The prediction of grass silage intake by beef cattle receiving barley-based supplements

Size: px
Start display at page:

Download "The prediction of grass silage intake by beef cattle receiving barley-based supplements"

Transcription

1 Livestock Production Science 68 (001) locte/ livprodsci The prediction of grss silge intke by beef cttle receiving brley-bsed supplements, b,b,b B.F. McNmee *, D.J. Kilptrick, R.W.J. Steen, F.J. Gordon Agriculturl Reserch Institute of Northern Irelnd, Hillsborough, Co. Down, BT6 6DP, UK b Deprtment of Agriculture for Northern Irelnd nd the Queen s University, Belfst, UK Received 1 July 1999; received in revised form 9 My 000; ccepted 8 June 000 Abstrct Dt on the intke by beef cttle of 11 silges either unsupplemented or supplemented with brley-bsed concentrtes were provided from six studies crried out t the Institute. An empiricl model ws developed from these dt which described n exponentil decrese in silge intke s concentrte intke ws incresed, with y-xis intercepts corresponding to unsupplemented silge intkes nd common x-xis intercept of 73. (S.E. 5.00) g/ kg W corresponding to concentrte intke when offered s sole feed. The model curvture (r prmeter) ws lso shown to be constnt for ll silges (1.05 (S.E )). When the model ws vlidted ginst externl dt (11 published studies), the reltionship between ctul nd predicted silge DMI gve n R of 0.89 with n intercept nd slope not significntly different from 0 nd 1, respectively. Seventy-six percent of silge DMIs predicted using the developed model were within 0.5 kg DM of the observed intkes in the vlidtion dt. The developed model showed n improvement over previously published model, s indicted by significnt reduction in the men squred prediction error. 001 Elsevier Science B.V. All rights reserved. Keywords: Beef cttle; Predicted grss silge d libitum intke; Concentrte supplementtion; Empiricl model; Substitution rte 1. Introduction diry systems. While some models im to directly predict the totl intke in mixed diets (Vdiveloo nd Estimtes of voluntry intke form n importnt Holmes, 1979; Agriculturl Reserch Council, 1980; prt of feed rtioning systems for ruminnts nd Rook nd Gill, 1990), Lewis (1981) hs rgued tht mny pproches hve been dopted for the develop- more logicl pproch in mixed grss silge/ conment of empiricl models to predict the d libitum dry mtter intke of grss silge (SDMI) in beef nd *Corresponding uthor. Present ddress: Glen Ltd, Segoe Industril Estte, Crigvon, BT63 5UA, Northern Irelnd, UK. Tel.: ; fx: E-mil ddress: bmcnmee@glen.co.uk (B.F. McNmee) / 01/ $ see front mtter 001 Elsevier Science B.V. All rights reserved. PII: S (00)0013-X centrte diets my be to dopt two-stge prediction. The first stge being to derive model to predict the intke potentil of silge when given s the sole feed, nd the second to correct this model for the substitution effect of concentrtes. This concept is supported by recognition tht the extent to which the intke of grss silge is reduced by supplementry concentrtes depends, to lrge extent, on the intke

2 6 B.F. McNmee et l. / Livestock Production Science 68 (001) 5 30 of the forge given s sole feed (Wilkinson, 1985; Irwin, 1970; Forbes nd Jckson, 1971; Steen nd Thoms, 1987). McIlmoyle, 198; Steen nd Kilptrick, 1999; Steen A number of models for predicting the intke of nd Kilptrick, unpublished; Ptterson et l., unsilge s sole feed re vilble in the literture. published). In the studies, 11 silges ( g/kg Such models hve included the independent vrites DM) were offered to totl of 681 heifers, bulls nd of silge digestibility nd dry mtter concentrtion steers of mixed breeds (initil liveweight (Bumgrdt et l., 1976; Lewis, 1981), whole diet kg) for periods rnging from 8 to 30 dys. Of the gross energy concentrtion nd metbolisbility (Ag- 11 silges exmined, eight were offered s sole riculturl Reserch Council, 1980), silge mmoni feed nd with, 3 or 4 levels of concentrte nitrogen concentrtion (Lewis, 1981), silge neutrl supplementtion. The other three silges were only detergent fibre concentrtion (Bumgrdt et l., offered to the nimls supplemented with 3, 4 or ) nd ner infrred reflectnce spectroscopy levels of concentrtes. The concentrte supplements (NIRS) (Steen et l., 1998). The ltter pproch hs offered in the studies were mostly brley bsed proved to be both ccurte nd simple nd pr- ( g/ kg brley) nd in ll cses were offered ticulrly suitble for use within technicl support seprtely to the silge portion of the diet. In ll role for the griculturl industry. The objective of studies the nimls were housed in open pens nd this pper is to develop this pproch further by were offered silge through brrier. Silge ws providing prediction model tht will djust d refreshed twice dily. libitum silge intke for the effect of level of The SDMIs (g/ kg W ) were nlysed using supplementry concentrtes offered in the diet of the Genstt nlysis of vrince procedures (Genstt 5 beef niml. If this cn be ccurtely chieved then Committee, 1989). Silge 3 concentrte mens from the combined prediction of silge intke s sole the nlysis of vrince were used in regression feed nd the effect of concentrte level on tht intke nlysis to investigte the reltionship between y 5 would enble more ccurte feed rtioning systems silge intke nd x 5 concentrte intke on g/kg to be developed. While Lewis (1981) hs followed W bsis. An exponentil reltionship of the form similr pproch, this hs proved to hve limited x y 5 1 br ws exmined, where ( 1 b) repreccurcy in previous independent vlidtions (Ag- sented silge intke, when silge ws offered s riculturl nd Food Reserch Council, 1991). sole feed. Three sets of models were fitted: 1. with seprte, b nd r prmeters for ech of. Mterils nd methods the 11 silges;. s (1) but with common r prmeter; The pproch dopted in the present study ws to 3. s () but extending to tke ccount of the develop n empiricl model from dt obtined from constrint tht the intercept of the eqution on the six studies crried out with growing cttle t this x-xis, equting to the concentrte intke t which Institute nd to vlidte the model ginst 11 pub- the silge intke ws zero, should be constnt for lished studies crried out outside the Institute. Be- ll silges i.e. the concentrte intke when concuse of the effect of liveweight on feed intke, ll centrte s the sole feed ws independent of dt were expressed in the form (kg silge DM silge type. This introduced the following con- intke/kg liveweight ) nd (kg supplement strint nd modified eqution: log ( /b )/log k x i e i i e DM intke/kg liveweight ) (r) 5 k giving y 5b (r r ) where k is constnt nd is equl to concentrte intke for zero silge intke nd i is silge type for i Model development The dt used to develop the model were derived from six studies crried out t the Agriculturl Reserch Institute of Northern Irelnd (Forbes nd Sttisticl tests, bsed on comprison of residul sum of squres, were crried out to compre the goodness of fit of the three sets of models.

