Influence of Knife Bevel Angle, Rate of Loading and Stalk Section on Some Engineering Parameters of Lilium Stalk

Size: px
Start display at page:

Download "Influence of Knife Bevel Angle, Rate of Loading and Stalk Section on Some Engineering Parameters of Lilium Stalk"

Transcription

1 Irni Journl of Energy & Environment 3 (4): , 01 ISSN IJEE n Offiil Peer Reviewed Journl of Bol Noshirvni University of Tehnology DOI: /idosi.ijee BUT Influene of Knife Bevel Angle, Rte of Loding nd Stlk Setion on Some Engineering Prmeters of Lilium Stlk Adel Heidri, Gholmrez Chegini, Mohmmd Hossein Kinmehr, Seyed Rez Hssn-Beygi nd Jvd Khzei Deprtment of Agrotehnology, College of Auoreihn, University of Tehrn, Tehrn, Irn (Reeived: Jnury 18, 011; Aepted in Revised Form: August 14, 01) Astrt: Some physil nd mehnil property testing of min stlks of Lilium ws onduted to provide informtion for future utomti mhine design. Sher, ompression nd ending properties of Lilium stlks were determined with using universl testing mhine. The experiments were onduted t three rte of loding levels from 30 to 50 mm/min, three knife evel ngle levels from 30 to 60 degree nd t two levels the stlk; upper nd lower. The results showed tht ll the mentioned ove prmeters hd signifint effet on the mesured mehnil properties (P<0.01). In ll three loding rte, n inresing the sher strength nd speifi utting energy were oserved s the knife evel ngle inresed. The highest ompression strength nd speifi ompressing energy were 6.86 MP nd 1.34 mj/mm t the lower level, while the lowest ompression strength nd speifi ompressing energy were.90 MP nd mj/mm t the upper level. As the loding rte of the stlk inresed, the ending strength deresed, inditing redution in the rittleness of the stlk. The verge vlues for modulus of elstiity were found to e 3.48 nd MP for stlk regions of upper nd lower, respetively. Key words: Bending Compression Lilium Physil properties Sher strength Stlk INTRODUCTION density nd frition [4, 5]. Methods nd proedures for determining most of mehnil nd rheologil properties Flower is one of the griulturl rops onsidering its of griulturl produts hve een desried. exporting potentil, Studying on post hrvesting losses Prsd nd Gupt [6] studied the mehnil of this rop hs speil importne. Nowdys using properties of mize stlk in reltion to utting under mehnized nd uto mehnized equipments is qusi-stti deformtion. They oserved tht for mize neessry in post hrvest proessing of ut flower [1]. stlks t moisture ontent of 74% w.. studies showed For this purpose mhine ws designed whih piks tht with inresing utting rte from 00 to 1000 mm/min lefs of ut flowers (Lilium). Before designing of this the sher strength of mize stlk deresed from 3.63 to mhine some physil nd mehnil properties of ut.10 MP. Khzei et l. [7] reported tht with inresing flower were determined. utting rte from 0 to 00 mm/min the sher strength of Most of studies on the physil nd mehnil pyrethrum stlk deresed. The mximum vlues of sher properties of plnts hve een rried out during their fore nd energy for utting of hemp were 43 N nd.1 growth using filure riteri (fore, stress nd energy) J, respetively. Ine et l. [8] reported tht the mximum or their Young's modulus nd the modulus of rigidity. sher stress nd speifi utting energy of sunflower stlk Studies hve foused on plnt ntomy, lodging were 1.07 MP nd mj/mm, respetively. proesses, hrvest optimiztion, niml nutrition, Chttopdhy nd Pndeyreported [9] reported tht the industril pplitions nd the deomposition of whet sher strength of sorghum stlk deresed from 3.74 to strw in soil [, 3]. The physil properties of the ellulr 1.94 MP t the forge stge nd deresed from 4.68 to mteril re importnt for utting, tension, ending,.0 MP t the seed stge when the utting rte ws Corresponding Author: Adel Heidri, Deprtment of Agrotehnology, College of Auoreihn, University of Tehrn, Tehrn, Irn. P.O. Box: Tel: , Fx: , E-mil: delheidri310@ut..ir. 333

2 Irni J. Energy & Environ., 3 (4): , 01 inresed from 10 to 100 mm/min t 30 knife evel ngle. MRndl nd MNulty [10] hve reported tht the verge vlues of sher strength nd sher energy of grsses were 16MP nd 1 mj/mm, respetively. Considering the ove points, there is need for informtion on the vrition in the physi-mehnil properties of Lilium stlk to design nd frition of new piking lef mhine. This study ws foused on determining the shering, ending nd ompression strength nd the speifi shering energy, speifi ompressing energy, speifi ending energy of Lilium stlks s funtion of vrious stlk regions, different rte of loding nd different knife evel ngle. Also the effet of stlk dimeter on modulus of elstiity in ompression ws investigted. Fig. 1: Instron Universl Testing Mhine. MATERIALS AND METHODS The Lilium flower were hrvested from Ashin-e-Sz greenhouse in Tehrn, Irn, from helthy mother stok plnts y shrp knife t height of 10 m ove the soil surfe in the morning of eh testing dte. Hrvested stlks were overed nd trnsported in n insulted ontiner to the iomehnil test devies, lortory in Tehrn University, Tehrn, Irn. Speimens were kept in the refrigertor t temperture 4 C. The dimeter of the Lilium stlk deresed towrds the top of the plnt. Therefore, it ws divided eqully into two levels s upper nd lower [] Test speimens were tken from two lotions: ner the growth tip (upper) nd ner the root internode (lower).testing ws ompleted s rpidly s possile in order to redue the effets of drying. An instron Universl Test Mhine (UTM) whih equipped with 50 N lod ell with n ury of ±0.001 N ws used to mesure the shering, ending nd ompression fore of Lilium stlk test (Figure 1). () () Mesurement of the Physil Properties of Lilium Stlk: A venire liper with m divisions nd 5 m mximum reding ws used in mesuring the stlk dimeter. The weights of the stlk speimens were reorded using weight lne with n ury of 0.01 g. The density of the stlk ws found y displement method using toluene insted of wter to void wter sorption y the speimen. The weight of the speimen in the ir nd the weight of the toluene displed were reorded nd density ws lulted y the following eqution (1) [11]. = W /W S (1) movle lmp k k () Fig. : Apprtus for the mesurement of Sher strength: - shemti of pprtus, - fixed lmp, - 334

3 The moisture ontent nd mss per unit length of the speimen were determined y the use of oven method. The oven temperture ws set t 105±3 C for 4 h. The moisture ontent nd mss per unit length n e expressed y the following eqution [11]: Irni J. Energy & Environ., 3 (4): , 01 W. ( i W MC d w = ) 100 Wi md M = 1 () (3) Mesurement of the Mehnil Properties of Lilium Stlk Sher: The frited fixture (fixed lmp) ws fixed Fig. 3: Shemti of ompression test of Lilium stlk rigidly on the se pltform of the test mhine under the rosshed (movle lmp) with the help of four olts. A flt knife of 3 mm thikness, 50 mm width, 70 mm length nd 0.05 mm edge rdius ws fitted on the rosshed of UTM perpendiulr to the length of stlk speimen (Figure ). The flt knives were frited out of high ron steel nd hd 30, 45 nd 60 degree evel ngle. The stlk speimen ws held on the fixture with the help of two stlk supports of fixed lmp t oth ends of the speimen. During the downwrd movement of the rosshed, the knife ut the speimen y sher nd pssed through the slots provided in the fixture elow the speimen. The fore required for shering the stlk t the Fig. 4: Shemti of ending test of Lilium stlk rosshed speeds of 30, 40 nd 50 mm/min ws reorded ginst time on the UTM hrt reorder. The fore - displement urve ws reorded on the The sher strength nd speifi utting energy were hrt reorder. The liner portion of the fore - determined from the fore-displement urve for different displement urve ws used to ompute the modulus of loding rte nd knife evel ngles using Eqs. (4) nd (5). elstiity in ompression using Eq. (6) [9]. The shering energy ws lulted y integrting the urves of sher fore nd displement [9]. Fd = A L (6) F s = (4) The ompressive energy is found y determining the A re under the liner portion of the ompressive fore vs. 1 f Ess = F. dx = n (5) displement urve. Here, the ompressive energy E ws A A found y Eq. (7) [9]. Compression: A prllel plte pprtus with oth plte 1. f E = F dx = n (7) A surfes lrger thn the mjor dimension of the stlk A speimen were used, Therefore stlk speimens were Bending: Speimens were pled in the three-point pled etween flt steel pltes in the following mnner, loding pprtus under the Instron proe nd the fore speimen support plte, 100 mm squre, upon whih the ws pplied to the enter of the stlk (Figure 4). The speimen is pled nd loding plte, 0 mm squre, for movle plte ws moved t the speeds of 30, 40 nd 50 pplying the fore. The speimen Lilium stlk of 60 mm mm/min nd the fore - displement urve reorded. length ws pled on the se pltform (Figure 3). The ending energy ws determined from the This rrngement llowed for more onentrted pplied fore - displement urve using Eq. (8) [9]. lod on the enter of the speimen. The ompressive fore on the stlk speimen ws pplied y fore plte (proe) 1. nf E = F dx = (8) A t the deformtion rtes of 30, 40 nd 50 mm/min. A 335

