli 2 There re igrm lsses tht on-free hypergrph grmmrs nnot esrie, e.g., finite stte mhines, see Figures For these lsses, DiGen uses on-sensitive trnsformtions whih generte the itionl grph omponents tht nnot e expresse y onfree hypergrph grmmrs; see Setion 5.

3 Digrm Eitor Groups Derivtion grph Lyout ttriutes Grphil interfe Grphil ojets Group efinition Digrm representtion n trnsformtion Constrint stisftion moules Intertion t ll t flow Group types Speifition Event utomt Grmmr n trnsformtions Lyout onitions Imge of terminl symols trget of speifition Figure3: Overview of igrm eitor generte with DiGen n its speifition. P 1 P 2 NSD P 5.x = f.x.x = i.x.y = e.y =.y f.y = g.y f.x+0.5 = g.x h.x+0.5 = i.x f y e g Con h n i P 3 P 6 P 7 retngle(,,,).x+0.25 = e.x e Con e P 4 retngle(,,,).y-.y.h.x-.x.w retngle(,,,) stns for.x =.x.x =.x.y =.y.y =.y P 8 retngle(,,,).x+0.25 = e.x Con on retngle(,,,).y-.y on.h.x-.x on.w Con Figure 4: Con-free hypergrph grmmr for NSDs. Noes re shown s lk irles. Ft lines n rk she res lele with, on, y, n n re terminl hypereges, light she res re nonterminl hypereges. Nonterminls n stn for sttement sequene resp. sttement, Con for onition. The formuls re onstrints for lyout.

4 igrms. The hypergrph in Fig. 2 is suh erivtion grph onsisting of terminl eges only. These eges epite s ft lines n rk she res in Fig. 2 re mppe on the sreen s esrie in the speifition, see Fig. 3. As result of this mpping the grphil representtion (see the upper NSD in Fig. 1) onsists of set of grphil ojets. E.g., hyperege is mppe to n re ontining ritrry s, i.e., the sttements in Fig. 1. The sttement s re not prt of the hypergrph moel, ut property of this grphil ojet. Hypergrph grmmrs n esrie the syntti struture of igrms, ut lyout requirements re not inlue euse hypergrphs o not hve ny lyout. For onfree (string) grmmrs lyout n e esrie using ttriute grmmrs [11]. Constrints were me populr y Borning [12] for lyout in intertive environments. Their vntge is the multiiretionl nture, wheres in ttriute grmmrs hnges re propgte only into one iretion. Vner Znen [7] omine onstrints with on-free (string) grmmrs. Hypergrph grmmrs re ttriute in similr wy. However, not only hypereges, whih orrespon to lphet symols in string grmmrs, rry ttriutes, ut lso noes. Sine ny numer of hypereges n e onnete to noe, noe ttriutes re ommon ttriutes for ll hypereges visiting this noe. With using hypergrphs only few onstrints re neee ompre to [7]. Furthermore, onstrints n e liner inequlities in DiGen. Equtions etermine reltions etween ttriute vlues in efinite wy, wheres inequlity onstrints permit whole rnge of vlues s solutions. This is onvenient wy to omine utomti lyout of igrms provie y the system with user-efine moifitions. Detils on lyout n the inrementl lgorithm for onstrint stisftion uilt into our genertor n e foun in [13]. The onstrints for lyout of NSDs re shown in Fig. 4. Every noe n hs ttriutes x n y for the noe s position. They re referre to y n:x n n:y. The only ege ttriutes re.h,.w, on.h, non.w for the miniml height n with of loks resp. onitions. The smll numer of onstrints shown in Fig. 4 is suffiient for lyout ue to noe ttriutes, whih re shre mong ll visiting hypereges. 4 Diret Mnipultion The min feture onerning user intertion is tht igrm n e moifie very onveniently in iret mnipultion style y just moving igrm elements roun on the sreen. This is not the se for other systems like PAGG or Constrints [6, 7], in whih eiting opertions hve to e hosen from menu. In igrm eitor generte with DiGen the intertion moule (see Fig. 3) is responsile for the retion on user s tions with mouse NSD P 1 P 3 P 6 Con P 3 Figure 5: Prt of the erivtion for the hypergrph in Fig. 2 using the proutions from Fig. 4. n keyor. They n, e.g., use lyout hnges, seletion of igrm elements, or trnsformtions of the igrm s struture. Lyout hnges hve een isusse in [13]. Seletion of igrm elements is possile in ifferent wys n prt of the speifition. In our NSD eitor, e.g., susequent selete sttements (whih my e omplex) re utomtilly omine into single entity lle group, see Fig. 1 n [14]. Trnsformtions will e presente in setion 5. Our NSD eitor serves for emonstrting iret mnipultion. As n exmple, we wnt to remove the group in Fig. 1 from its position n insert it into the upper NSD s the first sttements of the while. Fig. 6 shows the result. The only wy to hieve this in other systems like [6, 7] is solely se on seletion n pressing uttons or hoosing menu items in the following style: 1. Press the Cut-utton 2. Selet the line immeitely elow the while sonition to inite the estintion 3. Press the Insert-utton The onept is the sme s in the Synthesizer Genertor [15] for syntx-irete eiting. It is suffiient there, ut for igrms more nturl wy of eiting is esirle. With DiGen igrm eitors offering true iret mnipultion n e speifie using event utomt, see Fig. 3 n [14]. E.g., the moifition from Fig. 1 to Fig. 6 n e me y simply pressing the mouse utton while the mouse pointer is lote over the selete group, rgging this group to its estintion,

