Optimality of a Threshold Policy in theM/M/ queue with repeated vacations

Consider anM/M/1 queueing system with server vacations where the server is turned off as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding cost ofh per unit of time and per customer in the system and a fixed cost of each time the server is turned on. We show that there exists a threshold policy that minimizes the long-run average cost criterion. The approach we use was first proposed in Blanc et al. (1990) and enables us to determine explicitly the optimal threshold and the optimal long-run average cost in terms of the model parameters.     

The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Scale invariant amplitude modulated phase-only filtering

A new synthetic discriminant-function-based amplitude modulated phase-only filtering technique is proposed for scale invariant pattern recognition. This technique has been found to yield improved correlation output when compared with the alternate techniques. The proposed technique is inherently suitable for optical implementation using the currently available spatial light modulators. Simulation results confirm the effectiveness of the proposed technique.     

Density of states of superlattices with multiple layers per period

Density-of-states (DOS) investigations of polytype superlattices (SLs), whose period consists of more than two different layers, are presented. Local DOS (LDOS) is computed as a function of both the electron energy and the space coordinate, which illustrates — in a direct way — the spatial localization, over the SL period, of states forming the energy minibands. A few examples of AlGaAs-based polytype SLs with a coupled-well, step-well and δ-doped basis are analysed, indicating that various LDOS distributions within SL minibands can be arranged. By changing the basis geometry, the electronic DOS can either be selectively confined to a particular SL layer or extend over the whole SL period, which provides a means of modifying the spatial overlap of states from different SL minibands and thus, tuning the respective interband transitions. In particular, polytype SLs with similar miniband structures may exhibit essentially different LDOS features and, consequently, the different transport and optical characteristics. Therefore, it is emphasized that — for a particular device application of a complex-basis SL — not only the electronic level structure should be appropriately designed, but also the corresponding space-charge distributions should be carefully considered.     

Non-partial-wave Coulomb-Born theory for the excitation of many-electron atomic ions II: Numerical description and application

A non-partial-wave Coulomb-Born theory is recently formulated to treat the excitation of many-electron atomic ions for impact by an arbitrary charged particle [Y.B. Duan et al., Phys. Rev. A 56, 2431 (1997)]. The multiple expansion of the transition matrix element is decomposed into the target form factor and the projectile form factor. These are the matrix elements of the tensor operators between quantum states so that any complicated wave function for the target ion can be employed. In this formal theory, an infinitesimally small positive quantity is introduced artificially to guarantee the convergence of integrals. As a supplementary part of the theory, we discuss how to choose the value of . It is found that the should be taken as functions of the momentum transfer and multipolarity . Illustrations are carried out by calculating the cross-sections for some typical transitions n _a l _a -n _b l _b of hydrogen-like ions for impact by electron, positron, and proton, respectively. The resulting cross-sections are in good agreement with ones produced by using a method available for ion targets with Slater-type orbitals [N.C. Deb, N.C. Sil, Phys. Rev. A 28, 2806 (1993)]. Comparisons demonstrate that the Coulomb-Born theory with non-partial wave analysis provides a powerful method to treat the excitation of many-electron atomic ions impact by an arbitrary charged particle. Received 6 April 1999     

Consequences of the center–of–mass correction in nuclear mean–field models

We study the influence of the scheme for the correction for spurious center–of–mass motion on the fit of effective interactions for self–consistent nuclear mean–field calculations. We find that interactions with very simple center–of–mass correction have significantly larger surface coefficients than interactions for which the center–of–mass correction was calculated for the actual many–body state during the fit. The reason for that is that the effective interaction has to counteract the wrong trends with nucleon number of all simplified schemes for center–of–mass correction which puts a wrong trend with mass number into the effective interaction itself. The effect becomes clearly visible when looking at the deformation energy of largely deformed systems, e.g. superdeformed states or fission barriers of heavy nuclei. Received: 6 September 1999     

Non-equilibrium dynamics of simple spherical spin models

We investigate the non-equilibrium dynamics of spherical spin models with two-spin interactions. For the exactly solvable models of the d-dimensional spherical ferromagnet and the spherical Sherrington-Kirkpatrick (SK) model the asymptotic dynamics has for large times and large waiting times the same formal structure. In the limit of large waiting times we find in both models an intermediate time scale, scaling as a power of the waiting time with an exponent smaller than one, and thus separating the time-translation-invariant short-time dynamics from the aging regime. It is this time scale on which the fluctuation-dissipation theorem is violated. Aging in these models is similar to that observed in spin glasses at the level of correlation functions, but different at the level of response functions, and thus different at the level of experimentally accessible quantities like thermoremanent magnetization. Received 22 April 1999     

Self-consistent field theory of collisions I. Scattering channels

The conventional Hartree and Hartree-Fock approaches for treating many-electron bound systems have been extended recently to positive energy scattering problems, in which both the bound and continuum orbitals are determined by the requirement of full self-consistency. Serious consequences of such a theory are that the target orbitals become energy dependent and the asymptotic boundary conditions are satisfied only approximately, in lowest order. It is important therefore to test the theory for its convergence under configuration mixing. This self-consistent field (SCF) theory for scattering has been tested here for scattering from hydrogenic target as a model where the target function is determined dynamically. Penetration of the projectile inside the bound target orbital is manifest through the SCF for the bound state. Our results show that the theory converges to the correct amplitudes and to the exact boundary conditions as more configurations are added. The use of the amputated functions and the weak asymptotic condition (WAC) upon which the SCF theory is based, is justified as the WAC converges to the correct limit. It is then applied to the positron-helium and electron-helium scattering systems where the helium function is calculated simultaneously together with the scattering function. The resulting phase shifts and the SCF target functions are compared with those obtained with the pre-determined target functions in the conventional approaches. Received 22 September 1999     

Evolution of the N = 20 and N = 28 shell closures in neutron-rich nuclei

The isospin dependence of shell closure phenomena is studied for light neutron-rich nuclei within a microscopic self-consistent approach using the Gogny force. Introducing configuration mixing, ³²Mg is found to be dynamically deformed, although the N = 20 spherical shell closure persists at the mean-field level for all N = 20 isotones. In contrast, the N = 28 spherical shell closure is found to disappear for N - Z≥ 10 whereas deformed shell closures are preserved and lead to shape coexistence in ⁴⁴ S. Configuration mixing shows that the ground state of this nucleus is triaxially deformed. The first 2⁺ excitation energy E_x = 1.46 MeV and the reduced transition probability B(E2;0⁺ _gs→ 2⁺ ₁)= 420 e ² fm ⁴ obtained with our approach are in good agreement with experimental data. Received: 26 July 2000 / Accepted: 30 August 2000