3 B.F. McNmee et l. / Livestock Production Science 68 (001) Model vlidtion the model in estblishing the reltionship between silge nd concentrte DMI. A strong exponentil The developed model ws vlidted ginst dt reltionship ws identified, which when fitted in its from 11 published studies, crried out t vrious unconstrined form, showed n R vlue of loctions outside this Institute (Lever, 1973; Dren- Sttisticl tests used to compre the prmeters for nn nd Lwlor, 1976; Flynn, 1978; Drennn, 1979; the individul silges showed tht common r-vlue Aston nd Tyler, 1980; Petchey nd Brodbent, of 1.05 (S.E ) could be ssumed for the 1980; Veir et l., 1983, 1985, 1990; Drennn nd exponentil reltionship. Kene, 1987,b). These studies incorported 15 grss When fitted in its constrined form, the R vlue silges ( g/kg DM) offered to totl of 919 ws 0.98, with corresponding estimte for k of 73. steers, bulls nd wenlings of mixed breeds nd (S.E.5.00) g concentrte DM/ kg W. The differrnging from 93 to 491 kg liveweight for periods of ence in goodness of fit between the unconstrined dys. Silges were offered either unsup- nd constrined forms ws non-significnt (P.0.05). plemented or with brley-bsed supplements (.875 The SDMIs for the 11 silges used to develop the g/ kg fresh brley) t 1,, 3 or 4 levels ( g/ kg model re presented in Fig. 1. The plotted points W / dy). represent the observed SDMIs t the rnge of CDMIs In the vlidtion exercise, predicted silge intkes for the 11 silges while the plotted curves represent (P) in supplemented diets, using the developed the predicted SDMIs for the sme 11 silges in model, were compred ginst ctul observed silge ccordnce with the bove constrined eqution. intkes (A), using the men-squre prediction error (MSPE) defined s 3.. Model vlidtion 1 MSPE 5] O sa Pd In order to pply the developed model to the dt n vlidtion set, it ws necessry to evlute the silgewhere n is the number of pirs of vlues of A nd P specific prmeters in the model using the silge dry being compred. The MSPE cn be regrded s the mtter intke when silge i ws offered s the sole sum of the men bis, the line bis nd the rndom feed (SDMImx), thus: vrition bout the regression line (Rook et l., k 1990). Results re presented in terms of the proportionl SDMImxi5 b i(r 1) contribution of ech of these three components giving the eqution: to the MSPE. The squre root of the MSPE is the k x k men prediction error (MPE) nd is reported s y 5 SDMImx(r r )/(r 1). proportion of the men observed silge intke. Finlly the predicted silge intkes using the present This eqution ws pplied to clculte the premodel were compred ginst silge intkes predicted silge intkes for the vlidtion dt using the dicted using the Lewis (1981) model. Agin the SDMImx for the prticulr silges nd the vlues MSPE ws used s the prmeter of ccurcy. for k, the concentrte intke for zero silge intke estimted from the development dt set, nd the estimted vlue for r. This gives the eqution 3. Results nd discussion (ARINI model): x y 5 SDMImx i( ) Model development The reltionship between ctul nd predicted The wide rnge of SDMIs recorded for the 11 silge intkes ws found to be liner with intercepts silges when offered s the sole feed (50.6 to 88.8 g non-significntly (P.0.05) different from zero nd DM/ kg W ), together with the rnge of concen- regression coefficients non-significntly (P.0.05) trte supplementtion offered to the nimls (8.8 to different from unity i.e. 458 lines through the origin g DM/kg W ) fcilitted the development of This is shown in Fig..

4 8 B.F. McNmee et l. / Livestock Production Science 68 (001) 5 30 Fig. 1. The observed nd predicted silge DMI of 11 silges in supplemented diets with vrious levels of DMI when offered s sole feed. Fig.. Actul versus predicted silge DMI using the ARINI model from 11 published feeding studies crried out t vrious loctions outside the Institute. The SDMI predicted for the vlidtion set using the bove model, showed men difference between ctul nd predicted intke of 8.9%61.87 nd men bis of 1.0% Substitution rtes chrcteristic of the ARINI model re shown in Tble 1. A feture of this model is the incresing substitution rte s concentrte DMI is incresed nd s silge intke s sole feed is incresed. The ccurcy of the ARINI model ws compred with tht of the Lewis (1981) model

5 B.F. McNmee et l. / Livestock Production Science 68 (001) Tble 1 b Exmple substitution rtes (SR ) nd corresponding mrginl substitution rtes (MSR ) s determined by the ARINI model (ll intkes re expressed s g/kg W ) Concentrte DMI SDMI s sole feed SDMI SR SDMI SR MSR SDMI SR MSR SDMI SR MSR SDMI SR MSR SDMI SR MSR kg of silge DM reduced per kg of concentrte offered. b The difference in SR by incresing the concentrte intke by 10 g/kg W. which ws developed from similr stndpoint. The wide rnge of weights were used. This lrge vrivlidtion prmeters re shown in Tble, together tion necessittes ccurte correction of intkes for with the MSPE nd the proportion of MSPE ttribut- liveweight differences correction which is not ble to men bis, line bis nd rndom error. The tken into ccount in the Lewis (1981) model. In men bis nd the MPE re expressed s propor- ddition, the Lewis eqution is bsed on series of tion of the observed silge intke. The men pre- prllel curves, of SDMI versus concentrte DMI, dicted intke using the Lewis (1981) model ws for silges with differing intkes s sole feed considerbly lower thn the ctul men intke with wheres, the ARINI model uses series of con- bis of 4.9 g/kg W compred to 1.01 g/kg vergent curves. It is expected tht the use of con- W for the ARINI model. This lrge men bis vergent curves, to describe the decresing SDMI s ws responsible for the inccurcies encountered CDMI is incresed, is biologiclly more pproprite with the Lewis model when vlidted using these s it reflects the decresing significnce of the silge dt, with the men bis ccounting for 30% of the qulity (nd hence its intke s sole feed) s silge clculted MSPE. The result ws tht the MPE for represents decresing proportion of the totl diet. the Lewis model ws compred to for the ARINI model. Furthermore, the R of the predicted versus ctul SDMIs for the vlidtion dt 4. Conclusions set showed significnt improvement from 0.76 to 0.89 with the ARINI s compred to the Lewis A model hs been developed to predict the SDMI model indicting tht the new model ccounts for t given level of concentrte supplementtion more of the vrince. providing the intke of the silge when consumed s The poor reltive performnce of the Lewis sole feed is known or my be ccurtely predicted (1981) model in the present vlidtion exercise my from silge compositionl prmeters. Vlidtion of hve been due to the fct tht the vlidtion dt the model with independent dt reveled tht 76% were derived from experiments in which nimls of of SDMI predictions were within 8% of the ctul Tble Prediction precision of ARINI model s compred to the Lewis (1981) model (ctul men intke555.7 (S.E..71; n533) g DM/ kg W ) Model Predicted intke Proportion of MSPE b Men S.E. MSPE Bis Line Rndom Bis MPE ARINI Lewis gdm/kgw. (g DM/kg W ). b