5 s: t: l:line l:line s: t: line Figure 7: Smple trnsformtion rule in the NSD eitor for inserting t t line l. For pplying this rule the lhs hs to mth the igrm s urrent struture. The rhs esries the moifition. Corresponing sutrees of the lhs n rhs re emphsize the sme wy. This enles more powerful trnsformtions n reusge of primitives. E.g., mny trnsformtions in the NSD eitor re se on primitives for eleting or inserting sequene of (ompoun) sttements. Figure 6: Sitution fter moving the group selete in Fig. 1 to the eginning of the while. n relesing the mouse utton over the line elow the while s onition. In the sme wy ny prt of igrm n e remove n inserte t ny other spot. A igrm prt n lso e me new NSD of its own, or n entire NSD n e inserte into nother igrm in similr fshion. A numer of other eiting opertions y iret mnipultion hve een speifie for the NSD eitor: The then-nelse-rnh ofn if n eswithey pressing the mouse utton over the if s tringle with y insie, rgging it to the right, n relesing it over the orresponing n (or the other wy roun). A while n e hnge into n until y moving the while s onition own to the en of the while n relesing the mouse utton there. Similrly, n until n e moifie into while. 5 Trnsformtions Digrm moifitions initite y iret mnipultion re esrie y trnsformtions: trnsformtion is trnsition from set of igrms to nother set of igrms. The struture of one or more igrms n e hnge, ut the user of igrm eitor only sees vli igrms, i.e., igrms elonging to the speifie igrm lss. In ontrst to [7], trnsformtions in DiGen n e omplex n onsist of severl primitive steps. An exmple of simple trnsformtion rule in the NSD eitor is given in Fig. 7. Trnsformtion rules esrie the moifition of the erivtion whih stns ehin eh igrm eing isplye on the sreen. In these rules erivtion (like tht in Fig. 5) is written s tree. A trnsformtion onsists of sequene of rules. The user of igrm eitor inites the trnsformtion n its lotion y iret mnipultion using mouse n keyor. The user woul inite t n line l where t hs to e inserte in the ove exmple. The system tries to pply the trnsformtion y mthing the left hn sies of the trnsformtion s rules in the sequene given. The first mthing lhs etermines the moifition to e me. Different rules in trnsformtion tke re of ifferent ons of the positions inite y the user (here t n line l). In the urrent implementtion the progrmmer of igrm eitor, i.e., the user of our genertor, hs to mke sure tht trnsformtions, whih re prt of n eitor speifition, ontin ll relevnt rules. If the progrmmer fils to provie omplete set of rules, this only mens tht for ertin ons trnsformtion oes not use ny hnge. An nlysis uring prsing the speifition woul e helpful to prevent suh pitflls. Trnsformtion rules s illustrte in Fig. 7 re suffiient for tree struture igrms like NSDs. For other igrm lsses, e.g., finite stte mhines, onfree hypergrph grmmr (see Fig. 4) is too wek. In suh ses on-sensitive proutions resp. trnsformtions re neee. They ritrry grph omponents to the hypergrph erive from the grmmr s strting grph. The on-sensitive trnsformtions re not llowe to elete sugrphs n therefore nnot istur the erivtion of hypergrphs in the hypergrph grmmr. Their priniple is out the sme s for the trnsformtions esrie ove. In igrm eitors generte with DiGen trnsformtions n lso e use to speify exeution of igrms. This is possile if

6 Figure 8: Snpshot of n FSM eitor session. te 1 is the initil n lso finl stte. The initil stte is mrke y thik orer line, finl sttes y oule orer line. Figure 10: Sitution rising from Fig. 9 fter pressing utton ep one. Figure 9: The FSM eitor session of Fig. 8 fter pressing utton rt. The urrent stte is set to the initil stte, whih is inite y the ft orer line. exeuting igrm, i.e., semntilly evluting igrm, n e synttilly represente, n ll the igrms rete uring the exeution re memers of the igrm lss. For n intuitive illustrtion we use our smple eitor for finite stte mhines (FSMs), see Figures Using the eitor, the user n rete n moify n FSM onsisting of sttes (irles) n trnsitions (rrows). A single stte hs to e mrke s initil stte, t lest one s terminl. But moreover, the user n exeute the eite FSM: n input string n e type in, n trnsitions n e rrie out step y step, eh onsuming one hrter of the input string. When the lst hrter is proesse n the FSM is in terminl stte, the string is onsiere epte. Exeution etils re represente n rrie out Figure 11: Termintion sitution fter proessing the lst igit of the string from Fig. 9. using trnsformtions on the erivtion grph of the urrent FSM: The remining string is represente s ontents of hyperege. Consuming the string hrter y hrter shortens the ontents. The urrent stte is inite y n itionl terminl ege ( ursor ) whih is mppe s fille irle or thik orer line on the sreen just ove the irle representing the urrent stte. epping initites trnsformtion on the erivtion grph tht looks up the first remining hrter n serhes for suitle trnsition. If more thn one trnsition fits, n ritrry one is hosen. Then the ursor is move to the new stte, n the string s first hrter is remove. opping the FSM y either rejeting or epting