4 Irni J. Energy & Environ., 3 (4): , 01 Tle 1: Dependent nd independent vriles studied in the reserh Dependent vriles Independent vriles Vlues Shering strength nd Speifi utting energy Loding rte, mm/min 30,40 nd 50 Knife evel ngle, deg 30, 45 nd 60 Stlk region Upper nd Lower Compression strength nd Speifi ompressing energy Loding rte, mm/min 30,40 nd 50 Stlk region Upper nd Lower Bending strength nd Speifi ending energy Loding rte, mm/min 30,40 nd 50 Stlk region Upper nd Lower Modulus of elstiity Stlk region Upper nd Lower Experimentl Design nd Sttistil Anlysis: The ontent nd density Speimens thn from the upper of the reserh ws onduted in order to determine shering utting (Tle ). The results of nlysis of vrine strength nd the speifi shering energy, ompression (ANOVA) showed tht Speimens group hd signifint strength nd the speifi ompression energy, ending effet on the ll mesured physil properties (P < 0.01). strength nd the speifi ending energy s funtion of Oservtions indite differenes in the woody versus vrious stlk regions, different rte of loding nd suulent nture of tissue depending upon the different knife evel ngle. physiologil ge of the stlk setion [1]. A omplete rndomized lok design ws used in ftoril experiment with five replitions using the Mehnil Property sttistil pkges SAS10. Experimentl dt were Sher Strength: The sher strength nd speifi utting nlyzed using nlysis of vrine (ANOVA) nd the energy deresed with inreses in the loding rte for ll mens were seprted t the 1% level pplying Dunn s levels (Tle 3). This effet of loding rte ws lso multiple rnge tests in SAS softwre. The vlues of reported y Hssn-Beygi et l. [13] for sffron stlk. independent vriles disussed in the study re detiled The sher strength nd speifi utting energy lso in Tle 1. deresed towrds the upper level. The vlue of the sher strength nd speifi utting energy t low stlk regions RESULTS AND DISCUSSIONS ws pproximtely times higher thn t the upper stlk regions. Vlues vried from 0.58 to 1.5 MP nd.36 to The men vlues for the physil properties re 6.79 mj/mm for the upper level nd 0.73 to.4 MP nd presented in Tle. The effets of loding rte nd stlk 3.78 to mj/ mm for the lower level, respetively, t region on shering strength nd the speifi shering the different loding rte studied. The vlues of the sher energy, ompression strength nd the speifi strength nd speifi utting energy were signifintly ompression energy, ending strength nd the speifi ffeted y loding rte, knife evel ngle nd stlk ending energy were signifint t the 1% proility regions t the 1% proility level. Aording to levels. The effet of knife evel ngle on shering Dunn s multiple rnge test results, with inresing strength nd the speifi shering energy ws signifint loding rte from 30 to 50 mm/min the sher strength nd t the 1% proility levels. The intertion of loding speifi utting energy deresed signifintly (P < 0.01) rte nd knife evel ngle on sher strength nd speifi in the rnges of 1.15 to 0.83 MP nd 6.91 to 4.36 mj/mm shering energy ws signifint t 1% level while the respetively (Tle 3). Prsd nd Gupt [6] lso reported effet on ompression strength nd the speifi tht for mize, the mximum sher strength deresed with ompression energy, ending strength nd the speifi the rte of loding from 0 to 100 m/min. Similr results ending energy ws not signifint. Also, the intertion were reported y Heidri nd Chegini [14]. of loding rte nd stlk region, knife evel ngle nd With inresing of the knife evel ngle from 30 to stlk region on the ll mesured mehnil properties 60 degree the sher strength nd speifi utting energy were not signifint t 1% level. The results otined re of the stlk inresed in the rnges of 0.76 to 1.31 MP disussed in detil elow. nd 4.0 to 7.34 mj/mm, respetively (Tle 4). Similr inrese in sher strength with respet to knife evel Physil Property: For physil properties, Speimens ngle ws reported y Chnellor [15]. He found the were tken from the lower were greter in dimeter nd mximum sher strength t moisture ontent of 35% w.. mss per unit length lso, those were smller in moisture MRndl nd MNulty [10] suggested men speifi 336

5 Irni J. Energy & Environ., 3 (4): , 01 Tle : Physil properties of Lilium stlk Stlk region Upper Lower Men 1 Sd Men Sd Moisture ontent, % Dimeter, mm Mss per unit length, gr/m Density, kg/m signifint t 1% level Tle 3: Effet of loding rte on the sher strength nd speifi utting energy Loding rte (mm/min) Sher strength (MP) Speifi utting energy (mj/mm ) Common letter mens tht there ws non-signifint t 1% proility level y Dunn's test Tle 4: Effet of knife evel ngle on the sher strength nd speifi utting energy Knife evel ngle (deg) Sher strength (MP) Speifi utting energy (mj/mm ) Common letter mens tht there ws non-signifint t 1% proility level y Dunn's test sher strength of 1.5MP for field grsses nd 15.7MP for greenhouse grown grsses. Prsd nd Gupt [6] found men vlue of 8.0 MP for mize t moisture ontent of 73% w.. The results of nlysis of vrine (ANOVA) lso showed tht the intertive effet of loding rte nd knife evel ngle were signifint t 1% onfidene on the sher strength nd speifi utting energy nd, in ll three loding rte, n inresing the sher strength nd speifi utting energy were oserved s the knife evel ngle inresed (Figures 5 nd 6). The reson for deresing sher strength nd sher energy with n inrese in utting rte ould e ontriuted to this phenomenon tht t low utting rte the stlk ws ompressed ginst the lde. However, t higher loding rte elsti wll of ells ws not enough time to trnsmit the sher fores to visous fluid within the ells so the stlk ut with lower fore. Similr results were reported y previous reserhers like Prsd nd Gupt [6] hve reported tht the sher strength of mize stlk ws deresed with inresing rte of loding from 00 to 1000 mm/min. The investigtions of Chttopdhyy nd Pndey [9] showed tht with inresing utting rte from 10 to 100 mm/min the sher strength of sorghum stlk deresed from 3.74 to 1.94 MP. Hssn-Beygi et l. [13] reported with inresing rte of loding from 00 to 1000 mm/min Fig. 5: Effet of loding rte on Lilium stlk sher energy for different knife evel ngle Fig. 6: Effet of loding rte on Lilium stlk speifi utting energy for different knife evel ngle the sher strength nd speifi utting energy of sffron stlk ws deresed. Also, with inresing utting rte the sher strength nd speifi utting energy were deresed for ll of the evel ngle levels. 1 Stndrd devition 337

