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Journal articles on the topic 'Neumann expansion'

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Published: 6 September 2023

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1

Exton, Harold. "Generalized Neumann and Kapteyn expansions." Journal of Applied Mathematics and Stochastic Analysis 8, no. 4 (January 1, 1995): 415–21. http://dx.doi.org/10.1155/s1048953395000384.

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Certain formal series of a most general nature are specialized so as to deduce expansions in terms of a class of generalized hypergeometric functions. These series generalize the Neumann and Kapteyn series in the theory of Bessel functions, and their convergence is investigated. An example of a succinct expansion is also given.

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2

Yang, Q. W. "Model reduction by Neumann series expansion." Applied Mathematical Modelling 33, no. 12 (December 2009): 4431–34. http://dx.doi.org/10.1016/j.apm.2009.02.012.

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3

Marksteiner, P., E. Badralexe, and A. J. Freeman. "Neumann-Type Expansion of Coulomb Functions." Journal of Computational Physics 111, no. 1 (March 1994): 49–52. http://dx.doi.org/10.1006/jcph.1994.1042.

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4

Lallemand, B., G. Plessis, T. Tison, and P. Level. "Neumann expansion for fuzzy finite element analysis." Engineering Computations 16, no. 5 (August 1999): 572–83. http://dx.doi.org/10.1108/02644409910277933.

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5

Yamazaki, Fumio, Associate Member, Masanobu Shinozuka, and Gautam Dasgupta. "Neumann Expansion for Stochastic Finite Element Analysis." Journal of Engineering Mechanics 114, no. 8 (August 1988): 1335–54. http://dx.doi.org/10.1061/(asce)0733-9399(1988)114:8(1335).

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6

Chakraborty, Subrata, and Santi Sekhar Dey. "Stochastic Finite Element Simulation of Uncertain Structures Subjected to Earthquake." Shock and Vibration 7, no. 5 (2000): 309–20. http://dx.doi.org/10.1155/2000/730364.

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In present study, the stochastic finite element simulation based on the efficient Neumann expansion technique is extended for the analysis of uncertain structures under seismically induced random ground motion. The basic objective is to investigate the possibility of applying the Neumann expansion technique coupled with the Monte Carlo simulation for dynamic stochastic systems upto that extent of parameter variation after which the method is no longer gives accurate results compared to that of the direct Monte carlo simulation. The stochastic structural parameters are discretized by the local averaging method and then simulated by Cholesky decomposition of the respective covariance matrix. The earthquake induced ground motion is treated as stationary random process defined by respective power spectral density function. Finally, the finite element solution has been obtained in frequency domain utilizing the advantage of Neumann expansion technique.

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7

Marušić, S. "An asymptotic expansion for the Neumann sieve problem." Russian Journal of Mathematical Physics 15, no. 1 (March 2008): 89–97. http://dx.doi.org/10.1134/s106192080801010x.

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8

López, José L., and Ester Pérez Sinusía. "The Liouville–Neumann expansion in singular eigenvalue problems." Applied Mathematics Letters 25, no. 1 (January 2012): 72–76. http://dx.doi.org/10.1016/j.aml.2011.07.011.

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9

Wang, Xiangyu, Song Cen, and Chenfeng Li. "Generalized Neumann Expansion and Its Application in Stochastic Finite Element Methods." Mathematical Problems in Engineering 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/325025.

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An acceleration technique, termed generalized Neumann expansion (GNE), is presented for evaluating the responses of uncertain systems. The GNE method, which solves stochastic linear algebraic equations arising in stochastic finite element analysis, is easy to implement and is of high efficiency. The convergence condition of the new method is studied, and a rigorous error estimator is proposed to evaluate the upper bound of the relative error of a given GNE solution. It is found that the third-order GNE solution is sufficient to achieve a good accuracy even when the variation of the source stochastic field is relatively high. The relationship between the GNE method, the perturbation method, and the standard Neumann expansion method is also discussed. Based on the links between these three methods, quantitative error estimations for the perturbation method and the standard Neumann method are obtained for the first time in the probability context.

