Performance of Stirling Engines * (Arranging Method of Experimental Results and Performance Prediction) Abstract. 1. Introduction
|
|
- Augustine Lyons
- 6 years ago
- Views:
Transcription
1 1 Performace of Stirlig Egies (Arragig Method of Experimetal Results ad Performace Predictio) Shoichi IWAMOTO Koichi HIRATA ad Fujio TODA Key Words: Stirlig Egie, Heat Exchager, Frictio, Egie Desig, Mechaical Loss, Pressure Loss Trasactios of the Japa Society of Mechaical Egieers, No.65, Vol.635, B, p Advaced Research Istitute for Sciece ad Egieerig, Waseda Uiversity, Okubo 3-4-1, Shijuku, Tokyo , Japa Ship Research Istitute, Shikawa , Mitaka, Tokyo , Japa, Saitama Uiversity, Shimo-okubo 255, Urawa, Saitama , Japa Abstract We have developed five kids of high- ad low-temperature differetial Stirlig egies ad their egie performace was ivestigated experimetally. I order to determie the parameters that affect egie performace, experimetal results were discussed ad compared with results calculated usig aalytical methods. We show a arragig method for the experimetal results, ad cosider the performace of geeral Stirlig egies. After usig the arragig method with odimesioal umbers obtaied by a dimesioal aalysis, a predictio method, which is used at the early desig stage, is formulated. Oe of the odimesioal umbers i this predictio method is calculated based o egie specificatios, icludig the properties of the workig gas. The predictio method ca predict egie speed, output power, the effect of workig gas ad operatig coditios. 1. Itroductio Recetly, evirometal pollutio ad eergy utilizatio have become serious problems worldwide. As Stirlig egies are a potetial solutio to the above problems, they have bee developed actively, ad the results of may studies have bee reported (1)-(9). However, to our kowledge, o systematic ivestigatio ad research o the parameters that affect egie performace have bee coducted to date. It is importat that egie performace be predicted accurately from the mai specificatios that are determied from the target performace durig egie desig. Geerally, the calculatio for egie performace is iitiated after the mai specificatios are determied ad the desig for heat exchagers ad mechaical devices is fiished. But, i actual practice, it is ecessary that the egie performace be determied at the same time as egie specificatios, ad also before fiishig the desig for heat exchagers ad mechaical devices. We have developed five kids of high- ad low-temperature differetial Stirlig egies, ad measured their performace. The measured performace is compared with results calculated usig aalytical methods. The parameters that affect egie performace are ivestigated. We suggest a arragig method for the experimetal results, discuss the performace of geeral Stirlig egies ad develop a simple method for predictig egie performace. 2. Previous Performace Predictio Methods As methods for predictig output power, LS, from egie specificatios, two simple methods utilizig the Beale Number (8) ad the West Number (9) are well kow. i) Beale Number, BN; This method for predictig output power was suggested by Beale (8), where BN is defied by Eq. (1). B L P V m S N = (1) SE Here, Pm is mea pressure i the workig space (Pa), VSE is swept volume of a expasio space (m 3 ),
2 2 is egie speed per uit secod (rps). It is kow that BN at the egie speed where maximum output power is realized, is about 0.15 i the case of high-temperature differetial Stirlig egies whose heater wall temperature is about 650 C (8). ii) West Number, WN; This method was suggested by West (9), where WN is defied by Eq. (2) with revisio of BN. LS W N = (2) T E TC PmVSE TE + TC Here, TE is expasio space gas temperature, ad TC is compressio space gas temperature. It was foud that WN is about 0.25 i the case of 5~150 kw class Stirlig egies, ad is about 0.35 i the case of smaller power egies (9). Output power ca be predicted from egie specificatios usig the BN or WN. However, it is ecessary to determie the egie speed at which maximum output power is realized. The, i order to predict egie performace accurately, the relatioship betwee output power, LS, ad egie speed,, ad that betwee the kid of workig gas ad the output power must be determied, with cosideratio of egie type ad operatig coditios. 3. Arragemet for Experimetal Results We have developed high- ad low-temperature differetial Stirlig egies ad measured their performace (10)-(14). Also, egie performace has bee aalyzed ad calculated usig aalytical methods (15)-(17). After compariso ad discussio, the parameters that affect output power sigificatly were clarified. As we have foud that pressure loss of the workig gas ad mechaical loss due to frictio i the mechaical devices affect output power sigificatly, the experimetal results ca be arraged as follows. 3.1 Pressure loss of workig gas The pressure of the workig gas decreases whe the gas flows through heat exchagers cosistig of a heater, a regeerator ad a cooler. The pressure drop is treated as pressure loss. Work doe by the egie depeds maily o the mea pressure of the workig gas, Pm, the egie size, the expasio space gas temperature, TE, ad the compressio space gas temperature, TC. Furthermore, work is affected strogly by pressure loss at heat exchagers. Pressure loss is affected by the egie type ad operatig coditios such as the egie speed, the desity of the workig gas i heat exchagers, ρ, the kietic viscosity, ν, ad the shape of heat exchagers. Thus, pressure loss should be calculated precisely at the fial desig stage, that is, after determiig the detailed sizes of heater ad cooler tubes ad the specificatios of the regeerator matrix. However, it is cosidered that the size of heat exchagers is depedet o egie size, because similar types of heat exchagers have bee adapted i geeral Stirlig egies. Thus, the swept volume of the expasio space, VSE, is used as the typical parameter that expresses as the size of heat exchagers, because VSE is geerally determied at the early desig stage. Also, the gas costat, R, ad the kietic viscosity of the workig gas, ν, are used as the typical parameters that express the properties of pressure loss, based o the fuctio, ρm Pm/(RTE), where ρm is the mea desity i the expasio space, TE is the expasio space gas temperature, Pm is the mea pressure, ad R is the gas costat. 3.2 Mechaical loss by frictio It ca be cosidered that mechaical loss cosists of Coulomb frictio loss ad viscosity frictio loss. The Coulomb frictio coefficiet, µco, ad the viscosity frictio coefficiet, cvi, are parameters that affect output power. The Coulomb frictio coefficiet, µco, is the same for Stirlig egies that cosist of the same type of mechaical elemets. Also, the viscosity frictio coefficiet, cvi, is depedet o the swept volume of the expasio space, VSE, because cvi is affected strogly by the egie size. The, the swept volume of the expasio space, VSE, is determied to be a typical parameter that expresses mechaical loss. 3.3 Derivatio of odimesioal umbers From the above cosideratios, it is assumed that egie performace cosists of the followig fuctio.