6 Irni J. Energy & Environ., 3 (4): , 01 Tle 5: Effet of loding rte on the Compression strength nd speifi Compressing energy Loding rte (mm/min) Compression strength (MP) Speifi Compressing energy (mj/mm ) Common letter mens tht there ws non-signifint t 1% proility level y Dunn's test Tle 6: Effet of loding rte on the ending strength nd speifi ending energy Loding rte (mm/min) Bending strength (MP) Speifi ending energy (mj/mm ) Common letter mens tht there ws non-signifint t 1% proility level y Dunn's test Compression Strength: The highest ompression strength nd speifi ompressing energy were 6.86 MP nd 1.34 mj/mm t the lower level, while the lowest ompression strength nd speifi ompressing energy were.90 MP nd mj/mm t the upper level. The ompression strength nd speifi ompressing energy deresed towrds the upper levels of the stlk. The differenes in the vlues of the ompression strength nd speifi ompressing energy in the stlk levels redued s the loding rte inresed. The nlysis of vrine showed tht loding rte nd stlk regions hd Fig. 7: Effet of stlk dimeter on the modulus of elstiity signifint effet on stlk shering stress t 1% proility level. In ddition, ording to Dunn s 4.43 To 6.8 mj/mm for ner the root internode multiple rnge tests, with inresing loding rte from speimens, respetively. Aording to the Dunn s 30 to 50 mm/min the ompression strength nd speifi multiple rnge test with inresing loding rte from 30 to ompressing energy deresed signifintly (P < 0.01) in 50 mm/min the required ending strength nd speifi the rnges of 5.49 to 4.33 MP nd to 7.07 mj/mm ending energy deresed signifintly (P < 0.01) in the respetively (Tle 5). Similr results were reported y rnges of 1.5 to 0.95 MP nd 4.84 to 3.09 mj/mm Simonton [16] for gernium. respetively (Tle 6). Results the ending strength nd The ompression strength nd speifi ompressing speifi ending energy vlues re sttistilly different energy lso vried towrds the stlk regions. With from eh other. inresing the stlk dimeter the ompression strength nd speifi ompressing energy were inresed Modulus of Elstiity: Modulus of elstiity in signifintly (P < 0.01). The verge vlues of the ompression ws determined t vrious stlk regions ompression nd speifi ompression energy were 3.73 (stlk levels). O Dogherty et l. [18] showed tht modulus MP nd 8.14 mj/mm for upper speimen nd 6.7 MP of elstiity for whet strw ws etween 4.76 GP nd nd 9.90 mj/mm for lower speimen, respetively GP. The effet of stlk region on modulus of elstiity ws signifint t 1% proility level. The Bending: The ending strength ws evluted s verge vlue for modulus of elstiity were found to e funtion of loding rte nd stlk regions. As the loding 3.48 MP nd MP for stlk regions of upper nd rte of the stlk inresed, the ending strength lower, respetively. However, with inresing the stlk deresed, inditing redution in the rittleness of the dimeter (hnge in stlk levels) the modulus of elstiity stlk. A similr result ws lso reported y Annoussmy ws inresed (Figure 7). et l. [] nd Nzri Gledr et l. [17]. The ending strength lso deresed towrds the upper level. The CONCLUSIONS vrition rnge of ending strength nd speifi ending energy were 0.6 to 1.45 MP nd 0.76 To 3.7 mj/mm for For physil properties, Speimens were tken from ner the growth tip speimen nd 0.97 to 1.66 MP nd the lower were greter in dimeter nd mss per unit 338

7 3 length lso, those were smller in moisture ontent nd Density of stlk (kg/m ) density Speimens thn from the upper of the utting. Modulus of elstiity in ompression (MP) The verge vlues of the shering nd required speifi s Sher strength (MP) shering energy were 0.81 MP nd 4.37 mj/mm for upper speimen nd 1.13 MP nd 6.9 mj/mm for lower REFERENCES speimen, respetively. With inresing of the knife evel ngle from 30 to 60 degree the sher strength nd speifi utting energy of the stlk inresed in the rnges of 0.76 to 1.31 MP nd 4.0 to 7.34 mj/mm, respetively. The highest ompression strength nd speifi ompressing energy were 6.86 MP nd 1.34 mj/mm t the lower level, while the lowest ompression strength nd speifi ompressing energy were.90 MP nd mj/mm t the upper level. The vrition rnge of ending strength nd speifi ending energy were 0.6 to 1.45 MP nd 0.76 To 3.7 mj/mm for ner the growth tip speimen nd 0.97 to 1.66 MP nd 4.43 To 6.8 mj/mm for ner the root internode speimens, respetively. The verge vlue for modulus of elstiity were found to e 3.48 MP nd MP for stlk regions of upper nd lower, respetively. ACKNOWLEDGEMENTS The uthors would like to thnk the University of Tehrn for full support of the projet. Arevitions: A Cross-setionl re of stlk (m ) d Dimeter of the stlk t the point of ompression (mm) Ess Speifi shering energy (mj/mm ) f Sle ftor of unit re F Bending fore t whih the stlk fils (N); F Compressive fore(n) Fs Shering fore (N) l Length of speimen(m) M.Cw Moisture ontent (%) M Mss per unit length(g/m) md Dried mss of speimen (g) n Numer of units under fore-displement urve on the universl testing mhine (UTM) hrt 3 Sk Mss density of kerosene (kg/m ) W Weight of stlk in ir (kg) Wd Dried weight of speimen (kg) Wi Initil weight of speimen (kg) Wk Weight of toluene displed y speimen (kg) x Knife displement (mm) L Trnsverse deformtion due to ompressive fore (mm) Irni J. Energy & Environ., 3 (4): , Ige, M.T. nd M.F. Finner, Effets nd intertion etween ftors ffeting the shering hrteristi of forge hrvesters. Trnstions of the ASABE., 18(6): Annoussmy, M., G. Rihrd, S. Reous nd J. Guerif, 000 Chnge in mehnil properties of whet strw due to deomposition nd moisture. Applied Engineering in Agriulture, 16(6): Skuisz, G., T.I. Krvtsov nd L.P. Veliknov, 007. Anlysis of the strength properties of pe stlks. Int. Agrophysis, 1: Yiljep, Y.D. nd U.S. Mohmmed, 005. Effet of Knife Veloity on Cutting Energy nd Effiieny during Impt Cutting of Sorghum Stlk. Agriulturl Engineering Interntionl, the CIGR Journl, Mnusript PM, , Vol. VII. eommons. ornell.edu... Journls CIGR E-Journl Volume Shw, M.D. nd L.G. Til, 007. Compression, Relxtion nd Adhesion Properties of Seleted Biomss Grinds. Agriulturl Engineering Interntionl, the CIGR Ejournl, Mnusript FP , Vol. IX. 6. Prsd, J. nd C.B. Gupt, Mehnil properties of mize stlks s relted to hrvesting. J. Agri. Eng. Res., 0(1): Khzei, J., H. Rni, A. Edi nd F. Golei, 00. Determining the sher strength nd piking fore of pyrethrum flower. Irnin J. Agri. Si., 33(3): Ine, A., S. Ugurluy, E. Guzel nd M.T. Ozn, 005. Bending nd shering hrteristis of sunflower stlk residue. Biosystlks Eng., 9(): Chttopdhyy, P.S. nd K.P. Pndey, Mehnil properties of sorghum stlk in reltion to qusi-stti deformtion. J. Agri. Eng. Res., 73: MNulty, P.B. nd N.N. Moshenin, Comption of ulk orn rnl to filure. Trnstion of the ASAE, (): Mohsenin, N.N., Physil Properties of Plnt nd Animl Mteril. Gordon nd Brnh. New York, USA. 1. Grossmn, H.H., 198 Antomy nd Morphology. In Gerniums Mstlerz nd Holom, pp:

8 Irni J. Energy & Environ., 3 (4): , Hssn-Beygi, S.R., H. Vle Ghozhdi nd J. Khzei, 16. Simonton, W., 199. Physil properties of zonl 010. Piking Fore of Sffron Flower nd Sher gernium uttings. Trns of the ASAE., Strength of Sffron Stlk. Eletroni Journl of 35(6): Polish Agriulturl Universities. Volume Nzri, Gledr, M., A. Jfri, S.S. Mohtsei, A. Tteefr, A. Shrifi, M.J. O Dogherty, 14. Heidri, A. nd G.H.R. Chegini, 008. Determining the S. Rfiee nd G. Rihrd, 008. Effets of moisture sher strength nd piking fore of rose flower. ontent nd level in the rop on the engineering Eletroni Journl of Polish Agriulturl Universities, properties of lflf stlks. Biosyst. Eng., pp: volume14/ issue/ 101: rt-13.html. 18. O Dogherty, M.J., J.A. Huert, J. Dyson nd 15. Chnellor, W.J., Energy requirements for C.J. Mrshll, A study of the physil nd utting forge. Agriulturl Engineering, mehnil properties of whet strw. J. Agri. Eng. 39(10): Res., 6:

First compression (0-6.3 GPa) First decompression ( GPa) Second compression ( GPa) Second decompression (35.

First compression (0-6.3 GPa) First decompression ( GPa) Second compression ( GPa) Second decompression (35. 0.9 First ompression (0-6.3 GP) First deompression (6.3-2.7 GP) Seond ompression (2.7-35.5 GP) Seond deompression (35.5-0 GP) V/V 0 0.7 0.5 0 5 10 15 20 25 30 35 P (GP) Supplementry Figure 1 Compression

More information

Review Topic 14: Relationships between two numerical variables

Review Topic 14: Relationships between two numerical variables Review Topi 14: Reltionships etween two numeril vriles Multiple hoie 1. Whih of the following stterplots est demonstrtes line of est fit? A B C D E 2. The regression line eqution for the following grph

More information

Roughness Coefficients for Selected Residue Materials

Roughness Coefficients for Selected Residue Materials University of Nersk - Linoln DigitlCommons@University of Nersk - Linoln Biologil Systems Engineering: Ppers nd Pulitions Biologil Systems Engineering 8-1991 Roughness Coeffiients for Seleted Residue Mterils

More information

Effects of Applying Accumulator Straw in Soil on Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris under Cadmium Stress

Effects of Applying Accumulator Straw in Soil on Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris under Cadmium Stress Interntionl Conferene on Mnufturing Siene nd Engineering (ICMSE 2015) Effets of Applying Aumultor Strw in Soil on Nutrient Uptke nd Soil Enzyme Ativity of Cpsell burs-pstoris under Cdmium Stress Jin Wng1,,

More information

THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL

THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL P3.1 Kot Iwmur*, Hiroto Kitgw Jpn Meteorologil Ageny 1. INTRODUCTION Jpn Meteorologil Ageny

More information

Activities. 4.1 Pythagoras' Theorem 4.2 Spirals 4.3 Clinometers 4.4 Radar 4.5 Posting Parcels 4.6 Interlocking Pipes 4.7 Sine Rule Notes and Solutions

Activities. 4.1 Pythagoras' Theorem 4.2 Spirals 4.3 Clinometers 4.4 Radar 4.5 Posting Parcels 4.6 Interlocking Pipes 4.7 Sine Rule Notes and Solutions MEP: Demonstrtion Projet UNIT 4: Trigonometry UNIT 4 Trigonometry tivities tivities 4. Pythgors' Theorem 4.2 Spirls 4.3 linometers 4.4 Rdr 4.5 Posting Prels 4.6 Interloking Pipes 4.7 Sine Rule Notes nd

More information

University of Sioux Falls. MAT204/205 Calculus I/II

University of Sioux Falls. MAT204/205 Calculus I/II University of Sioux Flls MAT204/205 Clulus I/II Conepts ddressed: Clulus Textook: Thoms Clulus, 11 th ed., Weir, Hss, Giordno 1. Use stndrd differentition nd integrtion tehniques. Differentition tehniques

More information

SIDESWAY MAGNIFICATION FACTORS FOR STEEL MOMENT FRAMES WITH VARIOUS TYPES OF COLUMN BASES

SIDESWAY MAGNIFICATION FACTORS FOR STEEL MOMENT FRAMES WITH VARIOUS TYPES OF COLUMN BASES Advned Steel Constrution Vol., No., pp. 7-88 () 7 SIDESWAY MAGNIFICATION FACTORS FOR STEEL MOMENT FRAMES WIT VARIOUS TYPES OF COLUMN BASES J. ent sio Assoite Professor, Deprtment of Civil nd Environmentl

More information

Compressive behavior of hemp fiber (Cannabis sativa L.) stalks

Compressive behavior of hemp fiber (Cannabis sativa L.) stalks The Cndin Society for ioengineering The Cndin society for engineering in griculturl, food, environmentl, nd iologicl systems. L Société Cndienne de Génie grolimentire et de ioingénierie L société cndienne

More information

Applying Hyperaccumulator Straw in Cd-Contaminated Soil Enhances Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris

Applying Hyperaccumulator Straw in Cd-Contaminated Soil Enhances Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris Interntionl Conferene on Mnufturing Siene nd Engineering (ICMSE 2015) Applying Hyperumultor Strw in Cd-Contminted Soil Enhnes Nutrient Uptke nd Soil Enzyme Ativity of Cpsell burs-pstoris Jin Wng1,, Keng

More information

Iowa Training Systems Trial Snus Hill Winery Madrid, IA

Iowa Training Systems Trial Snus Hill Winery Madrid, IA Iow Trining Systems Tril Snus Hill Winery Mdrid, IA Din R. Cohrn nd Gil R. Nonneke Deprtment of Hortiulture, Iow Stte University Bkground nd Rtionle: Over the lst severl yers, five sttes hve een evluting

More information

ANALYSIS AND MODELLING OF RAINFALL EVENTS

ANALYSIS AND MODELLING OF RAINFALL EVENTS Proeedings of the 14 th Interntionl Conferene on Environmentl Siene nd Tehnology Athens, Greee, 3-5 Septemer 215 ANALYSIS AND MODELLING OF RAINFALL EVENTS IOANNIDIS K., KARAGRIGORIOU A. nd LEKKAS D.F.

More information

for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx

for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx Applitions of Integrtion Are of Region Between Two Curves Ojetive: Fin the re of region etween two urves using integrtion. Fin the re of region etween interseting urves using integrtion. Desrie integrtion

More information

SECTION A STUDENT MATERIAL. Part 1. What and Why.?

SECTION A STUDENT MATERIAL. Part 1. What and Why.? SECTION A STUDENT MATERIAL Prt Wht nd Wh.? Student Mteril Prt Prolem n > 0 n > 0 Is the onverse true? Prolem If n is even then n is even. If n is even then n is even. Wht nd Wh? Eploring Pure Mths Are

More information

Restraint of purlins for various roof systems

Restraint of purlins for various roof systems NS009 Restrint of purlins for vrious roof systems T. Vrny, M. Brhm & A. Beli ulty of ivil Engineering, zeh Tehnil University, Prh, zehi Astron Buildings S.A., Diekirh, Luxemourg, A memer of the Lind Group

More information

Novel Fiber-Optical Refractometric Sensor Employing Hemispherically-Shaped Detection Element

Novel Fiber-Optical Refractometric Sensor Employing Hemispherically-Shaped Detection Element Novel Fier-Optil Refrtometri Sensor Employing Hemispherilly-Shped Detetion Element SERGEI KHOTIAINTSEV, VLADIMIR SVIRID Deprtment of Eletril Engineering, Fulty of Engineering Ntionl Autonomous University

More information

Table of Content. c 1 / 5

Table of Content. c 1 / 5 Tehnil Informtion - t nd t Temperture for Controlger 03-2018 en Tble of Content Introdution....................................................................... 2 Definitions for t nd t..............................................................