7 the string is inite y n itionl hyperege with Ok or Error. Sine eh exeution step is rrie out s trnsformtion on the erivtion grph, the user my hnge the igrm uring exeution. Lter exeution steps follow the new igrm struture. Fig. 8 shows the sitution fter onstruting n FSM n Fig. 9 the sitution fter pressing utton rt. The user ws ske to provie n input string for the FSM, n the urrent stte ws set to the initil stte. If there is suitle trnsition for the urrently first hrter in the input string, eh press on utton ep uses trnsition n removes the first hrter from the input, see Fig. 10. After repetely pressing on utton ep the FSM rehes its finl stte s in Fig. 11. Ok visulizes the FSM to hve epte the initilstring. 6 Cse uies A prototype of DiGen hs een implemente on Spr-Worksttions using C++ n X-Winows with OSF/Motif. Currently, DiGen onsists of pproximtely 100,000 lines of oe. Three smple igrm eitors hve een speifie n generte y DiGen: n NSD eitor s shown in Figures 1 n 6, n eitor for flowhrts, Fig. 12, n n FSM eitor, see Figures From these se stuies we got the following results: Con-free hypergrph grmmrs s introue in Setion 3 n esily n ompletely esrie NSDs n flowhrts. However, FSMs nnot e expresse y pure on-free hypergrph grmmr euse of their generl grph struture [10]. We use hypergrph grmmr to speify the igrm s skeleton n, itionlly, on-sensitive trnsformtion rules to esrie the FSMs grph prts. This exmple emonstrtes tht DiGen is useful even for igrm lsses tht on-free hypergrph grmmrs nnot ompletely esrie. Of ourse, utomti lyout oes not work for those igrm prts efine y on-sensitive trnsformtion rules. But sine DiGen provies user-justle lyout, the user n rrnge the igrm mnully. Speifitions in the urrent implementtion of DiGen re files. The speifition effort n thus e mesure in lines of. Tle 1 shows the totl numers of lines neee to speify the three smple eitors n for eh of the speifition prts. Oviously, the prt onsisting of grmmr n mpping terminl eges on the sreen is the shortest one in eh speifition. The longest prt is theesription of user intertion, whih onsists of ul Figure 12: Smple session with flowhrt eitor # lines for NSD FC FSM grmmr & lyout & groups mpping on sreen grph omponents 191 trnsformtions user intertion totl Tle 1: Numer of lines neee to speify the eitors for Nssi-Shneiermnn igrms (NSD), flowhrts (FC), n finite stte mhines (FSM). representtion of event utomt, speil kin of finite stte mhines. Using grphil speifition woul reue the speifition effort y gret extent. Speifying grph omponents is short: for FSMs 191 lines re neee to esrie rrows, i.e., trnsitions, etween ritrry sttes. A grphil speifition will further reue this speifition effort. The speifitions for the NSD n flowhrt eitors re pretty muh the sme. Atully, we hve uilt the flowhrt speifition y opying the NSD speifition n minly hnging the mpping of terminl hypereges on the sreen. We oul thus emonstrte tht generting igrm eitor is simple tsk if n eitor for similr igrm lss lrey

8 exists. 7 Conlusions DiGen genertes igrm eitors with iret mnipultion opertions from speifition. A igrm lss is speifie y hypergrph grmmr, whih is esp. useful for esriing multiimensionl reltionships etween igrm elements. Lyout is efine on high level y onstrints. Complex eiting opertions n even exeution of igrm n e speifie. A igrm eite y the user is lwys in onsistent stte, whih is hypergrph in the forml moel. This hypergrph n e use y other prts of the pplition; however, this ws not one yet. Three se stuies showe tht even using forml moel for esriing the igrm lss n utomtilly generting the eitor oes not leve the progrmmer without work: in our exmples, eh speifition onsists of some 2,000 lines of % of the speifition is neee to esrie trnsformtions n user intertion. Future work will reue this perentge: A file s use so fr is not the est hoie for esriing user intertion n trnsformtions. A grphil representtion will mke speifitions shorter n lerer. We wnt to hypergrph prsing lgorithm to DiGen, i.e., n lgorithm tht reonstruts the erivtion struture from hypergrph. Furthermore, DiGen will hve rwing progrm omponent. Then, the user n simply rw igrms y ritrrily omining igrm prts extrte from the speifition. Drwing will e n eitor s efult ehvior when trnsformtions n intertions hve not een speifie, n it will e the prsing lgorithm s tsk to fin the igrms erivtion struture in orer to ientify orret igrms resp. igrm prts. As onsequene, trnsformtions n intertion esriptions my e omitte for rpi prototyping purposes. Speifitions will shrink to 5 20% of the urrent length (see Tle 1), n very rpi prototyping will thus e possile. Of ourse, the user my rw inorret igrms n hs thus less eiting support thn esrie in Setion 4. But sine the prsing lgorithm will point out inorret igrms n igrm prts, this my e permissile for rpi prototyping. Referenes [1] A. Morse n G. Reynols, Overoming urrent growth limits in UI evelopment, Communitions of the ACM, vol. 36, pp , Apr [2] I. Nssi n B. Shneiermn, Flowhrt tehniques for struture progrmming, ACM SIGPLAN Noties, vol. 8, pp , Aug [3] A.A. Khwj n J.E. Urn, Apttion n moifition of Nssi-Shneiermn hrts to represent Desrtes speifitions visully, in 1992 Interntionl Workshop on Rpi Prototyping, Reserh Tringle Prk, NC, June 1992, pp IEEE Computer Soiety Press, [4] B.A. Myers, D.A. Giuse, R.B. Dnnenerg, et l., Grnet - Comprehensive support for grphil, highly intertive user interfes, Computer, vol. 23, pp , Nov [5] F. Arefi, C.E. Hughes, n D.A. Workmn, Automtilly generting visul syntx-irete eitors, Communitions of the ACM, vol. 33, pp , Mr [6] H. Göttler, Grph grmmrs, new prigm for implementing visul lnguges, in N. Dershowitz, eitor, Rewriting Tehniques n Applitions, vol. 355 of Leture Notes in Computer Siene, pp Springer, [7] B.T. Vner Znen, Constrint grmmrs - new moel for speifying grphil pplitions, in K. Bie n C. Lewis, eitors, Pro. CHI 89,vol.20 of SIGCHI Bulletin, pp , Mr [8] C. Berge, Hypergrphs, North-Holln, Amsterm, [9] D. Hrel, tehrts: A visul formlism for omplex systems, Siene of Computer Progrmming, vol. 8, pp , [10] F. Drewes n H.-J. Kreowski, A note on hyperege replement, in H. Ehrig, H.-J. Kreowski, n G. Rozenerg, eitors, Leture Notes in Computer Siene, vol. 532, pp Springer, [11] D.E. Knuth, Semntis of on-free lnguges, Mthemtil Systems Theory, vol. 2, pp , [12] A. Borning, The progrmming lnguge spets of ThingL, onstrint-oriente simultion lortory, ACM Trnstions on Progrmming Lnguges n Systems, vol. 3, pp , Ot [13] M. Mins n G. Viehstet, Speifition of igrm eitors proviing lyout justment with miniml hnge, in Pro IEEE Symposium on Visul Lnguges, pp IEEE Computer Soiety Press, [14] Gerhr Viehstet n Mrk Mins, Intertion in relly grphil user interfes, in Pro IEEE Symposium on Visul Lnguges, pp , Los Almitos, CA, USA, Ot IEEE Computer Soiety Press. [15] T.W. Reps n T. Teitelum, The Synthesizer Genertor, Springer, New York, 1989.