3 3 π1 π 2 π 3 π 4 π 5 π 6 π 7 π = Ws Pm VSE R TE ν, (3) where, Ws is output work (J), Pm is mea pressure of workig gas (Pa), VSE is swept volume of expasio space (m 3 ), R is gas costat (J/kgK), TE is expasio space gas temperature (K), ν is kietic viscosity at temperature, TE, ad pressure, Pm, ad is egie speed (rps). The compressio space gas temperature, TC, is assumed to be costat i the case of geeral Stirlig egies, because it was cofirmed that it does ot differ markedly regardless of the egie type. Equatio (3) ca be show as Eq. (4) usig fudametal uits with mass, M, legth, L, time, T, ad temperature, θ. 2 2 π1 1 2 π 2 3 π π 4 π π 6 1 π π = ML T ML T L L T θ θ L T T (4) [ ] [ ] [ ] [ ] [ ] [ ] [ ] 7 The, we focus o leadig odimesioal umbers that symbolize egie speed ad output power. After much discussio ad cosideratio, the followig three odimesioal umbers are suggested. VSE 2 3 (5) ν WS ws (6) P V m SE T RV 2 3 E SE s =, (7) 2 ν where, is defied as odimesioal speed, ad ws is defied as odimesioal output work. I the case of a egie of which cylider bore, D, is equal to pisto stroke, H, Eq. (5) ca be chaged to Eq. (8) with mea pisto speed, u (=2H). = k ud ν, (8) where, k is a fixed umber [=( /4) 2/3 /2]. Namely, the odimesioal speed,, is equivalet to the Reyolds umber, because it is a ratio of iertia force to viscosity force of the workig gas with a typical legth, D. The odimesioal output work, ws, is equal to the Beale Number, BN, defied by Eq. (1). O the other had, the size ad specificatios of seal devices such as a pisto rig ad a rod seal are determied from the mea pressure i the workig space at maximum load, Plim, at the early desig stage. Also, workig pressure ad temperature are set as the operatig coditios of the egie, ad both affect mechaical loss strogly. The, odimesioal pressure, P, ad odimesioal temperature, T, are defied by Eqs. (9) ad (10), respectively. They are the odimesioal umbers that express the operatig coditios. P T P m (9) P T T lim E E T C + T C Here, Pm is mea pressure of workig gas, Plim is limited maximum mea pressure, TE is expasio space gas temperature, ad TC is compressio space gas temperature. 4. Results of Arragemet ad Cosideratios We have developed a 100 W class small egie ad measured its performace (10),(16). The experimetal results are treated usig the odimesioal umbers as defied above. Figure 1 shows the relatioship betwee odimesioal speed,, ad odimesioal output work, ws, at odimesioal temperature, T, of 0.42 (TE=490 C, TC=40 C) usig helium as the workig gas. I the figure, each lie represets the calculated results based o the isothermal aalysis method with cosideratio of pressure loss ad mechaical loss (15) (called the secod-order model). The solid lie represets the result at odimesioal pressure, P =0.73 (Pm=0.8 MPa), the broke lie represets that at P =0.55 (Pm=0.6 MPa), ad the dot-dashed lie represets that at P =0.36 (Pm=0.4 MPa). Symbols represet the experimetal results at P =0.73, 0.64, 0.55, 0.45 or 0.36 (the mea pressure, Pm, is varied from 0.8 MPa to 0.4 MPa with 0.1 MPa steps). From the figure, the odimesioal output work, ws, decreases with icreasig odimesioal speed,. O the other had, it was cofirmed that the output power teds to decrease at higher egie speed, though the (10)
4 idicated power icreases at higher egie speed i this experimet (15). The decrease i ws with icreasig is caused by the icrease i pressure loss i the heat exchagers ad mechaical loss caused by viscosity frictio at higher, because pressure loss ad mechaical loss are affected by egie speed as described above. Also, the odimesioal output work, ws, decreases with decreasig odimesioal pressure, P. Because the specificatios of seal devices such as a pisto rig are determied based o P 1 at the desig stage, the rate of Coulomb frictio loss of the seal devices icreases with decreasig odimesioal pressure, P. Figure 2 shows the relatioship betwee odimesioal speed,, ad odimesioal output work, ws, at odimesioal pressure, P, of 0.73 (Pm=0.8 MPa) usig helium as the workig gas. I the figure, the solid lie represets the calculated result at T =0.42 (TE=490 C, TC=40 C), the broke lie represets that at T =0.38 (TE=430 C, TC=40 C), ad the dot-dashed lie represets that at T =0.35 (TE=370 C, TC=40 C). Symbols represet the experimetal results i the case of T at 0.42, 0.40, 0.38, 0.37 or 0.35 (the expasio space gas temperature, TE is varied from 490 to 370 C with 30 C steps). From the figure, the odimesioal output work, ws, decreases with icreasig odimesioal speed,, ad decreasig odimesioal temperature, T, similar to the case i Fig. 1. This is due to the fact that the mechaical loss is ot strogly affected by the expasio space gas temperature, TE, ad the odimesioal temperature, T ; furthermore the rate of mechaical loss per uit output power icreases with icreasig odimesioal speed,. Figure 3 shows the relatioship betwee odimesioal speed,, ad odimesioal output work, ws, at odimesioal pressure, P, of 0.73 (Pm=0.8 MPa) usig itroge as the workig gas. I the figure, the solid lie represets the calculated result at T =0.40 (TE=460 C, TC=40 C), the broke lie represets that at T =0.37 (TE=400 C, TC=40 C), ad the dot-dashed lie represets that at T =0.32 (TE=340 C, TC=40 C). Symbols represet the experimetal results whe T is set at 0.40, 0.38, 0.37, 0.35 or 0.32 (the expasio space gas temperature, TE is varied from 460 to 340 C with 30 C steps). From the figure, the odimesioal output work, ws, decreases with icreasig odimesioal speed,, ad decreasig odimesioal temperature, T, similar to the case i Fig. 2, though the effect becomes small at higher values of odimesioal egie speed,. This may be due to the strog effects of pressure loss i the heat exchagers. The calculated results agree with experimetal oes very well. Also, the rage of odimesioal egie speed,, is much higher, about 2000~6000, tha the rage of of about 100~800 whe helium is used as the workig gas, as show i Figs. 1 ad 2. This is because the kietic viscosity, ν, strogly affects odimesioal speed,, ad because is equivalet to the Reyolds umber, as described above. Figures 1, 2 ad 3 show two cases of the relatioship betwee odimesioal speed,, ad odimesioal output work, ws, as defied by Eqs. (5) ad (6), for the 100 W class Stirlig egie. 4
5 5 Oe is the case of chagig the mea pressure, Pm, while maitaiig the same gas temperature, TE ad TC. The other is the case of chagig the gas temperature, TE, while maitaiig the same mea pressure, Pm. Furthermore, we cofirmed that similar figures were obtaied i the case of other operatig coditios ad differet types of egies icludig low-temperature differetial Stirlig egies. Thus, it is cosidered that the experimetal results ca be arraged with ad ws. Also, it is cofirmed that the results of the aalytical method agree well with the experimetal results, ad that the method has high accuracy. 5. Performace of Prototype Egies ad Predictio Method From the above cosideratios, the odimesioal output work, ws, ca be arraged well accordig to the odimesioal speed,, with odim esioal pressure, P, ad temperature T, as parameters. I order to determie the relatioship betwee egie specificatios ad output power, aother odimesioal output work, WS, ad odimesioal output power, LS, are defied by Eqs. (11) ad (12), respectively. W L P V W S m SEP S s (11) S T = W (12) O the other had, assumig that the egie is operated at the limited maximum gas temperature, Tlim, Eq. (13) is derived by revisig Eq. (7), where the expasio space gas temperature, TE, is chaged to Tlim, ad the kietic viscosity, νlim is used at temperature, Tlim, ad pressure, Plim. 2 3 TlimRV S = SE (13) 2 ν lim Here, S is defied as a odimesioal egie specificatio, because it is a odimesioal umber which is calculated from the egie specificatios at the early desig stage. Table 1 shows the egie specificatios ad the operatig coditios of five kids of prototype egies. They have differet egie types, operatig temperatures, pressures ad output power levels. I the table, Egie A is the 100 W class gamma type (see Figs. 1~3), Egie B is a alpha type of a similar power ad temperature level as Egie A, ad Egie C is a 2 kw class beta type. They are the high-temperature differetial egies. Egie D is a 1 kw class alpha type, ad Egie E is a 300 W class gamma type, both of which are low-temperature differetial egies. Figure 4 shows the relatioship betwee odimesioal speed, ad odimesioal output power, LS based o the experimetal results of the prototype egies listed i Table 1. Each odimesioal egie specificatio, S, is show i the figure. I the case of Egie A, two types of operatig coditios, i which either helium or itroge is used as the workig gas, are idicated. From the figure, each egie exhibits a maximum value of the odimesioal output power, LS,max at a give ; i.e., the maximum value of LS,max is the optimal coditio. The odimesioal maximum output power, LS,max, is obtaied whe the egie reaches the maximum output power, LS,max, i each experimet. LS,max icreases ad appears i the rage of higher odimesioal speed,, with
