linear differential equations lde of second and higher order

Ngày tải lên: 22/06/2014, 18:20

Ngày tải lên: 14/03/2014, 13:20

... N 1 ,N 2 of N with N = N 1 ⊕N 2 and N i = F i for i =1, 2. Proof. The proof is similar to the proof of Proposition 3.17. Let S 1 and S 2 be the set of eigenvalues of E acting on F 1 and F 2 respectively. ... translates into Z L =(r a,b )G L . A proof of Lemma 1.29 finishes the proof of the theorem. ✷ Proof of lemma 1.29. The proof is rather similar to the one of lemma 1.23. The only thing that we have ... theory of torsors, of this weaker statement). Let K be the Picard-Vessiot extension of a scalar differential equation L(y)=0 of order n over k.LetG be the differential Galois group of the equation and...

Ngày tải lên: 31/03/2014, 15:56

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 23/06/2014, 00:20

... range of temperature. They calculated heats of transition from the DTA curves of these soaps and have since (Void, Grandine, and Void, 1948) de- lineated the polymorphic transformations of calcium ... METHODS OF IDENTIFYING CLAYS AND INTERPRETATION OF RESULTS 159 J. A. Pask: Is the spinel formed by a combination of the exchangeable cation and the aluminum of the lattice? R. A. Rowland: ... E., and Rowland, R. A., 1944, Differential thermal analysis of clays and shales, control and prospecting method: Am. Ceramic Soc. Jour., v. 27, pp. 65-76. Grim, R. E., Machiu, J. S., and Bradley,...

Ngày tải lên: 22/05/2014, 15:57

Ngày tải lên: 12/06/2014, 16:17

... Wong et al.: The differential mediating effects of pain and depression on the physical and mental dimension of quality of life in Hong Kong Chinese adults. Health and Quality of Life Outcomes 2010 ... Health and Quality of Life Outcomes 2010, 8:1 http://www.hqlo.com/content/8/1/1 Page 2 of 6 SHOR T REPOR T Open Access The differential mediating effects of pain and depression on the physical and ... life?. The Journal of nervous and mental disease 2006, 194(4):241-248. 13. Boelen PA, Prigerson HG: The influence of symptoms of prolonged grief disorder, depression, and anxiety on quality of life among...

Ngày tải lên: 18/06/2014, 19:20

Ngày tải lên: 21/06/2014, 20:20

Ngày tải lên: 09/08/2014, 20:21

... 5 Antiderivation of Taylor Models. For a polynomial , we denote by all terms of of orders up to (and including) and by a bound of the range of over the domain box . Then, the antiderivation of Taylor ... the constant parts and using the antiderivation: VERIFIEDHIGH-ORDERINTEGRATIONOFDAES AND HIGHER- ORDER ODES Jens Hoefkens Martin Berz Kyoko Makino Department of Physics and Astronomy and National Superconducting ... (Berz and Makino, 1998; Makino et al., 2000). Definition 5 For a -th order Taylor model and , let The antiderivative of is defined by Since is of order , the definition assures that for a -th order...

Ngày tải lên: 12/01/2014, 21:46

Ngày tải lên: 24/04/2014, 17:17

... Oscillation of solutions of non -linear neutral 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 ... of even -order neutral delay differential equations. Adv Differ Equ. 2010,1–9 (2010) 14. Li, T, Thandapani, E: Oscillation of solutions to odd -order nonlinear neutral functional differential equations. ... 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...

Ngày tải lên: 20/06/2014, 22:20

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Ngày tải lên: 06/07/2014, 15:18

Ngày tải lên: 12/01/2014, 22:19

... Condition The left-hand sideofEq.2.27consistsofvaluesofy[k] at instants k + n, k + n − 1,k+ n − 2, andsoon. Ther ight-handsideofEq.2.27consistsoftheinputatinstantsk +m, k +m−1,k+m−2, and so on. For ... r ight-hand side of Eq. 2.24 represents the unit step function, which is unity for t ≥ 0 and is 0 for t<0. The right-hand side of Eq. 2.24 is a linear combination of the derivatives of y o (t)u(t). ... ˙y o (0) = 1 and y o (0) = 0. Settingt = 0 in the above equations and using the initial conditions, we obtain K 1 + K 2 = 0 and − K 1 − 2K 2 = 1 Solution of these equations yields K 1 = 1 and K 2 =−1....

Ngày tải lên: 27/01/2014, 03:20

Ngày tải lên: 14/03/2014, 13:20

... conditions of stable and asymptotic equivalence (see [1-5]) of linear delay differential equations under nonlinear perturbation in Banach space. The obtained results thank to use of the theories of general ... equivalence of systems of differential equations, Results of mathematic science 40 (1985) 245 (Russian). [4] M. Svec, Itegral and asymptotic equivelence of two systems of diffrential equations, ... behavior of linear differential equations under nonlinear perturbation. Let’s consider the delay differential equations: dx dt = Ax + f(t, x t ), where t ∈ R + , A ∈ L(E), f : R + ì E E and (T...

Ngày tải lên: 22/03/2014, 11:20

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