Maximum area of polygon

Maximum area of polygon Mimum re of polygon Suppose I give you n stiks. They might e of ifferent lengths, or the sme length, or some the sme s others, et. Now there re lots of polygons you n form with those stiks. Your jo is

More information

The art of Paperarchitecture (PA). MANUAL

The art of Paperarchitecture (PA). MANUAL The rt of Pperrhiteture (PA). MANUAL Introution Pperrhiteture (PA) is the rt of reting three-imensionl (3D) ojets out of plin piee of pper or ror. At first, esign is rwn (mnully or printe (using grphil

More information

GENERAL OPERATING PRINCIPLES

GENERAL OPERATING PRINCIPLES KEYSECUREPC USER MANUAL N.B.: PRIOR TO READING THIS MANUAL, YOU ARE ADVISED TO READ THE FOLLOWING MANUAL: GENERAL OPERATING PRINCIPLES Der Customer, KeySeurePC is n innovtive prout tht uses ptente tehnology:

More information

1 Fractions from an advanced point of view

1 Fractions from an advanced point of view 1 Frtions from n vne point of view We re going to stuy frtions from the viewpoint of moern lger, or strt lger. Our gol is to evelop eeper unerstning of wht n men. One onsequene of our eeper unerstning

More information

Words Symbols Diagram. abcde. a + b + c + d + e

Words 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 information

MATH PLACEMENT REVIEW GUIDE

MATH PLACEMENT REVIEW GUIDE MATH PLACEMENT REVIEW GUIDE This guie is intene s fous for your review efore tking the plement test. The questions presente here my not e on the plement test. Although si skills lultor is provie for your

More information

SECTION 7-2 Law of Cosines

SECTION 7-2 Law of Cosines 516 7 Additionl Topis in Trigonometry h d sin s () tn h h d 50. Surveying. The lyout in the figure t right is used to determine n inessile height h when seline d in plne perpendiulr to h n e estlished

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

JCM TRAINING OVERVIEW Multi-Download Module 2

JCM TRAINING OVERVIEW Multi-Download Module 2 Multi-Downlo Moule 2 JCM Trining Overview Mrh, 2012 Mrh, 2012 CLOSING THE MDM2 APPLICATION To lose the MDM2 Applition proee s follows: 1. Mouse-lik on the 'File' pullown Menu (See Figure 35 ) on the MDM2

More information

S-Scrum: a Secure Methodology for Agile Development of Web Services

S-Scrum: a Secure Methodology for Agile Development of Web Services Worl of Computer Siene n Informtion Tehnology Journl (WCSIT) ISSN: 2221-0741 Vol. 3, No. 1, 15-19, 2013 S-Srum: Seure Methoology for Agile Development of We Servies Dvou Mougouei, Nor Fzli Moh Sni, Mohmm

More information

OUTLINE SYSTEM-ON-CHIP DESIGN. GETTING STARTED WITH VHDL August 31, 2015 GAJSKI S Y-CHART (1983) TOP-DOWN DESIGN (1)

OUTLINE SYSTEM-ON-CHIP DESIGN. GETTING STARTED WITH VHDL August 31, 2015 GAJSKI S Y-CHART (1983) TOP-DOWN DESIGN (1) August 31, 2015 GETTING STARTED WITH VHDL 2 Top-down 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 information

Fluent Merging: A General Technique to Improve Reachability Heuristics and Factored Planning

Fluent Merging: A General Technique to Improve Reachability Heuristics and Factored Planning Fluent Merging: A Generl Tehnique to Improve Rehility Heuristis n Ftore Plnning Menkes vn en Briel Deprtment of Inustril Engineering Arizon Stte University Tempe AZ, 85287-8809 menkes@su.eu Suro Kmhmpti

More information

Angles 2.1. Exercise 2.1... Find the size of the lettered angles. Give reasons for your answers. a) b) c) Example

Angles 2.1. Exercise 2.1... Find the size of the lettered angles. Give reasons for your answers. a) b) c) Example 2.1 Angles Reognise lternte n orresponing ngles Key wors prllel lternte orresponing vertilly opposite Rememer, prllel lines re stright lines whih never meet or ross. The rrows show tht the lines re prllel

More information

Word Wisdom Correlations to the Common Core State Standards, Grade 6

Word Wisdom Correlations to the Common Core State Standards, Grade 6 Reing Stnrs for Informtionl Text Key Ies n Detils 1 Cite textul eviene to support nlysis of wht the text sys expliitly s well s inferenes rwn from the text. 6, 7, 12, 13, 18, 19, 28, 29, 34, 35, 40, 41,

More information

You should have the following for this examination a multiple-choice answer sheet a pen with black or blue ink

You should have the following for this examination a multiple-choice answer sheet a pen with black or blue ink 8575-001 Aess Certifite in English Lnguge Tehing Fountions of English Lnguge Tehing Smple pper 2 You shoul hve the following for this exmintion multiple-hoie nswer sheet pen with lk or lue ink This question

More information

UNIVERSITY AND WORK-STUDY EMPLOYERS WEBSITE USER S GUIDE

UNIVERSITY AND WORK-STUDY EMPLOYERS WEBSITE USER S GUIDE UNIVERSITY AND WORK-STUDY EMPLOYERS WEBSITE USER S GUIDE Tble of Contents 1 Home Pge 1 2 Pge 2 3 Your Control Pnel 3 4 Add New Job (Three-Step Form) 4-6 5 Mnging Job Postings (Mnge Job Pge) 7-8 6 Additionl

More information

Equivalence Checking. Sean Weaver

Equivalence 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 information

PROJECTILE MOTION PRACTICE QUESTIONS (WITH ANSWERS) * challenge questions

PROJECTILE 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 information

- DAY 1 - Website Design and Project Planning

- 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 information

Clause Trees: a Tool for Understanding and Implementing Resolution in Automated Reasoning

Clause Trees: a Tool for Understanding and Implementing Resolution in Automated Reasoning Cluse Trees: Tool for Understnding nd Implementing Resolution in Automted Resoning J. D. Horton nd Brue Spener University of New Brunswik, Frederiton, New Brunswik, Cnd E3B 5A3 emil : jdh@un. nd spener@un.

