solutions of differential equations pdf

... 2Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow, Russia Page 10 of 10 18 I Ideses, L Yaroslavsky, Three methods that improve the visual quality of colour anaglyphs ... disparity map for each level of decomposition is computed by applying the NNI technique In this work, we propose using four levels of decomposition in DWT A block diagram of the proposed M-WAF framework ... algorithms in real-time modes using a DSP The core of the EVM DM642™ is a digital media processor that is characterized by a large set of integrated features of the card, such as: a TMS320DM642™ DSP at...

Ngày tải lên: 20/06/2014, 22:20

... follows Local solutions of anisotropic equations In this section, we prove a local regularity result for weak solutions of anisotropic equations 1,q Let u ∈ Wloc i Ω be a local solution of the anisotropic ... conditions depending on u, in the proof of the local regularity results, we have to estimate the integral of some power of |u| by means of |Du| To this, we will make use of the Sobolev inequality that ... is supported by Special Fund of Mathematics Research of Natural Science Foundation of Hebei Province no 07M003 and Doctoral Foundation of the Department of Education of Hebei Province B2004103...

Ngày tải lên: 22/06/2014, 18:20

Ngày tải lên: 11/03/2015, 07:57

... periodic solutions of differential equations have been studied since the very beginning of this century The theory of almost periodic solutions has been developed in connection with problems of differential ... fully nonlinear equations The conditions are given in terms of the dissipativeness of the equations under consideration In Chapter we present the existence of almost periodic solutions of almost periodic ... Periodic Solutions 2.3.3 When Does Boundedness Yield Uniform Continuity ? 2.3.4 Periodic Solutions of Partial Functional Differential Equations 2.3.5 Almost Periodic Solutions of Partial...

Ngày tải lên: 29/10/2015, 12:32

... differential equations The objective of this paper is to study the oscillatory and nonoscillatory behavior of solutions of (A) In Section we begin with the classification of nonoscillatory solutions of ... analysis of the structure of the set P of all possible positive solutions of (A) J Manojlovi´ and T Tanigawa c Classification of positive solutions Let y(t) be an eventually positive solution of (A) ... solution of (A) belonging to P(I j ) This completes the proof Unlike the solutions of class P(I) it seems to be very difficult (or impossible) to characterize the existence of solutions of class...

Ngày tải lên: 22/06/2014, 21:20

... stability properties equations (see [24] for a discussion of some of these methods for ODEs) A natural question to ask is “do the numerical solutions preserve the stability properties of the exact solution?” ... illustrate some of our results with trajectories of (3.1) Note that in [30] an absolute correspondence of asymptotic mean square stability of the trivial solution and convergence of trajectories ... integro-differential equations stability and numerical stability of θ-methods, Journal of Integral Equations and Applications 10 (1998), no 4, 397–416 [10] I I Gihman and A V Skorokhod, Stochastic Differential Equations, ...

Ngày tải lên: 22/06/2014, 22:20

... measurement of the amount of oedema as well as the area and volume of the ulcer wounds This is because without an accurate and objective means of measuring changes in the size or shape of ulcers, ... exponential functions The specific forms of A0 (u), An (u), Bn (u) and R(u, v) for the case of Equations (1) can be found in [17] and for the case of Equations (2) can be found in [21] The main ... modelling of human limbs affected by oedema and venous ulcers In what follows, we discuss two examples of shape modelling of human limbs namely modelling of an arm shape and modelling of a leg...

Ngày tải lên: 13/08/2014, 23:20

... example, we will obtain the bound of the solutions of an integral equation For the sake of proving the global existence of solutions of differential equations, we first recall some basic facts ... of the above results In the first example, we will try to prove the global existence of the solutions of a delay differential equation, while in the second example, we will obtain the bound of ... Zheng and Feng Journal of Inequalities and Applications 2011, 2011:20 http://www.journalofinequalitiesandapplications.com/content/2011/1/20 Page 13 of 15 uniqueness of solutions cannot be guaranteed...

Ngày tải lên: 21/06/2014, 01:20

... existence of almost automorphic solutions of first-order linear difference equations In Section 4, we discuss the existence of almost automorphic solutions of nonlinear difference equations of the ... automorphic solutions of difference equations, it remains to study discrete almost automorphic solutions of Volterra difference equations as well as discrete almost automorphic solutions of functional ... periodicity of difference equations of a general type,” Journal of Difference Equations and Applications, vol 2, no 3, pp 271–287, 1996 S Sugiyama, “On periodic solutions of difference equations, ”...

Ngày tải lên: 21/06/2014, 20:20

... follows Local solutions of anisotropic equations In this section, we prove a local regularity result for weak solutions of anisotropic equations 1,q Let u ∈ Wloc i Ω be a local solution of the anisotropic ... conditions depending on u, in the proof of the local regularity results, we have to estimate the integral of some power of |u| by means of |Du| To this, we will make use of the Sobolev inequality that ... is supported by Special Fund of Mathematics Research of Natural Science Foundation of Hebei Province no 07M003 and Doctoral Foundation of the Department of Education of Hebei Province B2004103...

Ngày tải lên: 22/06/2014, 06:20

... assumptions of Corollary 3.4, one of the following two conditions is true: (a) A preserves the K-negligibility of elements of the set Π; (b) A is continuous in the topology of X Then all the solutions of ... obvious that the set of solutions of problem (4.27), (4.28) coincides with that of the continuous solutions of (1.1), where λ = and b(t) := c + t a q(s)ds, t ∈ [a,b] (4.31) 24 Journal of Inequalities ... guarantee the solvability of (1.1) Proof of Theorem 4.1 Without loss of generality, we may suppose that relation (4.18) is true, for otherwise, in view of Theorem 3.1, the assertion of the theorem becomes...