6 6 icreasig odimesioal egie specificatio, S. As a result, the odimesioal speed, opt at which the odimesioal maximum output power, LS,max, is obtaied accordig to the odimesioal egie specificatio, S. Table 2 shows the results of odimesioal values, LS,max, opt ad S, based o the measured maximum output power, LS,max, ad egie speed, opt. Namely, the values of LS,max are the peak values (the optimal coditio) for each egie show i Fig. 4. Figure 5 shows the relatioship betwee opt ad LS,max give i Table 2. I the figure, circles represet the experimetal results, ad the solid lie represets the calculated result usig the method of least squares. From the figure, it is cosidered that the relatioship betwee maximum output power ad egie speed ca be arraged usig the odimesioal maximum output power, LS,max ad the odimesioal speed, opt. As the relatioship betwee opt ad LS,max is a liear oe, it is expressed by Eqs. (14) ad (15). L S, max al opt = (14) The coefficiet, al, is determied to be the value give below from Fig. 5. a = 0.24 (15) L Figure 6 shows the relatioship betwee odimesioal egie specificatio, S, ad odimesioal speed, opt. I the figure, circles represet the experimetal results, ad the solid lie represets the calculated result usig the method of least squares. From the figure, the relatioship betwee S ad opt is expressed by Eqs. (16) ad (17) i the same maer as i Fig.5. opt m = a S (16) The coefficiets, a ad m, are determied to be the followig values from Fig. 6. a m = = (17) Next, the relatioship betwee odimesioal egie specificatio, S, ad odimesioal maximum output power, LS,max, is derived as show i Eq. (18) from Eqs. (14)~(17). L S max, = S 0.60 (18) Also from Eq. (14), Eq. (12) ad the defiitios of the odimesioal umbers, we ca see that the coefficiet al=0.24 is equivalet to the West Number, WN, at P =1. I order to cofirm the propriety of Eqs. (14)~(18) based o the experimetal results of the five kids of egies, other experimetal results that have already bee published are arraged by the same method, ad they are compared with Figs. 5 ad 6. Table 3 lists the egie specificatios, the experimetal results ad the values of the odimesioal umbers of previously reported egies. I the table, there are several egies that do ot have the measured value of the expasio space gas temperature, TE. I the case of high-performace egies, the heater wall temperature is estimated
7 geerally istead of the expasio gas temperature, TE. Thus, the value of TE is estimated by a simple calculatio of the heat trasfer based o the specificatios of the heat exchagers, the heater wall temperature ad other measured values. Figure 7 shows the relatioship betwee odimesioal speed obtaied from the maximum output power, opt, ad odimesioal maximum output power, LS,max. Figure 8 shows the relatioship betwee odimesioal egie specificatio, S, ad odimesioal speed, opt. I these figures, white circles represet the experimetal results of the previously reported egies listed i Table 3, ad black circles represet those of our prototype egies listed i Table 2. The broke lies were obtaied usig Eqs. (14) ad (16), respectively. From the figures, most of the experimetal results of the previously reported egies lie o the opt - LS,max ad S -opt lies, i the same maer as that of our prototype egies listed i Table 2. As a result, it is cofirmed that the performace of geeral Stirlig egies ca be estimated usig Eqs. (14)~(18), because the experimetal results ca be arraged by the odimesioal umbers, opt, LS,max ad S i egies of differet types, sizes, workig gas ad operatig coditios. 7
8 8 6. Flowchart of Predictio Method As the relatioship betwee egie specificatios ad output power is clarified as described above, egie performace ca be predicted at the early desig stage. Figure 9 shows a flowchart of the performace predictio method for the egie desig. First, the odimesioal egie specificatio, S, ca be calculated usig Eq. (13) based o the desig coditio ad egie specificatios. After the odimesioal speed, opt, ad the odimesioal maximum output power, LS,max, are derived from Eqs. (14)~(18), the maximum output power, LS,max, ad the egie speed at a particular time, opt, ca be derived. Namely, the predictio method suggested i this paper ca simply predict the maximum output power ad egie speed at a particular time based o egie specificatios, though it was impossible to do so usig previous predictio methods. Also, this predictio method ca estimate the effects of the kid of workig gas ad the operatig coditios by the derivatio of the odimesioal egie specificatio, S ; thus, it is possible to predict the egie performace i detail. 7. Coclusio I this paper, we measured the performace of high- ad low-temperature differetial Stirlig egies, ad derived the odimesioal umbers i order to estimate egie performace. Fially, the performace predictio method based o egie specificatios was suggested. This study is summarized as follows. (1) The relatioship betwee output work ad egie speed ca be arraged usig the odimesioal speed,, ad the odimesioal output work, ws, with odimesioal pressure, P, ad temperature, T, as parameters (see Figs. 1~3). Also, because the calculated results agree well with the experimetal results, the aalytical method is prove to have sufficietly high accuracy. (2) From the relatioship betwee odimesioal speed,, ad odimesioal output power, Ls, the optimal value of the odimesioal speed, opt, is derived based o the odimesioal egie specificatio, S (see Fig. 4). Thus, there is a optimal egie speed, opt, at which maximum output power, LS,max, is obtaied. (3) The maximum output power, LS,max, ad the optimal egie speed, opt, are derived from Eqs. (5)~(18) whe the mai egie specificatios are determied. Egie performace ca be predicted by the flowchart show i Fig. 9. Additioally, as egie performace is affected by pressure loss i the heat exchagers ad mechaical loss caused by frictio i the mechaical devices, the effects of these should be clarified. However, egies with differet types of mechaical devices ad differet heat exchage situatios such as high- ad low-temperature heat source, were ivestigated i this study. I particular, the heater of a high-temperature differetial egie exchages heat betwee hot gas ad workig gas, i.e., from oe gas to aother gas, ad similar types of heat exchagers are used i such cases. I cotrast, the heat exchagers ad the mechaical devices of a low-temperature differetial egie are differet from those of the high-temperature differetial egie. The heater of the low-temperature differetial egie described i this paper exchages heat betwee hot water ad workig gas, i.e., from liquid to gas. I spite of the fact that various egies were estimated, egie performace agrees well, as show i the diagrams (see Figs. 4~8), based o the odimesioal umbers defied i this paper. The relatioship betwee egie specificatio ad output power is expressed by Eqs. (14)~(18). Namely, it is cosidered that the type of heat exchager ad the mechaical loss deped o the swept volume of the expasio space. As a result, it was foud that the predictio method suggested i this study has sufficietly high accuracy for use at the desig stage of the geeral Stirlig egies.