6 30 B.F. McNmee et l. / Livestock Production Science 68 (001) 5 30 intkes. The developed model hs been designed for Reference Mnul. Oxford Scientific Publictions, Clrendon use in nimls offered silge nd concentrtes of Press, Oxford. Lever, J.D., Rering of diry cttle 4. Effect of concentrte similr composition, nd in ccordnce with the supplementtion on the liveweight gin nd feed intke of feeding regimen, to tht dopted in the studies from clves offered roughges d libitum. Anim. Prod. 17, which the model ws derived, i.e. silge Lewis, M., Equtions predicting silge intke by beef nd g/kg DM, concentrtes g/kg brley nd diry cttle. In: Proceedings of the Sixth Silge Conference, silge provided d libitum, seprte to the concen- Edinburgh, pp Petchey, A.M., Brodbent, P.J., The performnce of fttentrte supplementtion. ing cttle offered brley nd grss silge in vrious proportions either s discrete feeds or s complete diet. Anim. Prod. 31, References Rook, A.J., Gill, M., Prediction of the voluntry intke of grss silges by beef cttle 1. Liner regression nlyses. Anim. Prod. 50, Agriculturl nd Food Reserch Council, AFRC Technicl Rook, A.J., Dhno, M.S., Gill, M., Prediction of the Committee on Responses to Nutrients. Report no. 8. Voluntry voluntry intke of grss silges by beef cttle 3. Precision of intke of cttle. Nutr. Abs. Rev. (Series B) 61, lterntive prediction models. Anim. Prod. 50, Agriculturl Reserch Council, The Nutrient Requirements Steen, R.W.J., Kilptrick, D.J., The reltive effects of grss of Ruminnt Livestock. Commonwelth Agriculturl Bureux, silge:concentrte rtio, metbolisbility of the diet nd d Slough. libitum versus restricted dry mtter intke t equivlent energy Aston, K., Tyler, J.C., Effects of supplementing mize nd intke on the performnce nd crcss composition of beef grss silges with brley, nd mize silge with ure or cttle. Livest. Prod. Sci., In press. mmoni, on the intke nd performnce of fttening bulls. Steen, R.W.J., McIlmoyle, W.A., 198. The effect of frequency of Anim. Prod. 31, hrvesting grss for silge nd level of concentrte supple- Bumgrdt, B.R., Crbill, L.F., Gobble, J.L., Wngness, J., menttion on the intke nd performnce of beef cttle. Anim. In: Proceedings 1st Interntionl Symposium on Feed Com- Prod. 35, position, Animl Nutrient Requirements nd Computeristion Steen, R.W.J., Gordon, F.J., Dwson, L.E.R., Prk, R.S., Myne, of Diets, pp C.S., Agnew, R.E. et l., Fctors ffecting the intke of Drennn, M.J., Compenstory growth in cttle 1. Influence grss silge by cttle nd prediction of silge intke. Anim. Sci. of feeding level during the first winter (9 to 14 months of ge) 66, on subsequent performnce nd crcss composition. Ir. J. Thoms, C., Fctors ffecting substitution rtes in diry Agric. Res. 18, cows on silge bsed rtions. In: Hrseign, W., Cole, D.J.A. Drennn, M.J., Kene, M.G., Concentrte feeding levels (Eds.), Recent Advnces in Animl Nutrition, pp for unimplnted nd implnted finishing steers fed silge. Ir. J. Vdiveloo, J., Holmes, W., The prediction of the voluntry Agric. Res. 6, feed intke of diry cows. J. Agric. Sci. Cmbr. 93, Drennn, M.J., Kene, M.G., 1987b. Responses to supplementry Veir, D.M., Butler, G., Ivn, M., Proulx, J.G., Utilistion of concentrtes for finishing steers fed silge. Ir. J. Agric. Res. 6, grss silge by cttle: effect of brley nd fishmel supple ments. Cn. J. Anim. Sci. 65, Drennn, M.J., Lwlor, M.J., Evlution of pelletted dried Veir, D.M., Fortin, A., Ivn, M., Butler, G., Proulx, J.G., grss s supplement to grss silge for fttening steers. Anim. Performnce of Hereford3Shorthorn bulls nd steers rised in Prod., Northern Ontrio nd fed different levels of grss silge nd Flynn, A.V., Supplementing erly nd lte cut silges with high moisture brley. Cn. J. Anim. Sci. 63, brley for store cttle. An Fors Tluntis. Anim. Prod. Res. Veir, D.M., Proulx, J.G., Seone, J.R., Performnce of beef Rep., steers fed grss silge with or without supplements of soyben Forbes, T.J., Irwin, J.H.D., Silge for winter fttening. J. Br. mel, fish mel nd brley. Cn. J. Anim. Sci. 70, Grssld. Soc. 5, Wilkinson, J.M., Evlution of conserved forges. In: Forbes, T.J., Jckson, N., A study of the utiliztion of Whittemore, C.T., Simpson, K. (Eds.), Beef Production from silges of different dry-mtter content by young beef cttle Silge nd Other Conserved Forges. Longmn, London, pp. with or without supplementry brley. J. Br. Grssld. Soc. 6, Genstt 5 Committee, In: Pyne, R.W. et l. (Ed.), Genstt 5

Tests for the Ratio of Two Poisson Rates

Tests for the Ratio of Two Poisson Rates Chpter 437 Tests for the Rtio of Two Poisson Rtes Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson

More information

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:

More information

Math 31S. Rumbos Fall Solutions to Assignment #16

Math 31S. Rumbos Fall Solutions to Assignment #16 Mth 31S. Rumbos Fll 2016 1 Solutions to Assignment #16 1. Logistic Growth 1. Suppose tht the growth of certin niml popultion is governed by the differentil eqution 1000 dn N dt = 100 N, (1) where N(t)

More information

CBE 291b - Computation And Optimization For Engineers

CBE 291b - Computation And Optimization For Engineers The University of Western Ontrio Fculty of Engineering Science Deprtment of Chemicl nd Biochemicl Engineering CBE 9b - Computtion And Optimiztion For Engineers Mtlb Project Introduction Prof. A. Jutn Jn

More information

NUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by.

NUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by. NUMERICAL INTEGRATION 1 Introduction The inverse process to differentition in clculus is integrtion. Mthemticlly, integrtion is represented by f(x) dx which stnds for the integrl of the function f(x) with

More information

Math 1B, lecture 4: Error bounds for numerical methods

Math 1B, lecture 4: Error bounds for numerical methods Mth B, lecture 4: Error bounds for numericl methods Nthn Pflueger 4 September 0 Introduction The five numericl methods descried in the previous lecture ll operte by the sme principle: they pproximte the

More information

Student Activity 3: Single Factor ANOVA

Student Activity 3: Single Factor ANOVA MATH 40 Student Activity 3: Single Fctor ANOVA Some Bsic Concepts In designed experiment, two or more tretments, or combintions of tretments, is pplied to experimentl units The number of tretments, whether

More information

The steps of the hypothesis test

The steps of the hypothesis test ttisticl Methods I (EXT 7005) Pge 78 Mosquito species Time of dy A B C Mid morning 0.0088 5.4900 5.5000 Mid Afternoon.3400 0.0300 0.8700 Dusk 0.600 5.400 3.000 The Chi squre test sttistic is the sum of

More information

Hybrid Group Acceptance Sampling Plan Based on Size Biased Lomax Model

Hybrid Group Acceptance Sampling Plan Based on Size Biased Lomax Model Mthemtics nd Sttistics 2(3): 137-141, 2014 DOI: 10.13189/ms.2014.020305 http://www.hrpub.org Hybrid Group Acceptnce Smpling Pln Bsed on Size Bised Lomx Model R. Subb Ro 1,*, A. Ng Durgmmb 2, R.R.L. Kntm

More information

3.4 Numerical integration

3.4 Numerical integration 3.4. Numericl integrtion 63 3.4 Numericl integrtion In mny economic pplictions it is necessry to compute the definite integrl of relvlued function f with respect to "weight" function w over n intervl [,

More information

Scientific notation is a way of expressing really big numbers or really small numbers.

Scientific notation is a way of expressing really big numbers or really small numbers. Scientific Nottion (Stndrd form) Scientific nottion is wy of expressing relly big numbers or relly smll numbers. It is most often used in scientific clcultions where the nlysis must be very precise. Scientific

More information

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007 A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H Thoms Shores Deprtment of Mthemtics University of Nebrsk Spring 2007 Contents Rtes of Chnge nd Derivtives 1 Dierentils 4 Are nd Integrls 5 Multivrite Clculus

More information

Improper Integrals. Type I Improper Integrals How do we evaluate an integral such as

Improper Integrals. Type I Improper Integrals How do we evaluate an integral such as Improper Integrls Two different types of integrls cn qulify s improper. The first type of improper integrl (which we will refer to s Type I) involves evluting n integrl over n infinite region. In the grph

More information

Population Dynamics Definition Model A model is defined as a physical representation of any natural phenomena Example: 1. A miniature building model.

Population Dynamics Definition Model A model is defined as a physical representation of any natural phenomena Example: 1. A miniature building model. Popultion Dynmics Definition Model A model is defined s physicl representtion of ny nturl phenomen Exmple: 1. A miniture building model. 2. A children cycle prk depicting the trffic signls 3. Disply of

More information

f(x) dx, If one of these two conditions is not met, we call the integral improper. Our usual definition for the value for the definite integral

f(x) dx, If one of these two conditions is not met, we call the integral improper. Our usual definition for the value for the definite integral Improper Integrls Every time tht we hve evluted definite integrl such s f(x) dx, we hve mde two implicit ssumptions bout the integrl:. The intervl [, b] is finite, nd. f(x) is continuous on [, b]. If one

More information

Acceptance Sampling by Attributes

Acceptance Sampling by Attributes Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire

More information

Credibility Hypothesis Testing of Fuzzy Triangular Distributions

Credibility Hypothesis Testing of Fuzzy Triangular Distributions 666663 Journl of Uncertin Systems Vol.9, No., pp.6-74, 5 Online t: www.jus.org.uk Credibility Hypothesis Testing of Fuzzy Tringulr Distributions S. Smpth, B. Rmy Received April 3; Revised 4 April 4 Abstrct

More information

A signalling model of school grades: centralized versus decentralized examinations

A signalling model of school grades: centralized versus decentralized examinations A signlling model of school grdes: centrlized versus decentrlized exmintions Mri De Pol nd Vincenzo Scopp Diprtimento di Economi e Sttistic, Università dell Clbri m.depol@unicl.it; v.scopp@unicl.it 1 The

More information

New Expansion and Infinite Series

New Expansion and Infinite Series Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University

More information

Driving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d

Driving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d Interntionl Industril Informtics nd Computer Engineering Conference (IIICEC 15) Driving Cycle Construction of City Rod for Hybrid Bus Bsed on Mrkov Process Deng Pn1,, Fengchun Sun1,b*, Hongwen He1, c,

More information

DETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING MOMENT INTERACTION AT MICROSCALE

DETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING MOMENT INTERACTION AT MICROSCALE Determintion RevAdvMterSci of mechnicl 0(009) -7 properties of nnostructures with complex crystl lttice using DETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING

More information

P 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0)

P 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0) 1 Tylor polynomils In Section 3.5, we discussed how to pproximte function f(x) round point in terms of its first derivtive f (x) evluted t, tht is using the liner pproximtion f() + f ()(x ). We clled this

More information

A Brief Review on Akkar, Sandikkaya and Bommer (ASB13) GMPE

A Brief Review on Akkar, Sandikkaya and Bommer (ASB13) GMPE Southwestern U.S. Ground Motion Chrcteriztion Senior Seismic Hzrd Anlysis Committee Level 3 Workshop #2 October 22-24, 2013 A Brief Review on Akkr, Sndikky nd Bommer (ASB13 GMPE Sinn Akkr Deprtment of