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10

Bae, Ha-Rok, and Edwin E. Forster. "Improved Neumann Expansion Method for Stochastic Finite Element Analysis." Journal of Aircraft 54, no. 3 (May 2017): 967–79. http://dx.doi.org/10.2514/1.c033883.

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11

López, José L. "The Liouville–Neumann expansion at a regular singular point." Journal of Difference Equations and Applications 15, no. 2 (February 2009): 119–32. http://dx.doi.org/10.1080/10236190801980750.

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12

Zeitoun, D. G., and C. Braester. "A Neumann expansion approach to flow through heterogeneous formations." Stochastic Hydrology and Hydraulics 5, no. 3 (September 1991): 207–26. http://dx.doi.org/10.1007/bf01544058.

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13

Gottlieb, H. P. W. "Eigenvalues of the Laplacian with Neumann boundary conditions." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 26, no. 3 (January 1985): 293–309. http://dx.doi.org/10.1017/s0334270000004525.

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AbstractVarious grometrical properties of a domain may be elicited from the asymptotic expansion of a spectral function of the Laplacian operator for that region with apporpriate boundary conditions. Explicit calculations, using analytical formulae for the eigenvalues, are performed for the cases fo Neumann and mixed boundary conditions, extending earlier work involving Dirichet boundary conditions. Two- and three-dimensional cases are considered. Simply-connected regions dealt with are the rectangle, annular sector, and cuboid. Evaluations are carried out for doubly-connected regions, including the narrow annulus, annular cylinder, and thin concentric spherical cavity. The main summation tool is the Poission summation formula. The calculations utilize asymptotic expansions of the zeros of the eigenvalue equations involving Bessel and related functions, in the cases of curved boundaries with radius ratio near unity. Conjectures concerning the form of the contributions due to corners, edges and vertices in the case of Neumann and mixed boundary conditions are presented.

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14

Purushotham, M. "Economic Transmission Expansion Planning by using Von Neumann-Morgestern Criterion." International Journal for Research in Applied Science and Engineering Technology 7, no. 10 (October 31, 2019): 246–55. http://dx.doi.org/10.22214/ijraset.2019.10037.

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15

Guo, Huan, Yoshino Tatsuo, Lulu Fan, Ao Ding, Tianshuang Xu, and Genyuan Xing. "Biobjective Optimization Algorithms Using Neumann Series Expansion for Engineering Design." Applied Bionics and Biomechanics 2018 (December 19, 2018): 1–13. http://dx.doi.org/10.1155/2018/7071647.

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In this paper, two novel algorithms are designed for solving biobjective optimization engineering problems. In order to obtain the optimal solutions of the biobjective optimization problems in a fast and accurate manner, the algorithms, which have combined Newton’s method with Neumann series expansion as well as the weighted sum method, are applied to deal with two objectives, and the Pareto optimal front is achieved through adjusting weighted factors. Theoretical analysis and numerical examples demonstrate the validity and effectiveness of the proposed algorithms. Moreover, an effective biobjective optimization strategy, which is based upon the two algorithms and the surrogate model method, is developed for engineering problems. The effectiveness of the optimization strategy is proved by its application to the optimal design of the dummy head structure in the car crash experiments.

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16

López, José L. "The Liouville–Neumann expansion in one-dimensional boundary value problems." Integral Transforms and Special Functions 21, no. 2 (February 2010): 125–33. http://dx.doi.org/10.1080/10652460903056436.

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17

Fang, Licai, and Defeng Huang. "Neumann Series Expansion Based LMMSE Channel Estimation for OFDM Systems." IEEE Communications Letters 20, no. 4 (April 2016): 748–51. http://dx.doi.org/10.1109/lcomm.2016.2526624.