More information

Data Quality Certification Program Administrator In-Person Session Homework Workbook 2015-2016

Data Quality Certification Program Administrator In-Person Session Homework Workbook 2015-2016 Dt Qulity Certifition Progrm Aministrtor In-Person Session Homework Workook 2015-2016 Plese Note: Version 1.00: Pulishe 9-1-2015 Any exerises tht my e upte fter this printing n e foun online in the DQC

More information

OxCORT v4 Quick Guide Revision Class Reports

OxCORT 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 information

National Firefighter Ability Tests And the National Firefighter Questionnaire

National Firefighter Ability Tests And the National Firefighter Questionnaire Ntionl Firefighter Aility Tests An the Ntionl Firefighter Questionnire PREPARATION AND PRACTICE BOOKLET Setion One: Introution There re three tests n questionnire tht mke up the NFA Tests session, these

More information

KEY SKILLS INFORMATION TECHNOLOGY Level 3. Question Paper. 29 January 9 February 2001

KEY SKILLS INFORMATION TECHNOLOGY Level 3. Question Paper. 29 January 9 February 2001 KEY SKILLS INFORMATION TECHNOLOGY Level 3 Question Pper 29 Jnury 9 Ferury 2001 WHAT YOU NEED This Question Pper An Answer Booklet Aess to omputer, softwre nd printer You my use ilingul ditionry Do NOT

More information

On Equivalence Between Network Topologies

On Equivalence Between Network Topologies On Equivlene Between Network Topologies Tre Ho Deprtment of Eletril Engineering Cliforni Institute of Tehnolog tho@lteh.eu; Mihelle Effros Deprtments of Eletril Engineering Cliforni Institute of Tehnolog

More information

Formal concept analysis-based class hierarchy design in object-oriented software development

Formal concept analysis-based class hierarchy design in object-oriented software development Forml onept nlysis-se lss hierrhy esign in ojet-oriente softwre evelopment Roert Goin 1, Petko Vlthev 2 1 Déprtement informtique, UQAM, C.P. 8888, su. Centre Ville, Montrél (Q), Cn, H3C 3P8 2 DIRO, Université

More information

BUSINESS PROCESS MODEL TRANSFORMATION ISSUES The top 7 adversaries encountered at defining model transformations

BUSINESS PROCESS MODEL TRANSFORMATION ISSUES The top 7 adversaries encountered at defining model transformations USINESS PROCESS MODEL TRANSFORMATION ISSUES The top 7 dversries enountered t defining model trnsformtions Mrion Murzek Women s Postgrdute College for Internet Tehnologies (WIT), Institute of Softwre Tehnology

More information

CSE 1400 Applied Discrete Mathematics Sets

CSE 1400 Applied Discrete Mathematics Sets CSE 1400 Applie Disrete Mthemtis Sets Deprtment of Computer Sienes College of Engineering Flori Teh Fll 2011 Set Bsis 1 Common Sets 3 Opertions On Sets 3 Preeene of Set Opertions 4 Crtesin Prouts 4 Suset

More information

Computing the 3D Voronoi Diagram Robustly: An Easy Explanation

Computing the 3D Voronoi Diagram Robustly: An Easy Explanation Computing the 3D Voronoi Digrm Roustly: An Esy Explntion Hugo Leoux Delft University of Tehnology (OTB setion GIS Tehnology) Jffln 9, 2628BX Delft, the Netherlns h.leoux@tuelft.nl Astrt Mny lgorithms exist

More information

Active Directory Service

Active 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) 967-3498. Or. Mil the nswers to the following

More information

1. Area under a curve region bounded by the given function, vertical lines and the x axis.

1. Area under a curve region bounded by the given function, vertical lines and the x axis. Ares y Integrtion. Are uner urve region oune y the given funtion, vertil lines n the is.. Are uner urve region oune y the given funtion, horizontl lines n the y is.. Are etween urves efine y two given

More information

2. Use of Internet attacks in terrorist activities is termed as a. Internet-attack b. National attack c. Cyberterrorism d.

2. Use of Internet attacks in terrorist activities is termed as a. Internet-attack 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 information

Arc-Consistency for Non-Binary Dynamic CSPs

Arc-Consistency for Non-Binary Dynamic CSPs Ar-Consisteny for Non-Binry Dynmi CSPs Christin Bessière LIRMM (UMR C 9928 CNRS / Université Montpellier II) 860, rue de Sint Priest 34090 Montpellier, Frne Emil: essiere@rim.fr Astrt. Constrint stisftion

More information

Orthopoles and the Pappus Theorem

Orthopoles and the Pappus Theorem Forum Geometriorum Volume 4 (2004) 53 59. FORUM GEOM ISSN 1534-1178 Orthopoles n the Pppus Theorem tul Dixit n Drij Grinerg strt. If the verties of tringle re projete onto given line, the perpeniulrs from

More information

Lesson 1: Getting started

Lesson 1: Getting started Answer key 0 Lesson 1: Getting strte 1 List the three min wys you enter t in QuikBooks. Forms, lists, registers 2 List three wys to ess fetures in QuikBooks. Menu r, Ion Br, Centers, Home pge 3 Wht ookkeeping

More information

Quick Guide to Lisp Implementation

Quick Guide to Lisp Implementation isp Implementtion Hndout Pge 1 o 10 Quik Guide to isp Implementtion Representtion o si dt strutures isp dt strutures re lled S-epressions. The representtion o n S-epression n e roken into two piees, the

More information

Ratio and Proportion

Ratio 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 information

1. Definition, Basic concepts, Types 2. Addition and Subtraction of Matrices 3. Scalar Multiplication 4. Assignment and answer key 5.

