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Statistical Wave Content of Radiative Transfer Theory
Published in L.A. Apresyan, Yu.A. Kravtsov, M.G. Edelev, Radiation Transfer, 2019
L.A. Apresyan, Yu.A. Kravtsov, M.G. Edelev
In the general case, equations (3.3.1) and (3.3.12) cannot be solved exactly. However, a general methods exists that allows one to express the solution of the problem as an infinite series expansion in powers of V. This method assumes that the operator V is small and uses it as a perturbation. The respective series of perturbation theory are also known as Neumann series. They can be obtained by iteration of the integral form of the initial equation. For example, iterating eqn (3.3.11) we have G=G0+G0VG0+G0VG0VG0+G0VG0VG0VG0+…=Σn=0∞G0(VG0)n⋅(3.3.17)
Stabilisation of non-diagonal infinite-dimensional systems with delay boundary control
Published in International Journal of Control, 2023
Following the ideas in Krstic (2009b, Section 2.2), we model the delay in (14) by the following first-order hyperbolic PDE System (14) can now be written as Then, we consider the backstepping transfomation with which we want to map the above system into the target system Performing similar computations as in Krstic (2009b, Equations (2.26)–(2.39)), and recalling that is Hurwitz, we get that So, the stabilising control is given in an implicit form as and We have to solve the above fixed point implicit equation. To this end, for any integrable vector F on , we define It follows that can be written as the Neumann series We can show the convergence of this series in a similar manner as in Prieur and Trelat (2019, Lemma 3).
Novel Detectors for Massive MU-MIMO Communications
Published in IETE Journal of Research, 2020
Ye-Shun Shen, Fang-Biau Ueng, Chin-Yang Kung
In massive MU-MIMO system, we have to solve the problem of huge channel information in receiver. Therefore, low-complexity signal detectors personate an important role. We employ three methods based on MMSE to solve this problem. The methods are Neumann series expansion, SOR, and SSOR. By MMSE equalizer, the equalized output signal can be denoted as follows: We can rewrite (40) as follows: where ,, and define .
New iterative reconstruction methods for fan-beam tomography
Published in Inverse Problems in Science and Engineering, 2018
Daniil Kazantsev, Valery Pickalov
The projection matrix can be decomposed as , where is some known approximation to the unknown operator . Using the Neumann series decomposition [27] one can re-write operator as