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18

Tomy, Gladwin Jos Kurupasseril, and Kalarickaparambil Joseph Vinoy. "Neumann-Expansion-Based FEM for Uncertainty Quantification of Permittivity Variations." IEEE Antennas and Wireless Propagation Letters 19, no. 4 (April 2020): 561–65. http://dx.doi.org/10.1109/lawp.2020.2971963.

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19

Lee, Jae Han, and Byung Man Kwak. "Reliability-based structural optimal design using the Neumann expansion technique." Computers & Structures 55, no. 2 (April 1995): 287–96. http://dx.doi.org/10.1016/0045-7949(94)00439-a.

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20

Färe, Rolf, Daniel Primont, and William L. Weber. "Technical change and the von Neumann coefficient of uniform expansion." European Journal of Operational Research 280, no. 2 (January 2020): 754–63. http://dx.doi.org/10.1016/j.ejor.2019.07.033.

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21

Beals, Richard, and Nancy K. Stanton. "The Heat Equation for the -Neumann Problem, II." Canadian Journal of Mathematics 40, no. 2 (April 1, 1988): 502–12. http://dx.doi.org/10.4153/cjm-1988-021-8.

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Let Ω be a compact complex n + 1-dimensional Hermitian manifold with smooth boundary M. In [2] we proved the following.THEOREM 1. Suppose satisfies condition Z(q) with 0 ≦ q ≦ n. Let □p,q denote the -Laplacian on (p, q) forms onwhich satisfy the -Neumann boundary conditions. Then as t → 0;,(0.1)(If q = n + 1, the -Neumann boundary condition is the Dirichlet boundary condition and the corresponding result is classical.)Theorem 1 is a version for the -Neumann problem of results initiated by Minakshisundaram and Pleijel [8] for the Laplacian on compact manifolds and extended by McKean and Singer [7] to the Laplacian with Dirichlet or Neumann boundary conditions and by Greiner [5] and Seeley [9] to elliptic boundary value problems on compact manifolds with boundary. McKean and Singer go on to show that the coefficients in the trace expansion are integrals of local geometric invariants.

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22

Zhuge, Jinping. "First-order expansions for eigenvalues and eigenfunctions in periodic homogenization." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 5 (March 20, 2019): 2189–215. http://dx.doi.org/10.1017/prm.2019.8.

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AbstractFor a family of elliptic operators with periodically oscillating coefficients, $-{\rm div}(A(\cdot /\varepsilon )\nabla )$ with tiny ε > 0, we comprehensively study the first-order expansions of eigenvalues and eigenfunctions (eigenspaces) for both the Dirichlet and Neumann problems in bounded, smooth and strictly convex domains (or more general domains of finite type). A new first-order correction term is introduced to derive the expansion of eigenfunctions in L2 or $H^1_{\rm loc}$. Our results rely on the recent progress on the homogenization of boundary layer problems.

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23

Karch, G. "Asymptotics of solutions to a convection—diffusion equation on the half-line." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 4 (August 2000): 837–53. http://dx.doi.org/10.1017/s0308210500000469.

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We study the behaviour, as t → ∞, of solutions to the convectiondiffusion equation on the half-line with the homogeneous Neumann boundary condition and with bounded initial data. The higher-order terms of the asymptotic expansion in Lp (R+) of solutions are derived.

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24

Kijowski, M., and L. Klinkenbusch. "Eigenmode analysis of the electromagnetic field scattered by an elliptic cone." Advances in Radio Science 9 (July 29, 2011): 31–37. http://dx.doi.org/10.5194/ars-9-31-2011.

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Abstract. The vector spherical-multipole analysis is applied to determine the scattering of a plane electromagnetic wave by a perfectly electrically conducting (PEC) semi-infinite elliptic cone. From the eigenfunction expansion of the total field in the space outside the elliptic cone, the scattered far field is obtained as a multipole expansion of the free-space type by a single integration over the induced surface currents. As for the evaluation of the free-space-type expansion it is necessary to apply suitable series transformation techniques, a sufficient number of eigenfunctions has to be considered. The eigenvalues of the underlying two-parametric eigenvalue problem with two coupled Lamé equations belong to the Dirichlet- or the Neumann condition and can be arranged as so-called eigenvalue curves. It has been observed that the eigenvalues are in two different domains: In the first one Dirichlet- and Neumann eigenvalues are either nearly coinciding, while in the second one they are strictly separated. The eigenfunctions of the first (coinciding) type look very similar to free-space modes and do not contribute to the scattered field. This observation allows to significantly improve the determination of diffraction coefficients.