1. 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 information

Lesson 2.1 Inductive Reasoning

Lesson 2.1 Inductive Reasoning Lesson.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 1, 16,,. 400, 00, 100, 0,,,. 1 8, 7, 1, 4,, 4.,,, 1, 1, 0,,. 60, 180, 10,

More information

Chapter. Contents: A Constructing decimal numbers

Chapter. Contents: A Constructing decimal numbers Chpter 9 Deimls Contents: A Construting deiml numers B Representing deiml numers C Deiml urreny D Using numer line E Ordering deimls F Rounding deiml numers G Converting deimls to frtions H Converting

More information

Module 5. Three-phase AC Circuits. Version 2 EE IIT, Kharagpur

Module 5. Three-phase AC Circuits. Version 2 EE IIT, Kharagpur Module 5 Three-hse A iruits Version EE IIT, Khrgur esson 8 Three-hse Blned Suly Version EE IIT, Khrgur In the module, ontining six lessons (-7), the study of iruits, onsisting of the liner elements resistne,

More information

SOLVING EQUATIONS BY FACTORING

SOLVING EQUATIONS BY FACTORING 316 (5-60) 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 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

ORGANIZER QUICK START GUIDE

ORGANIZER QUICK START GUIDE NOTES ON USING GOTOWEBINAR GoToWeinr orgnizers my hol Weinrs for up to 1,000 ttenees. The Weinr proess n e roken into three stges: Weinr Plnning, Weinr Presenttion n Weinr Follow-up. Orgnizers nee to first

More information

Interior and exterior angles add up to 180. Level 5 exterior angle

Interior and exterior angles add up to 180. Level 5 exterior angle 22 ngles n proof Ientify interior n exterior ngles in tringles n qurilterls lulte interior n exterior ngles of tringles n qurilterls Unerstn the ie of proof Reognise the ifferene etween onventions, efinitions

More information

PLWAP Sequential Mining: Open Source Code

PLWAP 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 information

ORGANIZER QUICK REFERENCE GUIDE

ORGANIZER 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 information

Data Security 1. 1 What is the function of the Jump instruction? 2 What are the main parts of the virus code? 3 What is the last act of the virus?

Data Security 1. 1 What is the function of the Jump instruction? 2 What are the main parts of the virus code? 3 What is the last act of the virus? UNIT 18 Dt Seurity 1 STARTER Wht stories do you think followed these hedlines? Compre nswers within your group. 1 Love ug retes worldwide hos. 2 Hkers rk Mirosoft softwre odes. 3 We phone sm. Wht other

More information

c b 5.00 10 5 N/m 2 (0.120 m 3 0.200 m 3 ), = 4.00 10 4 J. W total = W a b + W b c 2.00

c b 5.00 10 5 N/m 2 (0.120 m 3 0.200 m 3 ), = 4.00 10 4 J. W total = W a b + W b c 2.00 Chter 19, exmle rolems: (19.06) A gs undergoes two roesses. First: onstnt volume @ 0.200 m 3, isohori. Pressure inreses from 2.00 10 5 P to 5.00 10 5 P. Seond: Constnt ressure @ 5.00 10 5 P, isori. olume

More information

Application Note Configuring Integrated Windows Authentication as a McAfee Firewall Enterprise Authenticator. Firewall Enterprise

Application Note Configuring Integrated Windows Authentication as a McAfee Firewall Enterprise Authenticator. Firewall Enterprise Applition Note Configuring Integrte Winows Authentition s MAfee Firewll Enterprise Authentitor MAfee version 7.x n 8.x Firewll Enterprise Use this Applition Note to implement trnsprent rowser uthentition

More information

ORGANIZER QUICK REFERENCE GUIDE

ORGANIZER 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 information

WHAT HAPPENS WHEN YOU MIX COMPLEX NUMBERS WITH PRIME NUMBERS?

WHAT HAPPENS WHEN YOU MIX COMPLEX NUMBERS WITH PRIME NUMBERS? WHAT HAPPES WHE YOU MIX COMPLEX UMBERS WITH PRIME UMBERS? There s n ol syng, you n t pples n ornges. Mthemtns hte n t; they love to throw pples n ornges nto foo proessor n see wht hppens. Sometmes they

More information

Return of Organization Exempt From Income Tax

Return of Organization Exempt From Income Tax PUBLIC DISCLOSURE COPY Form 99 Return of Orgniztion Exempt From Inome Tx Uner setion 51, 527, or 4947(1) of the Internl Revenue Coe (exept privte fountions) OMB 1545-47 Do not enter Soil Seurity numers

More information

A dynamically SVC based compact control algorithm for load balancing in distribution systems

A 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 pitor-thyristorontrolled

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

Multi-level Visualization of Concurrent and Distributed Computation in Erlang

Multi-level Visualization of Concurrent and Distributed Computation in Erlang Multi-level Visuliztion of Conurrent nd Distriuted Computtion in Erlng Roert Bker r440@kent..uk Peter Rodgers P.J.Rodgers@kent..uk Simon Thompson S.J.Thompson@kent..uk Huiqing Li H.Li@kent..uk Astrt This

More information

Student Access to Virtual Desktops from personally owned Windows computers

Student 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 information

Corrigendum-II Dated:19.05.2011

Corrigendum-II Dated:19.05.2011 10(21)/2010-NICSI NATIONAL INFORMATICS CENTRE SERVICES In. (NICSI) (A Government of Ini Enterprise uner NIC) Ministry of Communition & Informtion Tehnology Hll 2 & 3, 6 th Floor, NBCC Tower 15, Bhikiji

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

Revised products from the Medicare Learning Network (MLN) ICD-10-CM/PCS Myths and Facts, Fact Sheet, ICN 902143, downloadable.