More information

8.2 ESTIMATING DETENTION VOLUMES

8.2 ESTIMATING DETENTION VOLUMES 8.. Plnning versus Design number of detention bsin plnning methods hve been proposed in the professionl literture. These provide estimtes of the reuired volume of detention storge. The outlet structure

More information

Euler, Ioachimescu and the trapezium rule. G.J.O. Jameson (Math. Gazette 96 (2012), )

Euler, Ioachimescu and the trapezium rule. G.J.O. Jameson (Math. Gazette 96 (2012), ) Euler, Iochimescu nd the trpezium rule G.J.O. Jmeson (Mth. Gzette 96 (0), 36 4) The following results were estblished in recent Gzette rticle [, Theorems, 3, 4]. Given > 0 nd 0 < s

More information

Estimation of Binomial Distribution in the Light of Future Data

Estimation of Binomial Distribution in the Light of Future Data British Journl of Mthemtics & Computer Science 102: 1-7, 2015, Article no.bjmcs.19191 ISSN: 2231-0851 SCIENCEDOMAIN interntionl www.sciencedomin.org Estimtion of Binomil Distribution in the Light of Future

More information

Intro to Nuclear and Particle Physics (5110)

Intro to Nuclear and Particle Physics (5110) Intro to Nucler nd Prticle Physics (5110) Feb, 009 The Nucler Mss Spectrum The Liquid Drop Model //009 1 E(MeV) n n(n-1)/ E/[ n(n-1)/] (MeV/pir) 1 C 16 O 0 Ne 4 Mg 7.7 14.44 19.17 8.48 4 5 6 6 10 15.4.41

More information

APPROXIMATE INTEGRATION

APPROXIMATE INTEGRATION APPROXIMATE INTEGRATION. Introduction We hve seen tht there re functions whose nti-derivtives cnnot be expressed in closed form. For these resons ny definite integrl involving these integrnds cnnot be

More information

Time Truncated Two Stage Group Sampling Plan For Various Distributions

Time Truncated Two Stage Group Sampling Plan For Various Distributions Time Truncted Two Stge Group Smpling Pln For Vrious Distributions Dr. A. R. Sudmni Rmswmy, S.Jysri Associte Professor, Deprtment of Mthemtics, Avinshilingm University, Coimbtore Assistnt professor, Deprtment

More information

An approximation to the arithmetic-geometric mean. G.J.O. Jameson, Math. Gazette 98 (2014), 85 95

An approximation to the arithmetic-geometric mean. G.J.O. Jameson, Math. Gazette 98 (2014), 85 95 An pproximtion to the rithmetic-geometric men G.J.O. Jmeson, Mth. Gzette 98 (4), 85 95 Given positive numbers > b, consider the itertion given by =, b = b nd n+ = ( n + b n ), b n+ = ( n b n ) /. At ech

More information

8 Laplace s Method and Local Limit Theorems

8 Laplace s Method and Local Limit Theorems 8 Lplce s Method nd Locl Limit Theorems 8. Fourier Anlysis in Higher DImensions Most of the theorems of Fourier nlysis tht we hve proved hve nturl generliztions to higher dimensions, nd these cn be proved

More information

Vyacheslav Telnin. Search for New Numbers.

Vyacheslav Telnin. Search for New Numbers. Vycheslv Telnin Serch for New Numbers. 1 CHAPTER I 2 I.1 Introduction. In 1984, in the first issue for tht yer of the Science nd Life mgzine, I red the rticle "Non-Stndrd Anlysis" by V. Uspensky, in which

More information

Non-Linear & Logistic Regression

Non-Linear & Logistic Regression Non-Liner & Logistic Regression If the sttistics re boring, then you've got the wrong numbers. Edwrd R. Tufte (Sttistics Professor, Yle University) Regression Anlyses When do we use these? PART 1: find

More information

Predict Global Earth Temperature using Linier Regression

Predict Global Earth Temperature using Linier Regression Predict Globl Erth Temperture using Linier Regression Edwin Swndi Sijbt (23516012) Progrm Studi Mgister Informtik Sekolh Teknik Elektro dn Informtik ITB Jl. Gnesh 10 Bndung 40132, Indonesi 23516012@std.stei.itb.c.id

More information

FEM ANALYSIS OF ROGOWSKI COILS COUPLED WITH BAR CONDUCTORS

FEM ANALYSIS OF ROGOWSKI COILS COUPLED WITH BAR CONDUCTORS XIX IMEKO orld Congress Fundmentl nd Applied Metrology September 6 11, 2009, Lisbon, Portugl FEM ANALYSIS OF ROGOSKI COILS COUPLED ITH BAR CONDUCTORS Mirko Mrrcci, Bernrdo Tellini, Crmine Zppcost University

More information

20 MATHEMATICS POLYNOMIALS

20 MATHEMATICS POLYNOMIALS 0 MATHEMATICS POLYNOMIALS.1 Introduction In Clss IX, you hve studied polynomils in one vrible nd their degrees. Recll tht if p(x) is polynomil in x, the highest power of x in p(x) is clled the degree of

More information

Estimation of Global Solar Radiation at Onitsha with Regression Analysis and Artificial Neural Network Models

Estimation of Global Solar Radiation at Onitsha with Regression Analysis and Artificial Neural Network Models eserch Journl of ecent Sciences ISSN 77-5 es.j.ecent Sci. Estimtion of Globl Solr dition t Onitsh with egression Anlysis nd Artificil Neurl Network Models Abstrct Agbo G.A., Ibeh G.F. *nd Ekpe J.E. Fculty

More information

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn

More information

du = C dy = 1 dy = dy W is invertible with inverse U, so that y = W(t) is exactly the same thing as t = U(y),

du = C dy = 1 dy = dy W is invertible with inverse U, so that y = W(t) is exactly the same thing as t = U(y), 29. Differentil equtions. The conceptul bsis of llometr Did it occur to ou in Lecture 3 wh Fiboncci would even cre how rpidl rbbit popultion grows? Mbe he wnted to et the rbbits. If so, then he would be

More information

Solution Manual. for. Fracture Mechanics. C.T. Sun and Z.-H. Jin

Solution Manual. for. Fracture Mechanics. C.T. Sun and Z.-H. Jin Solution Mnul for Frcture Mechnics by C.T. Sun nd Z.-H. Jin Chpter rob.: ) 4 No lod is crried by rt nd rt 4. There is no strin energy stored in them. Constnt Force Boundry Condition The totl strin energy