More information

Project 6: Minigoals Towards Simplifying and Rewriting Expressions

Project 6: Minigoals Towards Simplifying and Rewriting Expressions MAT 51 Wldis Projet 6: Minigols Towrds Simplifying nd Rewriting Expressions The distriutive property nd like terms You hve proly lerned in previous lsses out dding like terms ut one prolem with the wy

More information

Comparing the Pre-image and Image of a Dilation

Comparing the Pre-image and Image of a Dilation hpter Summry Key Terms Postultes nd Theorems similr tringles (.1) inluded ngle (.2) inluded side (.2) geometri men (.) indiret mesurement (.6) ngle-ngle Similrity Theorem (.2) Side-Side-Side Similrity

More information

A Study on the Properties of Rational Triangles

A Study on the Properties of Rational Triangles Interntionl Journl of Mthemtis Reserh. ISSN 0976-5840 Volume 6, Numer (04), pp. 8-9 Interntionl Reserh Pulition House http://www.irphouse.om Study on the Properties of Rtionl Tringles M. Q. lm, M.R. Hssn

More information

Spacetime and the Quantum World Questions Fall 2010

Spacetime and the Quantum World Questions Fall 2010 Spetime nd the Quntum World Questions Fll 2010 1. Cliker Questions from Clss: (1) In toss of two die, wht is the proility tht the sum of the outomes is 6? () P (x 1 + x 2 = 6) = 1 36 - out 3% () P (x 1

More information

Momentum and Energy Review

Momentum and Energy Review Momentum n Energy Review Nme: Dte: 1. A 0.0600-kilogrm ll trveling t 60.0 meters per seon hits onrete wll. Wht spee must 0.0100-kilogrm ullet hve in orer to hit the wll with the sme mgnitue of momentum

More information

Some Aspects of Non-Orthogonal Stagnation-Point Flow towards a Stretching Surface

Some Aspects of Non-Orthogonal Stagnation-Point Flow towards a Stretching Surface Engineering, 00,, 705-709 doi:0.436/eng.00.909 Published Online September 00 (http://www.sirp.org/journl/eng) Some Aspets of Non-Orthogonl Stgntion-Point Flow towrds Strething Surfe Abstrt Mothr Rez, Andi

More information

THE SIGNIFICANCE OF PROVIDING OF SHEAR WALLS IN TALL BUILDINGS

THE SIGNIFICANCE OF PROVIDING OF SHEAR WALLS IN TALL BUILDINGS THE SIGNIFICANCE OF PROVIDING OF SHEAR WALLS IN TALL BUILDINGS 1 V.Klpn, 2 N.R.Sngeeth, 3 M.Sheik Mohmed 1 Assistnt Professor, Civil Engineering Deprtment, AlimMuhmmedSlegh College of Engineering, Muthpudupet,

More information

Engr354: Digital Logic Circuits

Engr354: Digital Logic Circuits Engr354: Digitl Logi Ciruits Chpter 4: Logi Optimiztion Curtis Nelson Logi Optimiztion In hpter 4 you will lern out: Synthesis of logi funtions; Anlysis of logi iruits; Tehniques for deriving minimum-ost

More information

Effects of Drought on the Performance of Two Hybrid Bluegrasses, Kentucky Bluegrass and Tall Fescue

Effects of Drought on the Performance of Two Hybrid Bluegrasses, Kentucky Bluegrass and Tall Fescue TITLE: OBJECTIVE: AUTHOR: SPONSORS: Effets of Drought on the Performne of Two Hyrid Bluegrsses, Kentuky Bluegrss nd Tll Fesue Evlute the effets of drought on the visul qulity nd photosynthesis in two hyrid

More information

WORKSHOP 1 Composite Wing

WORKSHOP 1 Composite Wing WORKSHOP 1 Composite Wing WS1-1 WS1-2 Workshop Ojetives Beome fmilir with the si steps in doing omposites nlysis Softwre Version Ptrn 2011 MD Nstrn 2011.1 Required File: omposite_wing.d WS1-3 Prolem Desription

More information

A Non-parametric Approach in Testing Higher Order Interactions

A Non-parametric Approach in Testing Higher Order Interactions A Non-prmetri Approh in Testing igher Order Intertions G. Bkeerthn Deprtment of Mthemtis, Fulty of Siene Estern University, Chenkldy, Sri Lnk nd S. Smit Deprtment of Crop Siene, Fulty of Agriulture University

More information

H (2a, a) (u 2a) 2 (E) Show that u v 4a. Explain why this implies that u v 4a, with equality if and only u a if u v 2a.

H (2a, a) (u 2a) 2 (E) Show that u v 4a. Explain why this implies that u v 4a, with equality if and only u a if u v 2a. Chpter Review 89 IGURE ol hord GH of the prol 4. G u v H (, ) (A) Use the distne formul to show tht u. (B) Show tht G nd H lie on the line m, where m ( )/( ). (C) Solve m for nd sustitute in 4, otining

More information

Studying the morphological traits of winter barley varieties and lines in Ardabil using multivariate statistical methods

Studying the morphological traits of winter barley varieties and lines in Ardabil using multivariate statistical methods J. Bio. & Env. Si. 2014 Journl of Biodiversity nd Environmentl Sienes (JBES) ISSN: 2220-6663 (Print) 2222-3045 (Online) Vol. 4, No. 3, p. 309-318, 2014 http://www.innspu.net RESEARCH PAPER OPEN ACCESS

More information

AP Calculus BC Chapter 8: Integration Techniques, L Hopital s Rule and Improper Integrals

AP Calculus BC Chapter 8: Integration Techniques, L Hopital s Rule and Improper Integrals AP Clulus BC Chpter 8: Integrtion Tehniques, L Hopitl s Rule nd Improper Integrls 8. Bsi Integrtion Rules In this setion we will review vrious integrtion strtegies. Strtegies: I. Seprte the integrnd into

More information

SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS

SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS IN-SITU PROBING OF DOMAIN POLING IN Bi 4 Ti 3 O 12 THIN FILMS BY OPTICAL SECOND HARMONIC GENERATION YANIV BARAD, VENKATRAMAN GOPALAN Mterils Reserh Lortory

More information

Lecture Notes No. 10

Lecture Notes No. 10 2.6 System Identifition, Estimtion, nd Lerning Leture otes o. Mrh 3, 26 6 Model Struture of Liner ime Invrint Systems 6. Model Struture In representing dynmil system, the first step is to find n pproprite

More information

VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS

VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS AGRICULTURAL ENGINEERING VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS Ltvi University of Agriulture E-mil: ilze.pelee@llu.lv Astrt Use of solr energy inreses every

More information

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 CH 3. CH 3 C a. NMR spectroscopy. Different types of NMR

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 CH 3. CH 3 C a. NMR spectroscopy. Different types of NMR 6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht

More information

A Brief Note on Quasi Static Thermal Stresses In A Thin Rectangular Plate With Internal Heat Generation

A Brief Note on Quasi Static Thermal Stresses In A Thin Rectangular Plate With Internal Heat Generation Americn Journl of Engineering Reserch (AJER) 13 Americn Journl of Engineering Reserch (AJER) e-issn : 3-847 p-issn : 3-936 Volume-, Issue-1, pp-388-393 www.jer.org Reserch Pper Open Access A Brief Note

More information

Probability. b a b. a b 32.

