integral equations and the moment method

... vanishing moment, to the MoM used to solve EM integral equations In the first approach, or what is commonly known as the wavelet expansion method, the integral equation is directly expanded and tested ... within the interval [0, 1] Otherwise, either ‘integralright’ or ‘integralleft’ will be omitted in the summation for Zi j by setting the partition to the edge value The centre integral can then ... Under these assumptions, the electric field has only the z component and the magnetic field has only the transverse components, i.e.Ex and Ey within the cavity under the patch 3.3 Contour integral...

Ngày tải lên: 16/09/2015, 14:04

... modulus and the cross-sectional area, and f is either the friction or contact force on the surface of the bar), pipe flow (u is the hydrostatic pressure, a1 = 7rD4/128p, is the diameter, p is the ... electromagnetics, and many others Equations involving partial derivatives are called partial diferential equations (PDEs) The solutions to these equations are functions, as opposed to standard algebraic equations ... L2(s2).Then the integral :R, is interpreted as the duality pairing ( f , v) between H-'(R) and H,'(R) Equivalence of the strong and weak solutions Obviously the classical solution to the problem...

Ngày tải lên: 31/03/2014, 15:57

... convenience of the reader, we restate the main results of [7] as the following theorem Theorem 1.1 Let (A1, , Ak) and (B1 , , Bk ) be commuting k-tuples of m × m and n × n matrices, respectively The following ... of m × m and n × n matrices, respectively, and let F = O On Then the following are equivalent: (i) F ∈ {T1, , Tk } ; (ii) The homogeneous systems of Sylvester equations AiY − Y Bi = O and ZAi ... Below we extend the Parlett’s method to the case of functions of several commuting matrices and apply it to the problems of finding simultaneous solutions of Sylvester equations In the sequel, we...

Ngày tải lên: 16/10/2015, 09:33

... between the solution u(x) and the true function u(x), and seeks to make the mapping between these as close to the identity map as possible in the limit of error-free data The method is linear, so the ... every x, giving 818 Chapter 18 Integral Equations and Inverse Theory CITED REFERENCES AND FURTHER READING: Backus, G.E., and Gilbert, F 1968, Geophysical Journal of the Royal Astronomical Society, ... Chapter 18 Integral Equations and Inverse Theory u(x) = δ(x, x )u(x )dx (18.6.2) for some so-called resolution function or averaging kernel δ(x, x ) The BackusGilbert method seeks to minimize the width...

Ngày tải lên: 17/10/2013, 22:15

... ’s, so as to suppress the low-intensity ripple and sharpen the point sources 824 Chapter 18 Integral Equations and Inverse Theory Algorithms for MEM The goal is to find the vector u that minimizes ... Chapter 18 Integral Equations and Inverse Theory CITED REFERENCES AND FURTHER READING: Jaynes, E.T 1976, in Foundations of Probability Theory, Statistical Inference, and Statistical Theories of ... method or MEM, are unrelated Bayes’ Theorem, which follows from the standard axioms of probability, relates the conditional probabilities of two events, say A and B: 820 Chapter 18 Integral Equations...

Ngày tải lên: 24/10/2013, 15:15

... of equations We then return to Volterra equations (§18.2), and find that simple and straightforward methods are generally satisfactory for these equations In §18.3 we discuss how to proceed in the ... Fredholm equations of the second kind are much less often ill-conditioned Equation (18.0.4) can be rewritten as 790 Chapter 18 Integral Equations and Inverse Theory The Volterra equation of the first ... an eigenvalue — because the integral operator (or matrix) is singular then In integral equations this dichotomy is called the Fredholm alternative Fredholm equations of the first kind are often...

Ngày tải lên: 21/01/2014, 18:20

... that returns g(t) and another that returns λKij It then returns the solution f at the quadrature points It also returns the quadrature points and weights These are used by the second routine ... return g(t) and λK(t, s) The routine returns arrays t[1 n] and f[1 n] containing the abscissas ti of the Gaussian quadrature and the solution f at these abscissas Also returned is the array w[1 ... arrays t[1 n] and w[1 n] containing the abscissas and weights of the Gaussian quadrature, and given the solution array f[1 n] from fred2, this function returns the value of f at x using the Nystrom...

Ngày tải lên: 21/01/2014, 18:20

... Romberg integration The general consensus is that the best of the higher order methods is the block-by-block method (see [1]) Another important topic is the use of variable stepsize methods, which ... while calculating the first few moments of the kernel K(t, s) at the tabulation points ti In such a scheme the narrow width of the kernel becomes an asset, rather than a liability: The quadrature ... L.M., and Mohamed, J.L 1985, Computational Methods for Integral Equations (Cambridge, U.K.: Cambridge University Press) [2] 18.3 Integral Equations with Singular Kernels Many integral equations...

Ngày tải lên: 21/01/2014, 18:20

... = const, x, x2 , , xn−1 , and then solve these for the coefficients This can be done analytically, once and for all, if the moments of the weight function over the same range of integration, ... on the left of the diagonal, combined with a square-root discontinuity on the right The first step is to (analytically, in this case) the required moment integrals over the singular part of the ... the global variable x is the row We can take x as the lower limit of integration Thus, we return the moment integrals either purely to the left or purely to the right of the diagonal { double d,df,clog,x2,x3,x4,y2;...

Ngày tải lên: 26/01/2014, 15:20

... Agreement 18.4 Inverse Problems and the Use of A Priori Information 808 Chapter 18 Integral Equations and Inverse Theory The single central idea in inverse theory is the prescription minimize: A ... better methods, demonstrates most of the basic ideas that are used in inverse problem theory In general, there are two positive functionals, call them A and B The first, A, measures something like the ... also called the Phillips-Twomey method [1,2] , the constrained linear inversion method [3], the method of regularization [4], and Tikhonov-Miller regularization [5-7] (It probably has other names...

