nonlinear equations and extremum problems

... others:differential and integrodifferential equations in Banach spaces, linear and non-linear theory of semigroups, direct and inverse problems for regular and singu-lar elliptic and parabolic differential and/or ... Rings and Group Rings P Goeters and O Jenda, Abelian Groups, Rings, Modules, and Homological Algebra J Cannon and B Shivamoggi, Mathematical and Physical Theory of Turbulence A Favini and A Lorenzi, ... H Pavel, Differential Equations and Control Theory G Lyubeznik, Local Cohomology and Its Applications G Da Prato and L Tubaro, Stochastic Partial Differential Equations and Applications W A Carnielli

Ngày tải lên: 04/03/2019, 11:08

... Equations and Problems 20 Let p = the price of one shirt Then 2p = the price of another shirt p + 2p + 27 = 34 Solve: p = $25, so 2p = · $25 = $50 The prices of the other two shirts are $25 and ... Addison-Wesley 222 Chapter 11: Algebra: Solving Equations and Problems Check The second angle, 85◦ , is 50◦ more than the first angle, 35◦ , and the third angle, 60◦ , is 10◦ less than twice ... 2015 Pearson Education, Inc Publishing as Addison-Wesley 214 Chapter 11: Algebra: Solving Equations and Problems 18 24a − = · 3a − · = 8(3a − 1) 19 4x + 6y − = · 2x + · 3y − · = 2(2x + 3y − 1)

Ngày tải lên: 08/11/2019, 14:41

... point for ˙x = f (x) and Es and Eu are the stable and unstable manifolds of the linear system ˙x = Df (0)x Then there exists local stable and unstable manifolds Wlocs (0)and Wlocu (0) of the ... semi-trajectory, γ+(x), and the negative semi-trajectory,γ−(x) x, A(x), are the sets Λ(x) = {y ∈ Rn|∃tn with tn → ∞ and ϕ(x, tn) → y as n → ∞} and A(x) = {y ∈ Rn|∃sn with sn → −∞ and ϕ(x, sn) → y as ... argument with the terms of order r + 1 and so on.Exercise: Consider the case of systems in R2 and suppose thatDf (0)has eigenvalues λ1 and λ2 Then if λ1= 8 and λ2=-2 the system isresonant of order

Ngày tải lên: 23/12/2019, 16:17

... Solving Equations and Problems31 6 8, 4 8 9 ↑ The digit 8 is in the thousands place Considerthe next digit to the right Since the digit, 4, is 4 or lower round down, meaning that 8 thousands stay ... Solving Equations and Problems 20 Let p = the price of one shirt Then 2p = the price of anothershirt Solve: p + 2p + 27 p = $25, so 2p = 2 · $25 = $50 The prices of the other two shirts are $25 and ... thousands Then change all digits to the right of the thousands digit 2 1 8 3 8 3 to the nearest hundredth ↑ Thousandths digit is 5 orhigher ↓ 34 A numberis divisible by 6 if it is even and

Ngày tải lên: 31/01/2020, 15:26

... DIFFERENTIAL EQUATIONS SECTION 1.1 DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELS The main purpose of Section 1.1 is simply to introduce the basic notation and terminology of ferential equations, and ... differential equations We include here just some typical examples of such verifications 3 If y1cos 2x and y2 sin 2x, then y1  2sin 2x y2 2 cos 2x, so Trang 22 DIFFERENTIAL EQUATIONS AND MATHEMATICAL ... curves for each of these problems Trang 3y (0, 10) Problem 20 Trang 44 DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELS x y (1, 17) Problem 24 Trang 526 Substitution of x and  y0 into y x Ccosx

Ngày tải lên: 20/08/2020, 13:33

... Iterative method for solving boundary value problems for the nonlinear fourth-order differential equations Boundary value problems for the nonlinear fourth order equations with dif-ferent boundary conditions ... we study the existence, uniqueness and some properties for the solutions of some problems for fully or non-fully nonlinear fourth-order differential equations and systems Also on the basis of ... boundary value problems for fully or non-fully nonlinear fourth-order differential equations and systems by using the reduc-tion of them to the operator equareduc-tions for the right-hand side funcreduc-tions

Ngày tải lên: 01/04/2021, 19:17

... local stable and unstable manifolds Wloc (0) u and Wloc (0) of the same dimension as E s and E u respectively These manifolds are (respectively) tangential to E s and E u at the origin and as smooth ... Differential equations are an important discipline of mathematics and have many applications in the fields of science and technology, which are considered as the bridge between theory and application ... studying the stability of nonlinear systems is the linearization method, we perform a transformation convert nonlinear defferential equations to linear form Then, stability of nonlinear systems solutions

