Modelling of Integrated Systems for Modular Linearisation-Based Analysis And Design
|
|
- Gloria Townsend
- 6 years ago
- Views:
Transcription
1 Modelling of Integated Systems fo Modula ineaisation-based Analysis And Design D.J. eith, W.E. eithead Depatment of Electonic & Electical Engineeing, Univesity of Stathclyde, 5 Geoge St., Glasgo G QE, U.K. Tel , Fax , . doug@icu.stath.ac.uk Keyods Integated systems, lineaisation, modula analysis Abstact The selection of an appopiate epesentation fo lineaisation-based analysis and design of integated systems is consideed. It is shon that, in contast to conventional lineaisation-based epesentations, a velocity-based epesentation suppots the modula analysis and design methodologies equied ith complex integated systems.. Intoduction In esponse to inceasingly stingent pefomance equiements, the tend in a ide ange of engineeing systems is toads tighte integation of the elements constituting the system. Whilst this fequently leads to inceased dynamic inteaction beteen sub-systems, the design of a complex system in an efficient and flexible manne necessitates a modula methodology heeby each sub-system has a ell-defined inteface to the est of the system hich is insensitive to the implementation details of the system. Such an appoach enables the detailed design and implementation of each sub-system to be caied out sepaately and this is paticulaly impotant in pojects hee sub-contactos ae involved. Thee is, of couse, a coesponding equiement fo a epesentation hich suppots the analysis and design of systems in a modula fashion. Depending on the task at hand, a numbe of diffeent epesentations ae typically utilised fo the analysis and design of complex systems; fo example, Bond Gaphs, dinay Diffeential Equations and Tansfe Functions. Each epesentation possesses paticula advantages and disadvantages hich make it moe, o less, suitable fo a paticula pupose. Taditionally, lineaisation-based epesentations ae often employed fo the analysis and design of nonlinea systems. The system is appoximated by a suitable linea system hich, in the vicinity of an equilibium opeating point, exhibits simila dynamic chaacteistics (typically, the seies expansion lineaisation about the equilibium opeating point. Whilst conventional lineaisation-based analysis is only valid locally to a specific equilibium opeating point, it has the consideable advantage that it maintains continuity ith established linea analysis techniques fo hich a substantial body of expeience has been accumulated. In ode to detemine appopiate linea appoximations to a paticula sub-system, knoledge of the equilibium opeating points is equied. Hoeve, specifying a pioi the elationship beteen the equilibium inputs and outputs of a sub-system imposes, in geneal, a vey stong estiction on the chaacteistics of the sub-system. Fo example, conside the nonlinea system x F(x,, y G(x,. The functions, F(, and G(,, ae not independent since, F(x o, o, G(x o, o y o must be jointly satisfied fo all equilibium input-output pais (x o, o. Indeed, hen F(, is invetible so that the equilibium state, x o, is detemined by o, it follos that the output function, G(,, is, essentially, completely specified by the equilibium input-output elationship and the choice of F(,. Consequently, in pactice, a flexible equilibium specification is equied. Hoeve, since the equilibium opeating points ae not those of the isolated sub-system but athe those of the sub-system hen it is embedded in the oveall system, the equilibium opeating points of a sub-system ae, in geneal, stongly influenced by the chaacteistics of the oveall integated system and may change consideably as a esult of even elatively small changes in othe sub-systems. Hence, conventional lineaisation-based epesentations do not eadily suppot modula analysis and design appoaches. Whilst, in the context of integated systems, the foegoing is pehaps the pimay deficiency of conventional lineaisation-based epesentations, it should be noted that thee ae also a numbe of othe difficulties ith such techniques. Fistly, the epesentations ae only accuate in the vicinity of an equilibium opeating point hilst the equiement is usually to design a system hich functions ell not only hen opeating in the vicinity of a single equilibium point but also duing tansitions beteen equilibium opeating points and peiods of sustained non-equilibium opeation. Conventionally, this equiement is addessed by employing extensive simulation studies to iteatively efine the design, but this quickly becomes extemely time-consuming and inefficient fo any but the simplest nonlinea systems. Thee is, theefoe, a consideable incentive to diectly incopoate, into the analytical pat of the design pocedue, knoledge of the plant dynamics duing tansitions beteen equilibium opeating points and duing sustained non-equilibium opeation. Secondly, a numbe of distinct linea epesentations ae typically employed duing analysis and design (eith & eithead 998a hich ae not equivalent and hich can make it difficult to incopoate insight obtained fom the analysis into the design pocedue. Thidly, and at a moe pactical level, the detemination of the equilibium opeating point is time-consuming and highly non-tivial fo a complex
2 nonlinea system. Similaly, the numeical diffeentiation associated ith conventional numeical lineaisation about an equilibium point is an undesiable ill-conditioned opeation. The velocity-based epesentation ecently poposed by eith & eithead (998a igoously genealises and extends the conventional seies expansion lineaisation at an equilibium opeating point and associates a linea system ith evey opeating point, not just equilibium opeating points. An altenative desciption of a nonlinea system in tems of a family of linea systems is theeby established; namely, the velocity-based lineaisation family. It is emphasised that the velocity-based fomulation involves no loss of infomation and, in paticula, does not involve eithe an inheent slo vaiation estiction no is it confined to equilibium opeating points alone but instead encompasses evey opeating point, including those fa fom equilibium. The velocity-based appoach theeby elaxes the estiction to nea equilibium opeation hilst maintaining the continuity ith linea methods hich is a pinciple advantage of the conventional lineaisation-based analysis techniques. The velocity-based epesentation theefoe esolves many of the deficiencies of conventional lineaisation-based epesentations. Hoeve, the liteatue on the velocity-based epesentation is confined to monolithic systems fo hich thee is no equiement to conside a decomposition into component sub-systems. The aim of this pape is, theefoe, to