Computación y Sistemas ISSN: Instituto Politécnico Nacional México


 Lauren Clarke
 10 months ago
 Views:
Transcription
1 Computción y Sistems ISSN: Instituto Politécnico Ncionl México Btyrshin, Ildr Z.; Kubyshev, Nily; Solovyev, Vlery; VillVrgs, Luis A. Visuliztion of Similrity Mesures for Binry Dt nd 2 x 2 Tbles Computción y Sistems, vol. 20, núm. 3, 2016, pp Instituto Politécnico Ncionl Distrito Federl, México Avilble in: How to cite Complete issue More informtion bout this rticle Journl's homepge in redlyc.org Scientific Informtion System Network of Scientific Journls from Ltin Americ, the Cribben, Spin nd Portugl Nonprofit cdemic project, developed under the open ccess inititive
2 Visuliztion of Similrity Mesures for Binry Dt nd 2 x 2 Tbles Ildr Z. Btyrshin 1, Nily Kubyshev 1, Vlery Solovyev 2, Luis A. VillVrgs 1 1 Instituto Politécnico Ncionl, México, Centro de Investigción en Computción (CIC), Mexico 2 Kzn Federl University, Kzn, Russi Abstrct. We propose methods of 3D visuliztion of the min similrity mesures for binry dt nd 2 x 2 tbles. We present the shpes of Jccrd, Dice, Sokl & Sneth, Roger & Tnimoto nd other similrity mesures. Such visuliztion of the similrity mesures gives the direct, visul, method of comprison of these mesures nd helps to understnd the similrity nd the difference between them. Bsed on the visuliztion of the two known prmetric fmilies of similrity mesures the pper proposes the new prmetric fmily of mesures generlizing these two fmilies nd giving the possibility to construct similrity mesures occupying the intermedite position between them. Keywords. Similrity mesure, binry vrible, contingency tble, visuliztion. 1 Introduction Similrity mesures hve numerous pplictions in computtionl linguistics, ecology, medicine, biology, socil sciences, etc. They ply importnt role in pttern recognition, mchine lerning, clssifiction nd sttistics [1, 57, 10, 1214, 16, 18, 19]. Dozens of similrity (or dissimilrity) mesures for binry dt hve been proposed nd the problem of their comprison nd selection for specific ppliction is studied in mny works [210, 15, 1720]. In different ppers, such mesures re referred to s ssocition coefficients, similrity coefficients, resemblnce mesures etc. Different pproches for compring similrity mesures re bsed on: similrity of the properties of these mesures, similrity of formuls, possibility of trnsformtion of one mesure into nother one, ordering of the mesures, distnce between them etc. [2, 3, 612,1820]. To the best of our knowledge, there re not works on 3D visuliztion of the binry similrity mesures. Such visuliztion cn be useful for compring the shpes of similrity mesures nd selecting mesure more suitble for specific pplictions. The pper proposes the methods of 3D visuliztion of the most populr similrity mesures used for binry dt nd 2 x 2 tbles. Such visuliztion of similrity mesures gives the direct, visul, method of comprison of these mesures nd cn help to understnd the similrity nd the difference between them. Severl uthors hve proposed different prmetric fmilies of similrity nd dissimilrity mesures [3, 9, 19, 20]. Bsed on the visuliztion of the two known prmetric fmilies of similrity mesures the pper proposes the new prmetric fmily of the similrity mesures generlizing these two fmilies nd giving possibility to construct similrity mesures occupying intermedite position between them. The pper hs the following structure. Section 2 considers some bsic definition relted with the similrity mesures for binry dt nd describes the most populr similrity mesures. Section 3 proposes the methods of 3D visuliztion of similrity mesures for binry dt nd visulize the most populr mesures. Section 4 proposes the new prmetric fmily of similrity mesures. The lst section contins discussion nd conclusion.
3 346 Ildr Z. Btyrshin, Nily Kubyshev, Vlery Solovyev, Luis A. VillVrgs 2 Bsic Definitions Consider objects described by n binry ttributes, descriptors or properties. The object x is coded by the vector x = (x 1,, x n ) of n ttribute vlues such tht x k = 1 if the object possesses the property k nd x k = 0 otherwise. Such dt re clled lso presence/bsence dt [8, 11]. For ny two objects x = (x 1,, x n ) nd y = (y 1,, y n ) the following four numbers re clculted: is the number of ttributes such tht x k = 1, y k = 1; b is the number of ttributes such tht x k = 1, y k = 0; c is the number of ttributes such tht x k = 0, y k = 1; d is the number of ttributes such tht x k = 0, y k = 0. The numbers nd d lso referred to s the numbers of positive nd negtive mtches, correspondingly [9, 17]. Note tht the following is fulfilled for these four number: + b + c + d = n, (1) where n is the number of binry ttributes. These four numbers re represented in Tble 1 lso known s 2 2 contingency tble [1]. Below there re presented some populr similrity mesures defined for such tbles [4, 5, 10]. Jccrd (1908): S J (x, y) = +b+c. (2) Dice (1945), Czeknowski (1913), Sorensen (1948): S CDS (x, y) = Sokl & Sneth (1963): S SS I (x, y) = 2 2+b+c. (3) +2b+2c. (4) Sokl & Michener (1958) or simple mtching : x S SM (x, y) = +d +b+c+d Rogers & Tnimoto (1960): S RT (x, y) = Sokl & Sneth (1963): S SS II (x, y) = Rssel & Ro (1940): Fith (1983): Tble 1. 2 x 2 contingency tble S RR (x, y) = +d +2b+2c+d 2+2d 2+b+c+2d +b+c+d S F (x, y) = +0.5d +b+c+d 3 Visuliztion of Similrity Mesures (5) (6) (7) (8) (9) Let us consider prmetric fmilies of similrity mesures tht include the known similrity mesures s prticulr cses [9, 20]. The similrity mesures (2)(4) cn be generlized s follows: T θ = +θ(b+c), (10) where θ is some positive rel number. The similrity mesures (5)(7) cn be considered s the prticulr cses of the following prmetric fmily of functions: S θ = +d +d+θ(b+c), (11) y b 0 c d
4 Visuliztion of Similrity Mesures for Binry Dt nd 2 x 2 Tbles 347 Fig. 1(). Jccrd similrity mesure (view 1) Fig. 1(b). Jccrd similrity mesure (view 2) Fig. 2(). Rogers & Tnimoto similrity mesure (view 1) Fig. 2(b). Rogers & Tnimoto similrity mesure (view 2) For us it will be more convenient to use the following nottion of these prmetric fmilies of similrity mesures: S () (x, y) = +t(b+c), (12) S (+d) (x, y) = +d +d+t(b+c), (13) where t is some positive rel number. The similrity mesures (2)(4) re obtined from (12) for the prmeter vlues t= 1, 0.5, 2, correspondingly. The similrity mesures (5)(7) re obtined from (13)
