solving systems of linear equations with 3 variables calculator
Tài liệu Đề tài " Isomonodromy transformations of linear systems of difference equations" pptx
... solution of the difference Schlesinger equations (3. 1)– (3. 3) with the initial conditions {Bi (0) = Bi }, and let Bi (x1 , , xn ) be the solution of the classical Schlesinger equations (5.4) with ... difference Schlesinger equations (3. 1)– (3. 3) Remark 4.6 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, ... Lemma 4 .3 Finally, let us show that Bi (k1 , , kn ) = Ci (k1 , , ki , ki+1 − 1, , kn − 1) solves (3. 1)– (3. 3) The relation (3. 3) is equivalent to (4 .3) We will derive (3. 4) (and hence (3. 1),...
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Báo cáo hóa học: " Solving systems of nonlinear matrix equations involving Lipshitzian mappings" pdf
... 3. 3507 4.6806 4. 839 1 4 .34 03 ⎟ ⎜ ⎟ B3 = ⎜ 3. 3102 4. 839 1 5.2014 4. 739 6 ⎟ ⎜ ⎟ ⎝ 2.9201 4 .34 03 4. 739 6 4 .37 50 ⎠ 0 0 We use the iterative algorithm (14) to solve (12) for different values of X1(0): ⎞ ⎛ ... (X3 + B3 )1/4 A3 , ⎪ ⎨ 1/5 1 /3 1/4 X = In + A∗ (X1 + B1 )1/4 A1 + A∗ (X2 + B2 )1/2 A2 + A∗ (X3 + B3 )1 /3 A3 , ⎪ ⎪ ⎩ 1/4 1/5 1 /3 X3 = In + A∗ (X1 + B1 )1 /3 A1 + A∗ (X2 + B2 )1/4 A2 + A∗ (X3 + B3 ... 2.7 937 X1 (15) = ⎝ −4.4081 16.8 83 −6.6118 ⎠ , 2.7 937 −6.6118 9.7152 ⎛ ⎞ 11.512 −5.8429 3. 1922 X2 (15) = ⎝ −5.8429 19.485 −7. 930 8 ⎠ 3. 1922 −7. 930 8 10.68 and ⎞ 11. 235 3. 5241 3. 2712 X3 (15) = ⎝ 3. 5241...
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báo cáo hóa học:" Research Article Exponential Stability and Estimation of Solutions of Linear Differential Systems of Neutral Type with Constant Coefficients" pot
... α p5 α p4 α p3 α −0.2α2 − 3. 1219, −0.01α4 − 1 .31 05α2 −0.0998α4 0.5717α2 − 0.49 43, p2 α −0. 036 6α4 − 0.096828α2 p1 α p0 α 2.0 830 , −0.00420 438 2α4 0.0 538 58, 0.00 73 2 − 0.0028, −0.0001 539 2α4 − 0.00020116α2 ... stability of neutral delay-differential systems, ” Journal of the Franklin Institute, vol 33 6, no 3, pp 5 43 548, 1999 13 X.-x Liu and B Xu, “A further note on stability criterion of linear neutral ... 201/08/9469 of Czech Grant Agency, by the Council of Czech Government MSM 0021 630 5 03, MSM 0021 630 519, and by Grant FEKT-S-10 -3 of Faculty of Electrical Engineering and Communication, Brno University of...
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Báo cáo toán học: "Extremal subsets of {1, ..., n} avoiding solutions to linear equations in three variables" doc
... sets for linear equations, J Number Theory 102 (20 03) , 11-22 [10] I.Z Ruzsa, Solving a linear equation in a set of integers I, Acta Arith 65 (19 93) , 259-282 [11] I.Z Ruzsa, Solving a linear equation ... 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 ... < c when b = 3, and that for b > it yields (taking k = 3) that n ≤ b2 + 3b + + 6 ≤c+1+ b 3 b 3 This in turn yields that b+1 c n ≤b+1 (11) except when b = 4, c = 28 and n ∈ {34 , 35 } One easily...
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systems of linear inequalities (hệ bất phương trình tuyến tính) bởi a. s. solodovnikov
... of this small book to acquaint the reader with the various aspects of the theory of systems of linear inequalities, viz with the geometrical aspect of the matter and some of the methods for solving ... include a remarkable analogy between the properties of linear inequalities and those of systems of linear equations (everything connected with linear equations has been studied for a long time and ... inequalities is in the long run reduced to the solution of a number of systems of linear equations We shall regard the solution of a system of linear equations as something simple, as an elementary operation,...
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báo cáo hóa học: " Spatial estimates for a class of hyperbolic equations with nonlinear dissipative boundary conditions" doc
... 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 ... doi:10.1016/S 036 2-546X(98)00 034 -0 15 Quintanilla, R: On the spatial blow-up and decay for some nonlinear boundary conditions Z angew Math Phys 57, 595–6 03 (2006) doi:10.1007/s00 033 -005-0 035 -4 16 Quintanilla, ... Parana Math 27(2): 23 43 (2009) 19 Ammari, K, Tucsnak, M: Stabilization of second order evolution equations by a class of unbounded feedbacks, ESIM: Control Optim Calc Var 6, 36 1 38 6 (2001) 20 Haraux,...