Ngày tải lên: 22/06/2014, 18:20

... Evolution Equations Global Behavior of Solutions, vol 841 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1981 C Zhang and Y Guo [4] F L Huang, “Existence of almost periodic solutions ... uniqueness of slowly oscillating solutions for the differential equation (1.1) So in this paper, we give a sufficient, then a necessary condition for the existence and uniqueness of slowly oscillating solutions ... periodic solutions for dissipative differential equations, ” Annals of Differential Equations, vol 6, no 3, pp 271–279, 1990 [5] H Ishii, “On the existence of almost periodic complete trajectories for...

Ngày tải lên: 22/06/2014, 18:20

... zero of a degree of a map implies the existence of solutions of the operator equation (6.1) and consequently the existence of a solution of (4.10) ((6.1) at λ = 1) Theorem 4.3 is proved Proof of ... and γn is the operator of taking of the normal component of a trace on the boundary of a function defined on Ω0 The operator γn 236 On weak solutions of the equations of motion 1/2 is bounded ... R(L) of the operator L is dense in E∗ We give the proof of this theorem in Section From Theorems 3.6 and 3.8 the next result follows 0,t (3.11) 222 On weak solutions of the equations of motion...

Ngày tải lên: 23/06/2014, 00:20

... −8 −6 −4 −2 10 10 t (s) t (s) Figure 6: Time-frequency distribution of x(t) of Figure Figure 4: Solution of (6), real part of x(t), when the forcing term is f (t) = A exp(iβt /2) + B exp(iγ4 ... obtain the compact form of (18) and (19) The combined use of (24)–(27) allows one to obtain (17) Now, we take the bilinear distribution of the left- and right-hand sides of (15) to obtain CP(D)x,P(D)x ... recognition of speech,” Proceedings of the IEEE, vol 84, no 9, pp 1199–1215, 1996 [30] W Au, A Popper, and R Fay, Eds., Hearing by Whales and Dolphins, vol 12 of Springer Handbook of Auditory...

Ngày tải lên: 23/06/2014, 01:20

... approximating solutions to differential equations Linear Differential Equations The first special case of first order differential equations that we will look is the linear first order differential ... http://tutorial.math.lamar.edu/terms.asp Differential Equations To get a better idea of how all the solutions are behaving, let's put a few more solutions in Adding some more solutions gives the figure below The set of solutions ... http://tutorial.math.lamar.edu/terms.asp Differential Equations Linear Equations – Identifying and solving linear first order differential equations Separable Equations – Identifying and solving separable first order differential equations...

Ngày tải lên: 05/07/2014, 04:20

Ngày tải lên: 06/07/2014, 15:18

... Functional Equations with Iteration 6.1 6.2 Equations without Derivatives 6.1.1 Babbage Type Equations 6.1.2 Equations Involving Several Iterates 6.1.3 Equations of Invariant Curves Equations ... Analytic Solutions of Functional Equations 6755 tp.indd 1/30/08 3:15:20 PM This page intentionally left blank Analytic Solutions of Functional Equations Sui Sun Cheng National ... discussed Application of the implicit theorems for finding power series solutions of polynomial or rational type functional equations are illustrated • In Chapter analytic solutions for several...

Ngày tải lên: 04/08/2014, 22:25

... on the asymptotic behavior of solutions of ill-posed equations associated with C-semigroups The existence of almost periodic solutions to ill-posed evolution equations of the form (1) has not been ... The existence of periodic solutions of systems of differential equations, Duke Math J 17 (1950) 457–475 16 Nguyen Van Minh and Nguyen Minh Man, On the asymptotic behavior of solutions of neutral ... Minh, and J S Shin, Almost Periodic Solutions of Differential Equations in Banach Spaces, Taylor & Francis, London, New York, 2002 Almost Periodic Solutions Equations Associated with C-Semigroups...

Ngày tải lên: 06/08/2014, 05:20

... solution of equations (1.2) if and only if the matrix X = Q∗XV is a simultaneous solution of equations AiX − X Bi = Ci , with Ci = Q∗Ci V Thus, in finding simultaneous solutions of Sylvester equations ... method to the case of functions of several commuting matrices and apply it to the problems of finding simultaneous solutions of Sylvester equations In the sequel, we denote elements of F and T by ... is a k-tuple of m×m matrices, (B1 , , Bk ) is a k-tuple of n × n matrices and (C1, , Ck ) is a k-tuple of m × n matrices Then a matrix X is a simultaneous solution of the system of equations (1.2)...

Ngày tải lên: 16/10/2015, 09:33

... that the above proof remains valid if we interchange the roles of G j and g j as at the end of the proof of Lemma 2.6 The proof of Theorem 1.3 is completed Lemma for the proof of Theorem 1.6 Lemma ... every solution f ≡ of (1.2) satisfies (1.14) This completes the proof of Theorem 1.6 Proofs of corollaries Proof of Corollary 1.4 By Remark 2.7, we see that the hypotheses of Theorem 1.3 are satisfied ... differential equation of the form (4.2) whose coefficients are analytic in a neighborhood of z = ∞ and have at most a pole at z = ∞ Proof of Lemma 4.1 Using a method similar to the proof of Lemma 2.6,...

Ngày tải lên: 22/06/2014, 18:20