5 348 Ildr Z. Btyrshin, Nily Kubyshev, Vlery Solovyev, Luis A. VillVrgs for the prmeter vlues t= 1, 2, 0.5, correspondingly. Tking into ccount tht from (1) it follows b + c = n ( + d), (14) the formuls (12) nd (13) cn be given in such form: S () (x, y) = S (+d) (x, y) = +t(n d), (15) +d +d+t(n d), (16) The prmetric fmilies of the similrity mesures (15) nd (16) hve been considered in [20] in the following forms: S (A) (x, y) = S (A+D) (x, y) = A A+θ(1 A D), (17) A+D A+D+θ(1 A D), (18) where A =, D = d. Further we will use the n n formuls (15) nd (16) for the considered prmetric fmilies of similrity mesures tht will be referred to s ()fmily nd (+d)fmily of similrity mesures, correspondingly. We propose to use the reltionship (14) for representtion of other similrity mesures. The similrity mesures (8) nd (9) do not belong to the considered fmilies of mesures, but, using the reltion (1), they lso cn be written s the functions of nd d: S RR (x, y) = n, (19) S F (x, y) = +0.5d. (20) n As it is cler from the formuls (15), (16), (19), (20) for fixed numbers n nd t one cn build ll of these formuls in 3D spce s the functions of 2 vribles nd d. (The formul (19) will depend relly only from ). From (1) nd (14) we obtin: 0 + d n. (21) This condition defines restrictions on the domin of the considered functions. In ll figures below we use the vlue n = 100 nd build the grphics of ll functions for vlues nd d chnging from 0 to 100 with the step 1, with the domin restriction (21). Figures 1() nd 1(b) show in two different projections Jccrd similrity mesure obtined from the prmetric formuls (12) nd (15) for prmeter vlue t=1 s follows: S J (x, y) = n d. (22) The domin (21) is presented on the plne S=0 by tringle with bold sides. Two blck lines show the profiles of the surfce of the similrity mesure: 1) for vlue =50 nd ll vlues of d; 2) for vlue d=50 nd ll vlues of. The vlue S = 0.5 depicts the vlue of the mesure S for = 50 nd d= 0. When d = 0 we obtin in (22) S=/n tht corresponds on Figure 1() to the line incresing from 0 to 1 when d=0 nd is incresing from 0 to 100. Figure 1(b) is obtined from Figure 1() by rottion of the xis to show the profile of the surfce for smll vlues of nd lrge vlues of d. This sitution corresponds to lrge number of negtive mtches d nd hence to smll vlues of nomintor nd denomintor in (2). The similr comments cn be done for the figures of other similrity mesures shown lter. Figures 2() nd 2(b) show two projections of Rogers & Tnimoto similrity mesure. From (6), (13) nd (16) we obtin for t=2: S RT (x, y) = +d 2n d. (23) Figure 3 shows the surfces of the following similrity mesures belonging to the prmetric ()fmily of mesures (from the left to the right): 1) DiceCzeknowskiSorensen, 2) Jccrd, 3) SoklSnethI. Figure 4 shows the surfces of the following similrity mesures belonging to the prmetric (+d)fmily of mesures (from the left to the right): 1) SoklSnethII, 2) Sokl & Michener, 3) Rogers nd Tnimoto. For ll of these similrity mesures the formuls like (22) nd (23) cn be esily obtined from their originl definitions by replcement b+c by nd, see (1) nd (14).
6 Visuliztion of Similrity Mesures for Binry Dt nd 2 x 2 Tbles 349 Fig. 3. ()fmily of similrity mesures in 2 views Fig. 4. (+d)fmily of similrity mesures in 2 views Figure 5 depicts the surfces of Rssel & Ro nd Fith mesures in the sme projection s the similrity mesures shown on Figures 1() nd 2(). Rssel & Ro nd Fith mesures do not belong nor to ()fmily nor to (+d)fmily of similrity mesures nd one cn see tht they
7 350 Ildr Z. Btyrshin, Nily Kubyshev, Vlery Solovyev, Luis A. VillVrgs Fig. 5. Russel & Ro (on the left side) nd Fith (on the right side) similrity mesures Fig. 6. (+pd)fmily of similrity mesures: Jccrd (on the left side) nd Sokl & Michener (on the right side) Fig. 7. (+pd)fmily of similrity mesures: Dice & Czeknowski & Sorensen (on the left side) nd Sokl & Sneth II (on the right side) hve the shpes quite different from the shpes of similrity mesures from these fmilies shown on Figure 3 nd 4. The min problem with these two mesures tht they do not stisfy the reflexivity property S(x,x)= 1 tht requires tht reflexive similrity mesure should hve the vlue 1 on the border of the domin where +d= n nd b= c= 0. One cn see tht the similrity mesures both from ()fmily nd from (+d)fmily re reflexive.
8 Visuliztion of Similrity Mesures for Binry Dt nd 2 x 2 Tbles 351 Fig. 8. (+pd)fmily of similrity mesures: Sokl & Sneth I (on the left side) nd Rogers & Tnimoto (on the right side) 4 New Prmetric Fmily of Similrity Mesures As one cn see from Figures 3 nd 4 the shpes of the similrity mesures from ()fmily nd (+d)fmily re sufficiently different. The similrity mesures S(x,y) from ()fmily re bsed on the positive mtches of binry ttributes in x nd y. The similrity mesures from (+d)fmily re bsed both on positive nd on negtive mtches. Discussions pro nd contr of these two types of similrities mesures cn be found for exmple in [5, 10, 17, 19]. We propose the new prmetric fmily of binry similrity mesures formlly generlizing both these fmilies nd giving the possibility to build the similrity mesures intermedite between these two fmilies. Below re the two equivlent forms of the new prmetric fmily of mesures clled (+pd)fmily: S (+pd) (x, y) = S (+pd) (x, y) = +pd +pd+t(b+c), (24) +pd +pd+t(n d), (25) where t is the positive rel number nd p is the number from the intervl [0,1]. When p = 0 we obtin the ()fmily of similrity mesures nd when p = 1 we obtin the (+d) fmily of similrity mesures. Chnging prmeter p between 0 nd 1 one cn move similrity mesure from ()fmily to (+d) fmily. Generlly, the prmeters p nd t cn be tuned in some procedure of selection of suitble similrity mesure for specific ppliction. The selected vlue of the prmeter p cn reflect the trdeoff or reltive importnce of positive nd negtive mtches in the constructed similrity mesure. Figures 6, 7, 8 show the shpes of binry similrity mesures from (+pd)fmily when prmeter p is chnged from 0 (on the left sides) to 1 (on the right sides) such tht on the left sides we hve similrity mesures from ()fmily nd on the right sides the mesures from (+d)fmily. The prmeter t hs the vlues 1, 0.5 nd 2 on Figures 6, 7 nd 8, respectively. On Figure 6. the similty mesures re chnged from Jccrd (on the left side) to Sokl & Michener (on the right side). On Figure 7. the similty mesures re chnged from Dice & Czeknowski & Sorensen (on the left side) nd Sokl & Sneth II (on the right side). On Figure 8. the similty mesures re chnged from Sokl & Sneth I (on the left side) nd Rogers & Tnimoto (on the right side). 5 Discussion nd Conclusion The pper proposes the methods of visuliztion of the populr similrity mesures for binry dt nd contingency 2 x 2 tbles. Such visuliztion