9 9 Refereces (1) Edo, N., Hasegawa, Y., Shioyama, E., Taaka, A., Taaka, M., Yamada, Y., Takahashi, S. ad Yamashita, I., Test ad Evaluatio Method of the Kiematic Stirlig Egies ad Their Applicatio Systems Used i the Moo Light Project, 4th Iteratioal Coferece o Stirlig Egies (1988), p (2) Lista, P., First Experimetal Results Testig the V160DMA Stirlig Cogeeratio Uit, Proc. 6th Iteratioal Stirlig Egies Coferece (1993), p (3) Orga, A.J., Stirlig Egie Thermodyamics Desig - Without the Computer (1993), A.1.1, Regeerative Thermal Machies. (4) Hargreaves, C.M., The Philips Stirlig Egie (1991), Elsevier. (5) Yamashita, I., Taaka, S., Hasegawa, Y., Taaka, M., Suzuki, K. ad Yaagihara, S., Theoretical ad Experimetal Studies o Stirlig Egies, Techical Report of Mechaical Egieerig Laboratory, (i Japaese), No.128 (1983), p (6) Richey, A.E., Automotive Stirlig Egie Systems Developmet, Proc. 19th Itersociety Eergy Coversio Egieerig Coferece (1984), p (7) Wataabe, T., Yamaguchi, S., Yamaguchi, K., Momose, Y., Haramura, S., Kodoh, T. ad Ishizaki, Y., 50 kw Stirlig Egie, Proc. 17th Itersociety Eergy Coversio Egieerig Coferece (1982), p (8) Walker, G., Elemetary Desig Guidelies for Stirlig Egies, Proc. 14th Itersociety Eergy Coversio Egieerig Coferece (1979), p (9) West, C.D., Priciples ad Applicatios of Stirlig Egie (1986), p , Va Nostrad Reihold Compay. (10) Hirata, K., Kagawa, N., Yamashita, I. ad Iwamoto, S., Basic Study o Developmet of Stirlig Egie for Small Portable Geerator (1st Report, Egie Desig, Maufacturig, ad Performace), Tras. Jp. Soc. Mech. Eg.(i Japaese), Vol. 64, No. 621, B (1998), p (11) Iwamoto, S., Toda, F. ad Suzuki, S., Performace of 100W class small Stirlig egie, Proc. of Japa Society for Desig Egieerig (i Japaese), No. 96-Sprig (1996), p (12) Tsukahara, S., Isshiki, N., Kuwabara, M., Tamaki, H., Terada, F. ad Yoshikawa, K., Developmet of 2 kw Stirlig Egie, Proc. 4th Iteratioal Coferece o Stirlig Egies (1988), p (13) Iwamoto, S., Toda, F., Hirata, K. ad Takeuchi, M., Performace Characteristics of 1kW Class Low-Temperature Differece Stirlig Egie, Proc. The 1st Symposium o Stirlig Cycle, Jp. Soc. Mech. Eg. (i Japaese), No (1997), p (14) Iwamoto, S., Toda, F., Hirata, K., Takeuchi, M. ad Yamamoto, T., Compariso of Low- ad High Temperature Differetial Stirlig Egies, Proc. 8th Iteratioal Stirlig Egie Coferece ad Exhibitio (1997), p (15) Hirata, K., Hamaguchi, K. ad Iwamoto, S., Basic Study o Developmet of Stirlig Egie for Small Portable Geerator (2d Report, Egie Performace Predictio by Simulatio Model), Tras. Jp. Soc. Mech. Eg. (i Japaese), Vol. 64, No. 621, B (1998), p (16) Iwamoto, S. ad Toda, F., Performace Aalysis for Low-Temperature-Differece Stirlig Egie (Defiitio of Mechaism Efficiecy ad Effects of Various Factors o Egie Performace), Tras. Jp. Soc. Mech. Eg. (i Japaese), Vo. 63, No. 611, B (1997), p (17) Toda, F. ad Iwamoto, S., Performace Aalysis for Low-Temperature-Differece Stirlig Egie (Effect of Gas Flow Losses o Idicated Power), Tras. Jp. Soc. Mech. Eg. (i Japaese), Vol. 64, No. 619, B (1998), p
Comparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series
Applied Mathematical Scieces, Vol. 7, 03, o. 6, 3-337 HIKARI Ltd, www.m-hikari.com http://d.doi.org/0.988/ams.03.3430 Compariso Study of Series Approimatio ad Covergece betwee Chebyshev ad Legedre Series
More informationPOWER SERIES SOLUTION OF FIRST ORDER MATRIX DIFFERENTIAL EQUATIONS
Joural of Applied Mathematics ad Computatioal Mechaics 4 3(3) 3-8 POWER SERIES SOLUION OF FIRS ORDER MARIX DIFFERENIAL EQUAIONS Staisław Kukla Izabela Zamorska Istitute of Mathematics Czestochowa Uiversity
More informationEXPERIMENT OF SIMPLE VIBRATION
EXPERIMENT OF SIMPLE VIBRATION. PURPOSE The purpose of the experimet is to show free vibratio ad damped vibratio o a system havig oe degree of freedom ad to ivestigate the relatioship betwee the basic
More informationMathematical Modeling of Optimum 3 Step Stress Accelerated Life Testing for Generalized Pareto Distribution
America Joural of Theoretical ad Applied Statistics 05; 4(: 6-69 Published olie May 8, 05 (http://www.sciecepublishiggroup.com/j/ajtas doi: 0.648/j.ajtas.05040. ISSN: 6-8999 (Prit; ISSN: 6-9006 (Olie Mathematical
More informationSimilarity between quantum mechanics and thermodynamics: Entropy, temperature, and Carnot cycle
Similarity betwee quatum mechaics ad thermodyamics: Etropy, temperature, ad Carot cycle Sumiyoshi Abe 1,,3 ad Shiji Okuyama 1 1 Departmet of Physical Egieerig, Mie Uiversity, Mie 514-8507, Japa Istitut
More informationA statistical method to determine sample size to estimate characteristic value of soil parameters
A statistical method to determie sample size to estimate characteristic value of soil parameters Y. Hojo, B. Setiawa 2 ad M. Suzuki 3 Abstract Sample size is a importat factor to be cosidered i determiig
More informationEVALUATION OF GLASS FIBER/EPOXY INTERFACIAL STRENGTH BY THE CRUCIFORM SPECIMEN METHOD
EVALUATION OF GLASS FIBER/EPOX INTERFACIAL STRENGTH B THE CRUCIFORM SPECIMEN METHOD Ju KOANAGI, Hajime KATO, Akihiro KASHIMA, uichi IGARASHI, Keichi WATANABE 3, Ichiro UENO 4 ad Shiji OGIHARA 4 Istitute
More information62. Power series Definition 16. (Power series) Given a sequence {c n }, the series. c n x n = c 0 + c 1 x + c 2 x 2 + c 3 x 3 +
62. Power series Defiitio 16. (Power series) Give a sequece {c }, the series c x = c 0 + c 1 x + c 2 x 2 + c 3 x 3 + is called a power series i the variable x. The umbers c are called the coefficiets of
More informationCUMULATIVE DAMAGE ESTIMATION USING WAVELET TRANSFORM OF STRUCTURAL RESPONSE
CUMULATIVE DAMAGE ESTIMATION USING WAVELET TRANSFORM OF STRUCTURAL RESPONSE Ryutaro SEGAWA 1, Shizuo YAMAMOTO, Akira SONE 3 Ad Arata MASUDA 4 SUMMARY Durig a strog earthquake, the respose of a structure
More informationOrthogonal Gaussian Filters for Signal Processing
Orthogoal Gaussia Filters for Sigal Processig Mark Mackezie ad Kiet Tieu Mechaical Egieerig Uiversity of Wollogog.S.W. Australia Abstract A Gaussia filter usig the Hermite orthoormal series of fuctios
More informationResearch on real time compensation of thermal errors of CNC lathe based on linear regression theory Qiu Yongliang
d Iteratioal Coferece o Machiery, Materials Egieerig, Chemical Egieerig ad Biotechology (MMECEB 015) Research o real time compesatio of thermal errors of CNC lathe based o liear regressio theory Qiu Yogliag
More informationProvläsningsexemplar / Preview TECHNICAL REPORT INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE
TECHNICAL REPORT CISPR 16-4-3 2004 AMENDMENT 1 2006-10 INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE Amedmet 1 Specificatio for radio disturbace ad immuity measurig apparatus ad methods Part 4-3:
More informationStudy on Coal Consumption Curve Fitting of the Thermal Power Based on Genetic Algorithm
Joural of ad Eergy Egieerig, 05, 3, 43-437 Published Olie April 05 i SciRes. http://www.scirp.org/joural/jpee http://dx.doi.org/0.436/jpee.05.34058 Study o Coal Cosumptio Curve Fittig of the Thermal Based
More informationA NEW CLASS OF 2-STEP RATIONAL MULTISTEP METHODS
Jural Karya Asli Loreka Ahli Matematik Vol. No. (010) page 6-9. Jural Karya Asli Loreka Ahli Matematik A NEW CLASS OF -STEP RATIONAL MULTISTEP METHODS 1 Nazeeruddi Yaacob Teh Yua Yig Norma Alias 1 Departmet
More informationThe axial dispersion model for tubular reactors at steady state can be described by the following equations: dc dz R n cn = 0 (1) (2) 1 d 2 c.
