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descretizing the radiosity equation

Markov processes and the Kolmogorov equations

Markov processes and the Kolmogorov equations

Cao đẳng - Đại học

... plunked down the Kolmogorov backward equation without any justification In fact, one can use Itˆ ’s formula to prove the Feynman-Kac Theorem, and use o the Feynman-Kac Theorem to derive the Kolmogorov ... T , t 16.4 The Kolmogorov Backward Equation Consider dX t = at; X t dt + t; X t dBt; and let pt0; t1 ; x; y  be the transition density Then the Kolmogorov Backward Equation is: ... us to the equation vtt; x + rxvxt; x + 2x2vxxt; x = 0;  t T; x  0: This is a special case of Theorem 5.51 (Feynman-Kac) Along with the above partial differential equation, we have the terminal...
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Tài liệu EXACT SMALL SAMPLE THEORY IN THE SIMULTANEOUS EQUATIONS MODEL docx

Tài liệu EXACT SMALL SAMPLE THEORY IN THE SIMULTANEOUS EQUATIONS MODEL docx

Vật lý

... relevant to the various cases The starting point in the derivation of the p.d.f of these estimators of /3 is to write down the joint distribution of the matrix A in (3.13) To obtain the p.d.f of the ... the structural equation Thus, if we consider the hypothesis H,,: p = & in (3.3), we may define y* = y, - Y2& and rewrite the structural equation under the null hypothesis as y* = Z,y + u On the ... indicating that the adequacy of the critical regions (3.62)-(3.63) depends on the degree of overidentification of the equation under the identifiability hypothesis In particular, the adequacy of these...
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Đề tài

Đề tài " Propagation of singularities for the wave equation on manifolds with corners " ppt

Thạc sĩ - Cao học

... VASY the body of the paper are primarily written for Dirichlet boundary conditions, and the required changes are pointed out at the end of the various sections In addition, the hypotheses of the ... Remark 4.5 The point of this lemma is that on the one hand the new term ε dX Ar u can be absorbed on the left-hand side in the elliptic region, ˜ hence is negligible; on the other hand, there is ... for the second / b paragraph in the statement of Proposition 6.2 We deal with the weakened hypothesis q0 ∈ WF−1,s+1 (P u) at the end of the proof Returning to (6.21), / b the utility of the commutator...
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External Debt and Economic Growth Relationship Using the Simultaneous Equations doc

External Debt and Economic Growth Relationship Using the Simultaneous Equations doc

Cao đẳng - Đại học

... may affect the GNP in the following ways: the higher the level of indebtedness, the larger the country’s leverage, the more limited the external sources of credit, and the greater the number ... of the results conform with the theoretical analysis For the growth equation, both the direct effect and total effect of exogenous variables on the growth equation (YR) are the same sign The ... For the capital inflow equation, both the direct effect and total effect of exogenous variables on the capital inflow equation (YR) are the same sign Most of the results conform with the theoretical...
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Introduction to optical waveguide analysis solving maxwell's equation and the schrdinger equation   kenji kawano, tsutomu kitoh

Introduction to optical waveguide analysis solving maxwell's equation and the schrdinger equation kenji kawano, tsutomu kitoh

Vật lý

... discussed are the error factors of the FFT-BPM, the physical meaning of the Fresnel equation, the problems with the wide-angle FFT-BPM, and the stability of the FD-BPM Chapter discusses the ®nite-difference ... solving the Schrodinger equation Chapter discusses È how to solve the Schrodinger equation with the effective mass approxÈ imation Since the structure of the Schrodinger equation is the same ... component normal to the surface S of the volume V The ®rst two terms of the last equation correspond to the rate of the reduction of the stored energy in volume V per unit time, while the third term...
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Báo cáo hóa học:

Báo cáo hóa học: " Neumann problem on the semi-line for the Burgers equation" pdf

Hóa học - Dầu khí

... on the use of the contraction-mapping technique, analogously to what was done for the Eckhaus equation in [15] In particular, the main result of the present study is to prove the following Theorem ... boundary data for the Burgers equation (1) The Neumann problem on the semi-line for υ(x,t) is then in principle solved through the following prescription: Solve the Neumann problem on the semi-line ... nonlinear integro-differential equation like (11) On the other hand, the determination of the solution u(x,t) has been reduced to the solution of the nonlinear integral equation (10b)–with C(t) satisfying...
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báo cáo hóa học:

báo cáo hóa học:" Research Article A Discrete Equivalent of the Logistic Equation" potx

