brunauer emmett and teller bet isotherm equation

... Chapter Root Finding and Nonlinear Sets of Equations for (i=1;i

Ngày tải lên: 07/11/2013, 19:15

... trade@cup.cam.ac.uk (outside North America) a x2 x3 b x1 d c f e 351 9.1 Bracketing and Bisection 352 Chapter Root Finding and Nonlinear Sets of Equations #include #define FACTOR 1.6 #define NTRY 50 if ... float *x2) Given a function func and an initial guessed range x1 to x2, the routine expands the range geometrically until a root is bracketed by the returned values x1 and x2 (in which case zbrac ... subdivide the interval into n equally spaced segments, and search for zero crossings of the function nb is input as the maximum number of roots sought, and is reset to the number of bracketing pairs...

Ngày tải lên: 15/12/2013, 04:15

... Method, False Position Method, and Ridders’ Method f(x) 356 Chapter Root Finding and Nonlinear Sets of Equations f (x) Figure 9.2.3 Example where both the secant and false position methods will ... both reliability and speed, Ridders’ method is generally competitive with the more highly developed and better established (but more complicated) method of Van Wijngaarden, Dekker, and Brent, which ... REFERENCES AND FURTHER READING: Ralston, A., and Rabinowitz, P 1978, A First Course in Numerical Analysis, 2nd ed (New York: McGraw-Hill), §8.3 Ostrowski, A.M 1966, Solutions of Equations and Systems...

Ngày tải lên: 15/12/2013, 04:15

... problem by maintaining brackets on the root and checking where the interpolation would land before carrying out the division When the correction P/Q would not land within the bounds, or when the bounds ... bisection, and inverse quadratic interpolation to converge from the neighborhood of a zero crossing While the false position and secant methods assume approximately linear behavior between two ... Finding and Nonlinear Sets of Equations } a=b; fa=fb; if (fabs(d) > tol1) b += d; else b += SIGN(tol1,xm); fb=(*func)(b); Move last best guess to a Evaluate new trial root } CITED REFERENCES AND...

Ngày tải lên: 15/12/2013, 04:15

... x1, float x2, float xacc) Using a combination of Newton-Raphson and bisection, find the root of a function bracketed between x1 and x2 The root, returned as the function value rtsafe, will be ... convergence notwithstanding — is to investigate, for some particular equation, the set of starting values from which the method does, or doesn’t converge to a root Consider the simple equation z3 − ... (New York: McGraw-Hill), §8.4 Ortega, J., and Rheinboldt, W 1970, Iterative Solution of Nonlinear Equations in Several Variables (New York: Academic Press) Mandelbrot, B.B 1983, The Fractal Geometry...

Ngày tải lên: 15/12/2013, 04:15

... (outside North America) Given B and C, R and S can be readily found, by polynomial division (§5.3) We can consider R and S to be adjustable functions of B and C, and they will be zero if the quadratic ... coefficients, i=0 and the coefficients a[0 m] The method is to construct an upper Hessenberg matrix whose eigenvalues are the desired roots, and then use the routines balanc and hqr The real and imaginary ... rigorously derive) the Laguerre formulas we can note the following relations between the polynomial and its roots and derivatives 9.5 Roots of Polynomials 373 #include #include "complex.h"...

Ngày tải lên: 15/12/2013, 04:15

... δx2 and higher and by setting F(x + δx) = 0, we obtain a set of linear equations for the corrections δx that move each function closer to zero simultaneously, namely J · δx = −F (9.6.6) Matrix equation ... Root Finding and Nonlinear Sets of Equations no root here! two roots here f pos g pos M f=0 g pos g= g neg f pos f neg g neg = g g= g pos x Figure 9.6.1 Solution of two nonlinear equations in ... America) The matrix of partial derivatives appearing in equation (9.6.3) is the Jacobian matrix J: 382 Chapter Root Finding and Nonlinear Sets of Equations void ludcmp(float **a, int n, int *indx,...

