That is only conventional (straight-line) tomography is concerned. In this work, HOS is used to describe the scattered wavefield. So far the theory of diffraction tomography is limited to the linear case, using Born and Rytov approximation and only second-order statistics such as convolution and correlation is Cited by: 1. Electromagnetic Scintillation describes the phase and amplitude fluctuations imposed on signals that travel through the atmosphere. These volumes provide a modern reference and comprehensive tutorial for this subject, treating both optical and microwave propagation. Measurements and predictions are integrated at each step of the development. Second Order Differential Equations presents a classical piece of theory concerning hypergeometric special functions as solutions of second-order linear differential equations. The theory is presented in an entirely self-contained way, starting with an introduction of the solution of the second-order differential equations and then focusingon Cited by: This is formally equivalent to the second-order Rytov approximation for 1-D random media, which has the remarkable property of accounting for backscattered waves. A general description of scattering attenuation in 3-D anisotropic random media, which reduces in the layered-media limit to the results of the ODA approach, has not been reported so by:

Field guide to atmospheric optics. [Larry C Andrews] -- The material in this Field Guide includes a review of classical Kolmogorov turbulence theory, Gaussian-beam waves in free space, and atmospheric effects on a propagating optical wave. second-order statistics --Rytov approximation --Extended Huygens-Fresnel principle --Parabolic. Recognizing the inherent non‐linear characteristics of natural frequency constraints, a second order Taylor series approximation for each eigenvalue of the equations of motion is derived and applied successfully to improve stability and overall efficiency of the automated synthesis process. Second Order Approximation Methods for DSGE Models The University of York Dr. Nicola Branzoli June Contents 1 Introduction 2 2 Starting Examples 3. SECOND ORDER SOLUTION 5 2. THE GENERAL FORM OF THE MODEL We suppose a model that takes the form (1) K n×1 (wt n×1,wt−1,σεt m×1)+Πσηt p×1 =0, where Etηt+1 =0 and Etεt+1 =0. The equations hold for t =0,,∞, as does the Etεt+1 = 0 condition. The disturbances εt are exogenously given, while ηt is determined as a func- tion of εwhen the model is solved, if the solution exists.

A second-order accurate numerical approximation for the fractional diﬀusion equation Charles Tadjeran a, Mark M. Meerschaert b,*, Hans-Peter Scheﬄer c a Department of Physics, University of Nevada, Reno, NV , USA b Department of Mathematics and Statistics, University of Otago, Room A, Dunedin , New Zealand c Department of Mathematics and Statistics, University of Nevada, Reno. The approximation is computed around the non-stochastic steady state, where σ = 0. Without loss of generality, we will assume that f(0,0,0,0) = 0 3 Second-order Taylor expansions As stated in Magnus and Neudecker (), the second-order Taylor expansion of a twice diﬀerentiable function f: Rn → Rm is given by f(x) ≈ f(x0)+[Df(x0)](x Cited by: Expressive power. Second-order logic is more expressive than first-order logic. For example, if the domain is the set of all real numbers, one can assert in first-order logic the existence of an additive inverse of each real number by writing ∀x ∃y (x + y = 0) but one needs second-order logic to assert the least-upper-bound property for sets of real numbers, which states that every bounded.