investigate the application of the velocity-based epesentation to integated systems and, in paticula, conside the suppot, if any, povided by this epesentation fo modula analysis and design.. Velocity-based epesentation Befoe consideing integated systems, the velocitybased analysis and design epesentation is biefly summaised. Conside a nonlinea system x F(x,, y G(x, ( hee F(, and G(, ae diffeentiable nonlinea functions ith ipschit continuous fist deivatives and R m denotes the input to the plant, y R p the output and x R n the states. The set of equilibium opeating points of the nonlinea system, (, consists of those points, (x o, o, fo hich F(x o, o ( and the equilibium output is y o G(x o, o (3 et Φ:R n R m denote the space consisting of the union of the states, x, ith the inputs,. The set of equilibium opeating points of the nonlinea system, (, foms a locus of points, (x o, o, in Φ and the esponse of the system to a geneal time-vaying input, (t, is depicted by a tajectoy in Φ. The solution x to the linea system (the velocitybased lineaisation "x, " x F(x, F(x, (4 "y x G(x, G(x, (5 appoximates the solution x to the nonlinea system locally to the opeating point (x,. Since a linea system (4-(5 is associated ith evey opeating point of the nonlinea system, thee is a family of velocity-based lineaisations associated ith the nonlinea system. Whilst the solution to a single velocity-based lineaisation is only a local appoximation to the solution of the nonlinea system, the solutions to the membes of this family can be pieced togethe to obtain an abitaily accuately global appoximation to the solution of the nonlinea system. The elationship beteen the nonlinea system and its velocitybased lineaisation, (4-(5, is diect. Diffeentiating (, an altenative epesentation of the nonlinea system is x, x F(x, F(x, (6 y x G(x, G(x, (7 Dynamically, the velocity-fom (6-(7, ith appopiate initial conditions, and ( ae equivalent (have the same solution, x. Clealy, the velocity-based lineaisation, (4- (5, is simply the foen fom of (6-(7 at the opeating point, (x,. Hence, numeical diffeentiation is not equied in ode to lineaise a system in velocity-based fom; instead, the velocity-based lineaisation is obtained by simply feeing the velocity fom of the nonlinea system. The velocity-based fomulation, (6-(7, is of higheode than the diect fomulation, (. Hoeve, efomulate (, as x Ax B f(ρ, y Cx D g(ρ (8 hee A, B, C, D ae appopiately dimensioned constant matices, f( and g( ae nonlinea functions and ρ(x, R q, q mn, embodies the nonlinea dependence of the dynamics on the state and input ith x ρ, ρ functions of ρ alone. Tivially, this efomulation can alays be achieved by letting ρ [x T T ] T, in hich case qmn. The nonlineaity of the system is, hoeve, fequently dependent on only a subset of the elements of the state and input, in hich case the dimension, q, of the scheduling vaiable ρ is less than mn. Assume, ithout loss of geneality, that x ρ and ρ ae constant. The velocity-fom of the system, (8, is x (9 (Af(ρ x ρ (Bf(ρ ρ ( y (Cg(ρ x ρ (Dg(ρ ρ ( hich, as ( and ( depend only on, ρ and, may be efomulated, equivalently, as ρ x ρ ρ ( (Af(ρ x ρ (Bf(ρ ρ (3 y (Cg(ρ x ρ (Dg(ρ ρ (4 Since the dimension of the scheduling vaiable ρ is, typically, much loe than that of x, the ode of (-(4 is usually only slightly highe than the ode of (. Thee exists a igoous, and diect, elationship beteen the dynamic chaacteistics of a nonlinea system and those of its velocity-based lineaisation family. It is emphasised that the velocity-based lineaisation family embodies the entie dynamics of the nonlinea system, (,
3 ith no loss of infomation and povides an altenative epesentation of the nonlinea system. Thee is no estiction to nea equilibium opeation no any slo vaiation equiement. Whilst the velocity-based epesentation is equivalent to the diect epesentation, (, in the sense that they each embody the entie dynamics of the nonlinea system, they ae not necessaily equivalent ith espect to othe consideations. In paticula, the diect elationship beteen the velocity-fom of the nonlinea system and the velocity-based lineaisation family and the lineaity of the membes of the latte family povides continuity ith established linea theoy hich, fo example, facilitates analysis (eith & eithead 998a and design (eith & eithead 998b,c. With egad to design, it is noted that the velocitybased epesentation povides diect suppot fo divide and conque design appoaches, such as the gain-scheduling design methodology, heeby the design of a nonlinea system is decomposed into the design of an associated family of linea systems (eith & eithead 998b,c. Fo example, since a velocity-based lineaisation family is associated ith a nonlinea plant, a coesponding linea contolle family can be obtained by designing a linea contolle fo each membe of the plant family. A nonlinea contolle may then be detemined fo hich the velocity-based lineaisation family is the designed linea contolle family. This appoach esolves many of the deficiencies of the conventional gain-scheduling appoach including the estiction to an excessively small neighbouhood of the equilibium opeating points. By alloing infomation about the plant dynamics at nonequilibium opeating points to be diectly incopoated into the contolle design, both sustained non-equilibium opeation and dynamic tansitions beteen equilibium opeating points, including those hich take the system fa fom equilibium, can be accommodated. In paticula, the velocity-based gain-scheduling appoach can be employed to detemine a dynamic invesion contolle hich achieves global linea dynamics hen combined ith the nonlinea plant (eith & eithead 998c. f couse, the velocity-based gain-scheduling appoach is quite geneal and also diectly suppots the design of feedback configuations fo hich the closed-loop dynamics ae nonlinea. 