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nhóm 2 khi đi trên xe đò có một cụ già phải đứng vì hết ghế ngồi em sẽ ứng xử như thế nào khi gặp tình huống trên vì sao em ứng xử như vậy em có ý kiến gì khi có người không nhường ghế

ONE PARAMETER FAMILY OF LINEAR DIFFERENCE EQUATIONS AND THE STABILITY PROBLEM FOR THE NUMERICAL pdf

ONE PARAMETER FAMILY OF LINEAR DIFFERENCE EQUATIONS AND THE STABILITY PROBLEM FOR THE NUMERICAL pdf

Báo cáo khoa học

... (k + 1)! 2k + (k! )2 = , (2k + 2) ! k + 2( 2k)! 2 (k + 1)! (k − 1)! k = (2k + 2) ! k + 4 − k 2 (2k − 2) ! (3.8) Thus, relation (3.7) becomes σk+1 (z) = z + (k! )2 z+1 (z − 1 )2 (z − 1)k Lk − (2k)! z−1 ... obtain σ2m +2 eiθ = eiθ − eiθ + σ2m eiθ σ2m+1 eiθ − 4 − (2m + 1) 2 2 = eiθ + imθ eiθ − eimθ fm (θ) e gm (θ) − 4 − (2m + 1) 2 = ei(θ /2) ei(θ /2) + e−i(θ /2) = ei(m+1)θ cos θ 2 eimθ gm (θ) − ei(θ /2) ei(θ /2) ... m For m = 1, from Theorem 3 .2 it follows that eiθ − eiθ + σ1 eiθ − σ0 eiθ 12 eiθ − eiθ + − = 12 2 eiθ = =e iθ ei(θ /2) + e−i(θ /2) − ei(θ /2) − e−i(θ /2) (3 .21 ) 12 2 cos(θ /2) + + cosθ = eiθ = eiθ...
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báo cáo hóa học:

báo cáo hóa học:" Research Article Existence of Positive Solutions of Nonlinear Second-Order Periodic Boundary Value Problems" ppt

Hóa học - Dầu khí

... T, ≤ t ≤ s ≤ T 2. 4 Remark 2. 4 Notice that it is not necessary to assume that v / 2. 5 In fact, if a ∈ Λ , then from 13, Remark in Page 3 328 , we have π T λ1 a ≥ 1− a p K 2p∗ > 0, 2. 6 where λ1 a ... theorem, see 15, Theorem 19.3 , we may get the desired results Remark 3.4 Theorem 3 .2 is a partial generalization of Lemma 3.1 It is enough to prove that the condition i on f in Theorem 3 .2 holds ... 122 9– 123 6, 20 08 D Jiang, J Chu, and M Zhang, “Multiplicity of positive periodic solutions to superlinear repulsive singular equations,” Journal of Differential Equations, vol 21 1, no 2, pp 28 2–3 02, ...
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báo cáo hóa học:

báo cáo hóa học:" Nodal solutions of second-order two-point boundary value problems" potx

Hóa học - Dầu khí

... contradicts to Lemma 2. 3 Proof of main results Proof of Theorems 1.1 and 1 .2 We only prove Theorem 1.1 since the proof of Theorem 1 .2 is similar ν It is clear that any solution of (2. 4) of the form ... Lemma 2. 2 Spr(λk L) < 1, which is impossible since Spr(L) = λk f0 ν Lemma 2. 5 If (µ, u) ∈ E is a non-trivial solution of (2. 4), then u ∈ Sk for ν and some k ∈ N ν Proof Taking into account Lemma ... form u = λAu (2. 1) Equations of the form (2. 1) are usually called nonlinear eigenvalue problems L´pez-G´mez [7] studied a o o nonlinear eigenvalue problem of the form u = G(r, u), (2. 2) where r...
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Báo cáo hóa học:

Báo cáo hóa học: " Research Article Multiplicity of Positive Periodic Solutions of Singular Semipositone Third-Order Boundary Value Problems" doc