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25

Weiss, Chester J., and G. Bart van Bloemen Waanders. "On the convergence of the Neumann series for electrostatic fracture response." GEOPHYSICS 84, no. 2 (March 1, 2019): E47—E55. http://dx.doi.org/10.1190/geo2018-0564.1.

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The feasibility of Neumann-series expansion of Maxwell’s equations in the electrostatic limit is investigated for potentially rapid and approximate subsurface imaging of geologic features proximal to metallic infrastructure in an oilfield environment. Although generally useful for efficient modeling of mild conductivity perturbations in uncluttered settings, we have raised the question of its suitability for situations such as oilfields, in which metallic artifacts are pervasive and, in some cases, in direct electrical contact with the conductivity perturbation on which the Neumann series is computed. Convergence of the Neumann series and its residual error are computed using the hierarchical finite-element framework for a canonical oilfield model consisting of an L-shaped, steel-cased well, energized by a steady-state electrode, and penetrating a small set of mildly conducting fractures near the heel of the well. For a given node spacing [Formula: see text] in the finite-element mesh, we find that the Neumann series is ultimately convergent if the conductivity is small enough — a result consistent with previous presumptions on the necessity of small conductivity perturbations. However, we also determine that the spectral radius of the Neumann series operator grows as approximately [Formula: see text], thus suggesting that in the limit of the continuous problem [Formula: see text], the Neumann series is intrinsically divergent for all conductivity perturbations, regardless of their smallness. The hierarchical finite-element methodology itself is critically analyzed and shown to possess the [Formula: see text] error convergence of traditional linear finite elements, thereby supporting the conclusion of an inescapably divergent Neumann series for this benchmark example. Application of the Neumann series to oilfield problems with metallic clutter should therefore be done with careful consideration to the coupling between infrastructure and geology. The methods used here are demonstrably useful in such circumstances.

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26

Liu, Genqian, and Xiaoming Tan. "Spectral invariants of the magnetic Dirichlet-to-Neumann map on Riemannian manifolds." Journal of Mathematical Physics 64, no. 4 (April 1, 2023): 041501. http://dx.doi.org/10.1063/5.0088549.

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This paper is devoted to investigating the heat trace asymptotic expansion associated with the magnetic Steklov problem on a smooth compact Riemannian manifold (Ω, g) with smooth boundary ∂Ω. By computing the full symbol of the magnetic Dirichlet-to-Neumann map [Formula: see text], we establish an effective procedure, by which we can calculate all the coefficients a0, a1, …, a n−1 of the asymptotic expansion. In particular, we explicitly give the first four coefficients a0, a1, a2, and a3. They are spectral invariants, which provide precise information concerning the volume and curvatures of the boundary ∂Ω and some physical quantities.

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27

DOWKER, J. S., K. KIRSTEN, and P. B. GILKEY. "ON PROPERTIES OF THE ASYMPTOTIC EXPANSION OF THE HEAT TRACE FOR THE N/D PROBLEM." International Journal of Mathematics 12, no. 05 (July 2001): 505–17. http://dx.doi.org/10.1142/s0129167x01000927.

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The spectral problem where the field satisfies Dirichlet conditions on one part of the boundary of the relevant domain and Neumann on the remainder is discussed. It is shown that there does not exist a classical asymptotic expansion for short time in terms of fractional powers of t with locally computable coefficients.