9 352 Ildr Z. Btyrshin, Nily Kubyshev, Vlery Solovyev, Luis A. VillVrgs helps to understnd the reltionships between these mesures nd cn explin why these similrity mesures joined in clusters of similr mesures obtined in different works where the clustering of these mesures is pplied [6,12]. The new prmetric fmily of the similrity mesures is proposed. This fmily generlizes the two known prmetric fmilies of similrity mesures nd gives the possibility to construct similrity mesures intermedite between these two fmilies. Such intermedite position cn reflect the trdeoff or reltive importnce of positive nd negtive mtches in the construction of similrity mesures from the new prmetric clss of similrity mesures. The proposed methodology of visuliztion of binry similrity mesures cn be extended on other binry similrity nd ssocition mesures considered in literture. Acknowledgements The work is prtilly supported by the projects SIP of IPN, of CONACYT, Mexico, by RFBR project nd by the Russin Government Progrm of competitive growth of Kzn Federl University. References 1. Agresti, A. (2002). Ctegoricl dt nlysis. Wiley nd Sons. 2. Btgelj, V. & Bren, M. (1995). Compring resemblnce mesures. Journl of Clssifiction, Vol. 12, No. 1, pp DOI: /BF Bulieu, F.B. (1989). A clssifiction of presence/bsence bsed dissimilrity coefficients. Journl of Clssifiction, Vol. 6, No. 1, pp DOI: /BF Choi, S.S., Ch, S.H., & Chrles, C.T. (2010). A survey of binry similrity nd distnce mesures. Journl of Systemics, Cybernetics nd Informtics, pp Clifford, H.T. & Stephenson, W. (1975). An introduction to numericl clssifiction (Vol. 229). New York: Acdemic Press. 6. Durte, J.M., Sntos, J.B.D., & Melo, L.C. (1999). Comprison of similrity coefficients bsed on RAPD mrkers in the common ben. Genetics nd Moleculr Biology, Vol. 22, No. 3, pp DOI: /S Goodmn, L.A. & Kruskl, W.H. (1954). Mesures of ssocition for cross clssifictions. Journl of the Americn Sttisticl Assocition, Vol. 49, pp DOI: / _1. 8. Gower, J.C. (1971). A generl coefficient of similrity nd some of its properties. Biometrics, pp Gower, J.C. & Legendre, P. (1986). Metric nd Eucliden properties of dissimilrity coefficients. Journl of clssifiction, Vol. 3, No. 1, pp DOI: /BF Legendre, P. & Legendre, L.F. (1998). Numericl ecology, 2 nd English Ed., Elsevier. 11. Lesot, MJ., Rifqi, M., & Benhdd, H. (2009) Similrity mesures for binry nd numericl dt: survey. Int. J. Knowledge Engineering nd Soft Dt Prdigms, Vol. 1, No. 1, pp DOI: /IJKESDP Meyer, A.D.S., Grci, A.A.F., Souz, A.P.D., & Souz Jr, C.L.D. (2004). Comprison of similrity coefficients used for cluster nlysis with dominnt mrkers in mize (Ze mys L). Genetics nd Moleculr Biology, Vol. 27, No. 1, pp DOI: /S Pori, S., Cmbri, E., & Gelbukh, A. (2015). Deep convolutionl neurl network textul fetures nd multiple kernel lerning for utterncelevel multimodl sentiment nlysis. Proceedings of EMNLP, pp Pori, S., Gelbukh, A., Hussin, A., Howrd, N., Ds, D., & Bndyopdhyy, S. (2013). Enhnced SenticNet with ffective lbels for conceptbsed opinion mining. IEEE Intelligent Systems, Vol. 28, No. 2, pp RodríguezSlzr, M.E., ÁlvrezHernández, S., & BrvoNúñez, E. (2001). Coeficientes de socición. Plz y Vldés Editores, México. 16. Sidorov, G., Gelbukh, A., GómezAdorno, H., & Pinto, D. (2014). Soft similrity nd soft cosine mesure: Similrity of fetures in vector spce model. Computción y Sistems, Vol. 18, No. 3, pp DOI: /CyS Sokl, R.R. & Sneth, P.H.A. (1963). Principles of Numericl Txonomy. WH Freemn. 18. Tn, P.N., Kumr, V., & Srivstv, J. (2002). Selecting the right interestingness mesure for ssocition ptterns. Proceedings of the eighth ACM SIGKDD interntionl conference on Knowledge discovery nd dt mining, pp DOI: /
10 Visuliztion of Similrity Mesures for Binry Dt nd 2 x 2 Tbles Tversky, A. (1977). Fetures of similrity. Psychologicl review, Vol. 84, No. 4, pp DOI: / X Wrrens, M.J. (2013). A comprison of multiwy similrity coefficients for binry sequences. Interntionl Journl of Reserch nd Reviews in Applied Sciences, Vol. 16, No. 1, p. 12. Ildr Z. Btyrshin grduted from the Moscow PhysiclTechnicl Institute. He received PhD from the Moscow Power Engineering Institute nd Dr. Sci. (hbilittion) degree from the Highest Attesttion Committee of Russi. He is currently the Titulr Professor C of CIC IPN. He served s CoChir of 10 Interntionl Conferences on Soft Computing, Artificil Intelligence nd Computtionl Intelligence. He is n uthor nd editor of 20 books nd specil volumes of journls nd n uthor of more thn 200 ppers in journls nd conference proceedings. Nily Kubyshev recieved her PhD from Lobchevsky Stte University of Nizhny Novgorod, Russi, nd Dr. Sci. (hbilittion) degree from the Highest Attesttion Committee of Russi. She is currently with IPN, Mexico, s Postdoctorl Resercher. Vlery Solovyev did his reserch with the Higher School of Informtion Technologies nd Informtion Systems, University of Kzn, Russi. He grduted with Doctor of Science in Computer Science degree t the Russin Acdemy of Sciences in He is currently working s Senior Resercher nd hed of Lbortory of Medicl Informtics. His reserch interests include dt mining, computtionl linguistics, cognitive science. He is the President of The Assocition of Cognitive Science (Russi). Luis A. VillVrgs received his Ph.D. in computer science from the Polytechnic University of Ctloni in From December 1999 to Februry 2001 he ws with the Lbortory for Computer Science s Postdoctorl Fellow t the Msschusetts Institute of Technology. From October 2001 to Jnury 2007 he ws with the Mexicn Petroleum Institute. Since Jnury 2007 he hs been with the Center for Computer Reserch t The Ntionl Polytechnic Institute in Mexico, where he ws director from 2010 to Article received on 15/07/2016; ccepted 10/09/2016. Corresponding uthor is Ildr Z. Btyrshin.
