physical examples of first order systems

... Classification of First- Order Recurrent Neural Networks 143 class of rational-weighted first -order recurrent neural networks made up of McCulloch and Pitts cells, and provide a refined classification of the ... The obtained hierarchical classification of neural networks consists of a decidable pre-well ordering of width and height ω ω , and a decidability procedure of this hierarchy is provided Notably, ... irrespective of the fact that this sequence is periodic or not, some state will repeat finitely often whereas other will repeat infinitely often The (finite) set of states occurring infinitely often in...

Ngày tải lên: 28/04/2014, 10:06

... problems for first order integro-differential equations of mixed type J Math Anal Appl 300, 1–11 (2004) doi:10.1016/j.jmaa.2004.02.060 Xing, Y, Han, M, Zheng, G: Initial value problem for first order ... Tisdell, CC: Existence of solutions to first -order periodic boundary value problems J Math Anal Appl 323(2), 1325–1332 (2006) doi:10.1016/j.jmaa.2005.11.047 Tisdell, CC: On first- order discrete boundary ... fol2 lows from Corollary 2.2 In what follows we focus on the first- order integro-differential equations of mixed type in the form of (1.2) The results presented in the following three statements...

Ngày tải lên: 21/06/2014, 02:20

... that the time scale T is unbounded from above because of the definition of oscillation The object of the present paper is to study nonoscillation of the following delay dynamic equation: xΔ t Ai t ... 3.19 T is a positive solution of 3.2 , and −x is a negative solution to 3.3 The following three examples are special cases of the above result, and the first two of them are corollaries for the ... solutions of 4.11 and 4.13 illustrates the result of Theorem 4.5, √ here y t > x t for all t ∈ 3, ∞ √N Corollary 4.8 Let x be a solution of 3.1 , and Y ·, s > on s, ∞ fundamental solution of xΔ...

Ngày tải lên: 21/06/2014, 11:20

... FO systems and we propose a simple fractional -order controller to control of fractional -order interval systems It is obvious that the considered formation covers IO plant The remaining part of ... multiplicity of one The geometric multiplicity of an eigenvalue λ of the matrix A is the dimension of the subspace of vectors v for which Av λv Then, our robust stability test task for FO-LTI interval systems ... open-loop and closed-loop systems have different orders For this reason, a controller in order to change the order of the closed-loop system to a specific fractional order is designed In 12 , authors...

Ngày tải lên: 21/06/2014, 16:20

... there exists n0 ∈ N such that 2.11 holds, then every solution of 1.9 oscillates on t0 , ∞ T Proof The proof is an immediate consequence of Lemmas 2.1 and 2.2 We need the following lemmas in the ... and 2.11 hold Then, every solution of 1.9 is oscillatory on t0 , ∞ T Proof The proof follows from Lemmas 2.1, 2.2, and 2.5 Remark 2.7 We obtain the main results of 7, by letting n0 in Theorem 2.6 ... criterion for first order dynamic equations,” to appear in Functional Differential Equations 10 Y Sahiner and I P Stavroulakis, “Oscillations of first order delay dynamic equations,” Dynamic ¸ Systems and...

Ngày tải lên: 22/06/2014, 11:20

... properties of the set of solutions of initial and periodic problems In Section 3, we prove the existence of at least one N-periodic stable solution Finally, Section is devoted to give some examples ... optimality of the obtained results Preliminaries This paper is devoted to study the stability, by using the method of lower and upper solutions, of the N-periodic solutions of the following first -order ... see [1, 2], that the existence of α and β, a pair of lower and upper solutions of problem (PN ), such that α ≤ β in JN , does not imply the existence of a solution of this problem Alberto Cabada...

Ngày tải lên: 23/06/2014, 00:20

... Length of a first- order branch Foliar biomass of a first- order branch Woody biomass of a first- order branch Total (foliage and woody) biomass of a first- order branch Height of the base of a first- order ... first- order branch Ratio of the height of the base of a first- order branch to tree height Elongation of a first- order branch per year Increment in foliar biomass of a first- order branch per year ... terms of above-ground biomss per year Height increment per year Relative growth rate in terms of tree height per year Birth rate of first- order branches per tree per year Death rate of first- order...

