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Abstract: The time-dependent Vlasov–Maxwell equations are one of the most complete mathematical equations that model charged particle beams or plasma physics problems. However, the numerical solution of this system often requires a large computational effort. It is worthwhile, whenever possible, to take into account the geometrical or physical particularities of the problem to derive asymptotic simpler approximate models, leading to cheaper simulations. In this paper, we consider the case of high energy short beams, as for example the transport of a bunch of highly relativistic charged particles in the interior of a perfectly conducting hollow tube. We then derive and analyze a new paraxial asymptotic model, that approximates the Vlasov–Maxwell equations and is fourth order accurate with respect to a small parameter which reflects the physical characteristics of the problem. This approach promises to be very powerful in its ability to get an accurate and fast algorithm, easy to be developed. [Copyright &y& Elsevier]

Abstract: Let and be nontrivial involutions, i.e., and . A matrix is called -symmetric if . This paper presents a -symmetric matrix solution to the inverse eigenproblem with a leading principal submatrix constraint. The solvability condition of the constrained inverse eigenproblem is also derived. The existence, the uniqueness and the expression of the -symmetric matrix solution to the best approximation problem of the constrained inverse eigenproblem are achieved, respectively. An algorithm is presented to compute the -symmetric matrix solution to the best approximation problem. Two numerical examples are given to illustrate the effectiveness of our results. [Copyright &y& Elsevier]