Revised products from the Medicare Learning Network (MLN) ICD-10-CM/PCS Myths and Facts, Fact Sheet, ICN 902143, downloadable. DEPARTMENT OF HEALTH AND HUMAN SERVICES Centers for Meire & Meii Servies Revise prouts from the Meire Lerning Network (MLN) ICD-10-CM/PCS Myths n Fts, Ft Sheet, ICN 902143, ownlole. MLN Mtters Numer: SE1325

More information

DATABASDESIGN FÖR INGENJÖRER - 1056F

DATABASDESIGN FÖR INGENJÖRER - 1056F DATABASDESIGN FÖR INGENJÖRER - 06F Sommr 00 En introuktionskurs i tssystem http://user.it.uu.se/~ul/t-sommr0/ lt. http://www.it.uu.se/eu/course/homepge/esign/st0/ Kjell Orsorn (Rusln Fomkin) Uppsl Dtse

More information

European Convention on Products Liability in regard to Personal Injury and Death

European 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 information

Notes on Excess Burden (EB) most efficient lowest deadweight loss excess burden non-distorting tax system benchmark

Notes on Excess Burden (EB) most efficient lowest deadweight loss excess burden non-distorting tax system benchmark Notes on Exess Buren (EB) Our gol is to lulte the exess uren of tx system. This will llow us to juge one tx system ginst nother. All txes use inome effets simply euse they tke money wy tht oul hve een

More information

Start Here. Quick Setup Guide. the machine and check the components. NOTE Not all models are available in all countries.

Start Here. Quick Setup Guide. the machine and check the components. NOTE Not all models are available in all countries. Quik Setup Guie Strt Here MFC-9130CW / MFC-9330CDW MFC-9340CDW Thnk you for hoosing Brother, your support is importnt to us n we vlue your usiness. Your Brother prout is engineere n mnufture to the highest

More information

control policies to be declared over by associating security

control policies to be declared over by associating security Seure XML Querying with Seurity Views Wenfei Fn University of Edinurgh & Bell Lortories wenfei@infeduk Chee-Yong Chn Ntionl University of Singpore hny@ompnusedusg Minos Groflkis Bell Lortories minos@reserhell-lsom

More information

The remaining two sides of the right triangle are called the legs of the right triangle.

The remaining two sides of the right triangle are called the legs of the right triangle. 10 MODULE 6. RADICAL EXPRESSIONS 6 Pythgoren Theorem The Pythgoren Theorem An ngle tht mesures 90 degrees is lled right ngle. If one of the ngles of tringle is right ngle, then the tringle is lled right

More information

the machine and check the components Black Yellow Cyan Magenta Product Registration Sheet (USA only)

the machine and check the components Black Yellow Cyan Magenta Product Registration Sheet (USA only) Quik Setup Guie Strt Here MFC-J825DW MFC-J835DW Thnk you for hoosing Brother, your support is importnt to us n we vlue your usiness. Your Brother prout is engineere n mnufture to the highest stnrs to eliver

More information

Lecture 3: orientation. Computer Animation

Lecture 3: orientation. Computer Animation Leture 3: orienttion Computer Animtion Mop tutoril sessions Next Thursdy (Feb ) Tem distribution: : - :3 - Tems 7, 8, 9 :3 - : - Tems nd : - :3 - Tems 5 nd 6 :3 - : - Tems 3 nd 4 Pper ssignments Pper ssignment

More information

1 GSW IPv4 Addressing

1 GSW IPv4 Addressing 1 For s long s I ve een working with the Internet protools, people hve een sying tht IPv6 will e repling IPv4 in ouple of yers time. While this remins true, it s worth knowing out IPv4 ddresses. Even when

More information

Return of Organization Exempt From Income Tax

Return of Organization Exempt From Income Tax Form 990 Deprtment of the Tresury Internl Revenue Servie Return of Orgniztion Exempt From Inome Tx Uner setion 501(), 527, or 4947()(1) of the Interni Revenue Coe (exept lk lung enefit trust or privte

More information

Before you can use the machine, please read this Quick Setup Guide for the correct setup and installation.

Before you can use the machine, please read this Quick Setup Guide for the correct setup and installation. Quik Setup Guide Strt Here DCP-365CN DCP-373CW DCP-375CW DCP-377CW Before you n use the mhine, plese red this Quik Setup Guide for the orret setup nd instlltion. WARNING CAUTION Wrnings tell you wht to

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

McAfee Network Security Platform

McAfee Network Security Platform XC-240 Lod Blner Appline Quik Strt Guide Revision D MAfee Network Seurity Pltform This quik strt guide explins how to quikly set up nd tivte your MAfee Network Seurity Pltform XC-240 Lod Blner. The SFP+

More information

Enterprise Digital Signage Create a New Sign

Enterprise 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 information

Vectors Summary. Projection vector AC = ( Shortest distance from B to line A C D [OR = where m1. and m

Vectors Summary. Projection vector AC = ( Shortest distance from B to line A C D [OR = where m1. and m . Slr prout (ot prout): = osθ Vetors Summry Lws of ot prout: (i) = (ii) ( ) = = (iii) = (ngle etween two ientil vetors is egrees) (iv) = n re perpeniulr Applitions: (i) Projetion vetor: B Length of projetion

More information

Forensic Engineering Techniques for VLSI CAD Tools

Forensic Engineering Techniques for VLSI CAD Tools Forensi Engineering Tehniques for VLSI CAD Tools Jennifer L. Wong, Drko Kirovski, Dvi Liu, Miorg Potkonjk UCLA Computer Siene Deprtment University of Cliforni, Los Angeles June 8, 2000 Computtionl Forensi

More information

CHAPTER 31 CAPACITOR

CHAPTER 31 CAPACITOR . Given tht Numer of eletron HPTER PITOR Net hrge Q.6 9.6 7 The net potentil ifferene L..6 pitne v 7.6 8 F.. r 5 m. m 8.854 5.4 6.95 5 F... Let the rius of the is R re R D mm m 8.85 r r 8.85 4. 5 m.5 m

More information

Review guide for the final exam in Math 233

Review guide for the final exam in Math 233 Review guide for the finl exm in Mth 33 1 Bsic mteril. This review includes the reminder of the mteril for mth 33. The finl exm will be cumultive exm with mny of the problems coming from the mteril covered

More information

Practice Test 2. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn

Practice Test 2. a. 12 kn b. 17 kn c. 13 kn d. 5.0 kn e. 49 kn Prtie Test 2 1. A highwy urve hs rdius of 0.14 km nd is unnked. A r weighing 12 kn goes round the urve t speed of 24 m/s without slipping. Wht is the mgnitude of the horizontl fore of the rod on the r?