Contents TRIGONOMETRIC METHODS PROBABILITY DISTRIBUTIONS
ontents UNIT 7 TRIGONOMETRI METHODS Lesson 1 Trigonometric Functions................... 462 1 onnecting ngle Mesures nd Liner Mesures.............. 463 2 Mesuring Without Mesuring.........................
More informationAn Indian Journal FULL PAPER ABSTRACT KEYWORDS. Trade Science Inc. The tennis serve technology based on the AHP evaluation of consistency check
[Type text] [Type text] [Type text] ISSN : 0977 Volume 0 Issue 0 BioTechnology 0 An Indin Journl FULL PAPER BTAIJ, 0(0), 0 [7] The tennis serve technology bsed on the AHP evlution of consistency check
More informationAHPbased tennis service technical evaluation consistency test
Avilble online.jocpr.com Journl of Chemicl nd Phrmceuticl Reserch, 0, ():779 Reserch Article ISSN : 09778 CODEN(USA) : JCPRC AHPbsed tennis service technicl evlution consistency test Mio Zhng Deprtment
More informationOpen Access Regression Analysisbased Chinese Olympic Games Competitive Sports Strength Evaluation Model Research
Send Orders for Reprints to reprints@benthmscience.e The Open Cybernetics & Systemics Journl, 05, 9, 79735 79 Open Access Regression Anlysisbsed Chinese Olympic Gmes Competitive Sports Strength Evlution
More informationINVESTIGATION 2. What s the Angle?
INVESTIGATION 2 Wht s the Angle? In the previous investigtion, you lerned tht when the rigidity property of tringles is comined with the ility to djust the length of side, the opportunities for useful
More informationChapter 5. Triangles and Vectors
www.ck12.org Chpter 5. Tringles nd Vectors 5.3 The Lw of Sines Lerning Objectives Understnd how both forms of the Lw of Sines re obtined. Apply the Lw of Sines when you know two ngles nd nonincluded side
More informationERRATA for Guide for the Development of Bicycle Facilities, 4th Edition (GBF4)
Dvid Bernhrdt, P.E., President Commissioner, Mine Deprtment of Trnsporttion Bud Wright, Executive Director 444 North Cpitol Street NW, Suite 249, Wshington, DC 20001 (202) 6245800 Fx: (202) 6245806 www.trnsporttion.org
More informationExploring Impacts of Countdown Timers on Queue Discharge Characteristics of Through Movement at Signalized Intersections
Avilble online t www.sciencedirect.com ScienceDirect Procedi  Socil nd Behviorl Scienc es 96 ( 2013 ) 255 264 13th COTA Interntionl Conference of Trnsporttion Professionls (CICTP 2013) Exploring Impcts
More informationWorking Paper: Reversal Patterns
Remember to welcome ll ides in trding. AND remember to reserve your opinion until you hve independently vlidted the ide! Working Pper: Reversl Ptterns Working Pper In this pper I wnt to review nd (hopefully)
More informationChapter 4 Group of Volunteers
CHAPTER 4 SAFETY CLEARANCE, FREEBOARD AND DRAUGHT MARKS 41 GENERAL 41.1 This chpter specifies the minimum freebord for inlnd wterwy vessels. It lso contins requirements concerning the indiction of the
More information2014 WHEAT PROTEIN RESPONSE TO NITROGEN
2014 WHEAT PROTEIN RESPONSE TO NITROGEN Aron Wlters, Coopertor Ryford Schulze, Coopertor Dniel Hthcot, Extension Progrm Specilist Dr. Clrk Neely, Extension Stte Smll Grins Specilist Ryn Collett, Extension
More informationCS 188: Artificial Intelligence Spring Announcements
CS 188: Artificil Intelligence Spring 2011 Lecture 19: Dynmic Byes Nets, Nïve Byes 4/6/2011 Pieter Aeel UC Berkeley Slides dpted from Dn Klein. Announcements W4 out, due next week Mondy P4 out, due next
More informationCopyright 1983 by ASME NEGATIVE INCIDENCE FLOW OVER A TURBINE ROTOR BLADE
THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47 St., New York, N.Y. 7 83GT23 ^+ The Society shll not be responsible for sttements or opinions dvnced in ppers or in G discussion t meetings of the
More informationChp. 3_4 Trigonometry.notebook. October 01, Warm Up. Pythagorean Triples. Verifying a Pythagorean Triple... Pythagorean Theorem
Chp. 3_4 Trigonometry.noteook Wrm Up Determine the mesure of the vrile in ech of the following digrms: x + 2 x x 5 x + 3 Pythgoren Theorem  is fundmentl reltionship mongst the sides on RIGHT tringle.
More informationTHREE DIMENSIONAL GOLF BALL FLIGHT
TEHNOMUS  New Technologies nd Products in Mchine Mnufcturing Technologies THREE IMENSIONA GOF BA FIGHT Ansts Ino Julin Joro Todor Kbleshko Uniersity of Trnsport Sofi BUGARIA ii00@b.bg Uniersity of Chemicl
More informationRight Triangle Trigonometry
Right Tringle Trigonometry To the ncient Greeks, trigonometry ws the study of right tringles. Trigonometric functions (sine, cosine, tngent, cotngent, secnt, nd cosecnt) cn be defined s right tringle rtios
More informationWhy? DF = 1_ EF = _ AC
Similr Tringles Then You solved proportions. (Lesson 2) Now 1Determine whether two tringles re similr. 2Find the unknown mesures of sides of two similr tringles. Why? Simon needs to mesure the height
More informationStudy on Fish Migration through a StoneEmbedded Fish Passage Based on Preference
Journl of Wter nd Environment Technology, Vol.13, No.1, 2015 Study on Fish Migrtion through StoneEmbedded Fish ssge Bsed on reference Rin FEBRINA 1) 2), Mshiko SEKINE 2), Hiroshi KANEMOTO 2), Koichi YAMAMOTO
More informationA Step, Stride and Heading Determination for the Pedestrian Navigation System
Journl of Globl Positioning Systems (2004) Vol. 3,. 12: 273279 A Step, Stride nd Heding Determintion for the Pedestrin Nvigtion System Jeong Won Kim GNSS Technology Reserch Center, Chungnm Ntionl University,
More informationLesson 12.1 Right Triangle Trigonometry
Lesson 12.1 Right Tringle Trigonometr 1. For ech of the following right tringles, find the vlues of sin, cos, tn, sin, cos, nd tn. (Write our nswers s frctions in lowest terms.) 2 15 9 10 2 12 2. Drw right
More informationand that excessive pronation is one major cause of foot and leg problems of runners. The treatment modahties used on these runners are shown
Foot orthotic devices to modify selected spects of lower extremity mechnics* B. T. BATES,&dgger; Ph.D., L. R. OSTERNIG, Ph.D., B. MASON, M.S., AND L. S. JAMES, M.D., Eugene, Oregon From the BiomechnicsSports
More informationDesign and Calibration of Submerged Open Channel Flow Measurement Structures: Part 3  Cutthroat Flumes
Uth Stte University DigitlCommons@USU Reports Uth Wter Reserch Lbortory Jnury 1967 Design nd Clibrtion of Submerged Open Chnnel Flow Mesurement Structures: Prt 3  Cutthrot Flumes Gylord V. Skogerboe M.