Ngày tải lên: 08/08/2014, 14:22

... W e c a n w rite the first e q u a tio n o f the syste m (1 ) a s : (1.14) (a ) dt Obviously, the stability condition of the stationary solution a = a0y &(ơ0) = (1.14) is of the form: ' ( a o) ... ones “x and F ig : p h a se p ictu re T h e Nonlinear oscillations o f third order systems Part Ị 517 Influence of Coulomb Friction on Sclf-Exdtcd Oscillation In t h is S e c tio n the in fluen ... n s o f th e first a p p r o x im a t io n : * = acoscp, (5 ) dA ~dt = (Ệ2 + Q 2) d(p = Q dt A {\ EỆ A * ) - y - Q h 2A* ] • A = eQ 2(ề2 + Q 2) Considering in the first quadrant of the plane...

Ngày tải lên: 08/04/2015, 15:29

... third order systems Part II 129 i.e the n e ce ssa ry c o n d it io n fo r the sta b ility o f the s ta tio n a ry o s c illa t io n is : < (3 ) T h u s , fo r the D u ffin g case, o n ly the soft ... For this purpose, we represent the solution of Eq (4.1) in the form: (5 ) X =* a0cos(yt + ip0)+ b Q o sQ t9 131 Nonlinear oscillations o f third order systems Part II w h ere the firs t term is ... oscillations of a third order non-linear system, J Sound and Vibration, 36, 4, 1974 H R S r i r a n g a r a j a n , p S rin iv a s a n , Ultraspherical polynom ials approach to the study o f third-order...

Ngày tải lên: 08/04/2015, 15:29

... se r v e d on n n a lo ''- c o m p u te r t o o fig r Non-autonomous Systems (continued) Parametric Ocnillotion of third order non-linear System ?he f o llo w in g e q u a tio n i X - Q2 X + ... x n e T f th(r J ec ^ e r s e a the Van d e r To l c.-ise ii = ( - x ^ ) A the equations of the first approximations are t X * a c o s , > Rz-px^ For the D u ffin g case (2.6) v/e h a v e t h e...

Ngày tải lên: 08/04/2015, 15:30

... an important role in the development of theory of fractional dynamic systems [4,7,11] Using of half -order derivatives and integrals leads to a formulation of certain real-world problems in different ... [4,8-11] that allows the prediction of behavior of a differential system when the behavior of the null solution of a comparison system is known The application of Lyapunov’s direct method in boundedness ... among the fractional order derivatives, Caputo, Reimann-Liouville and Grünwald-Letnikov fractional order derivatives, necessary definition of initial value problems of fractional order differential...

Ngày tải lên: 20/06/2014, 22:20

... robust control of fractional differential systems with delays They delt with the BIBO stability of both retarded and neutral fractional delay systems Zhang [16] established the existence of a unique ... http://www.advancesindifferenceequations.com/content/2011/1/47 Page of Definition The Riemann-liouville fractional (arbitrary) order derivatives of order a, n

Ngày tải lên: 20/06/2014, 22:20

... coupled infinite systems of first order partial differential equations Rocky Mt J Math 10, 237–246 (1980) Kamont Journal of Inequalities and Applications 2011, 2011:15 http://www.journalofinequalitiesandapplications.com/content/2011/1/15 ... Journal of Inequalities and Applications 2011, 2011:15 http://www.journalofinequalitiesandapplications.com/content/2011/1/15 Page of 20 functions of one variable, which are solutions of ordinary ... Viscosity solutions of functional differential inequalities were studied in [14,15] The aim of this article is to add a new element to the above sequence of generalizations of classical theorems...

Ngày tải lên: 21/06/2014, 02:20

... our proof greatly It is easy to see from the proof that this main nonlinearity is used to guarantee the small twist condition 4 Boundary Value Problems The Proof of Theorem The proof of Theorem ... curve of the Poincare mapping, which guarantees the boundedness of solutions of the system 2.11 Hence, all the solutions of 1.9 are bounded References J Littlewood, “Unbounded solutions of y ... ×S1 be a finite part of cylinder C S1 ×R, where S1 R/2πZ, we denote by Γ the class of Jordan curves in C that are homotopic to the circle r constant The subclass of Γ composed of those curves lying...