5.4 Applicatio of Perturbatio Methods to the Dispersio Model for Tubular Reactors The axial dispersio model for tubular reactors at steady state ca be described by the followig equatios: d c Pe dz z =
More informationMechanical Efficiency of Planetary Gear Trains: An Estimate
Mechaical Efficiecy of Plaetary Gear Trais: A Estimate Dr. A. Sriath Professor, Dept. of Mechaical Egieerig K L Uiversity, A.P, Idia E-mail: sriath_me@klce.ac.i G. Yedukodalu Assistat Professor, Dept.
More informationIntermittent demand forecasting by using Neural Network with simulated data
Proceedigs of the 011 Iteratioal Coferece o Idustrial Egieerig ad Operatios Maagemet Kuala Lumpur, Malaysia, Jauary 4, 011 Itermittet demad forecastig by usig Neural Network with simulated data Nguye Khoa
More information11 Correlation and Regression
11 Correlatio Regressio 11.1 Multivariate Data Ofte we look at data where several variables are recorded for the same idividuals or samplig uits. For example, at a coastal weather statio, we might record
More information577. Estimation of surface roughness using high frequency vibrations
577. Estimatio of surface roughess usig high frequecy vibratios V. Augutis, M. Sauoris, Kauas Uiversity of Techology Electroics ad Measuremets Systems Departmet Studetu str. 5-443, LT-5368 Kauas, Lithuaia
More informationA New Method to Order Functions by Asymptotic Growth Rates Charlie Obimbo Dept. of Computing and Information Science University of Guelph
A New Method to Order Fuctios by Asymptotic Growth Rates Charlie Obimbo Dept. of Computig ad Iformatio Sciece Uiversity of Guelph ABSTRACT A ew method is described to determie the complexity classes of
More informationDESIGN, PRODUCTION, AND APPLICATION OF A STAND FOR TESTING FRICTION OF THE BEARINGS
Tome V (year 7), Fascicole, (ISSN 1584 665) DESIGN, PRODUCTION, AND APPLICATION OF A STAND FOR TESTING FRICTION OF THE BEARINGS Pavlia KATSAROVA, Stilia NIKOLOV, Miltso TASHEV TECHNICAL UNIVERSITY SOFIA,BRANCH
More informationMECHANICAL INTEGRITY DESIGN FOR FLARE SYSTEM ON FLOW INDUCED VIBRATION
MECHANICAL INTEGRITY DESIGN FOR FLARE SYSTEM ON FLOW INDUCED VIBRATION Hisao Izuchi, Pricipal Egieerig Cosultat, Egieerig Solutio Uit, ChAS Project Operatios Masato Nishiguchi, Egieerig Solutio Uit, ChAS
More informationMechatronics. Time Response & Frequency Response 2 nd -Order Dynamic System 2-Pole, Low-Pass, Active Filter
Time Respose & Frequecy Respose d -Order Dyamic System -Pole, Low-Pass, Active Filter R 4 R 7 C 5 e i R 1 C R 3 - + R 6 - + e out Assigmet: Perform a Complete Dyamic System Ivestigatio of the Two-Pole,
More informationCEE 522 Autumn Uncertainty Concepts for Geotechnical Engineering
CEE 5 Autum 005 Ucertaity Cocepts for Geotechical Egieerig Basic Termiology Set A set is a collectio of (mutually exclusive) objects or evets. The sample space is the (collectively exhaustive) collectio
More informationECE 8527: Introduction to Machine Learning and Pattern Recognition Midterm # 1. Vaishali Amin Fall, 2015
ECE 8527: Itroductio to Machie Learig ad Patter Recogitio Midterm # 1 Vaishali Ami Fall, 2015 tue39624@temple.edu Problem No. 1: Cosider a two-class discrete distributio problem: ω 1 :{[0,0], [2,0], [2,2],
More informationPrinciple Of Superposition
ecture 5: PREIMINRY CONCEP O RUCUR NYI Priciple Of uperpositio Mathematically, the priciple of superpositio is stated as ( a ) G( a ) G( ) G a a or for a liear structural system, the respose at a give
More informationx a x a Lecture 2 Series (See Chapter 1 in Boas)
Lecture Series (See Chapter i Boas) A basic ad very powerful (if pedestria, recall we are lazy AD smart) way to solve ay differetial (or itegral) equatio is via a series expasio of the correspodig solutio
More information567. Research of Dynamics of a Vibration Isolation Platform
567. Research of Dyamics of a Vibratio Isolatio Platform A. Kilikevičius, M. Jurevičius 2, M. Berba 3 Vilius Gedimias Techical Uiversity, Departmet of Machie buildig, J. Basaavičiaus str. 28, LT-03224
More informationVALIDATION OF A CFD MODEL OF A THREE- DIMENSIONAL TUBE-IN-TUBE HEAT EXCHANGER
Third Iteratioal Coferece o CFD i the Mierals ad Process Idustries CSIRO, Melboure, Australia 1-1 December 3 VALIDATION OF A CFD MODEL OF A THREE- DIMENSIONAL TUBE-IN-TUBE HEAT EXCHANGER Hilde VAN DER
More informationANALYSIS OF DAMPING EFFECT ON BEAM VIBRATION
Molecular ad Quatum Acoustics vol. 7, (6) 79 ANALYSIS OF DAMPING EFFECT ON BEAM VIBRATION Jerzy FILIPIAK 1, Lech SOLARZ, Korad ZUBKO 1 Istitute of Electroic ad Cotrol Systems, Techical Uiversity of Czestochowa,
More informationANALYSIS OF EXPERIMENTAL ERRORS
ANALYSIS OF EXPERIMENTAL ERRORS All physical measuremets ecoutered i the verificatio of physics theories ad cocepts are subject to ucertaities that deped o the measurig istrumets used ad the coditios uder
More informationPERFORMANCE OPTIMIZATION OF SOLAR PTC USING TAGUCHI METHOD
Iteratioal Joural of Mechaical Egieerig ad Techology (IJMET) Volume 9, Issue 2, February 2018, pp. 523 529 Article ID: IJMET_09_02_052 Available olie at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=9&itype=2
More informationExact Solutions for a Class of Nonlinear Singular Two-Point Boundary Value Problems: The Decomposition Method
Exact Solutios for a Class of Noliear Sigular Two-Poit Boudary Value Problems: The Decompositio Method Abd Elhalim Ebaid Departmet of Mathematics, Faculty of Sciece, Tabuk Uiversity, P O Box 741, Tabuki
More informationAN OPEN-PLUS-CLOSED-LOOP APPROACH TO SYNCHRONIZATION OF CHAOTIC AND HYPERCHAOTIC MAPS
http://www.paper.edu.c Iteratioal Joural of Bifurcatio ad Chaos, Vol. 1, No. 5 () 119 15 c World Scietific Publishig Compay AN OPEN-PLUS-CLOSED-LOOP APPROACH TO SYNCHRONIZATION OF CHAOTIC AND HYPERCHAOTIC
More informationTrue Nature of Potential Energy of a Hydrogen Atom
True Nature of Potetial Eergy of a Hydroge Atom Koshu Suto Key words: Bohr Radius, Potetial Eergy, Rest Mass Eergy, Classical Electro Radius PACS codes: 365Sq, 365-w, 33+p Abstract I cosiderig the potetial
More informationMAT1026 Calculus II Basic Convergence Tests for Series
MAT026 Calculus II Basic Covergece Tests for Series Egi MERMUT 202.03.08 Dokuz Eylül Uiversity Faculty of Sciece Departmet of Mathematics İzmir/TURKEY Cotets Mootoe Covergece Theorem 2 2 Series of Real
More informationCalculation of Geometrical Parameters of Geokhod Transmission With Hydraulic Cylinders
IO Coferece Series: Materials Sciece ad Egieerig AER OEN ACCESS Calculatio of Geometrical arameters of Geokhod Trasmissio With ydraulic Cyliders To cite this article: M Yu Blaschuk et al 016 IO Cof. Ser.:
More information1 Review of Probability & Statistics