Ngày tải lên: 15/12/2013, 04:15

... Systems of Equations 393 More Advanced Implementations CITED REFERENCES AND FURTHER READING: Dennis, J.E., and Schnabel, R.B 1983, Numerical Methods for Unconstrained Optimization and Nonlinear Equations ... (i=1;i

Ngày tải lên: 15/12/2013, 04:15

... Then all ξ1 , ξn , ζ1 , and ζn > Let θ1 denote the ˆ 1002 NEIL S TRUDINGER AND XU-JIA WANG angle between ξ and ζ at x, and θ2 the angle between ξ and the x1 -axis By ˆ (2.2) and (2.19), |∂γ u(ˆ)| ... maximal surface equation and affine mean curvature equation Introduction In a landmark paper [4], Caffarelli established interior W 2,p and C 2,α estimates for solutions of the Monge-Amp`re equation e ... follows directly from (2.1) and the boundary condition (1.2) For the lower bound, one requires that ϕ be C smooth, and ∂Ω be C and uniformly convex [22] For (2.1) and (2.2) we only need f to...

Ngày tải lên: 16/02/2014, 06:20

... Guillemin and Sternberg [1980], and Marsden and Weinstein [1982, 1983], but is explicit in Marsden, Weinstein, Ratiu and Schmid [1983], and in Holmes and Marsden [1983] Kazhdan, Kostant and Sternberg ... Ortiz and West [2000], Wendlandt and Marsden [1997] and references therein Discrete analogues of reduction theory have begun in Ge and Marsden [1988], Marsden, Pekarsky and Shkoller [1999], and ... functions and momentum maps play a key role in the stability theory of relative equilibria (see, for example, Marsden [1992] and Marsden and Ratiu [1999] and references therein and for references and...

Ngày tải lên: 24/04/2014, 16:49

... Point Theory and Applications and gave some existence and uniqueness results and iterative approximations of solutions for the functional equations in BB S Liu and Kang 14 and Liu and Ume 17 generalized ... results, which extend and improve substantially the results due to Bellman , Bhakta and Choudhury , Liu 12 , Liu and Kang 14, 15 , Liu and Ume 17 , Liu et al 18 , and others Lemmas and Algorithms Throughout ... 1.9 where opt denotes sup or inf, x and y stand for the state and decision vectors, respectively, a, b, and c represent the transformations of the processes, and f x represents the optimal return...

Ngày tải lên: 21/06/2014, 05:20

... has studied x t the equation −a t x t − r t , x t 1.3 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 ... “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, ... “Stability and fixed points: addition of terms,” Dynamic Systems and Applications, vol 13, no 3-4, pp 459–477, 2004 B Zhang, “Contraction mapping and stability in a delay-differential equation, ”...

Ngày tải lên: 21/06/2014, 11:20

... Inequalities and Applications and weak solutions of the anisotropic equations −divA x, u , Du − N i ∂fi , ∂xi 1, q u ∈ Wloc i Ω 1.4 We refer to the classical books by Ladyˇ enskaya and Ural’ceva ... in Ak,t and t − τ < The summation of the 1st and the 4th terms on the righthand side of 3.7 can be estimated as uα dx b u − ηw α dx ≤ 2b b Ak,t Ak,t uα dx 3.10 Ak,t Substituting 3.9 and 3.10 ... by Boccardo and Giachetti to the nonlinear case in For anisotropic cases, Giachetti and Porzio recently proved in the local Ls -summability for minima of anisotropic functionals and weak solutions...

Ngày tải lên: 22/06/2014, 06:20

... Inequalities and Applications and weak solutions of the anisotropic equations −divA x, u , Du − N i ∂fi , ∂xi 1, q u ∈ Wloc i Ω 1.4 We refer to the classical books by Ladyˇ enskaya and Ural’ceva ... in Ak,t and t − τ < The summation of the 1st and the 4th terms on the righthand side of 3.7 can be estimated as uα dx b u − ηw α dx ≤ 2b b Ak,t Ak,t uα dx 3.10 Ak,t Substituting 3.9 and 3.10 ... by Boccardo and Giachetti to the nonlinear case in For anisotropic cases, Giachetti and Porzio recently proved in the local Ls -summability for minima of anisotropic functionals and weak solutions...