More informationAnnouncements. CS 188: Artificial Intelligence Spring Today. P4: Ghostbusters. Exact Inference in DBNs. Dynamic Bayes Nets (DBNs)
CS 188: Artificil Intelligence Spring 2010 Lecture 21: DBNs, Viteri, Speech Recognition 4/8/2010 Written 6 due tonight Project 4 up! Due 4/15 strt erly! Announcements Course contest updte Plnning to post
More informationSmall Game Hunter Lead Shot Communication Study. Executive Summary. A cooperative study conducted by:
8 Smll Gme Hunter Led Shot Communiction Study Executive Summry A coopertive study conducted y: Minnesot Coopertive Fish nd Wildlife Reserch Unit Minnesot Deprtment of Nturl Resources 9 Smll Gme Hunter
More informationIntended Hydration Strategies and Knowledge of ExerciseAssociated Hyponatraemia in Marathon Runners: A QuestionnaireBased Study
Journl of Athletic Trining 2018;53(7):696 702 doi: 10.4085/1062605012517 Ó by the Ntionl Athletic Triners Assocition, Inc www.ntjournls.org Exertionl Het Illness Intended Hydrtion Strtegies nd Knowledge
More informationAcoustic measurements of bubbles in the wake of ship model in tank
Acoustic mesurements of bubbles in the wke of ship model in tnk A. Sutin,b, A. Benilov, H.S. Roh nd Y.I. Nh c Stevens Institute of Technology, Cstle Point on Hudson, Hoboken, NJ 07030, USA b Artnn Lbortories,
More informationMTH 112: Elementary Functions
1/14 MTH 112: Elementry Functions Section 8.1: Lw of Sines Lern out olique tringles. Derive the Lw os Sines. Solve tringles. Solve the miguous cse. 8.1:Lw of Sines. 2/14 Solving olique tringles Solving
More informationAPPLICATION OF POLISH CALCIUM SORBENTS IN CARBONATE LOOPING
Physicochem. Probl. Miner. Process. 49(), 203, 20 www.minproc.pwr.wroc.pl/journl/ Physicochemicl Problems of Minerl Processing ISSN 643049 (print) ISSN 20844735 (online) Received April 3, 202; reviewed;
More informationThe Discussion of this exercise covers the following points: The openloop ZieglerNichols method. The openloop ZieglerNichols method
Exercise 63 Level Process Control EXERCISE OBJECTIVE In this exercise, you will perform PID control of level process. You will use the openloop step response method to tune the controller. DISCUSSION
More informationPROTECTION FROM HANDARM TRANSMITTED VIBRATION USING ANTIVIBRATON GLOVES
PROTECTION FROM HANDARM TRANSMITTED VIBRATION USING ANTIVIBRATON GLOVES VLADO GOGLIA IGOR ĐUKIĆ JOSIP ŢGELA Abstrct There re vrious wys of reducing the helthhzrds of hndtrnsmitted vibrtion. One of the
More informationABSTRACT EXPERIMENTAL METHOD AND MODEL
Proceedings of The Twelfth () Interntionl Offshore nd Polr Engineering Conference Kitkyushu, Jpn, My 31, Copyright by The Interntionl Society of Offshore nd Polr Engineers ISBN 15353 (Set); ISSN 1919
More informationIGF Research Project N Safer High Heels
IGF Reserch Project 17868 N Sfer High Heels Survivl of compnies in the fshion nd sesonlly dependent sectors such s the footwer industry depends upon their ility to implement the ltest trends. Shoe ottoms
More informationbark bark bat bat Multiple Meaning Words: Kindergarten to Grade 2 More Teaching Tools at harsh sound made by a dog
the brk the brk bt bt hrsh sound mde by dog Mx, stop brking! outside cover of the trunks, brnches, nd roots of woody plnts The brk of this tree is very rough. club of wood or metl used to hit the bll in
More information1985 BFS CLINICS. BFS ClinicAssembly in Kamloops, British Columbia. Westsyde High School. Bob Bridges is the Football Coach.
1985 BFS CLINICS BFS ClinicAssembly in Kmloops, British Columbi. Westsyde High School. Bob Bridges is the Footbll Coch. BFS Clinicin Rick Anderson detils BFS Nutrition Progrm t Lke Hvsu High School in
More informationA Measurement Framework for National Key Performance Measures
MINISTERIAL COUNCIL ON EDUCATION, EMPLOYMENT, TRAINING AND YOUTH AFFAIRS Performnce Mesurement nd Reporting Tskforce Working for qulity eduction outcomes A Mesurement Frmework for Ntionl Key Performnce
More informationAn Analysis of the Visual Demands Associated with Aviation Maintenance Inspectors. The Ohio State University College of Optometry, Columbus, OH 2
An Anlysis of the Visul Demnds Associted with Avition Mintennce Inspectors Gregory W. Good 1, Json J. Nichols 1, Mnoj V. Subbrm 1, Vn B. Nkgwr 2, Ronld W. Montgomery 2 1 The Ohio Stte University College
More informationFitness, obesity and risk of heat illness among army trainees
Occuptionl Medicine Advnce Access published July 14, 2014 Occuptionl Medicine doi:10.1093/occmed/kqu062 Fitness, obesity nd risk of het illness mong rmy trinees S. A. Bedno 1, N. Urbn 2,3, M. R. Boivin
More informationGrade 6. Mathematics. Student Booklet SPRING 2011 RELEASED ASSESSMENT QUESTIONS. Record your answers on the MultipleChoice Answer Sheet.
Grde 6 Assessment of Reding, Writing nd Mthemtics, Junior Division Student Booklet Mthemtics SPRING 211 RELEASED ASSESSMENT QUESTIONS Record your nswers on the MultipleChoice Answer Sheet. Plese note:
More informationPCT MINIMUM DOCUMENTATION
Ref.: PCT Minimum Documenttion pge: 4.1.1 PCT MINIMUM TION INVENTORY S CCORDING TO PCT RULE 34.1 (PERIOD FROM 1920 TO 2000) Explntory Notes 1. On the following pges is given the inventory of ptent documents,
More informationThe Pythagorean Theorem and Its Converse Is That Right?