More information

1 Probability Density Functions

1 Probability Density Functions Lis Yn CS 9 Continuous Distributions Lecture Notes #9 July 6, 28 Bsed on chpter by Chris Piech So fr, ll rndom vribles we hve seen hve been discrete. In ll the cses we hve seen in CS 9, this ment tht our

More information

Entropy ISSN

Entropy ISSN Entropy 006, 8[], 50-6 50 Entropy ISSN 099-4300 www.mdpi.org/entropy/ ENTROPY GENERATION IN PRESSURE GRADIENT ASSISTED COUETTE FLOW WITH DIFFERENT THERMAL BOUNDARY CONDITIONS Abdul Aziz Deprtment of Mechnicl

More information

Math 8 Winter 2015 Applications of Integration

Math 8 Winter 2015 Applications of Integration Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl

More information

Review of Calculus, cont d

Review of Calculus, cont d Jim Lmbers MAT 460 Fll Semester 2009-10 Lecture 3 Notes These notes correspond to Section 1.1 in the text. Review of Clculus, cont d Riemnn Sums nd the Definite Integrl There re mny cses in which some

More information

13.4. Integration by Parts. Introduction. Prerequisites. Learning Outcomes

13.4. Integration by Parts. Introduction. Prerequisites. Learning Outcomes Integrtion by Prts 13.4 Introduction Integrtion by Prts is technique for integrting products of functions. In this Section you will lern to recognise when it is pproprite to use the technique nd hve the

More information

Job No. Sheet 1 of 8 Rev B. Made by IR Date Aug Checked by FH/NB Date Oct Revised by MEB Date April 2006

Job No. Sheet 1 of 8 Rev B. Made by IR Date Aug Checked by FH/NB Date Oct Revised by MEB Date April 2006 Job o. Sheet 1 of 8 Rev B 10, Route de Limours -78471 St Rémy Lès Chevreuse Cedex rnce Tel : 33 (0)1 30 85 5 00 x : 33 (0)1 30 5 75 38 CLCULTO SHEET Stinless Steel Vloristion Project Design Exmple 5 Welded

More information

Applicable Analysis and Discrete Mathematics available online at

Applicable Analysis and Discrete Mathematics available online at Applicble Anlysis nd Discrete Mthemtics vilble online t http://pefmth.etf.rs Appl. Anl. Discrete Mth. 4 (2010), 23 31. doi:10.2298/aadm100201012k NUMERICAL ANALYSIS MEETS NUMBER THEORY: USING ROOTFINDING

More information

Minimum Energy State of Plasmas with an Internal Transport Barrier

Minimum Energy State of Plasmas with an Internal Transport Barrier Minimum Energy Stte of Plsms with n Internl Trnsport Brrier T. Tmno ), I. Ktnum ), Y. Skmoto ) ) Formerly, Plsm Reserch Center, University of Tsukub, Tsukub, Ibrki, Jpn ) Plsm Reserch Center, University

More information

MATH SS124 Sec 39 Concepts summary with examples

MATH SS124 Sec 39 Concepts summary with examples This note is mde for students in MTH124 Section 39 to review most(not ll) topics I think we covered in this semester, nd there s exmples fter these concepts, go over this note nd try to solve those exmples

More information

The Regulated and Riemann Integrals

The Regulated and Riemann Integrals Chpter 1 The Regulted nd Riemnn Integrls 1.1 Introduction We will consider severl different pproches to defining the definite integrl f(x) dx of function f(x). These definitions will ll ssign the sme vlue

More information

INTRODUCTION. The three general approaches to the solution of kinetics problems are:

INTRODUCTION. The three general approaches to the solution of kinetics problems are: INTRODUCTION According to Newton s lw, prticle will ccelerte when it is subjected to unblnced forces. Kinetics is the study of the reltions between unblnced forces nd the resulting chnges in motion. The

More information

1.2. Linear Variable Coefficient Equations. y + b "! = a y + b " Remark: The case b = 0 and a non-constant can be solved with the same idea as above.

1.2. Linear Variable Coefficient Equations. y + b ! = a y + b  Remark: The case b = 0 and a non-constant can be solved with the same idea as above. 1 12 Liner Vrible Coefficient Equtions Section Objective(s): Review: Constnt Coefficient Equtions Solving Vrible Coefficient Equtions The Integrting Fctor Method The Bernoulli Eqution 121 Review: Constnt

More information

NUMERICAL INTEGRATION

NUMERICAL INTEGRATION NUMERICAL INTEGRATION How do we evlute I = f (x) dx By the fundmentl theorem of clculus, if F (x) is n ntiderivtive of f (x), then I = f (x) dx = F (x) b = F (b) F () However, in prctice most integrls

More information

On the Uncertainty of Sensors Based on Magnetic Effects. E. Hristoforou, E. Kayafas, A. Ktena, DM Kepaptsoglou

On the Uncertainty of Sensors Based on Magnetic Effects. E. Hristoforou, E. Kayafas, A. Ktena, DM Kepaptsoglou On the Uncertinty of Sensors Bsed on Mgnetic Effects E. ristoforou, E. Kyfs, A. Kten, DM Kepptsoglou Ntionl Technicl University of Athens, Zogrfou Cmpus, Athens 1578, Greece Tel: +3177178, Fx: +3177119,

More information

SUMMER KNOWHOW STUDY AND LEARNING CENTRE

SUMMER KNOWHOW STUDY AND LEARNING CENTRE SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18

More information

MIXED MODELS (Sections ) I) In the unrestricted model, interactions are treated as in the random effects model:

MIXED MODELS (Sections ) I) In the unrestricted model, interactions are treated as in the random effects model: 1 2 MIXED MODELS (Sections 17.7 17.8) Exmple: Suppose tht in the fiber breking strength exmple, the four mchines used were the only ones of interest, but the interest ws over wide rnge of opertors, nd

More information

Numerical integration

Numerical integration 2 Numericl integrtion This is pge i Printer: Opque this 2. Introduction Numericl integrtion is problem tht is prt of mny problems in the economics nd econometrics literture. The orgniztion of this chpter

More information

Lecture 14: Quadrature

Lecture 14: Quadrature Lecture 14: Qudrture This lecture is concerned with the evlution of integrls fx)dx 1) over finite intervl [, b] The integrnd fx) is ssumed to be rel-vlues nd smooth The pproximtion of n integrl by numericl

More information

The International Association for the Properties of Water and Steam. Release on the Ionization Constant of H 2 O