3. Integated systems The velocity-based epesentation esolves many of the deficiencies of conventional lineaisation-based analysis and design techniques. Hoeve, the existing liteatue on the velocity-based epesentation is confined to monolithic systems fo hich thee is no equiement to conside a decomposition into component sub-systems. With egad to integated systems, the velocity-based epesentation, in contast to conventional lineaisationbased epesentations, is not esticted to nea equilibium opeation and does not equie the equilibium opeating point of a system to be detemined befoe lineaisationbased analysis is possible. Rathe, application of velocitybased analysis and design techniques only involves the much eake equiement that the lagest opeating envelope of a system is knon. As noted peviously, it is non-tivial to detemine the equilibium opeating point of a sub-system hen it is embedded in the oveall system and, futhemoe, the equilibium opeating point is, in geneal, stongly influenced by the chaacteistics of the oveall integated system. Since the equiement to detemine an equilibium opeating point is elaxed in the velocity-based fameok, this fameok esolves one of the pincipal difficulties, in the context of integated systems, ith conventional lineaisation-based techniques. f couse, hilst this is necessay in ode to de-couple the analysis and design of the sub-systems, it is not sufficient to suppot modula analysis and design. It is, in addition, also equied that the analysis and design esults obtained ith a specific sub-system can be integated in a diect and tanspaent manne ith those obtained fo othe subsystems. In ode to investigate the integation of analysis and design esults obtained fo diffeent sub-systems, it is sufficient to conside the seies, paallel and feedback combination of sub-systems since these ae the pincipal classes of inteconnection in idespead use. 3. Seies combination Conside the nonlinea system F ( x,,, y G( x,, (5 fo hich the velocity-based fom is x x F (x,, F (x,, F (x,, (6 y x G (x,, G (x,, G (x,, and the nonlinea system F ( x,,, y G( x,, (7 fo hich the velocity-based fom is x x F (x,, F (x,, F (x,, (8 y x G (x,, G (x,, G (x,, The systems, (5 and (7, ae cascaded togethe by setting y. The esulting system is F( x,,, y G( x,, (9 hee x x y y N M x Q P N M Q P,,, F x F x G x G x G x N M ( (,, (,, F x G x Q P (,, (,,, (,, (,, (,, fo hich the velocity-based fom is
4 N M Q P N M Q P N M N M N M x F ( x,, F ( x,, G ( x,, F ( x,, x x F ( x,, F ( x,, G ( x,, F ( x,, Q P Q P N M Q P F ( x,, G ( x,, F ( x,, x x N M Q P y y G ( x,, G ( x,, G ( x,, G ( x,, G ( x,, Q P N M Q P N M Q P G x G x G x (,, (,, (,, y G( x,, Evidently, ( is just the system obtained hen the systems, (6 and (8, ae cascaded togethe. It follos that the velocity-based fom of a system consisting of to cascaded sub-systems is identical to the system obtained by cascading togethe the velocity-based foms of the to sub-systems. ( 3. Paallel combination The systems, (5 and (7, ae combined in paallel by setting. The esulting system is F( x,,, y G( x,, ( hee x y x y x,,, y F( x,, F ( x,, G x G x F ( x,,, (,, (,, G ( x,, (3 fo hich the velocity-based fom is y x F ( x,, F ( x,, x G ( x,, F ( x,, x F ( x,, F ( x,, G ( x,, y x G( x,, y F ( x,, F ( x,, x G ( x,, G( x,, G ( x,, G( x,, G ( x,, (4 Evidently, ( is just the system obtained hen the systems, (6 and (8, ae combined in paallel. Hence, the velocity-based fom of a system consisting of the paallel combination of to sub-systems is identical to the system obtained by combining in paallel the velocitybased foms of the to sub-systems. 3.3 Feedback combination Conside the nonlinea system ith inputs, and, F( x,,, y G( x,, (5 fo hich the coesponding velocity-based fom is x x F(x,, F(x,, F(x,, (6 y x G(x,, G(x,, G(x,, Assuming that yg(x,,y (7 has a suitable solution yn(x, (8 the system, (5, is enclosed in a feedback loop by setting y. The esulting closed-loop system is M( x,, y N( x, (9 ith M( x, F( x,, N( x, (3 The velocity-based fom of (9 is x x M(x, M(x, (3 y x N(x, N(x, Combining (7 and (8 N( x, G( x,, N( x, (3 Hence, M( x, F( x,, N( x, F( x,, N( x, N( x, x x x M( x, F( x,, N( x, F( x,, N( x, N( x, (33 N( x, G( x,, N( x, G( x,, N( x, N( x, x x x N( x, G( x,, N( x, G( x,, N( x, N( x, and, by substituting (33 into(3, the closed-loop system, (9, can be diectly efomulated as x x F(x,, F(x,, F(x,, (34 y x G(x,, G(x,, G(x,, y N(x, Since N(x, satisfies (3, it is clea that (34 is the system obtained hen the system, (6, is enclosed in a feedback loop by setting y. Consequently, the velocity-based fom of the closed-loop system is identical to the system obtained by enclosing the velocity-based fom of the openloop system in a feedback loop. 3.4 Example Conside to nonlinea dynamic systems F ( x, (35 F ( x, (36 hee 3 F ( x,. x x., F ( x,. x. tanh( x 65.. (37 The unfoced equilibium state of (35 is 3.93 and that of (36 is.. The coesponding equilibium lineaisations ae
5 δ δx δ (38 x" δx 393., δ. and δ -. δx. δ (39 x" δx., δ. Hoeve, suppose that the systems ae coupled togethe ith equal to x and equal to x. The equilibium value of (x, x is no (-.78, -.8 and the coesponding equilibium lineaisations ae δ δx δ N M δx (4 x" δx, x" -.78 δx -.8 In compaison, the dynamics obtained by coupling togethe the equilibium lineaisations (38 and (39, δ δ x δ δx (4 N M x" δ., " x 393 x δx. ae quite diffeent fom the linea dynamics, (4; fo example, the eigenvalues of (4 ae (4.846, hilst those of (4 ae (-.968±j.684. This aises because the unfoced equilibium opeating point changes hen the systems ae coupled togethe. In ode to apply conventional lineaisation-based analysis to a paticula sub-system, it is, theefoe, necessay to detemine the equilibium opeating point of the complete coupled system. This is highly non-tivial fo complex nonlinea systems (unlike the simple example pesented hee. Futhemoe, the equilibium opeating point is, in geneal, influenced by the chaacteistics of the evey sub-system. Consequently, conventional lineaisation-based analysis techniques do not eadily suppot a modula methodology. The nonlinea systems, (35 and (36, may be efomulated as the velocity-based foms,. 3x. d i (4 d i b g (43,.. tanh( x 33.. The velocity-based lineaisation families of (35 and (36 ae defined, espectively, by the foen foms of (4 and (43. The velocity-fom of the nonlinea system obtained hen the to systems ae coupled togethe ith equal to x and equal to x is x. 3x x... tanh( x (44 and the membes of the velocity-based lineaisation family of the coupled system consist of the foen foms of (44 (o, equivalently, ae obtained by coupling the elevant membes of the velocity-based lineaisation families of the individual nonlinea systems (35 and (36. The velocitybased lineaisation associated ith an opeating point indicates the dynamics of the nonlinea system at that opeating point. The impulse esponses of the velocitybased lineaisations associated ith a numbe of opeating points of coupled nonlinea systems ae depicted in figue : the vaiation of the dynamic chaacteistics ith the opeating point is clealy evident. The velocity-based epesentation does not equie an equilibium opeating point to be detemined in ode to analyse a system; athe, application of velocity-based analysis and design techniques only involves the much eake equiement that the lagest opeating envelope of a system is knon. In contast to conventional lineaisationbased epesentations, the velocity-based epesentation theefoe suppots modula lineaisation-based analysis/design heeby the analysis/design of a subsystem is, as fa as possible, insensitive to the intenal details of the othe sub-systems constituting an integated system. Futhemoe, the foegoing analysis establishes that the velocity-based lineaisation families of the seies, paallel and feedback combination of to nonlinea systems ae identical to the seies, paallel and feedback combination of the membes of the velocity-based lineaisation families of the individual nonlinea systems. Hence, in addition to de-coupling the analysis/design of sub-systems, analysis and design esults utilising the velocity-based epesentation of a specific sub-system can be integated in a diect and tanspaent manne ith those obtained fo othe sub-systems. 