Probability. b a b. a b 32. Proility If n event n hppen in '' wys nd fil in '' wys, nd eh of these wys is eqully likely, then proility or the hne, or its hppening is, nd tht of its filing is eg, If in lottery there re prizes nd lnks,

More information

Estimation of Global Solar Radiation in Onitsha and Calabar Using Empirical Models

Estimation of Global Solar Radiation in Onitsha and Calabar Using Empirical Models Communitions in Applied Sienes ISS 0-77 Volume, umer, 0, 5-7 Estimtion of Glol Solr dition in Onitsh nd Clr Using Empiril Models M.. nuhi, J. E. Ekpe nd G. F Ieh Deprtment of Industril Physis, Eonyi Stte

More information

(h+ ) = 0, (3.1) s = s 0, (3.2)

(h+ ) = 0, (3.1) s = s 0, (3.2) Chpter 3 Nozzle Flow Qusistedy idel gs flow in pipes For the lrge vlues of the Reynolds number typilly found in nozzles, the flow is idel. For stedy opertion with negligible body fores the energy nd momentum

More information

Forces on curved surfaces Buoyant force Stability of floating and submerged bodies

Forces on curved surfaces Buoyant force Stability of floating and submerged bodies Stti Surfe ores Stti Surfe ores 8m wter hinge? 4 m ores on plne res ores on urved surfes Buont fore Stbilit of floting nd submerged bodies ores on Plne res Two tpes of problems Horizontl surfes (pressure

More information

1B40 Practical Skills

1B40 Practical Skills B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need

More information

NEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE

NEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE NEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE V.S. Gordeev, G.A. Myskov Russin Federl Nuler Center All-Russi Sientifi Reserh Institute of Experimentl Physis (RFNC-VNIIEF)

More information

Something found at a salad bar

Something found at a salad bar Nme PP Something found t sld r 4.7 Notes RIGHT TRINGLE hs extly one right ngle. To solve right tringle, you n use things like SOH-H-TO nd the Pythgoren Theorem. n OLIQUE TRINGLE hs no right ngles. To solve

More information

Linear Algebra Introduction

Linear Algebra Introduction Introdution Wht is Liner Alger out? Liner Alger is rnh of mthemtis whih emerged yers k nd ws one of the pioneer rnhes of mthemtis Though, initilly it strted with solving of the simple liner eqution x +

More information

Dorf, R.C., Wan, Z. T- Equivalent Networks The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000

Dorf, R.C., Wan, Z. T- Equivalent Networks The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000 orf, R.C., Wn,. T- Equivlent Networks The Eletril Engineering Hndook Ed. Rihrd C. orf Bo Rton: CRC Press LLC, 000 9 T P Equivlent Networks hen Wn University of Cliforni, vis Rihrd C. orf University of

More information

AP CALCULUS Test #6: Unit #6 Basic Integration and Applications

AP CALCULUS Test #6: Unit #6 Basic Integration and Applications AP CALCULUS Test #6: Unit #6 Bsi Integrtion nd Applitions A GRAPHING CALCULATOR IS REQUIRED FOR SOME PROBLEMS OR PARTS OF PROBLEMS IN THIS PART OF THE EXAMINATION. () The ext numeril vlue of the orret

More information

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 H 3 CH3 C. NMR spectroscopy. Different types of NMR

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 H 3 CH3 C. NMR spectroscopy. Different types of NMR 6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht

More information

, g. Exercise 1. Generator polynomials of a convolutional code, given in binary form, are g. Solution 1.

, g. Exercise 1. Generator polynomials of a convolutional code, given in binary form, are g. Solution 1. Exerise Genertor polynomils of onvolutionl ode, given in binry form, re g, g j g. ) Sketh the enoding iruit. b) Sketh the stte digrm. ) Find the trnsfer funtion T. d) Wht is the minimum free distne of

More information

Bend Forms of Circular Saws and Evaluation of their Mechanical Properties

Bend Forms of Circular Saws and Evaluation of their Mechanical Properties ISSN 139 13 MATERIALS SCIENCE (MEDŽIAGOTYRA). Vol. 11, No. 1. 5 Bend Forms of Circulr s nd Evlution of their Mechnicl Properties Kristin UKVALBERGIENĖ, Jons VOBOLIS Deprtment of Mechnicl Wood Technology,

More information

MATH Final Review

MATH Final Review MATH 1591 - Finl Review November 20, 2005 1 Evlution of Limits 1. the ε δ definition of limit. 2. properties of limits. 3. how to use the diret substitution to find limit. 4. how to use the dividing out

More information

Lesson 2: The Pythagorean Theorem and Similar Triangles. A Brief Review of the Pythagorean Theorem.

Lesson 2: The Pythagorean Theorem and Similar Triangles. A Brief Review of the Pythagorean Theorem. 27 Lesson 2: The Pythgoren Theorem nd Similr Tringles A Brief Review of the Pythgoren Theorem. Rell tht n ngle whih mesures 90º is lled right ngle. If one of the ngles of tringle is right ngle, then we

More information

Journal of Chemical and Pharmaceutical Research, 2013, 5(12): Research Article

Journal of Chemical and Pharmaceutical Research, 2013, 5(12): Research Article Avilble online www.jopr.om Journl of Chemil nd Phrmeutil Reserh, 2013, 5(12):1283-1288 Reserh Artile ISSN : 0975-7384 CODEN(USA) : JCPRC5 Study on osion resistne of zin lloy oting of mehnil plting by eletrohemil

More information

ALTERATION OF GEOTECHNICAL PROPERTIES OF PORTLAND LIMESTONE AND MONK'S PARK LIMESTONE UNDER SIMULATED WEATHERING

ALTERATION OF GEOTECHNICAL PROPERTIES OF PORTLAND LIMESTONE AND MONK'S PARK LIMESTONE UNDER SIMULATED WEATHERING 739 ALTERATION OF GEOTECHNICAL PROPERTIES OF PORTLAND LIMESTONE AND MONK'S PARK LIMESTONE UNDER SIMULATED WEATHERING MURPHY,W. Deprtment of Geology, University of Portsmouth, Burnby Building, Burnby Rod,

More information

Formula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx

Formula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx Fill in the Blnks for the Big Topis in Chpter 5: The Definite Integrl Estimting n integrl using Riemnn sum:. The Left rule uses the left endpoint of eh suintervl.. The Right rule uses the right endpoint

More information

Chapter Gauss Quadrature Rule of Integration

Chapter Gauss Quadrature Rule of Integration Chpter 7. Guss Qudrture Rule o Integrtion Ater reding this hpter, you should e le to:. derive the Guss qudrture method or integrtion nd e le to use it to solve prolems, nd. use Guss qudrture method to

More information

8.3 THE HYPERBOLA OBJECTIVES

8.3 THE HYPERBOLA OBJECTIVES 8.3 THE HYPERBOLA OBJECTIVES 1. Define Hperol. Find the Stndrd Form of the Eqution of Hperol 3. Find the Trnsverse Ais 4. Find the Eentriit of Hperol 5. Find the Asmptotes of Hperol 6. Grph Hperol HPERBOLAS

More information

1.3 SCALARS AND VECTORS

1.3 SCALARS AND VECTORS Bridge Course Phy I PUC 24 1.3 SCLRS ND VECTORS Introdution: Physis is the study of nturl phenomen. The study of ny nturl phenomenon involves mesurements. For exmple, the distne etween the plnet erth nd

More information

ME311 Machine Design

ME311 Machine Design ME11 Mchine Design Lecture 10: Springs (Chpter 17) W Dornfeld 9Nov018 Firfield University School of Engineering A Free Body Digrm of coil spring (cutting through nywhere on the coil) shows tht there must

More information

Calculus Cheat Sheet. Integrals Definitions. where F( x ) is an anti-derivative of f ( x ). Fundamental Theorem of Calculus. dx = f x dx g x dx

Calculus Cheat Sheet. Integrals Definitions. where F( x ) is an anti-derivative of f ( x ). Fundamental Theorem of Calculus. dx = f x dx g x dx Clulus Chet Sheet Integrls Definitions Definite Integrl: Suppose f ( ) is ontinuous Anti-Derivtive : An nti-derivtive of f ( ) on [, ]. Divide [, ] into n suintervls of is funtion, F( ), suh tht F = f.

More information

On the Scale factor of the Universe and Redshift.