Hóa học - Dầu khí

... problem 2. 4 - 2. 5 Lemma 2. 1 see 12 The boundary value problem 2. 4 - 2. 5 is equivalent to integral equation 2 ut G t, s F s, J u s − ω ds, 2. 6 where G t, s ⎧ ⎪ 2e ρ /2 ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ 2e ρ /2 ⎪ ⎪ ... t0 2 dt n 3.9 for some t0 ∈ 0, 2 Then t un max un t 0≤t 2 max 0≤t 2 t0 t max 0≤t 2 ≤ Fn s, J un s Fn s, J un s 2 un s ds −ω t0 2 2 2 un s ds −ω 2 n 2 ds n ρ un t − un t0 ρun s − 2 un ... ⎪ ⎩ t−s sin 2 t−s √ e−ρπ sin 3 /2 ρ t − s , ≤ s ≤ t ≤ 2 , √ √ 3ρ eρπ e−ρπ − cos 3ρπ √ √ sin 3 /2 ρ s − t e−ρπ sin 3 /2 ρ 2 − s t , ≤ t ≤ s ≤ 2 √ √ 3ρ eρπ e−ρπ − cos 3ρπ 2. 7 √ 3 /2 ρ 2 − t s Moreover,...
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CONSTRUCTION OF UPPER AND LOWER SOLUTIONS FOR SINGULAR DISCRETE INITIAL AND BOUNDARY VALUE PROBLEMS potx

CONSTRUCTION OF UPPER AND LOWER SOLUTIONS FOR SINGULAR DISCRETE INITIAL AND BOUNDARY VALUE PROBLEMS potx

Báo cáo khoa học

... (2. 3) Thus ≤ u(k) ≤ M n0 for k ∈ N + (2. 20) Let β(k) ≡ u(k) for k ∈ N + Now (2. 7) and (2. 20) guarantee α(k) ≤ β(k) for k ∈ N + (2. 21) Now (2. 2) and (2. 20) imply f (k,β(k)) ≤ h(β(k)) ≤ h(M) ... k + 1) (2. 27) j =k Thus (2. 3) holds Theorem 2. 1 guarantees that (2. 23) has a solution u ∈ C(N + , R) with u(k) > for k ∈ N Next we present a result for initial value problems Theorem 2. 3 Let ... ϕ p β(k − 1) (2. 22) Now Theorem 1 .2 guarantees that (1.1) has a solution u ∈ C(N + , R) with u(k) ≥ α(k) > for k ∈ N 21 0 Discrete initial and boundary value problems Example 2. 2 Consider the...
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báo cáo hóa học:

báo cáo hóa học:" Research Article Exponential Stability and Estimation of Solutions of Linear Differential Systems of Neutral Type with Constant Coefficients" pot

Hóa học - Dầu khí

... −0 .2 2 − 3. 121 9, −0.01α4 − 1.3105 2 −0.0998α4 0.5717 2 − 0.4943, p2 α −0.0366α4 − 0.096 828 2 p1 α p0 α 2. 0830, −0.00 420 43 82 4 0.053858, 0.0073 2 − 0.0 028 , −0.000153 92 4 − 0.00 020 116 2 0.000059 723 ... e−0. 028 9t /2 e−0. 028 9t /2 , 4.6 e−0. 028 9t /2 e−0. 028 9t /2 hold on 0, ∞ Example 4 .2 We will investigate system 1.1 where n D 0.1 0 0.1 , A −3 2 , 2, τ B 1, 0. 621 3 0. 621 3 , 4.7 Boundary Value Problems ... G1 , H τ 2 G2 , H x ˙ x τ τ e−γt /2 τ 2 G2 , H x ˙ τ D i eγiτ /2 e−γt /2 i 2. 38 Since m−1 i D i eγiτ /2 < ∞ i D i eγiτ /2 D eγτ /2 , − D eγτ /2 2.39 Boundary Value Problems 11 inequality 2. 38 yields...
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Báo cáo hóa học:

Báo cáo hóa học: "Research Article Existence and Uniqueness of Solutions for Higher-Order Three-Point Boundary Value Problems" ppt

Hóa học - Dầu khí

... in Theorem 3 .2 are satisfied Therefore by Theorem 3 .2 BVP 3.70 , 3.71 has a unique solution x x t satisfying 2 ≤ x t ≤ 2, 2t ≤ x t ≤ −2t, t ∈ −1, , −t2 ≤ x t ≤ t2 , t ∈ −1, , −2t ≤ x t ≤ 2t, t ... no 2, pp 22 7 23 2, 20 02 22 W L Zhao, “Existence and uniqueness of solutions for third order nonlinear boundary value problems,” The Tohoku Mathematical Journal, vol 44, no 4, pp 545–555, 19 92 ... λf t, w0 t, x0 , , wn 2 t, xn 2 , xn−1 xn 2 − λwn 2 t, xn 2 φ |xn−1 | ≤ 3 .25 2Mn 2 φ |xn−1 | : φE |xn−1 | Furthermore, we obtain ∞ s φE s ∞ ds s ds 2Mn 2 φ s ∞ 3 .26 Thus, Fλ satisfies the...
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Báo cáo hóa học:

Báo cáo hóa học: "Research Article Asymptotic Representation of the Solutions of Linear Volterra Difference Equations" pdf

Báo cáo khoa học

... sequence K i 1/2iα , i ≥ 1, if and only if either ∞ A> i 1 2iα ςα 4 .29 or A < 2 − ∞ i −1 i 2iα 22 −1 −1 ∞ i 1 2iα where ς is the well-known Riemann function Proofs of the main theorems 5.1 Proof ... 1/n n c i 4 .21 q c i is the extended binomial i∈Z 4 .22 and by using the well-known properties of the μ− i 1 c 2 μ c−1 , if μ ≥ 4 .23 c2c−1 > 1, therefore by statement α of Theorem 3.3 we get ... of Theorem 3.1 To prove Theorem 3.1 we need the next result from 20 22 −1 −1 ς α , 4.30 I Gy˝ ri and L Horv´ th o a 11 Theorem A Let us consider the initial value problem 3.1 , 3 .2 Suppose...
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Báo cáo hóa học:

Báo cáo hóa học: "EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR SOME THREE-POINT NONLINEAR BOUNDARY VALUE PROBLEMS" pptx

Báo cáo khoa học

... (η) (2. 21) here we have used the fact pη,τ (1) = q1,τ (η) By (2. 20) and (2. 21), we have Lτ (η) ≥ q1,τ (η) p0,τ (η) , q1,τ (0) + q1,τ (η) p0,τ (1) + p0,τ (η) Lτ x (2. 22) By (2. 17) and (2. 22) , ... Theorem 2. 1 cannot be obtained by Theorems 1.1–1.4 and the abstract results in [ 12] Remark 2. 4 The nonlinear term f was assumed to be nondecreasing in Theorems 1 .2 and 1.4, but in Theorem 2. 2 in ... any t1 ,t2 ∈ [0,η], |t1 − t2 | < δ, η −δ R0 δ1 ε G(τ) t1 ,s − G(τ) t2 ,s a(s)ds < , [0,η] [0,η] R0 p0,τ t2 − p0,τ t1 p0,τ (η) ε < (2. 25) By (2. 24)– (2. 25), we have for any x ∈ B and t1 ,t2 ∈ [0,η],...
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Báo cáo hóa học:

Báo cáo hóa học: "REPRESENTATION OF SOLUTIONS OF LINEAR DISCRETE SYSTEMS WITH CONSTANT COEFFICIENTS AND PURE DELAY" ppt

Báo cáo khoa học

... j) em k −m ω( j) = B j =1 B(k−2m− j) em ω( j) + f (k) (3 .26 ) j =1 Since eB(−m) ≡ I and m k B(k−2m− j) em j =1 k −m ω( j) = B(k−2m− j) em j =1 k ω( j) + B(k−2m− j) em j =k−m+1 ω( j) , (3 .27 ) 12 ... Δ em k −m ω( j) = B B(k−2m− j) em j =1 ω( j) + f (k) j =1 (3 .24 ) Using formula (2. 8) we get B(k−m− j) em B(k−2m− j) = Bem , (3 .25 ) and the last relation becomes eB(−m) ω(k + 1) + B m k B(k−2m− ... · j (2. 24) Finally due to (2. 21), ΔeBk = B I + m Bj · j =1 k − m − ( j − 1)m j B(k = Bem −m) (2. 25) and formula (2. 16) is proved Remark 2. 2 Analyzing the formula (2. 8) we conclude that the discrete...
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Báo cáo hóa học:

Báo cáo hóa học: "Research Article Periodic and Almost Periodic Solutions of Functional Difference Equations with Finite Delay" pdf

Báo cáo khoa học

... no 2, pp 22 7 23 7, 20 03 [14] A O Ignatyev and O A Ignatyev, “On the stability in periodic and almost periodic difference systems,” Journal of Mathematical Analysis and Applications, vol 313, no 2, ... periodic system,” Funkcialaj Ekvacioj, vol 12, pp 23 –40, 1969 [2] R P Agarwal, Difference Equations and Inequalities, vol 22 8 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel ... York, NY, USA, 2nd edition, 20 00 [3] C T H Baker and Y Song, “Periodic solutions of discrete Volterra equations,” Mathematics and Computers in Simulation, vol 64, no 5, pp 521 –5 42, 20 04 [4] C Cuevas...
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Báo cáo hóa học:

Báo cáo hóa học: "SECOND-ORDER ESTIMATES FOR BOUNDARY BLOWUP SOLUTIONS OF SPECIAL ELLIPTIC EQUATIONS CLAUDIA ANEDDA, ANNA BUTTU, AND GIOVANNI " pot

Báo cáo khoa học

... 2F(s) f (s) f (s) 2 = + O(1)s−β (2. 8) Multiplying by (2F(s))−1 /2 we find − 2F(s) −1 /2 − + 2F(s) 2F(s) 1 /2 1 /2 f (s) f (s) −1 f (s) 2 = 2F(s) = 2F(s) −1 /2 −1 /2 + O(1) 2F(s) + O(1) 2F(s) −1 /2 ... s ∞ s −1 /2 2F(t) 2F(t) dt −1 /2 −β t dt −1 /2 −β s 2F(s) = lim s→∞ + βs−β−1 = + lim β s→∞ = + lim s→∞ −1 /2 2F(t) s s 2F(s) −β 2F(t) −1 /2 dt −1 /2 −β s 2F(s) ∞ ∞ s dt (2. 11) −1 /2 −1 − s 2F(s) f (s) ... f (s) 2 = + O(1)e−s (3.6) Claudia Anedda et al Multiplying by (2F(s))−1 /2 we find − 2F(s) −1 /2 − + 2F(s) 1 /2 2F(s) 1 /2 2 f (s) f (s) −1 f (s) = 2F(s) = 2F(s) −1 /2 −1 /2 −1 /2 −s + O(1) 2F(s) +...
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ON THE SOLVABILITY OF INITIAL-VALUE PROBLEMS FOR NONLINEAR IMPLICIT DIFFERENCE EQUATIONS PHAM KY ANH pdf

ON THE SOLVABILITY OF INITIAL-VALUE PROBLEMS FOR NONLINEAR IMPLICIT DIFFERENCE EQUATIONS PHAM KY ANH pdf

Báo cáo khoa học

... Vietnam J Math 29 (20 01), no 3, 28 1 28 6 M S Berger, Nonlinearity and Functional Analysis, Lectures on Nonlinear Problems in Mathematical Analysis Pure and Applied Mathematics, Academic Press, New ... systems of difference equations, J Difference Equ Appl (20 02) , no 12, 1085–1105 R M¨ rz, On linear differential-algebraic equations and linearizations, Appl Numer Math 18 a (1995), no 1–3, 26 7 29 2 ... following lemma Lemma 2. 1 The matrix Gn := An + Bn Qn−1,n is nonsingular if and only if Sn ∩ KerAn−1 = {0}, (2. 3) where, as in the DAE case, Sn := {ξ ∈ Rm : Bn ξ ∈ ImAn } The proof of Lemma 2. 1 repeats...
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NONOSCILLATORY HALF-LINEAR DIFFERENCE EQUATIONS AND RECESSIVE SOLUTIONS ˇ ´ MARIELLA CECCHI, pdf

NONOSCILLATORY HALF-LINEAR DIFFERENCE EQUATIONS AND RECESSIVE SOLUTIONS ˇ ´ MARIELLA CECCHI, pdf

Báo cáo khoa học

... solution of (1.1), then (2. 2) holds and un ∆un < for large n Proof Without loss of generality, assume u eventually positive If condition (2. 2) does not hold, from Lemma 2. 2 we obtain lim un = n ... contradiction with (3 .2) The second statement follows from Lemma 2. 2(i) The following uniqueness result will play an important role in our later consideration Theorem 3.4 Assume (1.10) For any fixed c ∈ R ... where Φ(u) = u2 sgnu and an = n(n + 1)(n + 2) 2 , bn = 8(n + 1)(n + 2) n (n + 1)(n + 2) − (4.10) We have Φ∗ 1 < , = ∗ n(n + 1) an Φ n(n + 1)(n + 2) (4.11) Mariella Cecchi et al 20 3 so ∞ 1/Φ∗ (an...
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Tài liệu Solution of Linear Algebraic Equations part 1 docx

Tài liệu Solution of Linear Algebraic Equations part 1 docx

Kỹ thuật lập trình

... (2. 0 .2) Here the raised dot denotes matrix multiplication, A is the matrix of coefficients, and b is the right-hand side written as a column vector,  a11  a21 A= aM a 12 a 22 ··· aM  a1N a2N ... symmetric positive-definite ( 2. 9), tridiagonal ( 2. 4), band diagonal ( 2. 4), Toeplitz ( 2. 8), Vandermonde ( 2. 8), sparse ( 2. 7) • Strassen’s “fast matrix inversion” ( 2. 11) 36 Chapter Solution ... call 1-800-8 72- 7 423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America) Some other topics in this chapter include • Iterative improvement of a solution ( 2. 5) • Various...
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Tài liệu Solution of Linear Algebraic Equations part 2 ppt