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28

Chen, Xi, Yongkang Wu, Yuzhen Yu, and Kok-Kwang Phoon. "Performance of Neumann Expansion Preconditioners for Iterative Methods with Geotechnical Elastoplastic Applications." International Journal of Geomechanics 16, no. 3 (June 2016): 04015069. http://dx.doi.org/10.1061/(asce)gm.1943-5622.0000561.

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29

Kasiselvanathan, M., S. Lakshminarayanan, J. Prasad, K. B. Gurumoorthy, and S. Allwin Devaraj. "Performance Analysis of MIMO System Using Fish Swarm Optimization Algorithm." International Journal of Electrical and Electronics Research 10, no. 2 (June 30, 2022): 167–70. http://dx.doi.org/10.37391/ijeer.100220.

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During the signal identification process, massive multiple-input multiple-output (MIMO) systems must manage a high quantity of matrix inversion operations. To prevent exact matrix inversion in huge MIMO systems, several strategies have been presented, which can be loosely classified into similarity measures and evolutionary computation. In the existing Neumann series expansion and Newton methods, the initial value will be taken as zero as a result wherein the closure speed will be slowed and the prediction of the channel state information is not done properly. In this paper, fish swarm optimization algorithm is proposed in which initial values are chosen optimally for ensuring the faster and accurate signal detection with reduced complexity. The optimal values are chosen between 0 to 1 value and the initial arbitrary values are chosen based on number of input signals. In the proposed work, Realistic condition based channel state information prediction is done by using machine learning algorithm. Simulation results demonstrate that the suggested receiver's bit error rate performance characteristics employing the Quadrature Amplitude Modulation (QAM) methodology outperform the existing Neumann series expansion and Newton methods.

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30

Newman, J. N. "Evaluation of the Wave-Resistance Green Function: Part 2—The Single Integral on the Centerplane." Journal of Ship Research 31, no. 03 (September 1, 1987): 145–50. http://dx.doi.org/10.5957/jsr.1987.31.3.145.

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Effective series expansions are derived for the evaluation of the single integral in the potential of a submerged source which moves with constant velocity, when the source and field point are in the same longitudinal centerplane. In conjunction with the polynomial approximations for the double integral component which have been derived in Part 1 of this work, the present results facilitate the computation of the source potential or Green function. Three complementary domains of the centerplane are considered, with different expansions developed for use in each domain. The principal expansion is based on a Neumann series which is effective for small or moderate distances from the origin, except in a thin region near the free surface. To deal with the latter domain an asymptotic expansion is derived in ascending powers of the vertical coordinate. Both of these expansions are refined by subtracting a simpler component with the same behavior at the origin, and relating this component to Dawson's integral. Special algorithms for the evaluation of the latter function are presented in the Appendix. The third and final expansion, based upon the method of steepest descents, is effective at large distances from the origin. This asymptotic series is derived by a systematic recursive scheme to permit an arbitrary order of the approximation. Used in conjunction with the first two expansions, this permits the single integral to be evaluated with an absolute accuracy of six decimals throughout the centerplane.

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31

Zare Hosseinzadeh, Ali, Gholamreza Ghodrati Amiri, and Seyed Ali Seyed Razzaghi. "Model-based identification of damage from sparse sensor measurements using Neumann series expansion." Inverse Problems in Science and Engineering 25, no. 2 (March 21, 2016): 239–59. http://dx.doi.org/10.1080/17415977.2016.1160393.

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32

Yuan, Jie, Giuliano Allegri, Fabrizio Scarpa, Sophoclis Patsias, and Ramesh Rajasekaran. "A novel hybrid Neumann expansion method for stochastic analysis of mistuned bladed discs." Mechanical Systems and Signal Processing 72-73 (May 2016): 241–53. http://dx.doi.org/10.1016/j.ymssp.2015.11.011.

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33

Quaba, Awf. "Reconstruction of a Posttraumatic Ear Defect Using Tissue Expansion: 30 Years after Neumann." Plastic and Reconstructive Surgery 82, no. 3 (September 1988): 521–24. http://dx.doi.org/10.1097/00006534-198809000-00029.

