Recovering an optimal LP basis from an optimal dual solution

Given a linear program, we describe an approach for crossing over from an optimal dual solution to an optimal basic primal solution. It consists in restricting the dual problem to a small box around the available optimal dual solution then, resolving the associated modified primal problem.     

Prospects for the formation of ultracold ground state polar molecules from mixed alkali atom pairs

Photoassociation rates of mixed cold alkali atom pairs and formation rates of cold heteronuclear alkali dimers in their ground state are computed within an approach where the wave functions are calculated exactly, and the laser field is treated as a perturbation. These rates are predicted to have the same magnitude for all heteronuclear species involving either Rb or Cs atoms. Moreover, these rates are found slightly smaller than, or similar to, the same rates for Cs₂ molecules, which is encouraging for future experiments. We studied the specific case of the photoassociation into excited molecular states coupled with spin-orbit interaction, emphasizing the role of the so-called resonant coupling in the formation of stable ultracold molecules with low vibrational levels. The comparison with recent experimental results on RbCs photoassociation and cold molecule formation show their reasonable agreement with our calculations.Received: 2 July 2004, Published online: 23 November 2004PACS: 32.80.Pj Optical cooling of atoms; trapping - 33.20.Tp Vibrational analysis - 33.70.Ca Oscillator and band strengths, lifetimes, transition moments, and Franck-Condon factors     

Toward the development of ionically controlled nanoscopic molecular gates

An ionically controlled nanoscopic molecular gate has been developed by using functionalized mesoporous materials. The system shows that control of mass transport at nanometric scale can be achieved by using suitable rigid solids and pH-active molecules. The design principle suggests new perspectives in the search of ionically tuned tailored materials and devices with a fine control of mass transport for new applications in fields such as drug delivery, selective removal of toxic species, sensing, or catalysis.     

Sur le rang du

On the rank of the -class group of . Let be a square-free positive integer and be a prime such that . We set , where or . In this paper, we determine the rank of the -class group of .

RÉSUMÉ. Soit , un corps biquadratique où ou bien un premier et étant un entier positif sans facteurs carrés. Dans ce papier, on détermine le rang du -groupe de classes de .

     

Semileptonic B<Subscript>s</Subscript>→D<Subscript>sJ</Subscript>(2460)lν decay in QCD

Using three point QCD sum rule methods, the form factors relevant to semileptonic B_s→D_sJ(2460)ℓν decay are calculated. The q² dependences of these form factors are evaluated and compared with the heavy quark effective theory predictions. The dependence of the asymmetry parameter α, characterizing the polarization of the D_sJ meson, on q² is studied. The branching ratio of this decay is also estimated, and it is shown that it can easily be detected at LHC.     

Almost f-maps and almost f-rings

In the beginning of the eighties, Buskes and Holland proved that any archimedean almost f-ring is commutative. One decade later, Steinberg showed that if G and H are ? with H archimedean, then any positive bilinear map G × G ${{\begin{array}{ll} B \\ \rightarrow \end{array}}}$ H such that ${x \wedge y = 0}$ implies B(x, y) = 0 is symmetric. At first sight, the Steinberg Theorem might seem to be a considerable generalization of the Buskes and Holland result. It turns out, surprisingly enough, that these two results are equivalent. The main purpose of this paper is to establish this equivalence. A second objective is to apply the aforementioned Steinberg Theorem to prove that if R is an f-ring with a unit element e and S is an archimedean f-ring, then an ?-homomorphism R ${{{\begin{array}{ll} h \\\rightarrow \end{array}}}}$ S is a ring homomorphism if and only if h(e) is idempotent in S. This extends a well-known result by Huijsmans and de Pagter, who obtained the same conclusion for semiprime f-algebras.     

A multi-state model to improve the design of an automated system to monitor the activity patterns of patients with bipolar disorder

This paper describes the role of mathematical modelling in the design and evaluation of an automated system of wearable and environmental sensors called PAM (Personalised Ambient Monitoring) to monitor the activity patterns of patients with bipolar disorder (BD). The modelling work was part of an EPSRC-funded project, also involving biomedical engineers and computer scientists, to develop a prototype PAM system. BD is a chronic, disabling mental illness associated with recurrent severe episodes of mania and depression, interspersed with periods of remission. Early detection of the onset of an acute episode is crucial for effective treatment and control. The aim of PAM is to enable patients with BD to self-manage their condition, by identifying the person's normal ‘activity signature’ and thus automatically detecting tiny changes in behaviour patterns which could herald the possible onset of an acute episode. PAM then alerts the patient to take appropriate action in time to prevent further deterioration and possible hospitalisation. A disease state transition model for BD was developed, using data from the clinical literature, and then used stochastically in a Monte Carlo simulation to test a wide range of monitoring scenarios. The minimum best set of sensors suitable to detect the onset of acute episodes (of both mania and depression) is identified, and the performance of the PAM system evaluated for a range of personalised choices of sensors.