The Pythgoren Theorem nd Its Converse Is Tht Right? SUGGESTED LEARNING STRATEGIES: Activting Prior Knowledge, Mrking the Text, Shred Reding, Summrize/Prphrse/Retell ACTIVITY 3.6 How did Pythgors get theorem
More informationStandard Weight (W s ) Equation and Length Categories for Shovelnose Sturgeon
North Americn Journl of Fisheries Mngement 18:9 7, 18 Copyright by the Americn Fisheries Society 18 Stndrd Weight (W s ) Eqution nd Length Ctegories for Shovelnose Sturgeon MICHAEL C. QUIST,* CHRISTOPHER
More informationLateral Earth Pressure on Lagging in Soldier Pile Wall Systems
Lterl Erth Pressure on Lgging in Soldier Pile Wll Systems Howrd A. Perko, Ph.D, P.E., CTL Thompson, Fort Collins, CO, USA hperko@ctlthompson.com John J Boulden, SGM, Inc., Grnd Junction, CO johnb@sgminc.com
More informationTubbs 06. Soft White Winter Wheat. Variety description
New Whet Vrieties Tubbs 06 Soft White Winter Whet EM 8993E December 2009 Michel Flowers, C. Jmes Peterson, Andrew Hulting, John Burns, Stephen Guy, nd John Kuehner Vriety description Tubbs 06 is common
More informationDepartment of Animal and Aquacultural Sciences, Norwegian University of life Science, POBox N1432 Ås, Norway.
Presenttion in session H11.5 * The ehviour of horses in different pddock sizes, with nd without exercise G.H.M. Jørgensen * & K.E. Bøe. Deprtment of Animl nd Aquculturl Sciences, Norwegin University of
More informationFirearm Safety. Links to Topics below XAVIER BECERRA THE SIX BASIC GUN SAFETY RULES. Attorney Genera] The. Six Basic Gun Safety Rules
firerm Sfety Stte of Cliforni  Deprtment of Justice  Office of the Attorney Generl Pge 1 of 14 Stte of Cliforni Deprtment of]ustice XAVIER BECERRA Attorney Gener] Serch Trnslte Website Trducir Sitio
More information1 Measurement. What you will learn. World s largest cylindrical aquarium. Australian Curriculum Measurement and Geometry Using units of measurement
Austrlin Curriulum Mesurement nd Geometry Using units of mesurement hpter 1 Mesurement Wht you will lern 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Conversion of units Perimeter Cirumferene Are Are of irle Surfe
More informationThe Effect of Sand Grain Size in the Aeolian Transport Processes of Transgressives Dunefields of the Coast of the Santa Catarina State Brazil
Journl of Costl Reserch SI 39 102106 ICS 2004 (Proceedings) Brzil ISSN 07490208 The Effect of Snd Grin Size in the Aeolin Trnsport Processes of Trnsgressives Dunefields of the Cost of the Snt Ctrin Stte
More informationInertial SensorBased Methods in Walking Speed Estimation: A Systematic Review
Sensors 2012, 12, 61026116; doi:10.3390/s120506102 OPEN ACCESS sensors ISSN 14248220 www.mdpi.com/journl/sensors Review Inertil SensorBsed Methods in Wlking Speed Estimtion: A Systemtic Review Shuozhi
More informationModels for Predicting Average Bubble Diameter and Volumetric Bubble Flux in Deep Fluidized Beds
This is n open ccess rticle published under n ACS AuthorChoice License, which permits copying nd redistribution of the rticle or ny dpttions for noncommercil purposes. Cite This: Ind. Eng. Chem. Res.
More informationGarden City Community Park  Bike Terrain Park Consultation Process
To: From: City of Richmond Prks, Recretion nd Culturl Services Committee Mike Redpth, Senior Mnger, Prks Report to Committee To V~ \Wht A 20 x>r3. \ Dte: My 13, 2013 File: 06234520 MNOR1NoI01 Re:
More informationDaytime Habitat Selection by Resident Golden Eagles in Southern Idaho, USA
Dytime Hbitt Selection by Resident Golden Egles in Southern Idho, USA Environmentl & Sttisticl Consultnts Chd LeBeu 10414 Ryn Nielson, Eric Hllingstd, nd Dve Young cwlebeu@westinc.com Introduction Risk
More informationMultiple Meaning Words: Kindergarten to Grade 2 More Teaching Tools at
n prk n prk prk prk re of public lnd, s in city, tht is set side for rest nd enjoyment Let s got for wlk in the prk. re devoted specified purpose My prents compny is locted in business prk. field or stdium
More informationSpecial Right Triangles
Pge of 5 L E S S O N 9.6 Specil Right Tringles B E F O R E Now W H Y? Review Vocbulr hpotenuse, p. 465 leg, p. 465 You found side lengths of right tringles. You ll use specil right tringles to solve problems.
More informationFor citation purposes, the electronic version is the definitive version of this article:
Professionl I s s u e s Use of Mouthgurds Among 12 to 14YerOld Ontrio Schoolchildren Kusr Sdi Fkhruddin, BDS, MSc; Hereni P. Lwrence, DDS, MSc, PhD; Dvid J. Kenny, DDS, PhD, FRCD(C); Dvid Locker, BDS,
More information2014 Victorian Shooting Championship
2014 Victorin Shooting Chmpionship VPCI, in conjunction with the Stte Coches nd the Stte Umpires invite ll PFA licensed petnque plyers in the Stte of Victori to tke prt in the 2014 Victorin Shooting Chmpionship.
More informationBypass Compensator Cartridge, Size 16
Bypss Compenstor Crtridge, Size 6 Q mx = 5 l/min, p mx = 42 br Direct cting, djustble compenstor spring Description These directcting bypss pressurecompenstor (hydrostt) crtridges, series DWDP2B 6,
More informationNumerical simulations of rip currents off arcshaped coastlines
Act Ocenol. Sin., 1, Vol. 37, No. 3, P. 1 3 DOI: 1.17/s13131111971 http://www.hyx.org.cn Emil: hyxe@3.net Numericl simultions of rip currents off rcshped costlines WANG Hong 1, 3, ZHU Shouxin *, LI
More information1. God 2. Family 3. Career
Attributes for Success 1. Congenil, Likes People 2. Positive Outlook, Visionry 3. Cpble, Willing 4. Motivted, Committed 5. Sincere, Professionl 6. High Integrity 7. Fmily Oriented Benefits of n MK Creer...
More informationRight Triangle Trigonometry
ONDENSED LESSON 1.1 Right Tringle Trigonometr In this lesson ou will lern out the trigonometri rtios ssoited with right tringle use trigonometri rtios to find unknown side lengths in right tringle use
More informationUnintentional Drownings Among New York State Residents,
Reserch Articles Unintentionl Drownings Among New York Stte Residents, 1988 1994 Mrilyn L. Browne, MS Elizbeth L. LewisMichl, PhD Alice D. Strk, MPH, DrPH SYNOPSIS Objective. This study exmines situtions
More informationRESEARCH ARTICLE The role of vision in odorplume tracking by walking and flying insects
4121 The Journl of Experimentl iology 214, 41214132 2011. Published by The Compny of iologists Ltd doi:10.1242/jeb.036954 RESEARCH ARTICLE The role of vision in odorplume trcking by wlking nd flying
More informationPhysical Processes of Tableting
Physicl Processes of Tbleting E. N. HIESTANDX, J. E. WELLS, C. B. PEOT, nd J. F. OCHS Abstrct Sher deformtion ws shown to occur during the decompression of lrge compcts mde by nonisosttic compression.