The International Association for the Properties of Water and Steam. Release on the Ionization Constant of H 2 O IAPWS R-7 The Interntionl Assocition for the Properties of Wter nd Stem Lucerne, Sitzerlnd August 7 Relese on the Ioniztion Constnt of H O 7 The Interntionl Assocition for the Properties of Wter nd Stem

More information

Chapter 5 Bending Moments and Shear Force Diagrams for Beams

Chapter 5 Bending Moments and Shear Force Diagrams for Beams Chpter 5 ending Moments nd Sher Force Digrms for ems n ddition to illy loded brs/rods (e.g. truss) nd torsionl shfts, the structurl members my eperience some lods perpendiculr to the is of the bem nd will

More information

Construction and Selection of Single Sampling Quick Switching Variables System for given Control Limits Involving Minimum Sum of Risks

Construction and Selection of Single Sampling Quick Switching Variables System for given Control Limits Involving Minimum Sum of Risks Construction nd Selection of Single Smpling Quick Switching Vribles System for given Control Limits Involving Minimum Sum of Risks Dr. D. SENHILKUMAR *1 R. GANESAN B. ESHA RAFFIE 1 Associte Professor,

More information

Deteriorating Inventory Model for Waiting. Time Partial Backlogging

Deteriorating Inventory Model for Waiting. Time Partial Backlogging Applied Mthemticl Sciences, Vol. 3, 2009, no. 9, 42-428 Deteriorting Inventory Model for Witing Time Prtil Bcklogging Nit H. Shh nd 2 Kunl T. Shukl Deprtment of Mthemtics, Gujrt university, Ahmedbd. 2

More information

Monte Carlo method in solving numerical integration and differential equation

Monte Carlo method in solving numerical integration and differential equation Monte Crlo method in solving numericl integrtion nd differentil eqution Ye Jin Chemistry Deprtment Duke University yj66@duke.edu Abstrct: Monte Crlo method is commonly used in rel physics problem. The

More information

The graphs of Rational Functions

The graphs of Rational Functions Lecture 4 5A: The its of Rtionl Functions s x nd s x + The grphs of Rtionl Functions The grphs of rtionl functions hve severl differences compred to power functions. One of the differences is the behvior

More information

Advanced Calculus: MATH 410 Notes on Integrals and Integrability Professor David Levermore 17 October 2004

Advanced Calculus: MATH 410 Notes on Integrals and Integrability Professor David Levermore 17 October 2004 Advnced Clculus: MATH 410 Notes on Integrls nd Integrbility Professor Dvid Levermore 17 October 2004 1. Definite Integrls In this section we revisit the definite integrl tht you were introduced to when

More information

Chapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses

Chapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses Chpter 9: Inferences bsed on Two smples: Confidence intervls nd tests of hypotheses 9.1 The trget prmeter : difference between two popultion mens : difference between two popultion proportions : rtio of

More information

Section 11.5 Estimation of difference of two proportions

Section 11.5 Estimation of difference of two proportions ection.5 Estimtion of difference of two proportions As seen in estimtion of difference of two mens for nonnorml popultion bsed on lrge smple sizes, one cn use CLT in the pproximtion of the distribution

More information

Design and Analysis of Single-Factor Experiments: The Analysis of Variance

Design and Analysis of Single-Factor Experiments: The Analysis of Variance 13 CHAPTER OUTLINE Design nd Anlysis of Single-Fctor Experiments: The Anlysis of Vrince 13-1 DESIGNING ENGINEERING EXPERIMENTS 13-2 THE COMPLETELY RANDOMIZED SINGLE-FACTOR EXPERIMENT 13-2.1 An Exmple 13-2.2

More information

Jim Lambers MAT 169 Fall Semester Lecture 4 Notes

Jim Lambers MAT 169 Fall Semester Lecture 4 Notes Jim Lmbers MAT 169 Fll Semester 2009-10 Lecture 4 Notes These notes correspond to Section 8.2 in the text. Series Wht is Series? An infinte series, usully referred to simply s series, is n sum of ll of

More information

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry LECTURE 14 Dr. Teres D. Golden University of North Texs Deprtment of Chemistry Quntittive Methods A. Quntittive Phse Anlysis Qulittive D phses by comprison with stndrd ptterns. Estimte of proportions of

More information

Estimation of the particle concentration in hydraulic liquid by the in-line automatic particle counter based on the CMOS image sensor

Estimation of the particle concentration in hydraulic liquid by the in-line automatic particle counter based on the CMOS image sensor Glyndŵr University Reserch Online Conference Presenttion Estimtion of the prticle concentrtion in hydrulic liquid by the in-line utomtic prticle counter bsed on the CMOS imge sensor Kornilin, D.V., Kudryvtsev,

More information

Design Data 1M. Highway Live Loads on Concrete Pipe

Design Data 1M. Highway Live Loads on Concrete Pipe Design Dt 1M Highwy Live Lods on Concrete Pipe Foreword Thick, high-strength pvements designed for hevy truck trffic substntilly reduce the pressure trnsmitted through wheel to the subgrde nd consequently,

More information

Measuring Electron Work Function in Metal

Measuring Electron Work Function in Metal n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd

More information

CHM Physical Chemistry I Chapter 1 - Supplementary Material

CHM Physical Chemistry I Chapter 1 - Supplementary Material CHM 3410 - Physicl Chemistry I Chpter 1 - Supplementry Mteril For review of some bsic concepts in mth, see Atkins "Mthemticl Bckground 1 (pp 59-6), nd "Mthemticl Bckground " (pp 109-111). 1. Derivtion

More information

New data structures to reduce data size and search time

New data structures to reduce data size and search time New dt structures to reduce dt size nd serch time Tsuneo Kuwbr Deprtment of Informtion Sciences, Fculty of Science, Kngw University, Hirtsuk-shi, Jpn FIT2018 1D-1, No2, pp1-4 Copyright (c)2018 by The Institute

More information

Chapter 4 Contravariance, Covariance, and Spacetime Diagrams

Chapter 4 Contravariance, Covariance, and Spacetime Diagrams Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz

More information

1. a) Describe the principle characteristics and uses of the following types of PV cell: Single Crystal Silicon Poly Crystal Silicon

1. a) Describe the principle characteristics and uses of the following types of PV cell: Single Crystal Silicon Poly Crystal Silicon 2001 1. ) Describe the principle chrcteristics nd uses of the following types of PV cell: Single Crystl Silicon Poly Crystl Silicon Amorphous Silicon CIS/CIGS Gllium Arsenide Multijunction (12 mrks) b)

More information

Comparison Procedures

Comparison Procedures Comprison Procedures Single Fctor, Between-Subects Cse /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects Two Comprison Strtegies post hoc (fter-the-fct) pproch You re interested in discovering

More information

Effects of peripheral drilling moment on delamination using special drill bits

Effects of peripheral drilling moment on delamination using special drill bits journl of mterils processing technology 01 (008 471 476 journl homepge: www.elsevier.com/locte/jmtprotec Effects of peripherl illing moment on delmintion using specil ill bits C.C. Tso,, H. Hocheng b Deprtment

More information

Decision Science Letters

Decision Science Letters Decision Science Letters 8 (09) 37 3 Contents lists vilble t GrowingScience Decision Science Letters homepge: www.growingscience.com/dsl The negtive binomil-weighted Lindley distribution Sunthree Denthet

More information

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3 2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is

More information

Z b. f(x)dx. Yet in the above two cases we know what f(x) is. Sometimes, engineers want to calculate an area by computing I, but...

