Optimizing a linear function over an integer efficient set

In this paper, a method for optimizing a linear function over the integer Pareto-optimal set without having to determine all integer efficient solutions is presented. The proposed algorithm is based on a simple selection technique that improves the linear objective value at each iteration. Two types of cuts are performed successively until the optimal value is obtained and the current truncated region contains no integer feasible solution.     

A class of subgrid-scale models preserving the symmetry group of Navier–Stokes equations

Navier–Stokes equations (NS) admit transformations which transform a solution to another solution (galilean transformation, scaling transformation, …). They also admit viscosity dependent transformations which transform a solution to a solution of another NS with different viscosity. These particular transformations are called symmetries of NS. Each of them has a physical role (such as conservation laws, …). A consistent turbulence model should then remain invariant under these symmetry transformations. Unfortunately, this is not the case of several models.In this article, a class of subgrid-scale models preserving the symmetries of NS is built. This class is then refined such that the models respect the second law of thermodynamics. One of the simplest models of the class is tested to the flow in a ventilated room. Better results than those provided by Smagorinsky and dynamic models are obtained.     

L-functions of second-order cusp forms

We discuss equivalent definitions of holomorphic second-order cusp forms and prove bounds on their Fourier coefficients. We also introduce their associated L-functions, prove functional equations for twisted versions of these L-functions and establish a criterion for a Dirichlet series to originate from a second order form. In the last section we investigate the effect of adding an assumption of periodicity to this criterion. 2000 Mathematics Subject Classification Primary—11F12, 11F66 G. Mason: Research supported in part by NSF Grant DMS 0245225. C. O’Sullivan: Research supported in part by PSC CUNY Research Award No. 65453-00 34.     

Electronic states of chromium carbene ions characterized by high-resolution translational energy loss spectroscopy

The electronic states of the unsaturated organometallic carbene CrCH₂⁺ are investigated using high-resolution translational energy loss spectroscopy. The observed energy loss feature (1.05 ±0.2 eV) is in good agreement with theoretical calculations which predict two higher lying states, ⁶B₁, and ⁶A₁ at 0.78 and 0.82 eV respectively, above the ⁴B₁ ground state of CrCH₂⁺.     

Conformally covariant composite operators in quantum chromodynamics

Conformal covariance is shown to determine renormalization properties of composite operators in QCD and in the ϕ₆³-model at the one-loop level. Its relevance to higher-order (renormalization group improved) perturbative calculations in the short-distance limit is also discussed. Light cone operator product expansions and spectral representations for wavefunctions in QCD are derived.     

Numerical simulation of solitons switching and propagating in asymmetric directional couplers

A numerical investigation, based on the use of split step Fourier transformation algorithm, of all-optical solitons switching in asymmetric directional couplers is presented. The numerical algorithm is described in details. The analysis highlights the influence of the different effective mode area, the phase- and group–velocity mismatch, the different dispersion between two cores on the switching and propagation of short pulses. The investigation indicates that the phase velocity mismatch and the different effective mode area can reduce the coupling length while the different group velocity and the different dispersion between two cores do not change the coupling length. We have also found that the increase of effective mode area ratio can lead to an increase of the switching threshold power but improve significantly the switching steepness, the increase of the phase velocity mismatch can cause a decrease of the switching threshold power but degrade the switching steepness, the increase of the ratio of dispersion can result in a decrease of the switching threshold power and vary the switching steepness, the increase of group velocity mismatch can give rise to an increase of the switching threshold power but improve obviously the switching steepness. Furthermore, the group velocity mismatch can induce solitons pulse to walk off or stretch in the asymmetric directional coupler.     

Krull property of generalized power series rings

Let D be an integral domain and let $(S,\le )$ be a torsion-free, ≤-cancellative, subtotally ordered monoid. We show that the generalized power series ring $?D^{S,\le }?$ is a Krull domain if and only if D is a Krull domain and S is a Krull monoid.     

Partial control of delay-coordinate maps

Nonlinear Dynamics - Delay-coordinate maps have been widely used recently to study nonlinear dynamical systems, where there is only access to the time series of one of their variables. Here, we...     

Upper limit for the electric charge of the photons from the millisecond pulsar 1937+21 observations

Radio signals of different frequencies emitted simultaneously by a pulsar 16000 ly away, arrive on the Earth within less than 2 μs, notwithstanding the galactic magnetic fields encountered along their path. It follows that photons cannot have an electric charge larger than about 10⁻³² times the electron charge.     

Monopoles connected by strings and the monopole problem

To clarify the status of proposed causality arguments limiting the annihilation rate of monopoles, we present a three-dimensional model for the formation of monopoles connected by strings. The length distribution of the strings has been found using a Monte carlo simulation of the phase transition. The result is that long strings connecting monopoles are exponentially suppressed in agreement with the theoretical predictions of Mitchell and Turok [1]. The implications of our results for the monopole problem are discussed.