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34

Budziński, J., and S. Prajsnar. "Neumann expansion of the interelectronic distance function for integer powers. I. General formula." Journal of Chemical Physics 101, no. 12 (December 15, 1994): 10783–89. http://dx.doi.org/10.1063/1.467891.

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35

Chen, Hua Yun. "Representations of efficient score for coarse data problems based on Neumann series expansion." Annals of the Institute of Statistical Mathematics 63, no. 3 (May 6, 2009): 497–509. http://dx.doi.org/10.1007/s10463-009-0231-7.

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36

Kawabata, Kiyoshi, and Takehiko Satoh. "Numerical computations of Neumann expansion coefficients of Chandrasekhar's H-function for isotropic scattering." Journal of Quantitative Spectroscopy and Radiative Transfer 47, no. 1 (January 1992): 1–8. http://dx.doi.org/10.1016/0022-4073(92)90074-e.

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37

Gottlieb, H. P. W. "Eigenvalues of the Laplacian for rectilinear regions." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 29, no. 3 (January 1988): 270–81. http://dx.doi.org/10.1017/s0334270000005804.

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AbstractFrom a knowledge of the eigenvalue spectrum of the Laplacian on a domain, one may extract information on the geometry and boundary conditions by analysing the asymptotic expansion of a spectral function. Explicit calculations are performed for isosceles right-angle triangles with Dirichlet or Neumann boundary conditions, yielding in particular the corner angle terms. In three dimensions, right prisms are dealt with, including the solid vertex terms.

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38

ZAKHARIAN, A. R., M. BRIO, J. K. HUNTER, and G. M. WEBB. "The von Neumann paradox in weak shock reflection." Journal of Fluid Mechanics 422 (November 3, 2000): 193–205. http://dx.doi.org/10.1017/s0022112000001609.

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We present a numerical solution of the Euler equations of gas dynamics for a weak-shock Mach reflection in a half-space. In our numerical solutions, the incident, reflected, and Mach shocks meet at a triple point, and there is a supersonic patch behind the triple point, as proposed by Guderley. A theoretical analysis supports the existence of an expansion fan at the triple point, in addition to the three shocks. This solution is in complete agreement with the numerical solution of the unsteady transonic small-disturbance equations obtained by Hunter & Brio (2000), which provides an asymptotic description of a weak-shock Mach reflection. The supersonic patch is extremely small, and this work is the first time it has been resolved in a numerical solution of the Euler equations. The numerical solution uses six levels of grid refinement around the triple point. A delicate combination of numerical techniques is required to minimize both the effects of numerical diffusion and the generation of numerical oscillations at grid interfaces and shocks.

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39

Wiegmann, P., and A. Zabrodin. "Dyson gas on a curved contour." Journal of Physics A: Mathematical and Theoretical 55, no. 16 (March 24, 2022): 165202. http://dx.doi.org/10.1088/1751-8121/ac5a8f.

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Abstract We introduce and study a model of a logarithmic gas with inverse temperature β on an arbitrary smooth closed contour in the plane. This model generalizes Dyson’s gas (the β-ensemble) on the unit circle. We compute the non-vanishing terms of the large N expansion of the free energy (N is the number of particles) by iterating the ‘loop equation’ that is the Ward identity with respect to reparametrizations and dilatation of the contour. We show that the main contribution to the free energy is expressed through the spectral determinant of the Neumann jump operator associated with the contour, or equivalently through the Fredholm determinant of the Neumann–Poincare (double layer) operator. This result connects the statistical mechanics of the Dyson gas to the spectral geometry of the interior and exterior domains of the supporting contour.

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40

Se-Yun Kim and Jung-Woong Ra. "Diffraction by a dielectric wedge with the neumann expansion of correction currents on interfaces." Electronics Letters 23, no. 12 (1987): 630. http://dx.doi.org/10.1049/el:19870451.

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41

Xu, Shengqiang, and Jinqiao Duan. "A Taylor expansion approach for solving partial differential equations with random Neumann boundary conditions." Applied Mathematics and Computation 217, no. 23 (August 2011): 9532–42. http://dx.doi.org/10.1016/j.amc.2011.03.137.