Ngày tải lên: 07/04/2021, 08:04

... Stopping, Scaling, and Testing In this chapter we discuss three issues that are peripheral to the basic mathematical considerations in the solution of nonlinear equations and minimization problems, but ... finite-precision arithmetic The third is how to debug, test, and compare nonlinear algorithms 7.1 SCALING An important consideration in solving many "real-world" problems is that some dependent or independent ... and minimization problems, but essential to the computer solution of actual problems The first is how to adjust for problems that are badly scaled in the sense that the dependent or independent

Ngày tải lên: 22/10/2022, 08:00

... Perturbations: Theory and Methods Ivar Ekeland and Roger Temam, Convex Analysis and Variational Problems Ivar Stakgold, Boundary Value Problems of Mathematical Physics, Volumes I and II J M Ortega and W C ... Differential-Algebraic Equations Charles L Lawson and Richard J Hanson, Solving Least Squares Problems J E Dennis, Jr and Robert B Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations ... NEWTON'S METHOD FOR NONLINEAR EQUATIONS AND UNCONSTRAINED MINIMIZATION 86 Newton's method for systems of nonlinear equations 86 Local convergence of Newton's method 89 The Kantorovich and contractive

Ngày tải lên: 22/10/2022, 08:06

... Furthermore, many other nonlinear evo-38 lution equations arising in mathematical physics and engineering can also be solved by this powerful, 39 reliable and capable method The nonlinear three dimensional ... earths 57 magnetotail and polar magnetosphere [2] etc The KdV equations 58 have several two dimensional weak variations Solitons and solitary 59 waves represent one of the famous and motivating features ... construct soliton 101 and solitary wave solutions of three-dimensional EZK equation 102 and modified KdV-ZK equation Consequently, more general and 103 new exact solutions in soliton and solitary wave

Ngày tải lên: 04/12/2022, 15:46

... research by Escobedo and Herrero, as well as Andreucci, Herrero, and Velázquez.[2], Merle and Zaag[43], Quittner [54], Phan and Souplet[49].Since the foundational research by Gidas and Sprick on the ... Autuori, G., and Pucci, P and Salvatori, M C (2009), “Asymptotic stabil- ity for nonlinear Kirchhoff systems”,Nonlinear Anal Real World Appl., 2,[5] Bartsch, T., and Polácik, P., and Quittner, ... vector-valued nonlinear heat equations and applications”,Math Ann., 1, 103–137.[44] Mitidieri, E., and Pohozaev, S I (2001), “A priori estimates and the ab- sence of solutions of nonlinear partial

Ngày tải lên: 24/11/2023, 14:37

... Trang 1LINEAR EQUATIONS AND LEAST-SQUARES PROBLEMSA DISSERTATIONSUBMITTED TO THE PROGRAM IN COMPUTATIONAL AND MATHEMATICAL ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES ... Emily;David, Ha, and baby Mike Saunders; Holly Jin, Neil, Danlin, and Hansen Lillemark; Lilian Lao,Michael and Victor Dang; Justin Wing Lok Wan and Winnie Wan Chu; Dulce Ponceleón, Walter,Emma and Sofia ... b|| (1.5) with symmetric A as in Figure 1.2 and Figure 1.3 We defineb = Az +22, where z\¡ and z2 are randomly generated with ||z\|1 13 and ||z|l2 10~12, and then we normalize b by its 2-norm Thus

Ngày tải lên: 02/10/2024, 01:47

... six-teen for many years and sixsix-teen-year-olds today are no less responsible than their parents and grandparents were at sixteen Many young people today who are fourteen and fifteen years old ... serving items such as burgers and fries, pizza, hot dogs, and fried chicken School districts nationwide are now address-ing this trend by incorporataddress-ing some simple and inexpensive options that ... series First, 2 is subtracted, then 4, then 2,and so on 9 c. In this simple alternating subtraction andaddition series; 1 is subtracted, then 2 isadded, and so on 10 d This alternating addition series

