application of higher order differential equation ppt

... “Existence of solutions for a class of third -order nonlinear boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 294, no. 1, pp. 104–112, 2004. 14 D. Guo, Semi-Ordered ... solutions of nonlinear singular third -order two-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 413–425, 2006. 12 Y. Sun, “Positive solutions of ... Gregus, “Third order linear Differential equations,” in Mathematics and Its Applications, Reidel, Dordrecht, the Netherlands, 1987. 2 L J. Guo, J P. Sun, and Y H. Zhao, “Existence of positive solutions...

... Difference Equations 2011, 2011:56 http://www.advancesindifferenceequations.com/content/2011/1/56 Page 8 of 8 RESEARC H Open Access Positive periodic solution of higher- order functional difference equation Mei-Lan ... Most of these discrete mathematical models are first -order functional difference equations. Rela- tively, few articles focused on the existence of positive periodic solutions of higher- order functional ... k, , m ẻ N where N denotes the set of positive integers. The purpose of this article is to consider the existence of positive periodic solution of higher -order functional differen ce equatio...

... delay differential equations of higher order for p(t) = ± 1. Arch Math. 40, 359–366 (2004) 16. Tang, S, Li, T, Thandapani, E: Oscillation of higher- order half-linear neutral differential equations. ... zero as t đ . Proof. The proof of the corollary is similar to the proof of Corollary 3.3 and so it is omitted. From the above results on the oscillation of odd -order differential equation and Lemma ... on the oscillation of odd -order differential equation and Lemma 2.5, we can easily obtain the following results regarding the oscillation of even- order neutral differential equations. Theorem...

... equicontinuity of E R , and it comp letes the proof of the discreteness of the spectrum of L 0 . 2 The derivation of the asymptotic formula for eigenvalue distribution of L 0 Suppose that the eigenvalues of ... of L 0 which are less than g k λ k ∼−h √ γ k . (2:9) Now, find the asymptotic of those solutions of Equation 2.3 which are greater than g k , i.e., the real roots of Equation 2.5. By virtue of ... integrand is an odd function. the order of its numerator in the vicinity of zero is O(z ν+1 ), and the order of its denominator is O(z ν ), the integral along the left part of contour vanishes. Now,...

... class of second -order Emden-Fowler delay dynamic equations on time scales,” Journal of Mathematical Analysis and Applications, vol. 334, no. 2, pp. 847–858, 2007. 13 Y. Sáahiner, Oscillation of ... integration of nonlinear dynamic equations,” Advances in Difference Equations, vol. 2008, Article ID 739602, 17 pages, 2008. 15 T. S. Hassan, “Oscillation of third order nonlinear delay dynamic equations ... Journal of Mathematics, vol. 34, no. 4, pp. 1239–1254, 2004. 6 L. Erbe, “Oscillation results f or second -order linear equations on a time scale,” Journal of Difference Equations and Applications,...