Ngày tải lên: 26/01/2014, 15:20

... summaries) differs from other regularization methods in the nature of its functionals A and B For B, the method seeks to maximize the stability of the solution u(x) rather than, in the first instance, ... “zero the values outside of the region of support.” The usefulness of these definitions is the following remarkable theorem: Let C be the intersection of m convex sets C1 , C2 , , Cm Then the ... technique further in §18.7, in the context of the (nonlinear) maximum entropy method Some of that discussion can apply here as well The conjugate gradient method notwithstanding, application of the unsophisticated...

Ngày tải lên: 26/01/2014, 15:20

... two-fold way: On the one hand they are either analytic or synthetic, and on the other they are either a priori or a posteriori The meaning of these distinctions is, in short, the following Propositions ... we hypothesize some other phenomenon as its cause and then see whether or not the hypothesized cause indeed preceded the effect in time A distinction exists between a historical and a theoretical ... dogmatic and unscientific Mises's view that economic theorems-like the law of marginal utili~ or the law of returns, or the time-preference theory of interest and the Austrian business cycle theory-can...

Ngày tải lên: 22/03/2014, 21:20

... impose narrow norms and methods on scientific practice and today emphasizes the diversity of methods and of the means of discovery and justification [4,5] The scientific method is what scientists ... only the testing of hypotheses, not their discovery, constitutes science and is covered by the scientific method This is an outdated idea The philosopher Hans Reichenbach [3] introduced the notions ... or acceptance of hypotheses, rather than an assessment of degrees of likelihood The p value in null hypothesis testing represents the probability of the data if the null hypothesis is true We believe...

Ngày tải lên: 20/06/2014, 01:20

... first approach the authors used the tracking method and in the second approach they introduced a discrete analogue of dichotomy and trichotomy in variation A new step in the study of the exponential ... associated integral equation and on the uniform boundedness of the norm of solution relative to the norm of the input function Using detailed and constructive methods we will prove that this assures the ... Difference Equations priori the existence of the projection families, without supposing the invariance with respect to the projection families or the invertibility on the unstable subspace or on the...

Ngày tải lên: 21/06/2014, 05:20

... Theorem 3.4 and relation (2.15) the proof immediately follows We are now ready to answer the question concerning the values assumed by the polynomials ρk−1 (z) and σk (z) on the unit circle Theorem ... 1) and (eiθ − 1) The stability problem for the top order family The results obtained in the previous section permit to attack the question concerning the stability problem for the k-step methods ... modulus and σk (z) has not roots of unit modulus Then, the assertions of the theorem follow from Remark 4.1 We are now in the position to give the main results related to the stability problem Theorem...

Ngày tải lên: 23/06/2014, 00:20

... –0.8 to –0.3 l/min), and QTTHERM never underestimated QTFICK In the study by Dhingra et al [31], looking at the data suggests that the thermodilution method and the metabolic method were probably ... (Fick) method (QTFICK) according to (a) the Bland and Altman graphic method [28], and (b) the Passing and Bablok regression method [29] Determined using the whole set of data after removal of ... determined using the metabolic (Fick) method (QTFICK) against cardiac output determined using the thermodilution method (QTTHERM) [29] restricted to (a) QTTHERM values < l/min and (b) QTTHERM values...

Ngày tải lên: 12/08/2014, 19:21

... general theorems and establish some new integral inequalities Also we will give some examples so as to illustrate the validity of the present integral inequalities Main results In the rest of the ... denote the set of real numbers as R, and R+ = [0, ∞) is a subset of R Dom(f) and Im(f) denote the definition domain and the image of f, respectively Theorem 2.1: Assume that x, a Î C(R+, R+) and ... completed the proof Remark 4: If h(s, t) ≡ 0, a1(t) = a2(t) = a(t), then Theorem 2.2 becomes Theorem C [10, Theorem 1] Now we will apply the concept of establishing Theorem 2.2 to the situation...

Ngày tải lên: 21/06/2014, 01:20

... concentrations and storm runoff loads The total pollutant loads during the observation period in the dry year of 2005 and the average year of 2003 became smaller than those in the rainy year of 2004 Therefore, ... trisections in the flowing water width Analytical Methods After measuring the water temperature, electrical conductivity, DO and turbidity of the three samples individually at the observation point and ... matter The water samples taken at the three points spanning the river during the five flooding-stages were analyzed individually, and the representative concentrations were determined as the arithmetical...

Ngày tải lên: 05/09/2013, 09:38

... x; y: (KBE) The variables t0 and x in KBE  are called the backward variables In the case that a and are functions of x alone, pt0; t1 ; x; y  depends on t0 and t1 only through their difference ... can use Itˆ ’s formula to prove the Feynman-Kac Theorem, and use o the Feynman-Kac Theorem to derive the Kolmogorov backward equation 16.6 Black-Scholes Consider the SDE dS t = rS t dt + S ... on t0 and t1 only through their difference t1 , t0 This is always the case when at; x and t; x don’t depend on t Example 16.4 (Geometric Brownian motion) Recall that the solution to the SDE...

Ngày tải lên: 18/10/2013, 03:20

... all global banks These banks vary widely in their structures and activities, and therefore in the nature and degree of risks they pose to the international financial system Hence, the quantitative ... commodities, CDS and unallocated) 47 The indicator for each bank is calculated as the ratio of the notional amount outstanding for the bank and the sum total of the amounts reported by all banks in the sample ... Assessment methodology and the additional loss absorbency requirement on the trial scores of the banks, the Basel Committee is of the view that four equal sized buckets between the cut-off score and the...

Ngày tải lên: 06/03/2014, 09:20