4. Conclusions It is shon that the velocity-based epesentation suppots modula lineaisation-based analysis and design of integated systems In paticula, and in contast to conventional lineaisation-based epesentations, the velocity-based epesentation does not equie an equilibium opeating point to be detemined in ode to analyse a system; athe, application of velocity-based analysis and design techniques only involves the much eake equiement that the lagest opeating envelope of a system is knon. Timming, hich is highly non-tivial fo complex nonlinea systems, is not equied. does not equie numeical diffeentiation; athe the velocity-based lineaisation is obtained by simply feeing the velocity fom of the nonlinea system. is not confined to nea equilibium opeation but athe accommodates both tansitions beteen equilibium opeating points and sustained non-equilibium opeation. povides a unified fameok fo analysis and design hich employs a single lineaisation, namely the velocity-based lineaisation. Futhemoe, the velocity-based epesentations of the seies, paallel and feedback combination of to nonlinea systems ae identical to the seies, paallel and feedback combination of the velocity-based epesentations of the individual nonlinea systems. Hence, in addition to decoupling the analysis/design of sub-systems, analysis and design esults utilising the velocity-based epesentation of
6 a specific sub-system can be integated in a diect and tanspaent manne ith those obtained fo othe subsystems. The velocity-based epesentation theefoe esolves many of the difficulties associated ith conventional lineaisation-based epesentations and povides diect suppot fo the modula analysis and design methodologies equied ith complex integated systems. Acknoledgement D.J.eith gatefully acknoledges the suppot povided by the Royal Society fo the ok pesented. Refeences EITH, D.J., EITHEAD, W.E., 998a, Gain-Scheduled & Nonlinea & Systems: Dynamic Analysis by Velocity- Based ineaisation Families. Int. J. Contol, 7, pp89-37; 998b, Gain-Scheduled Contolle Design: An Analytic Fameok Diectly Incopoating Non- Equilibium Plant Dynamics. ibid, 7, pp49-69; 998c, Input-utput ineaisation by Velocity-based Gain- Scheduling. ibid, in pess.; 998d, Analytic Fameok fo Blended Multiple Model Systems Using inea ocal Models. ibid, in pess. x (x,x (-.4, (x,x (, (x,x (5, x Figue Impulse esponses of the velocity-based lineaisations associated ith a numbe of opeating points. It should be noted that the dynamics ae stongly dependent on the value of x but quite insensitive to the value of x. Responses ae, theefoe, only depicted fo opeating points at hich x is equal to eo. p
A NEW VARIABLE STIFFNESS SPRING USING A PRESTRESSED MECHANISM
Poceedings of the ASME 2010 Intenational Design Engineeing Technical Confeences & Computes and Infomation in Engineeing Confeence IDETC/CIE 2010 August 15-18, 2010, Monteal, Quebec, Canada DETC2010-28496
More informationFUSE Fusion Utility Sequence Estimator
FUSE Fusion Utility Sequence Estimato Belu V. Dasaathy Dynetics, Inc. P. O. Box 5500 Huntsville, AL 3584-5500 belu.d@dynetics.com Sean D. Townsend Dynetics, Inc. P. O. Box 5500 Huntsville, AL 3584-5500
More informationHammerstein Model Identification Based On Instrumental Variable and Least Square Methods
Intenational Jounal of Emeging Tends & Technology in Compute Science (IJETTCS) Volume 2, Issue, Januay Febuay 23 ISSN 2278-6856 Hammestein Model Identification Based On Instumental Vaiable and Least Squae
More informationEM Boundary Value Problems
EM Bounday Value Poblems 10/ 9 11/ By Ilekta chistidi & Lee, Seung-Hyun A. Geneal Desciption : Maxwell Equations & Loentz Foce We want to find the equations of motion of chaged paticles. The way to do
More informationPearson s Chi-Square Test Modifications for Comparison of Unweighted and Weighted Histograms and Two Weighted Histograms
Peason s Chi-Squae Test Modifications fo Compaison of Unweighted and Weighted Histogams and Two Weighted Histogams Univesity of Akueyi, Bogi, v/noduslód, IS-6 Akueyi, Iceland E-mail: nikolai@unak.is Two
More informationAbsorption Rate into a Small Sphere for a Diffusing Particle Confined in a Large Sphere
Applied Mathematics, 06, 7, 709-70 Published Online Apil 06 in SciRes. http://www.scip.og/jounal/am http://dx.doi.og/0.46/am.06.77065 Absoption Rate into a Small Sphee fo a Diffusing Paticle Confined in
More informationNotes on McCall s Model of Job Search. Timothy J. Kehoe March if job offer has been accepted. b if searching
Notes on McCall s Model of Job Seach Timothy J Kehoe Mach Fv ( ) pob( v), [, ] Choice: accept age offe o eceive b and seach again next peiod An unemployed oke solves hee max E t t y t y t if job offe has
More informationDuality between Statical and Kinematical Engineering Systems
Pape 00, Civil-Comp Ltd., Stiling, Scotland Poceedings of the Sixth Intenational Confeence on Computational Stuctues Technology, B.H.V. Topping and Z. Bittna (Editos), Civil-Comp Pess, Stiling, Scotland.
More informationAn Exact Solution of Navier Stokes Equation
An Exact Solution of Navie Stokes Equation A. Salih Depatment of Aeospace Engineeing Indian Institute of Space Science and Technology, Thiuvananthapuam, Keala, India. July 20 The pincipal difficulty in
More information6 PROBABILITY GENERATING FUNCTIONS
6 PROBABILITY GENERATING FUNCTIONS Cetain deivations pesented in this couse have been somewhat heavy on algeba. Fo example, detemining the expectation of the Binomial distibution (page 5.1 tuned out to
More informationEncapsulation theory: radial encapsulation. Edmund Kirwan *
Encapsulation theoy: adial encapsulation. Edmund Kiwan * www.edmundkiwan.com Abstact This pape intoduces the concept of adial encapsulation, wheeby dependencies ae constained to act fom subsets towads
More informationLiquid gas interface under hydrostatic pressure
Advances in Fluid Mechanics IX 5 Liquid gas inteface unde hydostatic pessue A. Gajewski Bialystok Univesity of Technology, Faculty of Civil Engineeing and Envionmental Engineeing, Depatment of Heat Engineeing,