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báo cáo hóa học:" Research Article The Boundary Value Problem of the Equations with Nonnegative Characteristic Form" pdf
... illustrate the application of Theorem 3. 1 Example 3. 2 We consider the boundary value problem of odd order equation as follows: 3 u ∂x3 3 u − Δu ∂y3 u3 x, y ∈ Ω ⊂ R2 , f x, y , 3. 15 where Ω is an unit ... quasilinear elliptic equations of second order,” Differential and Integral Equations, vol 2, no 4, pp 37 9 38 8, 1989 Z C Chen, “The Keldys-Fichera boundary value problem for a class of nonlinear ... 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...
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báo cáo hóa học:" Research Article Existence and Uniqueness of Periodic Solutions for a Class of Nonlinear Equations with p-Laplacian-Like Operators" doc
... of periodic solutions to a p-Laplacian differential equation with a deviating argument,” Journal of Mathematical Analysis and Applications, vol 33 6, no 2, pp 1107–11 23, 2007 S Lu, “Existence of ... y t −g x t , 2 .31 e t Let x1 t and x2 t being two T -periodic solutions of 1.1 ; and yi t ϕ xi t ψ xi t , i 1, 2 .32 Then we obtain xi t ϕ−1 yi t − ψ xi t yi t −g xi t , i 1, 2 .33 e t Setting ... , v t u t y1 t − y2 t , 2 .34 it follows from 2 .33 that v t ϕ−1 y1 t − ψ x1 t − ϕ−1 y2 t − ψ x2 t u t − g x1 t − g x2 t , 2 .35 Now, we claim that u t ≤ 0, ∀t ∈ R 2 .36 If this is not true, we...
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Báo cáo hóa học: " Research Article On the Solutions of Systems of Difference Equations" ppt
... of lyness-type difference equations, ” Advances in Difference Equations, vol 2007, Article ID 31 272, 13 pages, 2007 12 B Iri´ anin and S Stevi´ , “Some systems of nonlinear difference equations of ... 188, no 1, pp 833 – 837 , 2007 G Papaschinopoulos and C J Schinas, “On the behavior of the solutions of a system of two nonlinear difference equations, ” Communications on Applied Nonlinear Analysis, ... yn−m−k ,” Journal of Mathematical Analysis and Applications, vol 32 3, no 1, pp 26 32 , yn 2006 ¨ a/yn 3 , yn byn 3 /xn−q yn−q ,” A Y Ozban, “On the system of rational difference equations xn Applied...
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Báo cáo hóa học: "Research Article Exponential Stability of Difference Equations with Several Delays: Recursive Approach" docx
... whenever 50 50 |d| < 1, or |d| < 23 3.11 Condition 3. 8 of Lemma 1.4 becomes 1 − 25 50 |d| < 50 3. 12 Advances in Difference Equations 11 for even n and −d 25
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Báo cáo hóa học: " Research Article Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth" pdf
... side of (3. 34) such that − B3R eC1 | f − fB3R | dx ≤ C2 (3. 35) Using (3. 35) we can conclude that (− B3R eC1 f dx − B3R e−C1 f dx = − B3R ≤ − B3R eC1 ( f − fB3R ) dx e C1 | f − fB3R | − B3R dx ... pB4R − pB v1 Ls (B4R ) 4R (3. 34) − − Note that pBr ≥ pB2r since Br ⊂ B2r , so that the right-hand side of (3. 34) is bounded The rest of the proof is standard Since (3. 34) holds for all balls B2r ... | − B3R dx e−C1 ( f − fB3R ) dx (3. 36) ≤ C2 , which implies that − B3R C v1 dx 1/C1 = − B3R 2/C1 ≤ C2 2/C1 = C2 eC1 f dx 1/C1 − e−C1 f dx − − v1 C1 dx B3R B3R −1/C1 (3. 37) −1/C1 , so that we can...
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solution of linear equations using gaussian elimination
... a 23 x3 + + a2N xN = d2 a31 x1 + a32 x2 + a 33 x3 + + a3N xN = d3 Programming exercise a11 x1 + a12 x2 + a 13 x3 + + a1N xN = d1 aM x1 + aM x2 + aM x3 + + aMN xN = dM Here we have a total of ... concept of simultaneous linear equations A set of linear simultaneous equations may be written as: a11 x1 + a12 x2 + a 13 x3 + + a1N xN = d1 a21 x1 + a22 x2 + a 23 x3 + + a2N xN = d2 a31 x1 + a32 x2 ... set of equations and unknowns, ie N =3 and M =3, in order to illustrate the Gaussian elimination method: a11 x1 + a12 x2 + a 13 x = d1 (4) a21 x1 + a22 x2 + a 23 x3 = d2 (5) a31 x1 + a32 x2 + a 33 x3...
