end of chapter iii exercises continued

... date: Teaching date: Period 26: END OF CHAPTER III EXERCISES I Objectives: By the end of the lesson, Students will be able to: - Consolidate the main point of the chapter - Practise the skill slove ... point of the lesson 5- Homework: - Memorize the lesson - Do the remaining exercise Preparation date: Teaching date: Period 27: END OF CHAPTER III EXERCISES( CONTINUED) I Objectives: By the end of ... set c) Note : ( text book) of roots of that equation y=− ≠ a c x+ b b When b 0, guiding student compute the value of y Determine the set of roots State the set of roots of liner equations with Read...

Ngày tải lên: 06/02/2017, 09:33

... If the ratios of eigenvalues of A0 are not real then Theorem 3.9, Lemma 4.2, and Proposition 4.4 provide a proof of Theorem 4.5 However, our goal is to provide an independent proof of this theorem, ... note, first of all, that it suffices to provide a proof if one of the κi ’s is equal to ±1 and one of the δj ’s is equal to ∓1 with all other κ’s and δ’s equal to zero The proof will consist of several ... ), Sp(T ) = Sp(X) The matrix elements of S and T are rational functions of the matrix elements of X and Y which not depend on the spectra of X and Y Proof Lemma 3.3 proves the uniqueness and...

Ngày tải lên: 14/02/2014, 17:20

... suggested to the study of stability and estimates of solutions of 1.1 Exponential Stability and Estimates of the Convergence of Solutions to Stable Systems First we give two definitions of stability to ... solution of 1.1 is exponentially stable in the metric C1 Estimates of Solutions in a General Case Now we will estimate the norms of solutions of 1.1 and the norms of their derivatives in the case of ... a positive scalar Delay independent criteria of stability for some classes of delay neutral systems are developed in 10 The stability of systems 1.1 with time dependent delays is investigated...

Ngày tải lên: 21/06/2014, 11:20

Ngày tải lên: 30/06/2013, 01:26

Ngày tải lên: 07/07/2013, 01:25

Ngày tải lên: 17/09/2013, 05:10

... Region of a System in Three Unknowns 44 Systems of Linear Inequalities in Any Number of Unknowns 52 The Solution of a System of Linear Inequalities 'by Successive Reduction of the Number of Unknowns ... respectively For example, the study of convex polyhedra, a part of geometry as old as the hills, turns thereby into one of the chapters of the theory of systems of linear inequalities, This theory ... some properties of systems of linear inequalities In this connection one can mention the names of such mathe- maticians as H Minkowski (one of the greatest geometers of the end of the last and...

Ngày tải lên: 08/04/2014, 10:42

... directed to the study of spatial behavior of solutions of partial differential equations and systems The history and development of this question is explained in the work of Horgan and Knowles ... lateral surface of the cylinder Payne and Schaefer [14] proved such results for some classes of heat conduction problems In [15], Quintanilla investigate the spatial behavior of several nonlinear ... nonlinear dissipative feedback terms on the boundary Our study is inspired by the results of [21] For the proof of our results, we will use the following Lemma Lemma [22]Let ψ be a monotone increasing...

Ngày tải lên: 21/06/2014, 00:20

... -Solutions of Degenerate Elliptic Equations We start with an abstract regularity result which is useful for the existence problem of W m,p Ω -solutions of degenerate quasilinear elliptic equations of ... 2δ/ δ The proof of Theorem 4.4 is parallel to that of Theorem 4.3; here we omit the detail Acknowledgment This project was supported by the National Natural Science Foundation of China no 10971148 ... Boundary Value Problems 23 References M V Keldys, “On certain cases of degeneration of equations of elliptic type on the boundry of a domain,” Doklady Akademii Nauk SSSR, vol 77, pp 181–183, 1951...

Ngày tải lên: 21/06/2014, 11:20

... space of all continuous functions from 0, → X endowed with a topology of uniform convergence with the norm denoted by · We remark that fractional boundary conditions result in the existence of ... densities, see 12 The concept of nonlocal multipoint boundary conditions is quite important in various physical problems of applied nature when the controllers at the end points of the interval under ... is independent of x So, Θ1 is relatively compact on Br Hence, By Arzela-Ascoli’s Theorem, Θ1 is compact on Br Thus all the assumptions of Theorem 3.2 are satisfied and the conclusion of Theorem...

Ngày tải lên: 21/06/2014, 16:20

... Then 1.1 has a unique T -periodic solution Proof Existence For the proof of existence, we use Lemma 1.1 First, let us consider the homotopic equation of 1.1 : ϕ x t λf x t x t λg x t λe t , λ ∈ ... the NSF of China, the NSF of Jiangxi Province of China 2008GQS0057 , the Youth Foundation of Jiangxi Provincial Education Department GJJ09456 , and the Youth Foundation of Jiangxi Normal University ... variants, where ϕp s of 1.1 However, there are seldom results about the existence of periodic solutions to 1.1 The main difficulty lies in the p-Laplacian-like operator ϕ of 1.1 , which is more...