1 Review of Probability & Statistics a. I a group of 000 people, it has bee reported that there are: 61 smokers 670 over 5 960 people who imbibe (drik alcohol) 86 smokers who imbibe 90 imbibers over 5
More informationThe target reliability and design working life
Safety ad Security Egieerig IV 161 The target reliability ad desig workig life M. Holický Kloker Istitute, CTU i Prague, Czech Republic Abstract Desig workig life ad target reliability levels recommeded
More informationJ. Serb. Chem. Soc. 82 (4) S208 S220 (2017) Supplementary material
J. Serb. Chem. Soc. 82 (4) S8 S2 (7) Supplemetary material SUPPLEMENARY MAERIAL O Experimetal measuremets ad modellig of solvet activity ad surface tesio of biary mixtures of poly(viyl pyrrolidoe) i water
More informationObtaining Constants of Johnson-Cook Material Model Using a Combined Experimental, Numerical Simulation and Optimization Method
Vol:0, No:9, 06 Obtaiig Costats of Johso-Cook Material Model Usig a Combied Experimetal, Numerical Simulatio ad Optimizatio Method F. Rahimi Dehgola, M. Behzadi, J. Fathi Sola Iteratioal Sciece Idex, Mechaical
More informationFree Space Optical Wireless Communications under Turbulence Channel Effect
IOSR Joural of Electroics ad Commuicatio Egieerig (IOSR-JECE) e-issn: 78-834,p- ISSN: 78-8735.Volume 9, Issue 3, Ver. III (May - Ju. 014), PP 01-08 Free Space Optical Wireless Commuicatios uder Turbulece
More informationTRACEABILITY SYSTEM OF ROCKWELL HARDNESS C SCALE IN JAPAN
HARDMEKO 004 Hardess Measuremets Theory ad Applicatio i Laboratories ad Idustries - November, 004, Washigto, D.C., USA TRACEABILITY SYSTEM OF ROCKWELL HARDNESS C SCALE IN JAPAN Koichiro HATTORI, Satoshi
More informationDiscrete-Time Systems, LTI Systems, and Discrete-Time Convolution
EEL5: Discrete-Time Sigals ad Systems. Itroductio I this set of otes, we begi our mathematical treatmet of discrete-time s. As show i Figure, a discrete-time operates or trasforms some iput sequece x [
More informationTemperature Distribution in a Cylindrical Core and Coil Assembly with Heat Generation
Temperature Distributio i a Cylidrical Core ad Coil Assembly with Heat Geeratio P. S. Yeh, Ph.D. Abstract A residetial distributio trasformer cosists of a cylidrical steel tak ad a core-ad-coil assembly
More informationSize, shape and temperature effect on nanomaterials
Idia Joural of Pure & Applied Physics Vol. 53, November 2015, pp. 768-775 Size, shape ad temperature effect o aomaterials G Sharma, S Bhatt, R Kumar & M Kumar* Departmet of Physics, G.B. Pat Uiversity
More informationFinite Difference Method for the Estimation of a Heat Source Dependent on Time Variable ABSTRACT
Malaysia Joural of Matematical Scieces 6(S): 39-5 () Special Editio of Iteratioal Worsop o Matematical Aalysis (IWOMA) Fiite Differece Metod for te Estimatio of a Heat Source Depedet o Time Variable, Allabere
More informationInfinite Sequences and Series
Chapter 6 Ifiite Sequeces ad Series 6.1 Ifiite Sequeces 6.1.1 Elemetary Cocepts Simply speakig, a sequece is a ordered list of umbers writte: {a 1, a 2, a 3,...a, a +1,...} where the elemets a i represet
More informationFinally, we show how to determine the moments of an impulse response based on the example of the dispersion model.
5.3 Determiatio of Momets Fially, we show how to determie the momets of a impulse respose based o the example of the dispersio model. For the dispersio model we have that E θ (θ ) curve is give by eq (4).
More informationDISTRIBUTION LAW Okunev I.V.
1 DISTRIBUTION LAW Okuev I.V. Distributio law belogs to a umber of the most complicated theoretical laws of mathematics. But it is also a very importat practical law. Nothig ca help uderstad complicated
More informationCO-LOCATED DIFFUSE APPROXIMATION METHOD FOR TWO DIMENSIONAL INCOMPRESSIBLE CHANNEL FLOWS
CO-LOCATED DIFFUSE APPROXIMATION METHOD FOR TWO DIMENSIONAL INCOMPRESSIBLE CHANNEL FLOWS C.PRAX ad H.SADAT Laboratoire d'etudes Thermiques,URA CNRS 403 40, Aveue du Recteur Pieau 86022 Poitiers Cedex,
More informationSome properties of Boubaker polynomials and applications
Some properties of Boubaker polyomials ad applicatios Gradimir V. Milovaović ad Duša Joksimović Citatio: AIP Cof. Proc. 179, 1050 (2012); doi: 10.1063/1.756326 View olie: http://dx.doi.org/10.1063/1.756326
More informationG. R. Pasha Department of Statistics Bahauddin Zakariya University Multan, Pakistan
Deviatio of the Variaces of Classical Estimators ad Negative Iteger Momet Estimator from Miimum Variace Boud with Referece to Maxwell Distributio G. R. Pasha Departmet of Statistics Bahauddi Zakariya Uiversity
More informationDamped Vibration of a Non-prismatic Beam with a Rotational Spring
Vibratios i Physical Systems Vol.6 (0) Damped Vibratio of a No-prismatic Beam with a Rotatioal Sprig Wojciech SOCHACK stitute of Mechaics ad Fudametals of Machiery Desig Uiversity of Techology, Czestochowa,
More informationNUMERICAL INVESTIGATION OF FEEDBACK CONTROL IN PLASMA PROCESSING REACTORS INTRODUCTION
NUMERICAL INVESTIGATION OF FEEDBACK CONTROL IN PLASMA PROCESSING REACTORS Shahid Rauf ad Mark J. Kusher Departmet of Electrical ad Computer Egieerig Uiversity of Illiois 1406 W. Gree Street, Urbaa, Illiois
More informationThermodynamical analysis for a variable generalized Chaplygin gas
Available olie at www.worldscietificews.com WS 66 (7) 49-6 EISS 9-9 hermodyamical aalysis for a variable geeralized haplygi gas Mauel Malaver Departmet of asic Scieces, Maritime iversity of the aribbea,
More informationIntroduction to Signals and Systems, Part V: Lecture Summary
EEL33: Discrete-Time Sigals ad Systems Itroductio to Sigals ad Systems, Part V: Lecture Summary Itroductio to Sigals ad Systems, Part V: Lecture Summary So far we have oly looked at examples of o-recursive
More informationModified Lilliefors Test
Joural of Moder Applied Statistical Methods Volume 14 Issue 1 Article 9 5-1-2015 Modified Lilliefors Test Achut Adhikari Uiversity of Norther Colorado, adhi2939@gmail.com Jay Schaffer Uiversity of Norther
More informationREGRESSION (Physics 1210 Notes, Partial Modified Appendix A)
REGRESSION (Physics 0 Notes, Partial Modified Appedix A) HOW TO PERFORM A LINEAR REGRESSION Cosider the followig data poits ad their graph (Table I ad Figure ): X Y 0 3 5 3 7 4 9 5 Table : Example Data
More informationWhat is Physical Chemistry. Physical Chemistry for Chemical Engineers CHEM251. Basic Characteristics of a Gas
7/6/0 hysical Chemistry for Chemical Egieers CHEM5 What is hysical Chemistry hysical Chemistry is the study of the uderlyig physical priciples that gover the properties ad behaviour of chemical systems
More information2C09 Design for seismic and climate changes
2C09 Desig for seismic ad climate chages Lecture 02: Dyamic respose of sigle-degree-of-freedom systems I Daiel Grecea, Politehica Uiversity of Timisoara 10/03/2014 Europea Erasmus Mudus Master Course Sustaiable