On the Scale factor of the Universe and Redshift. On the Sle ftor of the Universe nd Redshift. J. M. unter. john@grvity.uk.om ABSTRACT It is proposed tht there hs been longstnding misunderstnding of the reltionship between sle ftor of the universe nd

More information

Mathematics. Area under Curve.

Mathematics. Area under Curve. Mthemtics Are under Curve www.testprepkrt.com Tle of Content 1. Introduction.. Procedure of Curve Sketching. 3. Sketching of Some common Curves. 4. Are of Bounded Regions. 5. Sign convention for finding

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Nme Dte hpter 9 Mintining Mthemtil Profiieny Simplify the epression. 1. 500. 189 3. 5 4. 4 3 5. 11 5 6. 8 Solve the proportion. 9 3 14 7. = 8. = 9. 1 7 5 4 = 4 10. 0 6 = 11. 7 4 10 = 1. 5 9 15 3 = 5 +

More information

ILLUSTRATING THE EXTENSION OF A SPECIAL PROPERTY OF CUBIC POLYNOMIALS TO NTH DEGREE POLYNOMIALS

ILLUSTRATING THE EXTENSION OF A SPECIAL PROPERTY OF CUBIC POLYNOMIALS TO NTH DEGREE POLYNOMIALS ILLUSTRATING THE EXTENSION OF A SPECIAL PROPERTY OF CUBIC POLYNOMIALS TO NTH DEGREE POLYNOMIALS Dvid Miller West Virgini University P.O. BOX 6310 30 Armstrong Hll Morgntown, WV 6506 millerd@mth.wvu.edu

More information

Lecture 6: Coding theory

Lecture 6: Coding theory Leture 6: Coing theory Biology 429 Crl Bergstrom Ferury 4, 2008 Soures: This leture loosely follows Cover n Thoms Chpter 5 n Yeung Chpter 3. As usul, some of the text n equtions re tken iretly from those

More information

THE ASYMMETRY OF COASTAL WATER LEVEL RESPONSE TO LANDFALLING HURRICANES SIMULATED BY A THREE-DIMENSIONAL STORM SURGE MODEL

THE ASYMMETRY OF COASTAL WATER LEVEL RESPONSE TO LANDFALLING HURRICANES SIMULATED BY A THREE-DIMENSIONAL STORM SURGE MODEL THE ASYMMETRY OF COASTAL WATER LEVEL RESPONSE TO LANDFALLING HURRICANES SIMULATED BY A THREE-DIMENSIONAL STORM SURGE MODEL Mhun Peng *, Lin Xie nd Leonrd J. Pietrfes Deprtment of Mrine, Erth nd Atmospheri

More information

Distributed Generation Placement in Unbalanced Distribution System with Seasonal Load Variation

Distributed Generation Placement in Unbalanced Distribution System with Seasonal Load Variation Distriuted Genertion Plement in Unlned Distriution System with Sesonl Lod Vrition Rvi Tej Bhimrsetti Dept. of Eletril Engg., NT Kurukshetr Kurukshetr, ndi svrtej@gmil.om Ashwni Kumr, Memer, EEE Dept. of

More information

ANALYSIS OF MECHANICAL PROPERTIES OF COMPOSITE SANDWICH PANELS WITH FILLERS

ANALYSIS OF MECHANICAL PROPERTIES OF COMPOSITE SANDWICH PANELS WITH FILLERS ANALYSIS OF MECHANICAL PROPERTIES OF COMPOSITE SANDWICH PANELS WITH FILLERS A. N. Anoshkin *, V. Yu. Zuiko, A.V.Glezmn Perm Ntionl Reserch Polytechnic University, 29, Komsomolski Ave., Perm, 614990, Russi

More information

COMPARISON BETWEEN TWO FRICTION MODEL PARAMETER ESTIMATION METHODS APPLIED TO CONTROL VALVES. Rodrigo Alvite Romano and Claudio Garcia

COMPARISON BETWEEN TWO FRICTION MODEL PARAMETER ESTIMATION METHODS APPLIED TO CONTROL VALVES. Rodrigo Alvite Romano and Claudio Garcia 8th Interntionl IFAC Symposium on Dynmis nd Control of Proess Systems Preprints Vol., June 6-8, 007, Cnún, Mexio COMPARISON BETWEEN TWO FRICTION MODEL PARAMETER ESTIMATION METHODS APPLIED TO CONTROL VALVES

More information

Distance Measurement. Distance Measurement. Distance Measurement. Distance Measurement. Distance Measurement. Distance Measurement

Distance Measurement. Distance Measurement. Distance Measurement. Distance Measurement. Distance Measurement. Distance Measurement IVL 1101 Surveying - Mesuring Distne 1/5 Distne is one of the most si engineering mesurements Erly mesurements were mde in terms of the dimensions of the ody very old wooden rule - Royl Egyptin uit uits

More information

1 This question is about mean bond enthalpies and their use in the calculation of enthalpy changes.

1 This question is about mean bond enthalpies and their use in the calculation of enthalpy changes. 1 This question is out men ond enthlpies nd their use in the lultion of enthlpy hnges. Define men ond enthlpy s pplied to hlorine. Explin why the enthlpy of tomistion of hlorine is extly hlf the men ond

More information

Statistics in medicine

Statistics in medicine Sttistis in meiine Workshop 1: Sreening n ignosti test evlution Septemer 22, 2016 10:00 AM to 11:50 AM Hope 110 Ftm Shel, MD, MS, MPH, PhD Assistnt Professor Chroni Epiemiology Deprtment Yle Shool of Puli

More information

Nonuniform Flow in a Compressor Due to Asymmetric Tip Clearance

Nonuniform Flow in a Compressor Due to Asymmetric Tip Clearance Seung Jin Song e-mil: sjsong@snu..kr Seung Ho Cho Shool of Mehnil nd Aerospe Engineering, Seoul Ntionl University, Seoul 151-74, Kore Nonuniform Flow in Compressor Due to Asymmetri Tip Clerne This pper

More information

System Validation (IN4387) November 2, 2012, 14:00-17:00

System Validation (IN4387) November 2, 2012, 14:00-17:00 System Vlidtion (IN4387) Novemer 2, 2012, 14:00-17:00 Importnt Notes. The exmintion omprises 5 question in 4 pges. Give omplete explntion nd do not onfine yourself to giving the finl nswer. Good luk! Exerise

More information

Due to gravity and wind load, the post supporting the sign shown is subjected simultaneously to compression, bending, and torsion.

Due to gravity and wind load, the post supporting the sign shown is subjected simultaneously to compression, bending, and torsion. ue to grvit nd wind lod, the post supporting the sign shown is sujeted simultneousl to ompression, ending, nd torsion. In this hpter ou will lern to determine the stresses reted suh omined lodings in strutures

More information

Supporting Information

Supporting Information tom-thik Interlyer Mde of VD-Grown Grphene Film on Seprtor for dvned thium-sulfur tteries Zhenzhen Du 1, hengkun Guo 2, njun Wng 3, jun Hu 1, Song Jin 1, Timing Zhng 1, Honghng Jin 1, Zhiki Qi 1, Sen Xin

More information

PREDICTION OF THE MODULUS OF ELASTICITY OF HIGH STRENGTH CONCRETE *

PREDICTION OF THE MODULUS OF ELASTICITY OF HIGH STRENGTH CONCRETE * Irnin Journl of Siene & Tehnology, Trnstion B, ngineering, Vol. 9, No. B Printed in The Islmi Republi of Irn, Shirz University PRDICTION OF TH MODULUS OF LSTICITY OF HIGH STRNGTH CONCRT * D. MOSTOFINJD

More information

Available online at ScienceDirect. Procedia Engineering 172 (2017 )

Available online at  ScienceDirect. Procedia Engineering 172 (2017 ) Aville online t www.sciencedirect.com ScienceDirect Procedi Engineering 172 (2017 ) 218 225 Modern Building Mterils, Structures nd Techniques, MBMST 2016 Experimentl nd Numericl Anlysis of Direct Sher

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

For a, b, c, d positive if a b and. ac bd. Reciprocal relations for a and b positive. If a > b then a ab > b. then

For a, b, c, d positive if a b and. ac bd. Reciprocal relations for a and b positive. If a > b then a ab > b. then Slrs-7.2-ADV-.7 Improper Definite Integrls 27.. D.dox Pge of Improper Definite Integrls Before we strt the min topi we present relevnt lger nd it review. See Appendix J for more lger review. Inequlities:

More information

1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light.

