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1.
Christodoulos Athanasiadis Nikolaos Berketis 《Mathematical Methods in the Applied Sciences》2006,29(1):27-48
A spherical electromagnetic wave propagating in a chiral medium is scattered by a bounded chiral obstacle which can have any of the usual properties. Reciprocity and general scattering theorems, relating the scattered fields due to scattering of waves from a point source put in any two different locations are established. Applying the general scattering theorem for appropriate locations and polarizations of the point source we prove an associated forward scattering theorem. Mixed scattering relations, relating the scattered fields due to a plane wave and the far‐field patterns due to a spherical wave, are also established. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
2.
3.
A primal-relaxed dual global optimization algorithm is presented along with an extensive review for finding the global minimum energy configurations of microclusters composed by particles interacting with any type of two-body central forces. First, the original nonconvex expression for the total potential energy is transformed to the difference of two convex functions (DC transformation) via an eigenvalue analysis performed for each pair potential that constitutes the total potential energy function. Then, a decomposition strategy based on the GOP algorithm [1–4] is designed to provide tight upper and lower bounds on the global minimum through the solutions of a sequence of relaxed dual subproblems. A number of theoretical results are included which expedite the computational effort by exploiting the special mathematical structure of the problem. The proposed approach attains-convergence to the global minimum in a finite number of iterations. Based on this procedure global optimum solutions are generated for small Lennard-Jones and Morse (a=3) microclustersn7. For larger clusters (8N24 for Lennard-Jones and 8N30 for Morse), tight lower and upper bounds on the global solution are provided which serve as excellent initial points for local optimization approaches. 相似文献
4.
Christos A. Athanasiadis 《Journal of Algebraic Combinatorics》1996,5(1):5-11
The Laplacian of a directed graph G is the matrix L(G) = O(G) –, A(G) where A(G) is the adjaceney matrix of G and O(G) the diagonal matrix of vertex outdegrees. The eigenvalues of G are the eigenvalues of A(G). Given a directed graph G we construct a derived directed graph D(G) whose vertices are the oriented spanning trees of G. Using a counting argument, we describe the eigenvalues of D(G) and their multiplicities in terms of the eigenvalues of the induced subgraphs and the Laplacian matrix of G. Finally we compute the eigenvalues of D(G) for some specific directed graphs G. A recent conjecture of Propp for D(H
n
) follows, where H
n
stands for the complete directed graph on n vertices without loops. 相似文献
5.
For an irreducible, crystallographic root system in a Euclideanspace V and a positive integer m, the arrangement of hyperplanesin V given by the affine equations (, x) = k, for and k =0, 1, ..., m, is denoted here by . The characteristic polynomial of is related in the paper to that of the Coxeter arrangement A(corresponding to m = 0), and the number of regions into whichthe fundamental chamber of A is dissected by the hyperplanesof is deduced to be equal to the product , where e1,e2, ..., el are the exponents of and h is the Coxeter number.A similar formula for the number of bounded regions follows.Applications to the enumeration of antichains in the root posetof are included. 2000 Mathematics Subject Classification 20F55(primary), 05A15, 52C35 (secondary). 相似文献
6.
Let Φ be a finite root system of rank n and let m be a nonnegative integer. The generalized cluster complex Δm(Φ) was introduced by S. Fomin and N. Reading. It was conjectured by these authors that Δm(Φ) is shellable and by V. Reiner that it is (m + 1)-Cohen-Macaulay, in the sense of Baclawski. These statements are proved in this paper. Analogous statements are shown
to hold for the positive part Δ+m(Φ) of Δm(Φ). An explicit homotopy equivalence is given between Δ+m(Φ) and the poset of generalized noncrossing partitions, associated to the pair (Φ, m) by D. Armstrong. 相似文献
7.
The approximation of the convex envelope of nonconvex functions is an essential part in deterministic global optimization
techniques (Floudas in Deterministic Global Optimization: Theory, Methods and Application, 2000). Current convex underestimation
algorithms for multilinear terms, based on arithmetic intervals or recursive arithmetic intervals (Hamed in Calculation of
bounds on variables and underestimating convex functions for nonconvex functions, 1991; Maranas and Floudas in J Global Optim
7:143–182, (1995); Ryoo and Sahinidis in J Global Optim 19:403–424, (2001)), introduce a large number of linear cuts. Meyer
and Floudas (Trilinear monomials with positive or negative domains: Facets of convex and concave envelopes, pp. 327–352, (2003);
J Global Optim 29:125–155, (2004)), introduced the complete set of explicit facets for the convex and concave envelopes of
trilinear monomials with general bounds. This study proposes a novel method to underestimate posynomial functions of strictly
positive variables. 相似文献
8.
Density values for dilute aqueous solutions of five cyclic ethers obtained using the Anton Paar DSA 5000 vibrating-tube densimeter and the laboratory-made flow densimeter are presented together with partial molar volumes at infinite dilution (standard partial molar volumes) calculated from the measured results. The cyclic ethers were either five-members cycles with one or two oxygen atoms (oxolane, 1,3-dioxolane) or six-members cycles with one, two, or three oxygen atoms (oxane, 1,4-dioxane, 1,3,5-trioxane). The measurements were performed at temperatures from T = 278 K up to T = 373 K and at either atmospheric pressure or at p = 0.5 MPa. The group contribution method is proposed and values of group contributions are evaluated. Standard partial molar volumes predicted for several other cyclic ethers including large cycles (crown ethers) are compared with available data from the literature. 相似文献
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10.
Christodoulos Athanasiadis Gary F. Roach Ioannis G. Stratis 《Mathematische Nachrichten》2003,250(1):3-16
A time domain analysis of the equations governing wave propagation in an unbounded chiral medium is presented by a spectral family approach and by a direct eigenfunction expansion using Beltrami–Moses fields. 相似文献