More informationAppendix: The Laplace Transform
Appedix: The Laplace Trasform The Laplace trasform is a powerful method that ca be used to solve differetial equatio, ad other mathematical problems. Its stregth lies i the fact that it allows the trasformatio
More informationChemical Kinetics CHAPTER 14. Chemistry: The Molecular Nature of Matter, 6 th edition By Jesperson, Brady, & Hyslop. CHAPTER 14 Chemical Kinetics
Chemical Kietics CHAPTER 14 Chemistry: The Molecular Nature of Matter, 6 th editio By Jesperso, Brady, & Hyslop CHAPTER 14 Chemical Kietics Learig Objectives: Factors Affectig Reactio Rate: o Cocetratio
More informationTHE NUMERICAL SOLUTION OF THE NEWTONIAN FLUIDS FLOW DUE TO A STRETCHING CYLINDER BY SOR ITERATIVE PROCEDURE ABSTRACT
Europea Joural of Egieerig ad Techology Vol. 3 No., 5 ISSN 56-586 THE NUMERICAL SOLUTION OF THE NEWTONIAN FLUIDS FLOW DUE TO A STRETCHING CYLINDER BY SOR ITERATIVE PROCEDURE Atif Nazir, Tahir Mahmood ad
More informationCHAPTER 10 INFINITE SEQUENCES AND SERIES
CHAPTER 10 INFINITE SEQUENCES AND SERIES 10.1 Sequeces 10.2 Ifiite Series 10.3 The Itegral Tests 10.4 Compariso Tests 10.5 The Ratio ad Root Tests 10.6 Alteratig Series: Absolute ad Coditioal Covergece
More informationLOSS-MINIMIZATION CONTROL OF SCALAR- CONTROLLED INDUCTION MOTOR DRIVES
LOSS-MINIMIZATION CONTROL OF SCALAR- CONTROLLED INDUCTION MOTOR DRIVES Hussei Sarha, Rateb Al-Issa, ad Qazem Jaber Departmet of Mechatroics Egieerig, Faculty of Egieerig Techology Al-Balqa Applied Uiversity,
More informationMeasurement uncertainty of the sound absorption
Measuremet ucertaity of the soud absorptio coefficiet Aa Izewska Buildig Research Istitute, Filtrowa Str., 00-6 Warsaw, Polad a.izewska@itb.pl 6887 The stadard ISO/IEC 705:005 o the competece of testig
More informationPHYC - 505: Statistical Mechanics Homework Assignment 4 Solutions
PHYC - 55: Statistical Mechaics Homewor Assigmet 4 Solutios Due February 5, 14 1. Cosider a ifiite classical chai of idetical masses coupled by earest eighbor sprigs with idetical sprig costats. a Write
More information2. Neutronic calculations at uranium powered cylindrical reactor by using Bessel differential equation
Trasworld Research Network 37/661 (), Fort P.O. Trivadrum-695 03 Kerala, Idia Nuclear Sciece ad Techology, 01: 15-4 ISBN: 978-81-7895-546-9 Editor: Turgay Korkut. Neutroic calculatios at uraium powered
More informationECON 3150/4150, Spring term Lecture 3
Itroductio Fidig the best fit by regressio Residuals ad R-sq Regressio ad causality Summary ad ext step ECON 3150/4150, Sprig term 2014. Lecture 3 Ragar Nymoe Uiversity of Oslo 21 Jauary 2014 1 / 30 Itroductio
More informationSection 13.3 Area and the Definite Integral
Sectio 3.3 Area ad the Defiite Itegral We ca easily fid areas of certai geometric figures usig well-kow formulas: However, it is t easy to fid the area of a regio with curved sides: METHOD: To evaluate
More informationOBJECTIVES. Chapter 1 INTRODUCTION TO INSTRUMENTATION FUNCTION AND ADVANTAGES INTRODUCTION. At the end of this chapter, students should be able to:
OBJECTIVES Chapter 1 INTRODUCTION TO INSTRUMENTATION At the ed of this chapter, studets should be able to: 1. Explai the static ad dyamic characteristics of a istrumet. 2. Calculate ad aalyze the measuremet
More information1 Adiabatic and diabatic representations
1 Adiabatic ad diabatic represetatios 1.1 Bor-Oppeheimer approximatio The time-idepedet Schrödiger equatio for both electroic ad uclear degrees of freedom is Ĥ Ψ(r, R) = E Ψ(r, R), (1) where the full molecular
More informationA CONFINEMENT MODEL OF HIGH STRENGTH CONCRETE
3 th World Coferece o Earthquake Egieerig Vacouver, B.C., Caada August -6, 24 Paper No. 873 A CONFINEMENT MODEL OF HIGH STRENGTH CONCRETE Nobutaka NAKAZAWA, Kazuhiko KAWASHIMA 2, Gakuho WATANABE 3, Ju-ichi
More informationBayesian and E- Bayesian Method of Estimation of Parameter of Rayleigh Distribution- A Bayesian Approach under Linex Loss Function
Iteratioal Joural of Statistics ad Systems ISSN 973-2675 Volume 12, Number 4 (217), pp. 791-796 Research Idia Publicatios http://www.ripublicatio.com Bayesia ad E- Bayesia Method of Estimatio of Parameter
More informationGoodness-Of-Fit For The Generalized Exponential Distribution. Abstract
Goodess-Of-Fit For The Geeralized Expoetial Distributio By Amal S. Hassa stitute of Statistical Studies & Research Cairo Uiversity Abstract Recetly a ew distributio called geeralized expoetial or expoetiated
More informationThe Heisenberg versus the Schrödinger picture in quantum field theory. Dan Solomon Rauland-Borg Corporation 3450 W. Oakton Skokie, IL USA
1 The Heiseberg versus the chrödiger picture i quatum field theory by Da olomo Raulad-Borg Corporatio 345 W. Oakto kokie, IL 677 UA Phoe: 847-324-8337 Email: da.solomo@raulad.com PAC 11.1-z March 15, 24
More informationThe Random Walk For Dummies
The Radom Walk For Dummies Richard A Mote Abstract We look at the priciples goverig the oe-dimesioal discrete radom walk First we review five basic cocepts of probability theory The we cosider the Beroulli
More informationRotationally invariant integrals of arbitrary dimensions
September 1, 14 Rotatioally ivariat itegrals of arbitrary dimesios James D. Wells Physics Departmet, Uiversity of Michiga, A Arbor Abstract: I this ote itegrals over spherical volumes with rotatioally
More informationNumerical Methods in Fourier Series Applications
Numerical Methods i Fourier Series Applicatios Recall that the basic relatios i usig the Trigoometric Fourier Series represetatio were give by f ( x) a o ( a x cos b x si ) () where the Fourier coefficiets
More informationPAijpam.eu ON TENSOR PRODUCT DECOMPOSITION
Iteratioal Joural of Pure ad Applied Mathematics Volume 103 No 3 2015, 537-545 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://wwwijpameu doi: http://dxdoiorg/1012732/ijpamv103i314
More informationDifferential Equations of Gas-Phase Chemical Kinetics
Differetial Equatios of Gas-Phase Chemical Kietics Chemked A Program for Chemical Kietics of Gas-Phase Reactios M. Jeleziak ad I. Jeleziak Home page: http://www.chemked.com/, email: ifo@chemked.com 02
More informationThe Growth of Functions. Theoretical Supplement
The Growth of Fuctios Theoretical Supplemet The Triagle Iequality The triagle iequality is a algebraic tool that is ofte useful i maipulatig absolute values of fuctios. The triagle iequality says that
More informationOPTIMAL PIECEWISE UNIFORM VECTOR QUANTIZATION OF THE MEMORYLESS LAPLACIAN SOURCE
Joural of ELECTRICAL EGIEERIG, VOL. 56, O. 7-8, 2005, 200 204 OPTIMAL PIECEWISE UIFORM VECTOR QUATIZATIO OF THE MEMORYLESS LAPLACIA SOURCE Zora H. Perić Veljo Lj. Staović Alesadra Z. Jovaović Srdja M.