... Introduction Thepast20yearswitnessedanexpansionofpowerspectrumestimationtechniques,whichhave provedessentialinmanyapplications,suchascommunications,sonar,radar,speech/imageprocess- ing,geophysics,andbiomedicalsignalprocessing[13,11,7].Inpowerspectrumestimationthe processunderconsiderationistreatedasasuperpositionofstatisticallyuncorrelatedharmoniccom- ponents.Thedistributionofpoweramongthesefrequencycomponentsisthepowerspectrum.As such,phaserelationsbetweenfrequencycomponentsaresuppressed.Theinformationinthepower spectrumisessentiallypresentintheautocorrelationsequence,whichwouldsufceforthecomplete statisticaldescriptionofaGaussianprocessofknownmean.However,thereareapplicationswhere onewouldneedtoobtaininformationregardingdeviationsfromtheGaussianityassumptionand presenceofnonlinearities.Inthesecasespowerspectrumisoflittlehelp,andonewouldhaveto lookbeyondthepowerspectrumorautocorrelationdomain .Higher- OrderSpectra(HOS)(oforder greaterthan2),whicharedenedintermsofhigher-ordercumulantsofthedata,docontainsuch information[16].Thethird-orderspectrumiscommonlyreferredtoasbispectrum,thefourth -order oneastrispectrum,andinfact,thepowerspectrumisalsoamemberofthehigher-orderspectral class;itisthesecond-orderspectrum. HOSconsistofhigher-ordermomentspectra,whicharedenedfordeterministicsignals,and cumulantspectra,whicharedenedforrandomprocesses.Ingeneral,therearethreemotivations behindtheuseofHOSinsignalprocessing:(1)tosuppressGaussiannoiseofunknownmeanand variance;(2)toreconstructthephaseaswellasthemagnituderesponseofsignalsorsystems;and (3)todetectandcharacterizenonlinearitiesinthedata. TherstmotivationstemsfromthepropertyofGaussianprocessestohavezerohigher -order spectra.Duetothisproperty,HOSarehighsignal-to-noiseratiodomains,inwhichonecanperform detection,parameterestimation,orevensignalreconstructionevenifthetimedomainnoiseis spatiallycorrelated.Thesamepropertyofcumulantspectracanprovidemeansofdetectingand characterizingdeviationsofthedatafromtheGaussianmodel. c 1999byCRCPressLLC ... Introduction Thepast20yearswitnessedanexpansionofpowerspectrumestimationtechniques,whichhave provedessentialinmanyapplications,suchascommunications,sonar,radar,speech/imageprocess- ing,geophysics,andbiomedicalsignalprocessing[13,11,7].Inpowerspectrumestimationthe processunderconsiderationistreatedasasuperpositionofstatisticallyuncorrelatedharmoniccom- ponents.Thedistributionofpoweramongthesefrequencycomponentsisthepowerspectrum.As such,phaserelationsbetweenfrequencycomponentsaresuppressed.Theinformationinthepower spectrumisessentiallypresentintheautocorrelationsequence,whichwouldsufceforthecomplete statisticaldescriptionofaGaussianprocessofknownmean.However,thereareapplicationswhere onewouldneedtoobtaininformationregardingdeviationsfromtheGaussianityassumptionand presenceofnonlinearities.Inthesecasespowerspectrumisoflittlehelp,andonewouldhaveto lookbeyondthepowerspectrumorautocorrelationdomain .Higher- OrderSpectra(HOS)(oforder greaterthan2),whicharedenedintermsofhigher-ordercumulantsofthedata,docontainsuch information[16].Thethird-orderspectrumiscommonlyreferredtoasbispectrum,thefourth -order oneastrispectrum,andinfact,thepowerspectrumisalsoamemberofthehigher-orderspectral class;itisthesecond-orderspectrum. HOSconsistofhigher-ordermomentspectra,whicharedenedfordeterministicsignals,and cumulantspectra,whicharedenedforrandomprocesses.Ingeneral,therearethreemotivations behindtheuseofHOSinsignalprocessing:(1)tosuppressGaussiannoiseofunknownmeanand variance;(2)toreconstructthephaseaswellasthemagnituderesponseofsignalsorsystems;and (3)todetectandcharacterizenonlinearitiesinthedata. TherstmotivationstemsfromthepropertyofGaussianprocessestohavezerohigher -order spectra.Duetothisproperty,HOSarehighsignal-to-noiseratiodomains,inwhichonecanperform detection,parameterestimation,orevensignalreconstructionevenifthetimedomainnoiseis spatiallycorrelated.Thesamepropertyofcumulantspectracanprovidemeansofdetectingand characterizingdeviationsofthedatafromtheGaussianmodel. c 1999byCRCPressLLC ... modeling of the bispectrum have been shown to yield superior resolution [30, 31] than the ones obtained with conventional methods. 76.6 Applications/Software Available Applications of HOS span...