More informationWIENER MODELS OF DIRECTION-DEPENDENT DYNAMIC SYSTEMS. Singleton Park, Swansea, SA2 8PP, UK. University of Warwick, Coventry, CV4 7AL, UK
Copyight IFAC 5th Tiennial Wold Congess, Bacelona, Spain WIEER MOELS OF IRECTIO-EPEET YAMIC SYSTEMS H. A. Bake, A. H. Tan and K. R. Godfey epatment of Electical and Electonic Engineeing, Univesity of Wales,
More informationFresnel Diffraction. monchromatic light source
Fesnel Diffaction Equipment Helium-Neon lase (632.8 nm) on 2 axis tanslation stage, Concave lens (focal length 3.80 cm) mounted on slide holde, iis mounted on slide holde, m optical bench, micoscope slide
More informationA Comment on Increasing Returns and Spatial. Unemployment Disparities
The Society fo conomic Studies The nivesity of Kitakyushu Woking Pape Seies No.06-5 (accepted in Mach, 07) A Comment on Inceasing Retuns and Spatial nemployment Dispaities Jumpei Tanaka ** The nivesity
More informationA scaling-up methodology for co-rotating twin-screw extruders
A scaling-up methodology fo co-otating twin-scew extudes A. Gaspa-Cunha, J. A. Covas Institute fo Polymes and Composites/I3N, Univesity of Minho, Guimaães 4800-058, Potugal Abstact. Scaling-up of co-otating
More informationBasic Bridge Circuits
AN7 Datafoth Copoation Page of 6 DID YOU KNOW? Samuel Hunte Chistie (784-865) was bon in London the son of James Chistie, who founded Chistie's Fine At Auctionees. Samuel studied mathematics at Tinity
More informationFunctions Defined on Fuzzy Real Numbers According to Zadeh s Extension
Intenational Mathematical Foum, 3, 2008, no. 16, 763-776 Functions Defined on Fuzzy Real Numbes Accoding to Zadeh s Extension Oma A. AbuAaqob, Nabil T. Shawagfeh and Oma A. AbuGhneim 1 Mathematics Depatment,
More informationSurveillance Points in High Dimensional Spaces
Société de Calcul Mathématique SA Tools fo decision help since 995 Suveillance Points in High Dimensional Spaces by Benad Beauzamy Januay 06 Abstact Let us conside any compute softwae, elying upon a lage
More informationThermodynamic Head Loss in a Channel with Combined Radiation and Convection Heat Transfer
Jounal of Poe and Enegy Engineeing, 04,, 57-63 Published Online Septembe 04 in SciRes. http://.scip.og/jounal/jpee http://dx.doi.og/0.436/jpee.04.9009 hemodynamic Head Loss in a Channel ith Combined Radiation
More informationNOTE. Some New Bounds for Cover-Free Families
Jounal of Combinatoial Theoy, Seies A 90, 224234 (2000) doi:10.1006jcta.1999.3036, available online at http:.idealibay.com on NOTE Some Ne Bounds fo Cove-Fee Families D. R. Stinson 1 and R. Wei Depatment
More informationAn error estimation technique for the solution of ordinary differential equations in Chebyshev series
An eo estimation technique fo the solution of odinay diffeential equations in Chebyshev seies 57 By J. Olive* Most numeical methods fo poducing appoximate Chebyshev seies solutions to odinay diffeential
More informationModeling and Calculation of Optical Amplification in One Dimensional Case of Laser Medium Using Finite Difference Time Domain Method
Jounal of Physics: Confeence Seies PAPER OPEN ACCESS Modeling and Calculation of Optical Amplification in One Dimensional Case of Lase Medium Using Finite Diffeence Time Domain Method To cite this aticle:
More informationEncapsulation theory: the transformation equations of absolute information hiding.
1 Encapsulation theoy: the tansfomation equations of absolute infomation hiding. Edmund Kiwan * www.edmundkiwan.com Abstact This pape descibes how the potential coupling of a set vaies as the set is tansfomed,
More informationJournal of Inequalities in Pure and Applied Mathematics
Jounal of Inequalities in Pue and Applied Mathematics COEFFICIENT INEQUALITY FOR A FUNCTION WHOSE DERIVATIVE HAS A POSITIVE REAL PART S. ABRAMOVICH, M. KLARIČIĆ BAKULA AND S. BANIĆ Depatment of Mathematics
More informationMathematical Model of Magnetometric Resistivity. Sounding for a Conductive Host. with a Bulge Overburden
Applied Mathematical Sciences, Vol. 7, 13, no. 7, 335-348 Mathematical Model of Magnetometic Resistivity Sounding fo a Conductive Host with a Bulge Ovebuden Teeasak Chaladgan Depatment of Mathematics Faculty
More informationDetermining solar characteristics using planetary data
Detemining sola chaacteistics using planetay data Intoduction The Sun is a G-type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this investigation
More informationEffect of no-flow boundaries on interference testing. in fractured reservoirs
Effect of no-flo boundaies on intefeence testing in factued esevois T.Aa. Jelmet 1 1 epatement of petoleum engineeing and applied geophysics,, Noegian Univesity of Science and Tecnology, NTNU. Tondheim,
More information3.1 Random variables
3 Chapte III Random Vaiables 3 Random vaiables A sample space S may be difficult to descibe if the elements of S ae not numbes discuss how we can use a ule by which an element s of S may be associated
More informationHua Xu 3 and Hiroaki Mukaidani 33. The University of Tsukuba, Otsuka. Hiroshima City University, 3-4-1, Ozuka-Higashi
he inea Quadatic Dynamic Game fo Discete-ime Descipto Systems Hua Xu 3 and Hioai Muaidani 33 3 Gaduate School of Systems Management he Univesity of suuba, 3-9- Otsua Bunyo-u, oyo -0, Japan xuhua@gssm.otsua.tsuuba.ac.jp
More informationNumerical Inversion of the Abel Integral Equation using Homotopy Perturbation Method
Numeical Invesion of the Abel Integal Equation using Homotopy Petubation Method Sunil Kuma and Om P Singh Depatment of Applied Mathematics Institute of Technology Banaas Hindu Univesity Vaanasi -15 India
More informationContact impedance of grounded and capacitive electrodes
Abstact Contact impedance of gounded and capacitive electodes Andeas Hödt Institut fü Geophysik und extateestische Physik, TU Baunschweig The contact impedance of electodes detemines how much cuent can
More informationA Relativistic Electron in a Coulomb Potential
A Relativistic Electon in a Coulomb Potential Alfed Whitehead Physics 518, Fall 009 The Poblem Solve the Diac Equation fo an electon in a Coulomb potential. Identify the conseved quantum numbes. Specify
More informationarxiv: v1 [physics.gen-ph] 18 Aug 2018
Path integal and Sommefeld quantization axiv:1809.04416v1 [physics.gen-ph] 18 Aug 018 Mikoto Matsuda 1, and Takehisa Fujita, 1 Japan Health and Medical technological college, Tokyo, Japan College of Science
More informationExploration of the three-person duel
Exploation of the thee-peson duel Andy Paish 15 August 2006 1 The duel Pictue a duel: two shootes facing one anothe, taking tuns fiing at one anothe, each with a fixed pobability of hitting his opponent.