Tài liệu Solution of Linear Algebraic Equations part 2 ppt

Kỹ thuật lập trình

... b11  b21  b31 b41   b 12  b 22  b 32 b 42    x 12  x 22  x 32 x 42  x13  x23  x33 x43  b13  b23  b33 b43  0 0 y11  y21 y31 y41 0 0 y 12 y 22 y 32 y 42 y13 y23 y33 y43  y14 y24  y34 ... 37 2. 1 Gauss-Jordan Elimination Elimination on Column-Augmented Matrices  Consider the linear matrix equation      a 12 a 22 a 32 a 42 a13 a23 a33 a43 a14 x11 a24   x21  · a34 ... (in the case of a single right-hand side vector):       x1 b1 a11 a 12 a13 a14  a 22 a23 a24   x2   b2  (2. 2.1) ·  =    0 a33 a34 x3 b3 0 a44 x4 b4 Here the primes signify that...
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Tài liệu Solution of Linear Algebraic Equations part 11 ppt

Tài liệu Solution of Linear Algebraic Equations part 11 ppt

Kỹ thuật lập trình

... + a 22 ) × (b11 + b 22 ) Q2 ≡ (a21 + a 22 ) × b11 Q3 ≡ a11 × (b 12 − b 22 ) Q4 ≡ a 22 × (−b11 + b21 ) Q5 ≡ (a11 + a 12 ) × b 22 Q6 ≡ (−a11 + a21 ) × (b11 + b 12 ) Q7 ≡ (a 12 − a 22 ) × (b21 + b 22 ) (2. 11.3) ... they are written explicitly: c11 = a11 × b11 + a 12 × b21 c 12 = a11 × b 12 + a 12 × b 22 c21 = a21 × b11 + a 22 × b21 (2. 11 .2) c 22 = a21 × b 12 + a 22 × b 22 Do you think that one can write formulas for ... a seemingly simple question: How many individual multiplications does it take to perform the matrix multiplication of two × matrices, a11 a21 a 12 a 22 · b11 b21 b 12 b 22 = c11 c21 c 12 c 22 (2. 11.1)...
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Tài liệu Solution of Linear Algebraic Equations part 3 pdf

Tài liệu Solution of Linear Algebraic Equations part 3 pdf

Kỹ thuật lập trình

... equation (2. 3.1) would look like this:       α11  21 α31 α41 22 α 32 α 42 0 α33 α43 β11   · 0 α44 β 12 22 0 β13 23 β33 β14 24  β34 β44 a11 a =  21 a31 a41 a 12 a 22 a 32 a 42 a13 a23 a33 ... seen in 2. 2 (equation 2. 2.4) Thus, equation (2. 3.4) can be solved by forward substitution as follows, y1 = b1 α11   i−1  yi = αij yj  bi − αii j=1 (2. 3.6) i = 2, 3, , N while (2. 3.5) can ... equations (2. 2 .2) – (2. 2.4), yN xN = βNN   N (2. 3.7)  xi = βij xj  yi − i = N − 1, N − 2, , βii j=i+1 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-5)...
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Tài liệu Solution of Linear Algebraic Equations part 4 docx

Tài liệu Solution of Linear Algebraic Equations part 4 docx

Kỹ thuật lập trình

... i>j: αi1 β1j + αi2 β2j + · · · + αii βij = aij αi1 β1j + αi2 β2j + · · · + αii βjj = aij αi1 β1j + αi2 β2j + · · · + αij βjj = aij (2. 3.8) (2. 3.9) (2. 3.10) Equations (2. 3.8)– (2. 3.10) total N equations ... unity elements αii (equation 2. 3.11) are not stored at all.] In brief, Crout’s method fills in the combined matrix of α’s and β’s,  β11  21  α31 α41 β 12 22 α 32 α 42 β13 23 β33 α43  β14 24  ... (equation 2. 3.11) • For each j = 1, 2, 3, , N these two procedures: First, for i = 1, 2, , j, use (2. 3.8), (2. 3.9), and (2. 3.11) to solve for βij , namely i−1 βij = aij − αik βkj (2. 3. 12) k=1...
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