Ngày tải lên: 21/06/2014, 07:20

... of Second -order Linear Difference Equation II: the second case In the rest of this paper, we would like to give an example to show how to use the results of this paper to obtain error bounds of ... different two cases of , respectively In the rest of this section, we introduce the main results of in the case that k is positive In the next section, we give two lemmas on estimations of bounds for ... asymptotic solutions of second -order linear differential equations, the method used in Wong and Li’s papers cannot give us way to obtain error bounds of these asymptotic solutions Only order estimations...

Ngày tải lên: 21/06/2014, 11:20

... by Theorem 3.1 The proof of Theorem 5.1 is now complete Proof of main result Theorem 1.1 The proof of Theorem 1.1 is direct consequence of the following Theorem 6.1 Assume hypotheses (H1 ) through ... “Superlinear systems of second -order ODE’s,” to appear in Nonlinear Analysis: Theory, Methods ’ Applications M Conti, L Merizzi, and S Terracini, “On the existence of many solutions for a class of superlinear ... fixed points of the operator Fλ are the positive solutions of system 2.4 Lemma 4.1 The operator Fλ : X→X is compact, and the cone C is invariant under Fλ a Proof Outline The compactness of Fλ follows...

Ngày tải lên: 22/06/2014, 06:20

... Therefore, u is the unique solution of PBVP (2.41) The proof of Lemma 2.7 is complete Lemma 2.8 u ∈ Ω is a solution of PBVP (1.1) if and only if u ∈ PC[JT , R] is solution of the following integral equation: ... (2.57) The proof of Lemma 2.8 is similar to that of Lemma 2.6 and we will omit it here Main results In this section, we will use the monotone iterative technique to prove the existence of minimal ... “On first order impulsive dynamic equations on time scales,” Journal of Difference Equations and Applications, vol 10, no 6, pp 541–548, 2004 [6] F M Atici and D C Biles, First- and second-order...

Ngày tải lên: 22/06/2014, 19:20

... by Theorem 3.1 The proof of Theorem 5.1 is now complete Proof of main result Theorem 1.1 The proof of Theorem 1.1 is direct consequence of the following Theorem 6.1 Assume hypotheses (H1 ) through ... “Superlinear systems of second -order ODE’s,” to appear in Nonlinear Analysis: Theory, Methods ’ Applications M Conti, L Merizzi, and S Terracini, “On the existence of many solutions for a class of superlinear ... fixed points of the operator Fλ are the positive solutions of system 2.4 Lemma 4.1 The operator Fλ : X→X is compact, and the cone C is invariant under Fλ a Proof Outline The compactness of Fλ follows...

Ngày tải lên: 22/06/2014, 19:20

... solutions of a class of non-autonomous second -order systems, Journal of Mathematical Analysis and Applications 236 (1999), no 2, 227–235 Martin Schechter: Department of Mathematics, University of California, ... These methods allow us to improve the previous results Proofs of the theorems We now give the proof of Theorem 1.1 Proof Let X be the set of vector functions x(t) given by (1.2) and described above ... order systems with sublinear nonlinearity, [12] Proceedings of the American Mathematical Society 126 (1998), no 11, 3263–3270 [13] C.-L Tang and X.-P Wu, Periodic solutions for second order systems...

Ngày tải lên: 22/06/2014, 22:20

... The first eigenvalue of p-Laplacian systems Problems of such a type arise in a variety of applications, for example, non-Newtonian fluids, reaction-diffusion problems, theory of superconductors, ... 314 The first eigenvalue of p-Laplacian systems The eigenfunctions corresponding to λ1 In this section, we complete the proof of Theorem 2.2 establishing the simplicity of λ1 More precisely, we ... to ||| · |||m The proof of the following lemma is also provided in [14] Lemma 2.1 (i) If p≤r ≤ pN , N−p N > α ≥ N −r N−p , p (2.9) 310 The first eigenvalue of p-Laplacian systems then the embedding...

Ngày tải lên: 23/06/2014, 00:20