... theorem proving in higher- order logic than in first -order logic as claimed in the last point, the nature of proofs in higher- order logic is far from mysterious. For example, higher- order resolution ... that the higher- order representation should ac- tually simplify the process of finding proofs. In a more specific sense, there are sublogics of a higher- order logic in which the process of constructing ... kinds of analyses by considering an example of determining pronoun reference. 2. Higher- Order Logic The higher- order logic we study here, called T, can be thought of as being a subsystem of...

... 1 of 7 ECET- 462 Application of Computers in Process Control Purdue University, Calumet [LABORATORY 8] Tuning of a PID controller using Ziegler-Nichols Method Page 6 of ... Form of the PID Compensator Page 7 of 7 Conclusion: 1) Follow the steps describe above to tune the PID controller. 2) Find the values of K P , T I , T D. 3) What is the effect of changing ... Page 2 of 7 Tuning of a PID controller using Ziegler-Nichols Method LAB 8 Objective: 1) To demonstrate the use of PID controller using LabVIEW. 2) Finding the values of K P and...

... this book we attempt to cover some of the important facets of mobile communications design. We start of with five chapters covering various aspects of the design of the commu- Introduction 9 Figure ... inherent in many DSP applications. Though the application of this to physical layer processing in the handset is not apparent so far, these devices allow very efficient compilation of higher level code ... this growth and roll-out of 3G should begin within 1 year. The key feature of 3G systems is the integration of significant amounts of data communication with voice communication, all at higher user capacities...

... x), t  n−1 j=0 |r| j 2 j+1  ≥ N ′ (ϕ(x, 2x, x), (2 − |r|)t) . The rest of the proof is similar to the proof of Theorem 2.5.  Fuzzy stability of additive functional equation 9 Theorem 2.5. Assume that a mapping f ... inequality d(f, A) ≤ 1 2 − 2L . This implies that the inequality (2.7) holds. The rest of the proof is similar to that of the proof of Theorem 2.1.  Corollary 2.4. Let θ ≥ 0 and let p be a real number with ... in the theory of functional equations is the following: When is it true that a function which approximately satisfies a functional equation must be close to an exact solution of the equation? If...

... class of higher- order difference equations Huantao Zhu 1 and Weibing Wang ∗2 1 Hunan College of Information, Changsha, Hunan 410200, P.R. China 2 Department of Mathematics, Hunan University of Science ... functional difference equation; periodic solution; fixed point theo- rem. 1 (1.3). Our aim of this article is to study the existence of periodic solutions for the higher- order difference equations (1.1) ... existence of periodic solutions for first -order functional difference equations [8–12]. Only a few article have been published on the same problem for higher- order functional difference equations....

... a class of even -order differential equations Journal of Inequalities and Applications 2012, 2012:5 doi:10.1186/1029-242X-2012-5 Qi-Ming Zhang (zhqm20082008@sina.com) Xiaofei He (hexiaofei525@sina.com) ISSN ... for a class of even -order differential equations Qi-Ming Zhang ∗1 and Xiaofei He 2 1 College of Science, Hunan University of Technology, Zhuzhou, Hunan 412000, P.R. China 2 College of Mathematics ... inequalities for certain higher order differential equations. Appl. Math. Comput. 216, 368–373 (2010) [18] He, X, Tang, XH: Lyapunov-type inequalities for even order differential equations. Commun. Pure...

... (1.4). 3. Stability of the quadratic equation (1.4) For r = 1, the stability problem of Equation (1.4) has been investigated by Cholewa [15]. For r = 2, the stability problem of Equation (1.4) has ... Journal of Inequalities and Applications 2011, 2011:79 http://www.journalofinequalitiesandapplications.com/content/2011/1/79 Page 5 of 9 RESEARCH Open Access On the Ulam-Hyers stability of a quadratic functional ... >2. Lee et al. Journal of Inequalities and Applications 2011, 2011:79 http://www.journalofinequalitiesandapplications.com/content/2011/1/79 Page 8 of 9 including Equation (1.1). It is also...