Ngày tải lên: 02/11/2013, 16:20

... (Electronic) 240 ICA BY NONLINEAR DECORRELATION AND NONLINEAR PCA is a stochastic gradient algorithm and the other one a recursive least mean-square algorithm. 12.1 NONLINEAR CORRELATIONS AND INDEPENDENCE ... other contrast func- 252 ICA BY NONLINEAR DECORRELATION AND NONLINEAR PCA tions... input 260 ICA BY NONLINEAR DECORRELATION AND NONLINEAR PCA W1 W2 −W3 −W4 W5 W6 −W7 ... 12.1, Cichocki 244 ICA BY NONLINEAR DECORRELATION AND NONLINEAR PCA and Unbehauen proposed a feedforward network with weight matrix B , with the mixture vector x for input and with output y = Bx

Ngày tải lên: 23/12/2013, 07:19

... 2004, and in SISSA (Trieste) in June 2006 Their scope was to present problems and techniques of some of the most promising and fascinating areas of research related to nonlinear hyperbolic problems ... dimensional problems and control problems for hyperbolic systems”; from CIRAM (Research Center of Applied Mathematics) and the Fund for International Programs of University of Bologna; and from ... Bologna and the Department of Mathematics of Bologna for their kind hospitality and for all the help and support they have provided throughout the school Bologna, Trieste, Brescia, Ză rich, u and

Ngày tải lên: 17/02/2014, 17:20

... equation and some other elliptic partial differential equations, it is useful to write A = D + L + U, 210 Nonlinear Equations and Their Solution by Iteration where D is the diagonal part of A, L and ... of the solution with respect to the right hand side From T (u1 ) = b1 and T (u2 ) = b2 , we obtain T (u1 ) − T (u2 ) = b1 − b2 206 Nonlinear Equations and Their Solution by Iteration Then (T (u1 ... boundary value problems for nonlinear ordinary differential equations Multi-variate generalizations of this equation are obtained as reformulations of boundary value problems for nonlinear elliptic...

Ngày tải lên: 16/02/2015, 19:32

... smallest and greatest solutions of the second order initial and boundary value problems, and dependence of these solutions on the data are studied in Sections and Applications to impulsive problems ... differential equations may be singular, distributional and impulsive Differential equations, initial and boundary conditions and impulses may depend functionally on the unknown function and/ or on ... (c1), and (d1) hold Then, the BVP (6.1) has the smallest and greatest solutions in Z, and they are increasing with respect to f and d and decreasing with respect to c Proof: Because f, c and d...

Ngày tải lên: 20/06/2014, 22:20

... “Fixed points and stability in differential equations with variable delays,” Nonlinear Analysis: Theory, Methods and Applications, vol 63, no 5–7, pp e233–e242, 2005 L C Becker and T A Burton, ... Becker and Burton have studied the equation −a t f x t − r t x t , 1.4 b t x1/3 t − r2 t 1.5 Jin and Luo have studied the equation x t −a t x t − r1 t Burton and Zhang have also studied similar problems ... point methods for highly nonlinear delay equations, ” Fixed Point Theory, vol 5, no 1, pp 3–20, 2004 J K Hale and S M Verduyn Lunel, Introduction to Functional Differential Equations, Springer, New...

Ngày tải lên: 21/06/2014, 11:20

... W.-S Cheung and J Ren, “Periodic solutions for p-Laplacian Rayleigh equations, ” Nonlinear Analysis: Theory, Methods & Applications, vol 65, no 10, pp 2003–2012, 2006 B Liu, “Existence and uniqueness ... following assumptions hold: A1 g ∈ C1 R, R and g x < for all x ∈ R; A2 there exist a constant r ≥ and a function ε t ∈ C R, R such that for all t ∈ R and |x| > r, x g x −ε t T < 0, T ε t − e t ... Consider the following nonlinear equation: f x t x t ϕ x t g x t 2.49 e t, e−x , g x − x3 x , and e t sin t One can easily check where ϕ x 2xex − 2x, f x that ϕ satisfy H1 and H2 Obviously, A1...

Ngày tải lên: 21/06/2014, 18:20

... are valid for functional differential equations in general form and for some cases of unbounded right-hand side of the equation see 1, Remark and , 2, Remark and In 1998, Stanˇ k worked on the ... 2 Advances in Difference Equations In this paper, we discuss the nonlinear second-order discrete problems with minimum and maximum: Δ2 u k − f k, u k , Δu k , u k : k ∈ ... −Δu } 3.4 Now, if 1.5 and 3.2 have a solution u1 k , then Lemma 2.6 and 3.2 show that φ −Δu1 < C and max u1 k : k ∈ T − u1 k : k ∈ T C 3.5 So, u1 k is a solution of 1.5 and 2.4 , that is, u1...

Ngày tải lên: 22/06/2014, 11:20