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42

Shenavar, Hossein, and Kurosh Javidan. "A Modified Dynamical Model of Cosmology I Theory." Universe 6, no. 1 (December 19, 2019): 1. http://dx.doi.org/10.3390/universe6010001.

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Wheeler (1964) had formulated Mach’s principle as the boundary condition for general relativistic field equations. Here, we use this idea and develop a modified dynamical model of cosmology based on imposing Neumann boundary condition on cosmological perturbation equations. Then, it is shown that a new term appears in the equation of motion, which leads to a modified Poisson equation. In addition, a modified Hubble parameter is derived due to the presence of the new term. Moreover, it is proved that, without a cosmological constant, such a model has a late time-accelerated expansion with an equation of state converging to w < − 1 . Also, the luminosity distance in the present model is shown to differ from that of the Λ C D M model at high redshifts. Furthermore, it is found that the adiabatic sound speed squared is positive in radiation-dominated era and then converges to zero at later times. Theoretical implications of the Neumann boundary condition have been discussed, and it is shown that, by fixing the value of the conjugate momentum (under certain conditions), one could derive a similar version of modified dynamics. In a future work, we will confine the free parameters of the Neumann model based on hype Ia Supernovae, Hubble parameter data, and the age of the oldest stars.

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43

CAO, LI-QUN. "ASYMPTOTIC EXPANSION AND CONVERGENCE THEOREM OF CONTROL AND OBSERVATION ON THE BOUNDARY FOR SECOND-ORDER ELLIPTIC EQUATION WITH HIGHLY OSCILLATORY COEFFICIENTS." Mathematical Models and Methods in Applied Sciences 14, no. 03 (March 2004): 417–37. http://dx.doi.org/10.1142/s0218202504003295.

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In this paper, we shall study systems governed by the Neumann problem of second-order elliptic equation with rapidly oscillating coefficients and with control and observations on the boundary. The multiscale asymptotic expansions of the solution for considering problem in the case without any constraints, and homogenized equation in the case with constraints will be given, their rigorous proofs will also be proposed.

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44

Ardenghi, Juan Sebastián. "Entanglement entropy between virtual and real excitations in quantum electrodynamics." International Journal of Modern Physics A 33, no. 13 (May 9, 2018): 1850081. http://dx.doi.org/10.1142/s0217751x18500811.

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The aim of this work is to introduce the entanglement entropy of real and virtual excitations of fermion and photon fields. By rewriting the generating functional of quantum electrodynamics theory as an inner product between quantum operators, it is possible to obtain quantum density operators representing the propagation of real and virtual particles. These operators are partial traces, where the degrees of freedom traced out are unobserved excitations. Then the von Neumann definition of entropy can be applied to these quantum operators and in particular, for the partial traces taken over by the internal or external degrees of freedom. A universal behavior is obtained for the entanglement entropy for different quantum fields at zeroth order in the coupling constant. In order to obtain numerical results at different orders in the perturbation expansion, the Bloch–Nordsieck model is considered, where it is shown that for some particular values of the electric charge, the von Neumann entropy increases or decreases with respect to the noninteracting case.

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45

Bush, W. B., and L. Krishnamurthy. "Asymptotic analysis of the structure of a steady planar detonation: Review and extension." Mathematical Problems in Engineering 5, no. 3 (1999): 223–54. http://dx.doi.org/10.1155/s1024123x99001076.