More informationFrank J. Gouveia. Ron L.Baskett. This paper was prepared for submittal to the Nuclear Utility Meteorological Data Users Group Workshop (NUMUG)
UCRL JC 1237 17 PREPRNT COMPARSON OF DATA FROM COLOCATED SENSOR PACKAGES AND MPLCATONS FOR DSPERSON MODELNG: AN N STU CASE STUDY OF RUGGED VERSUS LOWTHRESHOLD ANEMOMETERS AND NATURALVERSUS FORCEDVENTLATON
More informationIn any rightangle triangle the side opposite to the right angle is called the Label the Hypotenuse in each diagram above.
9 Ademi Mth Dte: Pythgoren Theorem RIGHT ANGLE TRIANGLE  A right tringle is tringle with one 90 0 ngle. For exmple: In ny rightngle tringle the side opposite to the right ngle is lled the Lbel the Hypotenuse
More informationFREEWAY SYSTEM PROBLEMS AND DEFICIENCIES: PHYSICAL DESIGN, TRAFFIC SAFETY, AND TRAFFIC CONGESTION
Finl Drft s Approved by Technicl Subcommittee SEWRPC Plnning Report No. 7 A REGIONAL FREEWAY RECONSTRUCTION SYSTEM PLAN FOR SOUTHEASTERN WISCONSIN Chpter V FREEWAY SYSTEM PROBLEMS AND DEFICIENCIES: PHYSICAL
More informationPRESSURE LOSSES DUE TO THE LEAKAGE IN THE AIR DUCTS  A SAFETY PROBLEM FOR TUNNEL USERS?
 7  PRESSURE LOSSES DUE TO THE LEAKAGE IN THE AIR DUCTS  A SAFETY PROBLEM FOR TUNNEL USERS? Pucher Krl, Grz Uniersity of Technology, Austri EMil: pucherk.drtech@gmx.t Pucher Robert, Uniersity of Applied
More informationComparison of Theoretical and Experimental Power output of a Small 3bladed Horizontalaxis Wind Turbine
Mrslnd Press Journl of Americn Science 9;5(4):79 9 Comprison of Theoreticl nd Experimentl Power output of Smll 3blded Horizontlxis Wind Turbine K.R. Ajo Deprtment of Mechnicl Engineering, University
More informationABSTRACT VARIATION AMONG FISH SPECIES IN THE STOICHIOMETRY OF NUTRIENT EXCRETION. by Lisette Esmeralda Torres
ABSTRACT VARIATION AMONG FISH SPECIES IN THE STOICHIOMETRY OF NUTRIENT EXCRETION by Lisette Esmerld Torres This study investigtes how nutrient cycling rtes nd rtios vry mong fish species nd with body size,
More informationAvailable online at ScienceDirect. Procedia Materials Science 8 (2015 )
Aville online t www.sciencedirect.com ScienceDirect Procedi Mterils Science 8 (2015 ) 914 923 Interntionl Congress of Science nd Technology of Metllurgy nd Mterils, SAM  CONAMET 2013 Effect of Het Input
More informationSTATISTICAL ANALYSIS OF VISUAL WAVE OBSERVATIONS AND GAGE/RADAR MEASUREMENTS. w : :. 4 Ill. Marc Perlin
TA7 w : :. 4 Ill l o. CERf ~~4 6 cop MISCELLANEOUS PAPER CERC846 STATISTICAL ANALYSIS OF VISUAL WAVE OBSERVATIONS AND GAGE/RADAR MEASUREMENTS by Mrc Perlin Costl Engineering Reserch Center DEPARTMENT
More informationData Compression. Reduce the size of data. Reduces time to retrieve and transmit data. Compression ratio = original data size/compressed data size
Dt Compression Reduce the size of dt. Reduces storge spce nd hence storge cost. Compression rtio = originl dt size/compressed dt size Reduces time to retrieve nd trnsmit dt. Lossless And Lossy Compression
More informationCOMPARISON OF CORIOLIS AND TURBINE TYPE FLOW METERS FOR FUEL MEASUREMENT IN GAS TURBINE TESTING
THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 346 E. 47th St., New York, N.Y. 117 93GT7 The Society shll not be responsible for sttements or opinions dvnced in ppers or discussion t meetings of the Society
More informationAnnouncements. CS 188: Artificial Intelligence Spring Announcements II. P4: Ghostbusters 2.0. Today. Dynamic Bayes Nets (DBNs)
CS 188: Artificil Intelligence Spring 2011 Lecture 19: Dynmic Byes Nets, Nïve Byes 4/6/2011 Announcements W4 out, due next week Mondy P4 out, due next week Fridy Midsemester survey Pieter Aeel UC Berkeley
More informationCS 188: Artificial Intelligence Spring Announcements
CS 188: Artificil Intelligence Spring 2011 Lecture 19: Dynmic Byes Nets, Nïve Byes 4/6/2011 Pieter Aeel UC Berkeley Slides dpted from Dn Klein. Announcements W4 out, due next week Mondy P4 out, due next
More informationThis article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and
This rticle ppered in journl published by Elsevier. The ttched copy is furnished to the uthor for internl noncommercil reserch nd eduction use, including for instruction t the uthors institution nd shring
More informationGraphic Standards Guide
Grphic Stndrds Guide YOGA LOVE RUN PEACE 2 ABOUT This Grphic Stndrds Guide covers the bsic guidelines for the Lululemon Athletic s new grphic identity. The Guide provides summry of the primry fetures nd
More informationAvailable online at ScienceDirect. Procedia Engineering 112 (2015 )
Avilble online t www.sciencedirect.com ScienceDirect Procedi Engineering 112 (2015 ) 225 230 7th AsiPcific Congress on Sports Technology, APCST 2015 Dynmic clibrtion of n instrumented bike brke hood in
More informationRS γ γ. * Kevin D. Dayaratna is a doctoral candidate in Mathematical Statistics at the
The Pythgoren WonLoss Formul nd Hockey: A Sttisticl Justifiction for Using the Clssic Bsebll Formul s n Evlutive Tool in Hockey By Kevin D. Dyrtn nd Steven J. Miller * October 16, 2013 Abstrct Originlly
More information1991. George W. Sidebotham 1, Gerald L. Wolf 1, Jeffrey Stern 1, and Robert Aftel 1
George W. Sidebothm 1, Gerld L. Wolf 1, Jeffrey Stern 1, nd Robert Aftel 1 ENDOTRACHEAL TUBE FIRES: A FLAME SPREAD PHENOMENON REFERENCE: Sidebothm, G.W., Wolf, G.L., Stern, J., nd Aftel, R. "Endotrchel
More informationApply the Law of Sines. You solved right triangles. You will solve triangles that have no right angle.