1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light. 1 This igrm represents the energy hnge tht ours when eletron in trnsition metl ion is exite y visile light. Give the eqution tht reltes the energy hnge ΔE to the Plnk onstnt, h, n the frequeny, v, of the

More information

Final Exam Review. [Top Bottom]dx =

Final Exam Review. [Top Bottom]dx = Finl Exm Review Are Between Curves See 7.1 exmples 1, 2, 4, 5 nd exerises 1-33 (odd) The re of the region bounded by the urves y = f(x), y = g(x), nd the lines x = nd x = b, where f nd g re ontinuous nd

More information

QUADRATIC EQUATION. Contents

QUADRATIC EQUATION. Contents QUADRATIC EQUATION Contents Topi Pge No. Theory 0-04 Exerise - 05-09 Exerise - 09-3 Exerise - 3 4-5 Exerise - 4 6 Answer Key 7-8 Syllus Qudrti equtions with rel oeffiients, reltions etween roots nd oeffiients,

More information

Problems set # 3 Physics 169 February 24, 2015

Problems set # 3 Physics 169 February 24, 2015 Prof. Anhordoqui Problems set # 3 Physis 169 Februry 4, 015 1. A point hrge q is loted t the enter of uniform ring hving liner hrge density λ nd rdius, s shown in Fig. 1. Determine the totl eletri flux

More information

( ) as a fraction. Determine location of the highest

( ) as a fraction. Determine location of the highest AB/ Clulus Exm Review Sheet Solutions A Prelulus Type prolems A1 A A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f( x) Set funtion equl to Ftor or use qudrti eqution if qudrti Grph to

More information

AP Calculus AB Unit 4 Assessment

AP Calculus AB Unit 4 Assessment Clss: Dte: 0-04 AP Clulus AB Unit 4 Assessment Multiple Choie Identify the hoie tht best ompletes the sttement or nswers the question. A lultor my NOT be used on this prt of the exm. (6 minutes). The slope

More information

A Matlab/Simulink Model of a Langevin s Ultrasonic Power Transducers

A Matlab/Simulink Model of a Langevin s Ultrasonic Power Transducers Mtl/Simulink Model of Lngevin s Ultrsoni Power Trnsduers Igor Jovnović, Ugleš Jovnović nd Drgn Mnčić strt Ultrsoni sndwih trnsduer, lso known s Lngevin s trnsduer, is hlf-wve resonnt struture tht osilltes

More information

MECHANICS OF MATERIALS

MECHANICS OF MATERIALS 9 The cgrw-hill Compnies, Inc. All rights reserved. Fifth SI Edition CHAPTER 5 ECHANICS OF ATERIALS Ferdinnd P. Beer E. Russell Johnston, Jr. John T. DeWolf Dvid F. zurek Lecture Notes: J. Wlt Oler Texs

More information

5. Every rational number have either terminating or repeating (recurring) decimal representation.

5. Every rational number have either terminating or repeating (recurring) decimal representation. CHAPTER NUMBER SYSTEMS Points to Rememer :. Numer used for ounting,,,,... re known s Nturl numers.. All nturl numers together with zero i.e. 0,,,,,... re known s whole numers.. All nturl numers, zero nd

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

THERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION

THERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es

More information

THE PYTHAGOREAN THEOREM

THE PYTHAGOREAN THEOREM THE PYTHAGOREAN THEOREM The Pythgoren Theorem is one of the most well-known nd widely used theorems in mthemtis. We will first look t n informl investigtion of the Pythgoren Theorem, nd then pply this

More information

NANO-SCALE EFFECTS IN THE ADHERENCE, SLIDING AND ROLLING OF A CYLINDER ON A SUBSTRATE

NANO-SCALE EFFECTS IN THE ADHERENCE, SLIDING AND ROLLING OF A CYLINDER ON A SUBSTRATE Nno-Sle Effets in Clindril Contts Sri et l. NANO-SCALE EFFECTS IN THE ADHERENCE, SLIDING AND ROLLING OF A CYLINDER ON A SUBSTRATE Ö. T. Sri, G. G. Adms, S. Müftü Mehnil Engineering Deprtment Northestern

More information

(Thymus fallax Fisch.et C.A. Mey.)

(Thymus fallax Fisch.et C.A. Mey.) DOI: http://x.oi.org/10.22092/ijmpr.2014.982 (19) 519528 4 0 (Thymus fllx Fish.et C.A. Mey.) 2 2 *1 *1 Mohmmin5@yhoo.om : 2 191 : 191 : 190 :. Nepetoiee (Lmiee) (Thymus). Thymus fllx Fish.et C.A. Mey..

More information

Coimisiún na Scrúduithe Stáit State Examinations Commission

Coimisiún na Scrúduithe Stáit State Examinations Commission M 30 Coimisiún n Scrúduithe Stáit Stte Exmintions Commission LEAVING CERTIFICATE EXAMINATION, 005 MATHEMATICS HIGHER LEVEL PAPER ( 300 mrks ) MONDAY, 3 JUNE MORNING, 9:30 to :00 Attempt FIVE questions

More information

Finite Element Simulation on Frictional and Brittle Preseismic fault slip

Finite Element Simulation on Frictional and Brittle Preseismic fault slip Finite Element Simultion on Fritionl nd Brittle Preseismi fult slip Zhishen Wu (1) Yun Go (1) Yutk Murkmi (2) (1) Deprtment of Urn & Civil Engineering. Irki University, Jpn (e-mil: zswu@ip.irki..jp; goyun@hs.irki..jp,

More information

GM1 Consolidation Worksheet

GM1 Consolidation Worksheet Cmridge Essentils Mthemtis Core 8 GM1 Consolidtion Worksheet GM1 Consolidtion Worksheet 1 Clulte the size of eh ngle mrked y letter. Give resons for your nswers. or exmple, ngles on stright line dd up

More information

MCH T 111 Handout Triangle Review Page 1 of 3

MCH T 111 Handout Triangle Review Page 1 of 3 Hnout Tringle Review Pge of 3 In the stuy of sttis, it is importnt tht you e le to solve lgeri equtions n tringle prolems using trigonometry. The following is review of trigonometry sis. Right Tringle:

More information

Effects of Sowing Dates and CCC Application on Morphological Traits, Agronomical Indices and Grain Yield in Barley Cultivars

Effects of Sowing Dates and CCC Application on Morphological Traits, Agronomical Indices and Grain Yield in Barley Cultivars World Applied Sienes Journl 4 (): 77-73, 0 ISSN 88-495 IDOSI Pulitions, 0 Effets of Sowing Dtes nd CCC Applition on Morphologil Trits, Agronomil Indies nd Grin Yield in Brley Cultivrs 3 S. Dstn, H.R. Mosser,

More information

FORM FIVE ADDITIONAL MATHEMATIC NOTE. ar 3 = (1) ar 5 = = (2) (2) (1) a = T 8 = 81

FORM FIVE ADDITIONAL MATHEMATIC NOTE. ar 3 = (1) ar 5 = = (2) (2) (1) a = T 8 = 81 FORM FIVE ADDITIONAL MATHEMATIC NOTE CHAPTER : PROGRESSION Arithmetic Progression T n = + (n ) d S n = n [ + (n )d] = n [ + Tn ] S = T = T = S S Emple : The th term of n A.P. is 86 nd the sum of the first

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