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The structure of a steady planar Chapman–Jouguet detonation, which is supported by a direct first-order one-step irreversible exothermic unimolecular reaction, subject to Arrhenius kinetics, is examined. Solutions are studied, by means of a limit-process-expansion analysis, valid forΛ, proportional to the ratio of the reaction rate to the flow rate, going to zero, and forβ, proportional to the ratio of the activation temperature to the maximum flow temperature, going to infinity, with the productΛβ1/2going to zero. The results, essentially in agreement with the Zeldovich–von Neumann–Doring model, show that the detonation consists of (1) a three-region upstream shock-like zone, wherein convection and diffusion dominate; (2) an exponentially thicker five-region downstream deflagration-like zone, wherein convection and reaction dominate; and (3) a transition zone, intermediate to the upstream and downstream zones, wherein convection, diffusion, and reaction are of the same order of magnitude. It is in this transition zone that the ideal Neumann state is most closely approached.

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46

Nazarov, S. A., and O. R. Polyakova. "Asymptotic expansion of eigenvalues of the neumann problem in a domain with a thin bridge." Siberian Mathematical Journal 33, no. 4 (1992): 618–33. http://dx.doi.org/10.1007/bf00971127.

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Yang, QW. "A new biased estimation method based on Neumann series for solving ill-posed problems." International Journal of Advanced Robotic Systems 16, no. 4 (July 2019): 172988141987205. http://dx.doi.org/10.1177/1729881419872058.

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The ill-posed least squares problems often arise in many engineering applications such as machine learning, intelligent navigation algorithms, surveying and mapping adjustment model, and linear regression model. A new biased estimation (BE) method based on Neumann series is proposed in this article to solve the ill-posed problems more effectively. Using Neumann series expansion, the unbiased estimate can be expressed as the sum of infinite items. When all the high-order items are omitted, the proposed method degenerates into the ridge estimation or generalized ridge estimation method, whereas a series of new biased estimates can be acquired by including some high-order items. Using the comparative analysis, the optimal biased estimate can be found out with less computation. The developed theory establishes the essential relationship between BE and unbiased estimation and can unify the existing unbiased and biased estimate formulas. Moreover, the proposed algorithm suits for not only ill-conditioned equations but also rank-defect equations. Numerical results show that the proposed BE method has improved accuracy over the existing robust estimation methods to a certain extent.

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48

Salem, Mohamed A., Aladin H. Kamel, and Andrey V. Osipov. "Electromagnetic fields in the presence of an infinite dielectric wedge." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2072 (March 31, 2006): 2503–22. http://dx.doi.org/10.1098/rspa.2006.1691.

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Electromagnetic fields excited by a line source in the presence of an infinite dielectric wedge with refractive index N are determined by application of the Kontorovich–Lebedev transform. Singular integral equations for spectral functions are solved by perturbation procedure, and the solution is obtained in the form of a Neumann series in powers of . The devised numerical scheme permits evaluation of the higher-order terms and, thus, extends the perturbation solution to values of N not necessarily close to unity. Asymptotic approximations for the near and far fields inside and outside the dielectric wedge are derived. The combination of the Neumann-type expansion of the transform functions with the representation of the field as a Bessel function series extends solutions derived with the Kontorovich–Lebedev method to the case of real-valued wavenumbers and arbitrarily positioned source and observer. Numerical results showing the influence of wedges with various values of dielectric and magnetic constants on the directivity of a line source are presented and verified through finite-difference frequency-domain simulations.

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Wang, Aifeng, and Mingkang Ni. "The Step-Type Contrast Structure for High Dimensional Tikhonov System with Neumann Boundary Conditions." Discrete Dynamics in Nature and Society 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/4569198.

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We investigate the step-type contrast structure for high dimensional Tikhonov system with Neumann boundary conditions. We not only propose a key condition with the existence of the number of mutually independent first integrals under which there exists a step-type contrast structure, but also determine where an internal transition time is. Using the method of boundary function, we construct the formal asymptotic solution and give the analytical expression for the higher order terms. At the same time, the uniformly valid asymptotic expansion and the existence of such an available step-type contrast structure are obtained by sewing connection method.

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Wingham, D. J., and R. H. Devayya. "A note on the use of the Neumann expansion in calculating the scatter from rough surfaces." IEEE Transactions on Antennas and Propagation 40, no. 5 (May 1992): 560–63. http://dx.doi.org/10.1109/8.142632.

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