Hóa học - Dầu khí

... equation accompanied with initial or boundary conditions in the real or complex plane This method was successfully applied to the Duffing equation, the Lorenz system, and the Blasius equation The ... imposed on the parameters appearing in the equation Moreover, since it is a non linear equation, a fixed-point theorem would be useful Indeed, the following well-known theorems concerning the inversion ... discussed These differences concern their solutions see Figure , their bifurcation diagrams, and their stability Derivation of the Discrete Equivalent Logistic Equation In this section, the method...
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báo cáo hóa học:

báo cáo hóa học:" Research Article A Remark on the Blowup of Solutions to the Laplace Equations with Nonlinear Dynamical Boundary Conditions" pdf

Hóa học - Dầu khí

... where we have used 2.31 and the fact that ψ1 is the eigenfunction of the problem 1.1 – 1.4 , B1 and B2 are denoted as the expressions in the first and the second parenthesis, respectively From 2.32 ... Qualitative Theory of Differential Equations, no 13, pp 1–20, 2008 30 E Vitillaro, “On the Laplace equation with non-linear dynamical boundary conditions,” Proceedings of the London Mathematical ... of the solution for the Laplace equations with a hyperbolic type dynamical boundary inequality by the test function methods In this paper, we present some sufficient conditions of blowup of the...
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Báo cáo hoa học:

Báo cáo hoa học: " Research Article On Boundedness of Solutions of the Difference Equation xn 1 pxn qxn−1 / 1 xn for q 1 p 1" pot

Hóa học - Dầu khí

... follows 16 Theorem A If p q ≤ 1, then the zero equilibrium of 1.1 is globally asymptotically stable If q 1, then the equilibrium x p of 1.1 is globally asymptotically stable If < q < p, then every ... }∞ exactly one of the following n n They are both monotonically increasing They are both monotonically decreasing Eventually, one of them is monotonically increasing, and the other is monotonically ... for any n ≥ Let S be the set of all initial values x−1 , x0 ∈ 0, ∞ × 0, ∞ such that the positive solutions {xn }∞ −1 of 1.1 are bounded Then we have the following theorem n Theorem 3.6 S ∞ n Qn...
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Báo cáo hóa học:

Báo cáo hóa học: " Research Article Existence of Pseudo Almost Automorphic Solutions for the Heat Equation with Sp -Pseudo Almost Automorphic Coefficients" docx

Hóa học - Dầu khí

... use of the approximation 5.4 rather than 5.5 Throughout the rest of the paper, the constant k α denotes the bound of the embedding Xβ → Xα , that is, u α ≤k α u β for each u ∈ Xβ 5.24 Theorem ... solutions to the heat equation 1.1 in the case when the coefficients f, g are Sp -pseudo almost automorphic is an untreated original problem and constitutes the main motivation of the present paper ... Y The collection of such functions will be denoted by P AA R × Y A substantial result is the next theorem, which is due to Liang et al Theorem 2.19 see The space P AA X equipped with the...
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Báo cáo hóa học:

Báo cáo hóa học: "Research Article Variational Method to the Impulsive Equation with Neumann Boundary Conditions" docx

Hóa học - Dầu khí

... constants Then uj ∈ C tj , tj and uj ∈ C tj , tj Therefore, uj is a classical solution of 2.13 and u satisfies the equation in IBVP 2.1 a.e on 0, By the Boundary Value Problems previous equation, ... obtain the result Theorem 3.3 Suppose that the first inequalities in (H1), (H3), and (H4) hold Furthermore, one assumes that g t, u and the impulsive functions Ik u are odd about u and we have the ... bounded in X In the following, the proof of P S condition is the same as that in Theorem 3.1, and we omit it here Secondly, as in Theorem 3.1, we can obtain that condition A2 in Theorem 2.1 is...
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Báo cáo hóa học:

Báo cáo hóa học: " Research Article The Periodic Character of the Difference Equation xn 1 f xn−l 1, xn−2k 1" pdf

Báo cáo khoa học

... 2, , then 2.24 reduces to the equation i yn i i f yn−l , yn−2k , ≤ i ≤ s − 1, n 0, 1, 2, 2.25 It follows from Theorem 1.1 that for any ≤ i ≤ s − 1, every positive solution of the equation ... and H Xi Therefore, lim x2n M, lim x2n g M , n→∞ lim x2n n→∞ g M 2.22 or n→∞ lim x2n n→∞ M 2.23 The proof is complete Remark 2.2 The proofs of Lemma 2.1 and Theorem 1.1 draw on ideas from the proofs ... lim x→ ∞ g x a The main result of this paper is the following theorem Theorem 1.1 Every positive solution of 1.1 converges to (not necessarily prime) a 2-periodic solution Proof of Theorem 1.1 In...
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Báo cáo hóa học:

Báo cáo hóa học: "Research Article On the Difference Equation xn" pot

Báo cáo khoa học

... see how the parameters α and β affect the dynamics of 1.1 Furthermore, using the normal form theory, we drive a formula for determining the direction of the period-two bifurcation and the stability ... the second equation of 3.8 , using the first equation and the invariance of the center manifold, we get the following linear equation for ω2 : y V z A − E ω2 β The matrix A − E is invertible because ... the period-doubling bifurcation theorem Stuart and Humphries, 7, page 41, Theorem 1.4.5 , the bifurcation of a period-two solution occurs Direction of bifurcation of the period-two cycle In the...
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Báo cáo hóa học:

Báo cáo hóa học: " Research Article Global Existence and Uniqueness of Strong Solutions for the Magnetohydrodynamic Equations" potx

Báo cáo khoa học

... Problems p p ρ, θ the pressure, and e e ρ, θ the internal energy; λ and μ are the bulk and shear viscosity coefficients, υ is the magnetic viscosity, κ is the heat conductivity Notice that the longitudinal ... 1.1 The equations in 1.1 describe the macroscopic behavior of the magnetohydrodynamic flow This is a three-dimensional magnetohydrodynamic flow which is uniform in the transverse directions There ... of 1.1 , namely, we consider the magnetohydrodynamic equations for isentropic compressible fluids Thus, instead of the equations in 1.1 , we will study the following equations: ρt ρu ρu2 t ρw bt...
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Báo cáo hóa học:

Báo cáo hóa học: " Research Article The Periodic Character of the Difference Equation xn 1 f xn−l 1, xn−2k 1" pot

Báo cáo khoa học

... 2, , then 2.24 reduces to the equation i yn i i f yn−l , yn−2k , ≤ i ≤ s − 1, n 0, 1, 2, 2.25 It follows from Theorem 1.1 that for any ≤ i ≤ s − 1, every positive solution of the equation ... and H Xi Therefore, lim x2n M, lim x2n g M , n→∞ lim x2n n→∞ g M 2.22 or n→∞ lim x2n n→∞ M 2.23 The proof is complete Remark 2.2 The proofs of Lemma 2.1 and Theorem 1.1 draw on ideas from the proofs ... lim x→ ∞ g x a The main result of this paper is the following theorem Theorem 1.1 Every positive solution of 1.1 converges to (not necessarily prime) a 2-periodic solution Proof of Theorem 1.1 In...
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Báo cáo hóa học:

Báo cáo hóa học: " Research Article Global Existence and Uniqueness of Strong Solutions for the Magnetohydrodynamic Equations Jianwen Zhang" pptx

Báo cáo khoa học

... Problems p p ρ, θ the pressure, and e e ρ, θ the internal energy; λ and μ are the bulk and shear viscosity coefficients, υ is the magnetic viscosity, κ is the heat conductivity Notice that the longitudinal ... 1.1 The equations in 1.1 describe the macroscopic behavior of the magnetohydrodynamic flow This is a three-dimensional magnetohydrodynamic flow which is uniform in the transverse directions There ... of 1.1 , namely, we consider the magnetohydrodynamic equations for isentropic compressible fluids Thus, instead of the equations in 1.1 , we will study the following equations: ρt ρu ρu2 t ρw bt...
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Báo cáo hóa học:

Báo cáo hóa học: "ON THE DIFFERENCE EQUATION xn+1 = axn − bxn /(cxn − dxn−1 )" pptx

Báo cáo khoa học

... than one, then the equilibrium x of (1.2) is unstable Remark 1.4 The condition (1.9) implies that all the roots of the polynomial equation (1.8) lie in the open unite disk |λ| < Consider the following ... let x be an equilibrium of (1.2) Then the following statements are true (a) If all roots of the polynomial equation (1.8) lie in the open unite disk |λ| < 1, then the equilibrium x of (1.2) is asymptotically ... On the positive solutions of the difference equation xn+1 = axn−1 /1 + bxn xn−1 , Applied [3] Mathematics and Computation 156 (2004), no 2, 587–590 , On the positive solutions of the difference equation...
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