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Tài liệu Solution of Linear Algebraic Equations part 3 pdf
... 21 a31 a41 a12 a22 a32 a42 a 13 a 23 a 33 a 43 a14 a24 a34 a44 (2 .3. 2) We can use a decomposition such as (2 .3. 1) to solve the linear set A · x = (L · U) · x = L · (U · x) = b (2 .3. 3) by first solving ... For the case of a × matrix A, for example, equation (2 .3. 1) would look like this: α11 α21 31 α41 α22 32 α42 0 33 α 43 β11 · 0 α44 β12 β22 0 β 13 β 23 33 β14 β24 34 β44 a11 ... L·y=b (2 .3. 4) U·x=y (2 .3. 5) and then solving What is the advantage of breaking up one linear set into two successive ones? The advantage is that the solution of a triangular set of equations...
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Báo cáo hóa học: " Research Article Systems of Quasilinear Parabolic Equations with Discontinuous Coefficients and Continuous Delays" docx
... independent of m 0, Proof By Hypothesis H , 3. 20 , and 3. 27 , the proof similar to that of 15, Lemma 4.4 gives 3. 31 , and, by 3. 20 and 3. 28 , the proof similar to that of 15, Lemma 4 .3 gives ∗ ... , k 3. 32 1, , K, 3. 33 20 Advances in Difference Equations ∗ ∗ where β1 and β2 depend only on d and the parameters M, a0 , θ0 , α0 , μ1 , μ2 , ν M , μ M , and By using 3. 5 , 3. 32 , 3. 33 , and ... t − l l l l Um x, t − h x, t λ in 3. 4 Thus 3. 9 and 3. 10 follow from h x, t ζ in 3. 3 and φ 3. 8 and the proofs similar to those of 15, formulas 2.7 and 4.2 3. 3 Uniform Estimates on Ω × 0, T The...
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báo cáo hóa học:" Research Article Existence of Periodic Solutions of Linear Hamiltonian Systems with Sublinear Perturbation" ppt
... developments of the secondorder systems 1.1 , see In this paper, we use this kind of condition to consider the existence of periodic solutions of first-order linear Hamiltonian system with a nonlinear ... |dt 3. 9 C un ≤ C un μ∗ Lμ un C un Hence un ≤ C u n μ∗ Lμ 3. 10 C Therefore, using 3. 7 , we get un ≤ C un μ∗ /μ un ≤ C u n μ∗ /μ C 3. 11 C 3. 12 Similarly, we also have Combining 3. 8 , 3. 11 , and 3. 12 ... vol 30 of Itogi Nauki i Tekhniki, pp 3 1 03, Akad Nauk SSSR Vsesoyuz Inst Nauchn i Tekhn Inform., Moscow, Russia, 1987, Translated in Journal of Soviet Mathematics, vol 43, no 2, pp 2259– 233 9,...
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Báo cáo hóa học: " Research Article Nonexpansive Matrices with Applications to Solutions of Linear Systems by Fixed Point Iterations Teck-Cheong Lim" docx
... If λ is an eigenvalue of A with |λ| 1, λ / Then Ak v2 and index λ ≥ 3, then there exist nonzero vectors v1 , v2 and v3 such that Av1 λv1 , A v2 v2 λv3 By expanding Aj v3 , j 0, 1, 2, , k ... λ 1−λ v2 k v1 18 1−λ v3 k 1−λ which approaches to ∞ as k → ∞ This completes the proof We now consider applications of preceding theorems to approximation of solution of a linear system Ax b, where ... eigenvalue of B Proof As in the proof of Theorem 2, a and b are equivalent For < μ < 1, denote μI − μ B by B μ Suppose now that a holds Let λ be an eigenvalue of B Then μ 1− μ λ is an eigenvalue of...
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Báo cáo hóa học: "REPRESENTATION OF SOLUTIONS OF LINEAR DISCRETE SYSTEMS WITH CONSTANT COEFFICIENTS AND PURE DELAY" ppt
... x(k) = ϕ(k), k ∈ Z−m (3. 15) (3. 16) We get this solution, in accordance with the theory of linear equations, as the sum of the solution of adjoint homogeneous problem (3. 1), (3. 2) (satisfying the ... + k b(k 3 j) e3 j =1 k f ( j − 1) = ebk + b(k 3 j) je3 j =1 (3. 33) Concluding remarks Method of representation of solutions developed in the paper can be used to the investigation of some ... Example 3. 7 Let us represent the solution of the problem Δx(k) = bx(k − 3) + k + 1, (3. 32) x( 3) = x(−2) = x(−1) = x(0) = 1, b = 0, b ∈ R, by formula (3. 31) Taking into account the representation of...
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