More informationState tracking control for Takagi-Sugeno models
State tacing contol fo Taagi-Sugeno models Souad Bezzaoucha, Benoît Max,3,DidieMaquin,3 and José Ragot,3 Abstact This wo addesses the model efeence tacing contol poblem It aims to highlight the encouteed
More informationASTR415: Problem Set #6
ASTR45: Poblem Set #6 Cuan D. Muhlbege Univesity of Mayland (Dated: May 7, 27) Using existing implementations of the leapfog and Runge-Kutta methods fo solving coupled odinay diffeential equations, seveal
More informationT. Raja Rani. Military Technological College, Muscat, Oman. Abstract
ISSN: 78-8 Vol. Issue, Octobe - Fee Convection ove a Vaying all Vetical Cylinde embedded in a Poous medium ith effect of Radiation, Vaiable Fluid Popeties and Statification. T. Raja Rani Militay Technological
More informationApplication of homotopy perturbation method to the Navier-Stokes equations in cylindrical coordinates
Computational Ecology and Softwae 5 5(): 9-5 Aticle Application of homotopy petubation method to the Navie-Stokes equations in cylindical coodinates H. A. Wahab Anwa Jamal Saia Bhatti Muhammad Naeem Muhammad
More informationA Crash Course in (2 2) Matrices
A Cash Couse in ( ) Matices Seveal weeks woth of matix algeba in an hou (Relax, we will only stuy the simplest case, that of matices) Review topics: What is a matix (pl matices)? A matix is a ectangula
More information2 Governing Equations
2 Govening Equations This chapte develops the govening equations of motion fo a homogeneous isotopic elastic solid, using the linea thee-dimensional theoy of elasticity in cylindical coodinates. At fist,
More informationSupporting Information Wedge Dyakonov Waves and Dyakonov Plasmons in Topological Insulator Bi 2 Se 3 Probed by Electron Beams
Suppoting Infomation Wedge Dyakonov Waves and Dyakonov Plasmons in Topological Insulato Bi 2 Se 3 Pobed by Electon Beams Nahid Talebi, Cigdem Osoy-Keskinboa, Hadj M. Benia, Klaus Ken, Chistoph T. Koch,
More information( ) [ ] [ ] [ ] δf φ = F φ+δφ F. xdx.
9. LAGRANGIAN OF THE ELECTROMAGNETIC FIELD In the pevious section the Lagangian and Hamiltonian of an ensemble of point paticles was developed. This appoach is based on a qt. This discete fomulation can
More informationHow to Obtain Desirable Transfer Functions in MIMO Systems Under Internal Stability Using Open and Closed Loop Control
How to Obtain Desiable ansfe Functions in MIMO Sstems Unde Intenal Stabilit Using Open and losed Loop ontol echnical Repot of the ISIS Goup at the Univesit of Note Dame ISIS-03-006 June, 03 Panos J. Antsaklis
More informationComputers and Mathematics with Applications
Computes and Mathematics with Applications 58 (009) 9 7 Contents lists available at ScienceDiect Computes and Mathematics with Applications jounal homepage: www.elsevie.com/locate/camwa Bi-citeia single
More informationEFFECTS OF FRINGING FIELDS ON SINGLE PARTICLE DYNAMICS. M. Bassetti and C. Biscari INFN-LNF, CP 13, Frascati (RM), Italy
Fascati Physics Seies Vol. X (998), pp. 47-54 4 th Advanced ICFA Beam Dynamics Wokshop, Fascati, Oct. -5, 997 EFFECTS OF FRININ FIELDS ON SINLE PARTICLE DYNAMICS M. Bassetti and C. Biscai INFN-LNF, CP
More informationA matrix method based on the Fibonacci polynomials to the generalized pantograph equations with functional arguments
A mati method based on the Fibonacci polynomials to the genealized pantogaph equations with functional aguments Ayşe Betül Koç*,a, Musa Çama b, Aydın Kunaz a * Coespondence: aysebetuloc @ selcu.edu.t a
More informationAnalytical Solutions for Confined Aquifers with non constant Pumping using Computer Algebra
Poceedings of the 006 IASME/SEAS Int. Conf. on ate Resouces, Hydaulics & Hydology, Chalkida, Geece, May -3, 006 (pp7-) Analytical Solutions fo Confined Aquifes with non constant Pumping using Compute Algeba
More informationIn the previous section we considered problems where the
5.4 Hydodynamically Fully Developed and Themally Developing Lamina Flow In the pevious section we consideed poblems whee the velocity and tempeatue pofile wee fully developed, so that the heat tansfe coefficient
More informationHydroelastic Analysis of a 1900 TEU Container Ship Using Finite Element and Boundary Element Methods
TEAM 2007, Sept. 10-13, 2007,Yokohama, Japan Hydoelastic Analysis of a 1900 TEU Containe Ship Using Finite Element and Bounday Element Methods Ahmet Egin 1)*, Levent Kaydıhan 2) and Bahadı Uğulu 3) 1)
More informationMathematisch-Naturwissenschaftliche Fakultät I Humboldt-Universität zu Berlin Institut für Physik Physikalisches Grundpraktikum.
Mathematisch-Natuwissenschaftliche Fakultät I Humboldt-Univesität zu Belin Institut fü Physik Physikalisches Gundpaktikum Vesuchspotokoll Polaisation duch Reflexion (O11) duchgefüht am 10.11.2009 mit Vesuchspatne
More informationExplosive Contagion in Networks (Supplementary Information)
Eplosive Contagion in Netwoks (Supplementay Infomation) Jesús Gómez-Gadeñes,, Laua Loteo, Segei N. Taaskin, and Fancisco J. Péez-Reche Institute fo Biocomputation and Physics of Comple Systems (BIFI),
More informationAPPLICATION OF MAC IN THE FREQUENCY DOMAIN
PPLICION OF MC IN HE FREQUENCY DOMIN D. Fotsch and D. J. Ewins Dynamics Section, Mechanical Engineeing Depatment Impeial College of Science, echnology and Medicine London SW7 2B, United Kingdom BSRC he
More informationAbsolute Specifications: A typical absolute specification of a lowpass filter is shown in figure 1 where:
FIR FILTER DESIGN The design of an digital filte is caied out in thee steps: ) Specification: Befoe we can design a filte we must have some specifications. These ae detemined by the application. ) Appoximations
More informationyou of a spring. The potential energy for a spring is given by the parabola U( x)
Small oscillations The theoy of small oscillations is an extemely impotant topic in mechanics. Conside a system that has a potential enegy diagam as below: U B C A x Thee ae thee points of stable equilibium,
More informationLocalization of Eigenvalues in Small Specified Regions of Complex Plane by State Feedback Matrix
Jounal of Sciences, Islamic Republic of Ian (): - () Univesity of Tehan, ISSN - http://sciencesutaci Localization of Eigenvalues in Small Specified Regions of Complex Plane by State Feedback Matix H Ahsani
More informationANA BERRIZBEITIA, LUIS A. MEDINA, ALEXANDER C. MOLL, VICTOR H. MOLL, AND LAINE NOBLE
THE p-adic VALUATION OF STIRLING NUMBERS ANA BERRIZBEITIA, LUIS A. MEDINA, ALEXANDER C. MOLL, VICTOR H. MOLL, AND LAINE NOBLE Abstact. Let p > 2 be a pime. The p-adic valuation of Stiling numbes of the
More informationChapter 5 Force and Motion
Chapte 5 Foce and Motion In Chaptes 2 and 4 we have studied kinematics, i.e., we descibed the motion of objects using paametes such as the position vecto, velocity, and acceleation without any insights
