Towards a Novel Energy Density Functional for Beyond-mean-field Calculations with Pairing and Deformation

We take an additional step towards the optimization of the novel finite-range pseudopotential at a constrained Hartree–Fock–Bogolyubov level and implement an optimization procedure within an axial code using harmonic oscillator basis. We perform the optimization using three different numbers of the harmonic oscillator shells. We apply the new parameterizations in the O–Kr part of the nuclear chart and isotopic chain of Sn, and we compare the results with experimental values and those given by a parameterization obtained using a spherical code.Peer reviewe

A note on uniform asymptotic wave diffraction by a wedge

New expressions for asymptotically uniform Green’s functions for high-frequency wave diffraction when a plane, cylindrical or point wave field is incident on an ideal wedge are derived. They are useful for deriving a uniform asymptotic expression for the exact solution in terms of the high-frequency diffracted and geometrical optics far field. The present method is simple and consists of differentiating out the singularities of the integral representations and using new representations for trigonometrical sums that arise when the wedge angle is a rational multiple of π. The new results make explicit the continuity of the fields across shadow and reflection boundaries

Initial-boundary value problems for the defocusing nonlinear Schr\"odinger equation in the semiclassical limit

Initial-boundary value problems for integrable nonlinear partial differential equations have become tractable in recent years due to the development of so-called unified transform techniques. The main obstruction to applying these methods in practice is that calculation of the spectral transforms of the initial and boundary data requires knowledge of too many boundary conditions, more than are required make the problem well-posed. The elimination of the unknown boundary values is frequently addressed in the spectral domain via the so-called global relation, and types of boundary conditions for which the global relation can be solved are called \emph{linearizable}. For the defocusing nonlinear Schr\"odinger equation, the global relation is only known to be explicitly solvable in rather restrictive situations, namely homogeneous boundary conditions of Dirichlet, Neumann, and Robin (mixed) type. General nonhomogeneous boundary conditions are not known to be linearizable. In this paper, we propose an explicit approximation for the nonlinear Dirichlet-to-Neumann map supplied by the defocusing nonlinear Schr\"odinger equation and use it to provide approximate solutions of general nonhomogeneous boundary value problems for this equation posed as an initial-boundary value problem on the half-line. Our method sidesteps entirely the solution of the global relation. The accuracy of our method is proven in the semiclassical limit, and we provide explicit asymptotics for the solution in the interior of the quarter-plane space-time domain.Comment: 56 pages, 13 figures. To appear in Stud. Appl. Mat

Quantum dense coding by spatial state entanglement

We have presented a theoretical extended version of dense coding protocol using entangled position state of two particles shared between two parties. A representation of Bell states and the required unitary operators are shown utilizing symmetric normalized Hadamard matrices. In addition, some explicit and conceivable forms for the unitary operators are presented by using some introduced basic operators. It is shown that, the proposed version is logarithmically efficient than some other multi-qubit dense coding protocols.Comment: 4 pages, 1 figure, Revte

Quantum symmetries and the Weyl-Wigner product of group representations

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase-space. Each such phase-space representation is a Weyl-Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by `factorising' the Weyl-Wigner product. However, not every real, unitary representation on phase-space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl-Wigner product and can be factorised. The conditions under which this is possible are examined. Examples are presented.Comment: Latex2e file, 37 page

On Polynomial Kernels for Integer Linear Programs: Covering, Packing and Feasibility

We study the existence of polynomial kernels for the problem of deciding feasibility of integer linear programs (ILPs), and for finding good solutions for covering and packing ILPs. Our main results are as follows: First, we show that the ILP Feasibility problem admits no polynomial kernelization when parameterized by both the number of variables and the number of constraints, unless NP \subseteq coNP/poly. This extends to the restricted cases of bounded variable degree and bounded number of variables per constraint, and to covering and packing ILPs. Second, we give a polynomial kernelization for the Cover ILP problem, asking for a solution to Ax >= b with c^Tx <= k, parameterized by k, when A is row-sparse; this generalizes a known polynomial kernelization for the special case with 0/1-variables and coefficients (d-Hitting Set)

High frequency diffraction of an electromagnetic plane wave by an imperfectly conducting rectangular cylinder

Copyright @ 2011 IEEEWe shall consider the the problem of determining the scattered far wave field produced when a plane E-polarized wave is incident on an imperfectly conducting rectangular cylinder. By using the the uniform asymptotic solution for the problem of the diffraction of a plane wave by a right-angled impedance wedge, in conjunction with Keller's method, the a high frequency far field solution to the problem is given