Ngày tải lên: 21/06/2014, 18:20

... } be solutions of 1.9 with the initial values x0 , x0 , , x0 Assume that k x0 , x0 , , x0 > 1, 2.15 then all solutions of 1.9 are positive k Proof We consider solutions of 1.9 with the ... −∞ and {x2n } → 1− Proof From 2.21 , 2.22 , and 2.24 , the proof is clear Example 2.13 Let k Then the solutions of 1.9 , with the initial values x0 x0 r, in its invertal of periodicity can be ... well-defined solutions of the difference equation xn xn 1.8 xn − are periodic with period two Motivated by 1.8 , we investigate the periodic character of the following two systems of difference equations:...

Ngày tải lên: 22/06/2014, 11:20

... Ministry of Absorption and by the NSERC Research Grant References V L Koci´ and G Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with c Applications, vol 256 of Mathematics ... easily deduced from the recursive representation of solutions To this end we consider the equation m x n al n x hl n , 2.16 l which is a different form of 1.1 We recall that we assume n − hl n ≤ T ... Theorems 2.1, 2.2, 2.17, and 2.18 but the boundedness of the delay Since the solution x n with x tends to as n → ∞, then the zero solution of 3.3 is neither asymptotically nor exponentially stable...

Ngày tải lên: 22/06/2014, 11:20

... which the constants depend are given in the statements of the theorems and lemmas A dependence on p Boundary Value Problems includes dependence on the log-H¨ lder-constant of p Note also that due ... Finally we observe that This completes the proof Lemma 3.4 can be used in the proof of the supremum estimate in [7] in the same way as in the proof of Lemma 3.5 Combining this with the weak Harnack ... depends on n, p, q, and Lq s (B4R )-norm of u Remark 3.8 (1) The main difference compared to Alkhutov’s result in [7, 9] is that the constant and the exponent depend on the Lq s (B4R )-norm of...

Ngày tải lên: 22/06/2014, 22:20

... number of extremal sets, all of whose symmetric differences with An,3 consist of a bounded number of elements (both bounds are independent of both n and c) These results were partly extended in ... proof of Lemma 2.1 Lemma 2.2 Let A be an L-avoiding subset of [1, n] of maximum size Let s = sA and t := max{i ∈ N : ri ≥ s} If n b,c then t = Proof : Just follow the reasoning in the proof of ... either multiples of b in [1, z0 ] or not divisible by b This implies that |B| ≤ |An | and completes the proof of part (i) of Theorem 3.1 Proof of Part (ii) : We divide the proof into two cases...

Ngày tải lên: 07/08/2014, 15:23

...        bM       x M  If the number of unknowns is equal to the number of equations, N=M, we may be able to solve the set of equations, provided that the equations are unique ... procedure Programming exercise Make a FORTRAN program consisting of a main program, that reads the coefficients of the system of equations (n, a1,1…an,n , d1…dn) from an input file (IN.DAT) and ... elimination method in order to solve the set of equations and returns n values of x to the main program Resources Test the program on the following set of equations: Push 2x +3y +4z -5s +7t = -35...

Ngày tải lên: 24/10/2014, 21:28

Ngày tải lên: 11/03/2015, 07:57

... xanh dương màu đỏ - Trên bảng có thẻ từ ghi tên loại mạch máu tim - Phiếu thảo luận nhóm cho nhóm III Mục đích sử dụng: Thông qua mô hình HS có thể: - Chỉ đường máu sơ đồ vòng tuần hoàn tuần hoàn ... Khung làm gỗ - Vẽ tranh - Cước đính vật để kéo - Kẽm cột sợi sợi lại Giá trị kinh tế : 100.000 đồng III. Mục đích sử dụng Thông qua tranh động, giúp HS có hứng thú học tập tiếp thu nhanh , nhớ lâu,...

Ngày tải lên: 06/07/2015, 22:13

... express my deepest thanks to my supervisor Prof Xiao Chi, who has helped me so much at every stage of my working on this thesis More than that, Prof Xiao Chi has shown me all the diligence, ambition, ... self The world in Zhang’s Tao’an mengyi and Dong’s “county of dreams” are both such imaginary worlds The main body of this thesis (chapter 2-4) explores respectively the self-expression in Zhang’s ... China）中专门讨论《西游补》的章节、 李前程（Li Qiancheng）《启悟小说：〈西游记〉、〈西游补〉、〈红楼梦〉》 （ Fictions of Enlightenment: Journey to the west, Towers of Myriad Mirrors, and Dream of the Red Chamber）中专门讨论《西游补》的一章。这三位学 者在分析中都谈到了“梦”在这部小说中的重要作用，并点明了小说对“梦...

Ngày tải lên: 16/10/2015, 15:35

Ngày tải lên: 24/06/2016, 22:08