More informationarxiv: v1 [math.nt] 12 May 2017
SEQUENCES OF CONSECUTIVE HAPPY NUMBERS IN NEGATIVE BASES HELEN G. GRUNDMAN AND PAMELA E. HARRIS axiv:1705.04648v1 [math.nt] 12 May 2017 ABSTRACT. Fo b 2 and e 2, let S e,b : Z Z 0 be the function taking
More informationChapter 5 Force and Motion
Chapte 5 Foce and Motion In chaptes 2 and 4 we have studied kinematics i.e. descibed the motion of objects using paametes such as the position vecto, velocity and acceleation without any insights as to
More informationF-IF Logistic Growth Model, Abstract Version
F-IF Logistic Gowth Model, Abstact Vesion Alignments to Content Standads: F-IFB4 Task An impotant example of a model often used in biology o ecology to model population gowth is called the logistic gowth
More informationA Backward Identification Problem for an Axis-Symmetric Fractional Diffusion Equation
Mathematical Modelling and Analysis Publishe: Taylo&Fancis and VGTU Volume 22 Numbe 3, May 27, 3 32 http://www.tandfonline.com/tmma https://doi.og/.3846/3926292.27.39329 ISSN: 392-6292 c Vilnius Gediminas
More informationSafety variations in steel designed using Eurocode 3
JCSS Wokshop on eliability Based Code Calibation Safety vaiations in steel designed using Euocode 3 Mike Byfield Canfield Univesity Swindon, SN6 8LA, UK David Nethecot Impeial College London SW7 2BU, UK
More informationBifurcation Analysis for the Delay Logistic Equation with Two Delays
IOSR Jounal of Mathematics (IOSR-JM) e-issn: 78-578, p-issn: 39-765X. Volume, Issue 5 Ve. IV (Sep. - Oct. 05), PP 53-58 www.iosjounals.og Bifucation Analysis fo the Delay Logistic Equation with Two Delays
More informationThe Substring Search Problem
The Substing Seach Poblem One algoithm which is used in a vaiety of applications is the family of substing seach algoithms. These algoithms allow a use to detemine if, given two chaacte stings, one is
More informationAnalytical time-optimal trajectories for an omni-directional vehicle
Analytical time-optimal tajectoies fo an omni-diectional vehicle Weifu Wang and Devin J. Balkcom Abstact We pesent the fist analytical solution method fo finding a time-optimal tajectoy between any given
More informationELASTIC ANALYSIS OF CIRCULAR SANDWICH PLATES WITH FGM FACE-SHEETS
THE 9 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS ELASTIC ANALYSIS OF CIRCULAR SANDWICH PLATES WITH FGM FACE-SHEETS R. Sbulati *, S. R. Atashipou Depatment of Civil, Chemical and Envionmental Engineeing,
More information1 Similarity Analysis
ME43A/538A/538B Axisymmetic Tubulent Jet 9 Novembe 28 Similaity Analysis. Intoduction Conside the sketch of an axisymmetic, tubulent jet in Figue. Assume that measuements of the downsteam aveage axial
More informationSecret Exponent Attacks on RSA-type Schemes with Moduli N = p r q
Secet Exponent Attacks on RSA-type Schemes with Moduli N = p q Alexande May Faculty of Compute Science, Electical Engineeing and Mathematics Univesity of Padebon 33102 Padebon, Gemany alexx@uni-padebon.de
More informationA Comparison and Contrast of Some Methods for Sample Quartiles
A Compaison and Contast of Some Methods fo Sample Quatiles Anwa H. Joade and aja M. Latif King Fahd Univesity of Petoleum & Mineals ABSTACT A emainde epesentation of the sample size n = 4m ( =, 1, 2, 3)
More informationModeling Fermi Level Effects in Atomistic Simulations
Mat. Res. Soc. Symp. Poc. Vol. 717 Mateials Reseach Society Modeling Femi Level Effects in Atomistic Simulations Zudian Qin and Scott T. Dunham Depatment of Electical Engineeing, Univesity of Washington,
More informationNuclear size corrections to the energy levels of single-electron atoms
Nuclea size coections to the enegy levels of single-electon atoms Babak Nadii Nii a eseach Institute fo Astonomy and Astophysics of Maagha (IAAM IAN P. O. Box: 554-44. Abstact A study is made of nuclea
More informationUsing Laplace Transform to Evaluate Improper Integrals Chii-Huei Yu
Available at https://edupediapublicationsog/jounals Volume 3 Issue 4 Febuay 216 Using Laplace Tansfom to Evaluate Impope Integals Chii-Huei Yu Depatment of Infomation Technology, Nan Jeon Univesity of
More informationResearch Article On Alzer and Qiu s Conjecture for Complete Elliptic Integral and Inverse Hyperbolic Tangent Function
Abstact and Applied Analysis Volume 011, Aticle ID 697547, 7 pages doi:10.1155/011/697547 Reseach Aticle On Alze and Qiu s Conjectue fo Complete Elliptic Integal and Invese Hypebolic Tangent Function Yu-Ming
More information0606 ADDITIONAL MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS Intenational Geneal Cetificate of Seconday Education MARK SCHEME fo the Octobe/Novembe 011 question pape fo the guidance of teaches 0606 ADDITIONAL MATHEMATICS
More informationCentral Coverage Bayes Prediction Intervals for the Generalized Pareto Distribution
Statistics Reseach Lettes Vol. Iss., Novembe Cental Coveage Bayes Pediction Intevals fo the Genealized Paeto Distibution Gyan Pakash Depatment of Community Medicine S. N. Medical College, Aga, U. P., India
More informationGain-Scheduled Controller Design: An Analytic Framework Directly Incorporating Non-Equilibrium Plant Dynamics
Gain-Sheduled Contolle Design: An Analyti Fameok Dietly Inopoating Non-Equilibium Plant Dynamis D.J.Leith W.E.Leithead Abstat Depatment of Eletoni & Eletial Engineeing, Univesity of Stathlyde, GLASGOW
More informationChapter 3: Theory of Modular Arithmetic 38
Chapte 3: Theoy of Modula Aithmetic 38 Section D Chinese Remainde Theoem By the end of this section you will be able to pove the Chinese Remainde Theoem apply this theoem to solve simultaneous linea conguences
More informationSwissmetro: design methods for ironless linear transformer
Swissmeto: design methods fo ionless linea tansfome Nicolas Macabey GESTE Engineeing SA Scientific Pak PSE-C, CH-05 Lausanne, Switzeland Tel (+4) 2 693 83 60, Fax. (+4) 2 693 83 6, nicolas.macabey@geste.ch
More informationLight Time Delay and Apparent Position
Light Time Delay and ppaent Position nalytical Gaphics, Inc. www.agi.com info@agi.com 610.981.8000 800.220.4785 Contents Intoduction... 3 Computing Light Time Delay... 3 Tansmission fom to... 4 Reception
More informationLong-range stress re-distribution resulting from damage in heterogeneous media
Long-ange stess e-distibution esulting fom damage in heteogeneous media Y.L.Bai (1), F.J.Ke (1,2), M.F.Xia (1,3) X.H.Zhang (1) and Z.K. Jia (1) (1) State Key Laboatoy fo Non-linea Mechanics (LNM), Institute
More informationNumerical Integration
MCEN 473/573 Chapte 0 Numeical Integation Fall, 2006 Textbook, 0.4 and 0.5 Isopaametic Fomula Numeical Integation [] e [ ] T k = h B [ D][ B] e B Jdsdt In pactice, the element stiffness is calculated numeically.