Ngày tải lên: 22/06/2014, 18:20

... established to neutral and nonneutral differential difference and dynamic equations Y Sahiner ¸ References [1] R P Agarwal, M Bohner, and S H Saker, Oscillation of second order delay dynamic equations, to ... Sahiner and I P Stavroulakis, Oscillations of first order delay dynamic equations, to appear in ¸ Dynamic Systems and Applications [11] B G Zhang and X Deng, Oscillation of delay differential equations ... monotone and deviating arguments τ(t) and δ(t) are variable functions of t Moreover, in case r(t) > (t/2)γ for sufficiently large t, Theorems 3.1 and 3.4 are stronger than Theorems 2.2 and 2.3 Example...

Ngày tải lên: 22/06/2014, 22:20

... theorem and application and it follows that b(t) = t (1 − L)2 ω2 (t,s)ds − 0, → as t − ∞ → (4.24) Furthermore, it follows from (4.23) and (H3 )(iii) that +∞ b(s)ds < +∞ (4.25) On the other hand, ... of Differential Equations 2003 (2003), no 5, 1–15 [2] C Avramescu and C Vladimirescu, Asymptotic stability results for certain integral equations, Electronic Journal of Differential Equations 2005 ... r2n > αβ Put Dn = x ∈ X : x n ≤ r2n , D= Dn (2.11) n∈N∗ Then u0 ∈ D and D is bounded, closed, and convex in X For each x ∈ D and for each n ∈ N∗ , as above we also consider two cases If x − u0...

Ngày tải lên: 22/06/2014, 22:20

... Kirschner and G F Webb, Understanding drug resistance for monotherapy treatment of HIV infection, Bull Math Biol 59 (1997), no 4, 763–785 A R McLean and C A Michie, In vivo estimates of division and ... an unavoidable AIDS epidemic Indeed, from (2.1), and mutatis mutandis also from (2.2), if we start, as is reasonable, with A = 0, we have A > 0, and thus A grows as long as A < µI/λ The only fixed ... of the quadratic equation shows that they are of opposite signs Thus, it suffices, at each step, to discard the negative solution and keep only the physical one, yn > Figures 2.1 and 2.2 show a typical...

Ngày tải lên: 23/06/2014, 00:20

... then Ꮿ J1 = y : J1 −→ R : y and y ∆ are continuous on J1 , + + Ꮿ J2 = y : J2 −→ R : y and y ∆ are continuous on J2 and y t1 and y ∆ t1 exist , A = y : J −→ R : y1 ∈ Ꮿ J1 and y2 ∈ Ꮿ J2 (3.7) For ... introduce the concept of lower and upper solutions of problem (3.1)–(3.5) as follows F M Atici and D C Biles 127 Definition 3.1 The functions α and β are, respectively, a lower and an upper solution of ... and convex set, in view of the Tychonoff-Schauder fixed point theorem, there is at least one fixed point of Q Theorem 3.3 Assume that conditions (F) and (I) are satisfied Let α and β be a lower and...

Ngày tải lên: 23/06/2014, 00:20

Ngày tải lên: 06/07/2014, 15:18

... the two functions tions Chapter The Markoff equation and Generalized Markoff equations The Markoff equation x2 + y + z = xyz (4.1) and generalized Markoff equations x2 + y + z = xyz + µ (4.2) for µ ... hyperbolic tori by Bowditch in [7, 9] and Tan et al in [42, 44] We review results on the Markoff equation in [7, 9] and the generalized Markoff equations in [44] and present a simple identity which ... on C3 36 Chapter The Markoff equation and Generalized Markoff equations is defined as follows: for any i ∈ {1, 2, 3} and (x1 , x2 , x3 ) ∈ C3 , si (xj ) = xj if j = i and si (xi ) = x1 x2 x3 xi −...

Ngày tải lên: 10/09/2015, 09:09