13.5 pply te Lw of Sines TEKS.1,.4, 2.4.; P.3.E efore Now You solved rigt tringles. You will solve tringles tt ve no rigt ngle. Wy? So you n find te distne etween frwy ojets, s in Ex. 44. Key Voulry lw
More informationNanobiophysical exploration of transthyretin amyloid fibrils Final report
Nnoiophysicl explortion of trnsthyretin myloid firils Finl report Summry In this work we used AFM to follow the myloidogenetic pthwy of trnsthyretin (TTR) y imging the events leding to the formtion of
More informationQuantitative assessment of surfproduced sea spray aerosol
Quntittive ssessment of surfproduced se spry erosol Filip P. Neele', Gerrit de Leeuw', Mrtijn Jnsen2 nd Mrcel Stive2' 1TNO Physics nd Electronics Lbortory, The Hgue, The Netherlnds 2Delft Hydrulics, Delft,
More informationLesson 8: Application Technology
The type of ppliction equipment used must suit the type of ppliction. In this module, you ll lern the prts of the most common types of ppliction equipment used by ssistnt pplictors, s well s how to properly
More informationDIE DESIGN AND CONSTRUCTION SPECIFICATIONS STAMPING  EUROPE MINIMUM CORE HOLE SIZE TO PULL PUNCHES WITH WINDOWS
MINIMUM CORE HOLE SIZE TO PULL PUNCHES WITH WINDOWS THE MINIMUM DIMENSIONS FOR THE HOLE IN THE PD REQUIRED TO INSERT THE PUNCHPULLER ND THE BLLLIFTER RE GIVEN IN THE TBLE BELOW. C CORE HOLE ØB MIN. SECTION
More informationSUMMER ASSIGNMENT FOR FUNCTIONS/TRIGONOMETRY Bring to school the 1 st day of class!
SUMMER ASSIGNMENT FOR FUNCTIONS/TRIGONOMETRY Bring to school the st d of clss! This summer ssignment is designed to prepre ou for Functions/Trigonometr. Nothing on the summer ssignment is new. Everthing
More informationSt Ac Ex Sp TOPICS (Text and Practice Books) 4.1 Triangles and Squares Pythagoras' Theorem  
MEP: Demonstrtion Projet UNIT 4 Trigonometry N: Shpe, Spe nd Mesures e,f St Ex Sp TOPIS (Text nd Prtie ooks) 4.1 Tringles nd Squres    4. Pythgors' Theorem   4.3 Extending Pythgors' Theorem   4.4
More informationRenewable Energy xxx (2011) 1e10. Contents lists available at SciVerse ScienceDirect. Renewable Energy
Renewle Energy xxx () e Contents lists ville t SciVerse ScienceDirect Renewle Energy journl homepge: www.elsevier.com/locte/renene Wke effect in wind frm performnce: Stedystte nd dynmic ehvior F. GonzálezLongtt
More informationA Universal Zombie RPG AddOn
A Universl Zombie RPG AddOn Brk Blckburn Assuming you re plying gme tht uses dice for tsk resolution, the Zombie Die cn be semlessly integrted into your gme. Zombies! Thnks to George Romero, Zombies re
More informationMultiple Meaning Words: Grade 3 to 5 More Teaching Tools at
pool pool pool pool smll re of still wter, typiclly one formed nturlly Pools of wter formed on the street fter the rin. smll, shllow ptch of liquid lying on surfce There s pool of oil under our cr. deep
More informationNick Willis Discipline: Middle distance running Specialist events: 800m and 1500m
Olympic Eduction Discipline: Middle distnce running Specilist events: 800m nd 1500m ws born in Lower Hutt (ner Wellington) in 1983.Running tlent obviously runs in the Willis fmily, s Nick nd his brother
More informationThe development of a truck concept to allow improved direct vision of vulnerable road users by drivers
Loughorough University Institutionl Repository The development of truck concept to llow improved direct vision of vulnerle rod users y drivers This item ws sumitted to Loughorough University's Institutionl
More informationSupplement of Populationspecific responses in physiological rates of Emiliania huxleyi to a broad CO 2 range
Supplement of Biogeosciences, 15, 3691 371, 21 https://doi.org/1.519/bg15369121supplement Author(s) 21. This work is distributed under the Cretive Commons Attribution. License. Supplement of Popultionspecific
More informationApply the Pythagorean Theorem
8. Apply the Pythgoren Theorem The Pythgoren theorem is nmed fter the Greek philosopher nd mthemtiin Pythgors (580500 B.C.E.). Although nient texts indite tht different iviliztions understood this property
More informationCharacteristics, Expenditures, and Economic Impact of Resident and Nonresident Hunters and Anglers in North Dakota, , Season and Trends
Agriculturl Economics Report No. 389 June 1998 Chrcteristics, Expenditures, nd Economic Impct of Resident nd Nonresident Hunters nd Anglers in North Dkot, 199697, Seson nd Trends Tin D. Lewis Jy A. Leitch
More informationCS 253: Algorithms. LZW Data Compression
CS : Algorithms LZW Dt Compression Dt Compression Reduce the size of dt Reduces storge spce nd hence storge cost. Reduces time to retrieve nd trnsmit dt. Compression rtio = originl dt size / compressed
More informationANNEX 1 CLASSIFICATION AND LABELLING SUMMARY TABLES
ANNEX CLASSIFICATION AND LABELLING SUMMARY TABLES ANNEX CLASSIFICATION AND LABELLING SUMMARY TABLES NOTE: The codifiction of hzrd s is further explined in Annex 3 (Section ). The hzrd re intended to be
More informationSamba. Brief History. Characteristics and Technique. Timing
Smb Brief History Smb is dnce nd musicl genre originting in Brzil, with roots from Afric vi the West Africn slve trde nd Africn religious trditions, prticulrly Angol nd the Congo. Introduced in 97, the
More informationTHERMOFLO FLUID PUMPS& SYSTEMS THERMOFLO FOR HEATING, COOLING AND WATER SUPPLY APPLICATIONS TO BS7074 SEALED SYSTEMS EXPANSION VESSELS PRESSURIZERS
THERMOFLO S E A L E D S Y S T E M S THERMOFLO SEALED SYSTEMS FOR HEATING, COOLING AND WATER SUPPLY APPLICATIONS TO BS7074 EXPANSION VESSELS PRESSURIZERS PUMPS& SYSTEMS WALL OR BASE MOUNTING PRESSURIZERS
More informationParadoxical Euler or Integration by Differentiation:
Prdoicl Euler or Integrtion by Differentition: A Synopsis of E36 Andrew Fbin nd Hieu Nguyen Rown University The Euler Society 008 Annul Conference July 1, 008 E36 Eposition de quelques prdoes dns le clcul
More information