More informationSensor and Simulation Notes. Note 525. Oct Lens Design for a Prolate-Spheroidal Impulse radiating Antenna (IRA)
Senso and Simulation Notes Note 55 Oct 7 Lens Design fo a Polate-Spheoidal Impulse adiating Antenna (IRA) Sehat Altunc, Cal E. Baum, Chistos G. Chistodoulou and Edl Schamiloglu Univesity of New Mexico
More informationON INDEPENDENT SETS IN PURELY ATOMIC PROBABILITY SPACES WITH GEOMETRIC DISTRIBUTION. 1. Introduction. 1 r r. r k for every set E A, E \ {0},
ON INDEPENDENT SETS IN PURELY ATOMIC PROBABILITY SPACES WITH GEOMETRIC DISTRIBUTION E. J. IONASCU and A. A. STANCU Abstact. We ae inteested in constucting concete independent events in puely atomic pobability
More informationSteady State and Transient Performance Analysis of Three Phase Induction Machine using MATLAB Simulations
Intenational Jounal of Recent Tends in Engineeing, Vol, No., May 9 Steady State and Tansient Pefomance Analysis of Thee Phase Induction Machine using MATAB Simulations Pof. Himanshu K. Patel Assistant
More informationGradient-based Neural Network for Online Solution of Lyapunov Matrix Equation with Li Activation Function
Intenational Confeence on Infomation echnology and Management Innovation (ICIMI 05) Gadient-based Neual Netwok fo Online Solution of Lyapunov Matix Equation with Li Activation unction Shiheng Wang, Shidong
More informationReading Assignment. Problem Description for Homework #9. Read Chapters 29 and 30.
Reading Assignment Read Chaptes 29 and 30. Poblem Desciption fo Homewok #9 In this homewok, you will solve the inhomogeneous Laplace s equation to calculate the electic scala potential that exists between
More informationSTABILITY AND PARAMETER SENSITIVITY ANALYSES OF AN INDUCTION MOTOR
HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY VESZPRÉM Vol. 42(2) pp. 109 113 (2014) STABILITY AND PARAMETER SENSITIVITY ANALYSES OF AN INDUCTION MOTOR ATTILA FODOR 1, ROLAND BÁLINT 1, ATTILA MAGYAR 1, AND
More informationMath 2263 Solutions for Spring 2003 Final Exam
Math 6 Solutions fo Sping Final Exam ) A staightfowad appoach to finding the tangent plane to a suface at a point ( x, y, z ) would be to expess the cuve as an explicit function z = f ( x, y ), calculate
More informationBounds on the performance of back-to-front airplane boarding policies
Bounds on the pefomance of bac-to-font aiplane boading policies Eitan Bachmat Michael Elin Abstact We povide bounds on the pefomance of bac-to-font aiplane boading policies. In paticula, we show that no
More informationElectrostatics (Electric Charges and Field) #2 2010
Electic Field: The concept of electic field explains the action at a distance foce between two chaged paticles. Evey chage poduces a field aound it so that any othe chaged paticle expeiences a foce when
More informationUnobserved Correlation in Ascending Auctions: Example And Extensions
Unobseved Coelation in Ascending Auctions: Example And Extensions Daniel Quint Univesity of Wisconsin Novembe 2009 Intoduction In pivate-value ascending auctions, the winning bidde s willingness to pay
More informationAn Application of Fuzzy Linear System of Equations in Economic Sciences
Austalian Jounal of Basic and Applied Sciences, 5(7): 7-14, 2011 ISSN 1991-8178 An Application of Fuzzy Linea System of Equations in Economic Sciences 1 S.H. Nassei, 2 M. Abdi and 3 B. Khabii 1 Depatment
More informationTo Feel a Force Chapter 7 Static equilibrium - torque and friction
To eel a oce Chapte 7 Chapte 7: Static fiction, toque and static equilibium A. Review of foce vectos Between the eath and a small mass, gavitational foces of equal magnitude and opposite diection act on
More informationLead field theory and the spatial sensitivity of scalp EEG Thomas Ferree and Matthew Clay July 12, 2000
Lead field theoy and the spatial sensitivity of scalp EEG Thomas Feee and Matthew Clay July 12, 2000 Intoduction Neuonal population activity in the human cotex geneates electic fields which ae measuable
More informationPerturbation to Symmetries and Adiabatic Invariants of Nonholonomic Dynamical System of Relative Motion
Commun. Theo. Phys. Beijing, China) 43 25) pp. 577 581 c Intenational Academic Publishes Vol. 43, No. 4, Apil 15, 25 Petubation to Symmeties and Adiabatic Invaiants of Nonholonomic Dynamical System of
More informationCentripetal Force OBJECTIVE INTRODUCTION APPARATUS THEORY
Centipetal Foce OBJECTIVE To veify that a mass moving in cicula motion expeiences a foce diected towad the cente of its cicula path. To detemine how the mass, velocity, and adius affect a paticle's centipetal
More informationForce between two parallel current wires and Newton s. third law
Foce between two paallel cuent wies and Newton s thid law Yannan Yang (Shanghai Jinjuan Infomation Science and Technology Co., Ltd.) Abstact: In this pape, the essence of the inteaction between two paallel
More informationarxiv:gr-qc/ v1 1 Sep 2005
Radial fall of a test paticle onto an evapoating black hole Andeas Aste and Dik Tautmann Depatment fo Physics and Astonomy, Univesity of Basel, 456 Basel, Switzeland E-mail: andeas.aste@unibas.ch June
More informationLINEAR AND NONLINEAR ANALYSES OF A WIND-TUNNEL BALANCE
LINEAR AND NONLINEAR ANALYSES O A WIND-TUNNEL INTRODUCTION BALANCE R. Kakehabadi and R. D. Rhew NASA LaRC, Hampton, VA The NASA Langley Reseach Cente (LaRC) has been designing stain-gauge balances fo utilization
More information