More informationUsing An Accelerating Method With The Trapezoidal And Mid-Point Rules To Evaluate The Double Integrals With Continuous Integrands Numerically
ISSN -50 (Paper) ISSN 5-05 (Olie) Vol.7, No., 017 Usig A Acceleratig Method With The Trapezoidal Ad Mid-Poit Rules To Evaluate The Double Itegrals With Cotiuous Itegrads Numerically Azal Taha Abdul Wahab
More informationa b c d e f g h Supplementary Information
Supplemetary Iformatio a b c d e f g h Supplemetary Figure S STM images show that Dark patters are frequetly preset ad ted to accumulate. (a) mv, pa, m ; (b) mv, pa, m ; (c) mv, pa, m ; (d) mv, pa, m ;
More informationSimilarity Solutions to Unsteady Pseudoplastic. Flow Near a Moving Wall
Iteratioal Mathematical Forum, Vol. 9, 04, o. 3, 465-475 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/imf.04.48 Similarity Solutios to Usteady Pseudoplastic Flow Near a Movig Wall W. Robi Egieerig
More informationTHE SYSTEMATIC AND THE RANDOM. ERRORS - DUE TO ELEMENT TOLERANCES OF ELECTRICAL NETWORKS
R775 Philips Res. Repts 26,414-423, 1971' THE SYSTEMATIC AND THE RANDOM. ERRORS - DUE TO ELEMENT TOLERANCES OF ELECTRICAL NETWORKS by H. W. HANNEMAN Abstract Usig the law of propagatio of errors, approximated
More informationl -State Solutions of a New Four-Parameter 1/r^2 Singular Radial Non-Conventional Potential via Asymptotic Iteration Method
America Joural of Computatioal ad Applied Mathematics 8, 8(): 7-3 DOI:.593/j.ajcam.88. l -State Solutios of a New Four-Parameter /r^ Sigular Radial No-Covetioal Potetial via Asymptotic Iteratio Method
More informationBoundary layer problem on conveyor belt. Gabriella Bognár University of Miskolc 3515 Miskolc-Egyetemváros, Hungary
Boudary layer problem o coveyor belt Gabriella Bogár Uiversity of Miskolc 355 Miskolc-Egyetemváros, Hugary e-mail: matvbg@ui-miskolc.hu Abstract: A techologically importat source of the boudary layer pheomeo
More informationAdded mass estimation of open flat membranes vibrating in still air
Added mass estimatio of ope flat membraes vibratig i still air *Yua-qi Li 1),Yi Zhou ), Akihito YOHIDA 3) ad Yukio TAMURA 4) 1), ) Departmet of Buildig Egieerig, Togji Uiversity, haghai, 9, Chia 1) liyq@togji.edu.c
More information8. СОВЕТУВАЊЕ. Охрид, септември ANALYSIS OF NO LOAD APPARENT POWER AND FREQUENCY SPECTRUM OF MAGNETIZING CURRENT FOR DIFFERENT CORE TYPES
8. СОВЕТУВАЊЕ Охрид, 22 24 септември Leoardo Štrac Frajo Keleme Kočar Power Trasformers Ltd. ANALYSS OF NO LOAD APPARENT POWER AND FREQENCY SPECTRM OF MAGNETZNG CRRENT FOR DFFERENT CORE TYPES ABSTRACT
More informationApproximate Confidence Interval for the Reciprocal of a Normal Mean with a Known Coefficient of Variation
Metodološki zvezki, Vol. 13, No., 016, 117-130 Approximate Cofidece Iterval for the Reciprocal of a Normal Mea with a Kow Coefficiet of Variatio Wararit Paichkitkosolkul 1 Abstract A approximate cofidece
More informationL 5 & 6: RelHydro/Basel. f(x)= ( ) f( ) ( ) ( ) ( ) n! 1! 2! 3! If the TE of f(x)= sin(x) around x 0 is: sin(x) = x - 3! 5!
aylor epasio: Let ƒ() be a ifiitely differetiable real fuctio. At ay poit i the eighbourhood of =0, the fuctio ca be represeted as a power series of the followig form: X 0 f(a) f() ƒ() f()= ( ) f( ) (
More informationStreamfunction-Vorticity Formulation
Streamfuctio-Vorticity Formulatio A. Salih Departmet of Aerospace Egieerig Idia Istitute of Space Sciece ad Techology, Thiruvaathapuram March 2013 The streamfuctio-vorticity formulatio was amog the first
More informationNew Version of the Rayleigh Schrödinger Perturbation Theory: Examples
New Versio of the Rayleigh Schrödiger Perturbatio Theory: Examples MILOŠ KALHOUS, 1 L. SKÁLA, 1 J. ZAMASTIL, 1 J. ČÍŽEK 2 1 Charles Uiversity, Faculty of Mathematics Physics, Ke Karlovu 3, 12116 Prague
More information1 Inferential Methods for Correlation and Regression Analysis
1 Iferetial Methods for Correlatio ad Regressio Aalysis I the chapter o Correlatio ad Regressio Aalysis tools for describig bivariate cotiuous data were itroduced. The sample Pearso Correlatio Coefficiet
More informationMETHOD OF FUNDAMENTAL SOLUTIONS FOR HELMHOLTZ EIGENVALUE PROBLEMS IN ELLIPTICAL DOMAINS
Please cite this article as: Staisław Kula, Method of fudametal solutios for Helmholtz eigevalue problems i elliptical domais, Scietific Research of the Istitute of Mathematics ad Computer Sciece, 009,
More informationCENTRIFUGAL PUMP SPECIFIC SPEED PRIMER AND THE AFFINITY LAWS Jacques Chaurette p. eng., Fluide Design Inc. November 2004
CENTRIFUGAL PUMP SPECIFIC SPEE PRIMER AN THE AFFINITY LAWS Jacques Chaurette p. eg., Fluide esig Ic. November 004 www.fluidedesig.com There is a umber called the specific speed of a pump whose value tells
More information7 Sequences of real numbers
40 7 Sequeces of real umbers 7. Defiitios ad examples Defiitio 7... A sequece of real umbers is a real fuctio whose domai is the set N of atural umbers. Let s : N R be a sequece. The the values of s are
More information