Z b. f(x)dx. Yet in the above two cases we know what f(x) is. Sometimes, engineers want to calculate an area by computing I, but... Chpter 7 Numericl Methods 7. Introduction In mny cses the integrl f(x)dx cn be found by finding function F (x) such tht F 0 (x) =f(x), nd using f(x)dx = F (b) F () which is known s the nlyticl (exct) solution.

More information

Lecture 20: Numerical Integration III

Lecture 20: Numerical Integration III cs4: introduction to numericl nlysis /8/0 Lecture 0: Numericl Integrtion III Instructor: Professor Amos Ron Scribes: Mrk Cowlishw, Yunpeng Li, Nthnel Fillmore For the lst few lectures we hve discussed

More information

Numerical Integration

Numerical Integration Chpter 5 Numericl Integrtion Numericl integrtion is the study of how the numericl vlue of n integrl cn be found. Methods of function pproximtion discussed in Chpter??, i.e., function pproximtion vi the

More information

Research on the Quality Competence in Manufacturing Industry

Research on the Quality Competence in Manufacturing Industry Reserch on the Qulity Competence in Mnufcturing Industry Xioping M, Zhijun Hn Economics nd Mngement School Nnjing University of Science nd Technology Nnjing 210094, Chin Tel: 86-25-8431-5400 E-mil: hnzhij4531@sin.com

More information

Discrete Mathematics and Probability Theory Summer 2014 James Cook Note 17

Discrete Mathematics and Probability Theory Summer 2014 James Cook Note 17 CS 70 Discrete Mthemtics nd Proility Theory Summer 2014 Jmes Cook Note 17 I.I.D. Rndom Vriles Estimting the is of coin Question: We wnt to estimte the proportion p of Democrts in the US popultion, y tking

More information

Operations with Polynomials

Operations with Polynomials 38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: How to identify the leding coefficients nd degrees of polynomils How to dd nd subtrct polynomils How to multiply polynomils

More information

The Wave Equation I. MA 436 Kurt Bryan

The Wave Equation I. MA 436 Kurt Bryan 1 Introduction The Wve Eqution I MA 436 Kurt Bryn Consider string stretching long the x xis, of indeterminte (or even infinite!) length. We wnt to derive n eqution which models the motion of the string

More information

Lecture INF4350 October 12008

Lecture INF4350 October 12008 Biosttistics ti ti Lecture INF4350 October 12008 Anj Bråthen Kristoffersen Biomedicl Reserch Group Deprtment of informtics, UiO Gol Presenttion of dt descriptive tbles nd grphs Sensitivity, specificity,

More information

Physics 116C Solution of inhomogeneous ordinary differential equations using Green s functions

Physics 116C Solution of inhomogeneous ordinary differential equations using Green s functions Physics 6C Solution of inhomogeneous ordinry differentil equtions using Green s functions Peter Young November 5, 29 Homogeneous Equtions We hve studied, especilly in long HW problem, second order liner

More information

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response

More information

5.7 Improper Integrals

5.7 Improper Integrals 458 pplictions of definite integrls 5.7 Improper Integrls In Section 5.4, we computed the work required to lift pylod of mss m from the surfce of moon of mss nd rdius R to height H bove the surfce of the

More information

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018 Physics 201 Lb 3: Mesurement of Erth s locl grvittionl field I Dt Acquisition nd Preliminry Anlysis Dr. Timothy C. Blck Summer I, 2018 Theoreticl Discussion Grvity is one of the four known fundmentl forces.

More information

SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 2014

SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 2014 SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 014 Mrk Scheme: Ech prt of Question 1 is worth four mrks which re wrded solely for the correct nswer.

More information

Shear and torsion interaction of hollow core slabs

Shear and torsion interaction of hollow core slabs Competitive nd Sustinble Growth Contrct Nº G6RD-CT--6 Sher nd torsion interction of hollow core slbs HOLCOTORS Technicl Report, Rev. Anlyses of hollow core floors December The content of the present publiction

More information

7.2 The Definite Integral

7.2 The Definite Integral 7.2 The Definite Integrl the definite integrl In the previous section, it ws found tht if function f is continuous nd nonnegtive, then the re under the grph of f on [, b] is given by F (b) F (), where

More information

Probability Distributions for Gradient Directions in Uncertain 3D Scalar Fields

Probability Distributions for Gradient Directions in Uncertain 3D Scalar Fields Technicl Report 7.8. Technische Universität München Probbility Distributions for Grdient Directions in Uncertin 3D Sclr Fields Tobis Pfffelmoser, Mihel Mihi, nd Rüdiger Westermnn Computer Grphics nd Visuliztion

More information

HOMEWORK SOLUTIONS MATH 1910 Sections 7.9, 8.1 Fall 2016

HOMEWORK SOLUTIONS MATH 1910 Sections 7.9, 8.1 Fall 2016 HOMEWORK SOLUTIONS MATH 9 Sections 7.9, 8. Fll 6 Problem 7.9.33 Show tht for ny constnts M,, nd, the function yt) = )) t ) M + tnh stisfies the logistic eqution: y SOLUTION. Let Then nd Finlly, y = y M

More information

Numerical Analysis: Trapezoidal and Simpson s Rule

Numerical Analysis: Trapezoidal and Simpson s Rule nd Simpson s Mthemticl question we re interested in numericlly nswering How to we evlute I = f (x) dx? Clculus tells us tht if F(x) is the ntiderivtive of function f (x) on the intervl [, b], then I =

More information

The Velocity Factor of an Insulated Two-Wire Transmission Line

The Velocity Factor of an Insulated Two-Wire Transmission Line The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the

More information