More information

the machine and check the components Black Yellow Cyan Magenta Starter Ink Cartridges Product Registration Sheet (USA only)

the machine and check the components Black Yellow Cyan Magenta Starter Ink Cartridges Product Registration Sheet (USA only) Quik Setup Guide Strt Here DCP-J140W Thnk you for hoosing Brother, your support is importnt to us nd we vlue your usiness. Your Brother produt is engineered nd mnuftured to the highest stndrds to deliver

More information

Calculating Principal Strains using a Rectangular Strain Gage Rosette

Calculating 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 information

Finite Automata. Informatics 2A: Lecture 3. John Longley. 25 September School of Informatics University of Edinburgh

Finite Automata. Informatics 2A: Lecture 3. John Longley. 25 September School of Informatics University of Edinburgh Lnguges nd Automt Finite Automt Informtics 2A: Lecture 3 John Longley School of Informtics University of Edinburgh jrl@inf.ed.c.uk 25 September 2015 1 / 30 Lnguges nd Automt 1 Lnguges nd Automt Wht is

More information

On the Utilization of Spatial Structures for Cognitively Plausible and Efficient Reasoning

On the Utilization of Spatial Structures for Cognitively Plausible and Efficient Reasoning To pper in: Proeeings of the IEEE Interntionl Conferene on Systems, Mn, n Cyernetis. Chigo, 18-21 Otoer 1992. On the Utiliztion of Sptil Strutures for Cognitively Plusile n Effiient Resoning Christin Freks

More information

Rotating DC Motors Part II

Rotating DC Motors Part II Rotting Motors rt II II.1 Motor Equivlent Circuit The next step in our consiertion of motors is to evelop n equivlent circuit which cn be use to better unerstn motor opertion. The rmtures in rel motors

More information

A sufficient statistic approach to disability insurance with application to the United States Social Security Disability Insurance program

A sufficient statistic approach to disability insurance with application to the United States Social Security Disability Insurance program Insurne Mrkets n Compnies: Anlyses n Aturil Computtions, Volume, Issue, 202 Henry R. Hytt (USA) A suffiient sttisti pproh to isility insurne with pplition to the Unite Sttes Soil Seurity Disility Insurne

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

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

Bypassing Space Explosion in Regular Expression Matching for Network Intrusion Detection and Prevention Systems

Bypassing Space Explosion in Regular Expression Matching for Network Intrusion Detection and Prevention Systems Bypssing Spce Explosion in Regulr Expression Mtching for Network Intrusion Detection n Prevention Systems Jignesh Ptel, Alex Liu n Eric Torng Dept. of Computer Science n Engineering Michign Stte University

More information

Innovation in Software Development Process by Introducing Toyota Production System

Innovation 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 information

Start Here. Quick Setup Guide MFC-9460CDN MFC-9465CDN. the machine and check the components WARNING CAUTION. Note

Start Here. Quick Setup Guide MFC-9460CDN MFC-9465CDN. the machine and check the components WARNING CAUTION. Note Quik Setup Guie Strt Here MFC-9460CDN MFC-9465CDN Before using this mhine for the first time, re this Quik Setup Guie to setup n instll your mhine. To view the Quik Setup Guie in other lnguges, plese visit

More information

the machine and check the components Black Yellow Cyan Magenta

the machine and check the components Black Yellow Cyan Magenta Quik Setup Guie Strt Here MFC-J425W MFC-J430W MFC-J435W Thnk you for hoosing Brother, your support is importnt to us n we vlue your usiness. Your Brother prout is engineere n mnufture to the highest stnrs

More information

The Cat in the Hat. by Dr. Seuss. A a. B b. A a. Rich Vocabulary. Learning Ab Rhyming

The Cat in the Hat. by Dr. Seuss. A a. B b. A a. Rich Vocabulary. Learning Ab Rhyming MINI-LESSON IN TION The t in the Ht y Dr. Seuss Rih Voulry tme dj. esy to hndle (not wild) LERNING Lerning Rhyming OUT Words I know it is wet nd the sun is not sunny. ut we n hve Lots of good fun tht is

More information

Lock Free Linked List using Compare & Swap. Final Project Distributed Algorithms and Systems

Lock Free Linked List using Compare & Swap. Final Project Distributed Algorithms and Systems Lok Free Linke List using Compre & Swp Finl Projet Distriute Algorithms n Systems Lwrene Bush Computer Siene Deprtment Rensseler Polytehni Institute Troy, New York April 30, 2002 Astrt For my projet, I

More information

Stroke-Based Performance Metrics for Handwritten Mathematical Expressions

Stroke-Based Performance Metrics for Handwritten Mathematical Expressions Stroke-Bse Performnce Metrics for Hnwritten Mthemticl Expressions Richr Znii rlz@cs.rit.eu Amit Pilly p2731@rit.eu eprtment of Computer Science Rochester Institute of Technology, NY, SA Hrol Mouchère hrol.mouchere@univ-nntes.fr

More information

VMware Horizon FLEX Administration Guide

VMware 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 information

THE LONGITUDINAL FIELD IN THE GTEM 1750 AND THE NATURE OF THE TERMINATION.

THE 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 information

Unit 6: Exponents and Radicals

Unit 6: Exponents and Radicals Eponents nd Rdicls -: The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N): - counting numers. {,,,,, } Whole Numers (W): - counting numers with 0. {0,,,,,, } Integers (I): -

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

Volumes by Cylindrical Shells: the Shell Method

Volumes by Cylindrical Shells: the Shell Method olumes Clinril Shells: the Shell Metho Another metho of fin the volumes of solis of revolution is the shell metho. It n usull fin volumes tht re otherwise iffiult to evlute using the Dis / Wsher metho.

More information

the machine and check the components Starter Ink Cartridges Basic User s Guide Product Safety Guide Telephone Line Cord

the machine and check the components Starter Ink Cartridges Basic User s Guide Product Safety Guide Telephone Line Cord Quik Setup Guide Strt Here MFC-J450DW MFC-J470DW Thnk you for hoosing Brother, your support is importnt to us nd we vlue your usiness. Your Brother produt is engineered nd mnuftured to the highest stndrds

More information