Synthesis of dialkyl 2,5-dihydro-5-oxo-1,2-azaphosphole-3,4-dicarboxylates

The adducts produced in the reaction between triphenylphosphine and dialkyl acetylenedicarboxylates were trapped by arylsulfonyl isocyanates to produce dialkyl 2,5-dihydro-5-oxo-1,2-azaphosphole-3,4-dicarboxylates in good yields.     

A miniaturized matrix-assisted laser desorption/ionization time of flight mass spectrometer with mass-correlated acceleration focusing

Mass correlated acceleration (MCA) has now been integrated into a 4 in (10.2 cm) matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometer to achieve high resolving power across a broader mass range, without sacrificing detection of higher mass ions. The goal was to combine MCA with a custom-built miniaturized instrument such as those that might be used for field-portable applications. Unlike other pulsed extraction methods, MCA is not mass dependent and mass spectra can be achieved with a single tuning of instrument parameters. Additionally, the multi-channel recording advantage is better realized because ions of all masses can be brought into focus simultaneously. The MCA dual-stage ion source compensates dynamically for the mass dependence by incorporating an extraction pulse region followed by an acceleration region that contains a time-dependent waveform correlated with mass. The technique was validated with applications in peptide mixtures and protein digestions. Diagnostic studies for the instrument include m/z range and limits of detection.     

Fluorescence spectroscopic studies on the multicomponent system coumarin 1/fluorescein/rhodamine B in ethanol

The steady-state fluorescence spectra of the three-component system coumarin 1/fluorescein/rhodamine B in 95% ethanol were studied at room temperature. In the appropriate concentration ranges, upon the excitation of coumarin 1 at 377 nm, the ternary dye mixture solution emitted simultaneously with three bands centered at 443, 528, and 575 nm, respectively. The analysis of the data seems to indicate that there is significant energy transfer between these three dyes and that the main contribution corresponds to the Förster nonradiative mechanism. The critical transfer distances between each two of the three components were calculated to be 48.4 Å for the coumarin 1/fluorescein pair, 42.2 Å for the coumarin 1/rhodamine B pair, and 65.5 Å between fluorescein and rhodamine B dyes. The system can potentially be used to obtain three primary outputs at different wavelengths in a dye laser system.     

Quasi-steady flight to quasi-steady flight transition for abort landing in a windshear: Trajectory optimization and guidance

This paper is concerned with the optimal transition and the near-optimum guidance of an aircraft from quasi-steady flight to quasi-steady flight in a windshear. The abort landing problem is considered with reference to flight in a vertical plane. In addition to the horizontal shear, the presence of a downdraft is considered.It is assumed that a transition from descending flight to ascending flight is desired; that the initial state corresponds to quasi-steady flight with absolute path inclination of –3.0 deg; and that the final path inclination corresponds to quasi-steady steepest climb. Also, it is assumed that, as soon as the shear is detected, the power setting is increased at a constant time rate until maximum power setting is reached; afterward, the power setting is held constant. Hence, the only control is the angle of attack. Inequality constraints are imposed on both the angle of attack and its time derivative.First, trajectory optimization is considered. The optimal transition problem is formulated as a Chebyshev problem of optimal control: the performance index being minimized is the peak value of the modulus of the difference between the instantaneous altitude and a reference value, assumed constant. By suitable transformations, the Chebyshev problem is converted into a Bolza problem. Then, the Bolza problem is solved employing the dual sequential gradient-restoration algorithm (DSGRA) for optimal control problems.Two types of optimal trajectories are studied, depending on the conditions desired at the final point. Type 1 is concerned with gamma recovery (recovery of the value of the relative path inclination corresponding to quasi-steady steepest climb). Type 2 is concerned with quasi-steady flight recovery (recovery of the values of the relative path inclination, the relative velocity, and the relative angle of attack corresponding to quasi-steady steepest climb). Both the Type 1 trajectory and the Type 2 trajectory include three branches: descending flight, nearly horizontal flight, and ascending flight. Also, for both the Type 1 trajectory and the Type 2 trajectory, descending flight takes place in the shear portion of the trajectory; horizontal flight takes place partly in the shear portion and partly in the aftershear portion of the trajectory; and ascending flight takes place in the aftershear portion of the trajectory. While the Type 1 trajectory and the Type 2 trajectory are nearly the same in the shear portion, they diverge to a considerable degree in the aftershear portion of the trajectory.Next, trajectory guidance is considered. Two guidance schemes are developed so as to achieve near-optimum transition from quasi-steady descending flight to quasi-steady ascending flight: acceleration guidance (based on the relative acceleration) and gamma guidance (based on the absolute path inclination).The guidance schemes for quasi-steady flight recovery in abort landing include two parts in sequence: shear guidance and aftershear guidance. The shear guidance is based on the result that the shear portion of the trajectory depends only mildly on the boundary conditions. Therefore, any of the guidance schemes already developed for Type 1 trajectories can be employed for Type 2 trajectories (descent guidance followed by recovery guidance). The aftershear guidance is based on the result that the aftershear portion of the trajectory depends strongly on the boundary conditions; therefore, the guidance schemes developed for Type 1 trajectories cannot be employed for Type 2 trajectories. For Type 2 trajectories, the aftershear guidance includes level flight guidance followed by ascent guidance. The level flight guidance is designed to achieve almost complete velocity recovery; the ascent guidance is designed to achieve the desired final quasi-steady state.The numerical results show that the guidance schemes for quasi-steady flight recovery yield a transition from quasi-steady flight to quasi-steady flight which is close to that of the optimal trajectory, allows the aircraft to achieve the final quasi-steady state, and has good stability properties.This research was supported by NASA Langley Research Center, Grant No. NAG-1-516, by Boeing Commercial Airplane Company, and by Air Line Pilots Association.The authors are indebted to Dr. R. L. Bowles (NASA-LRC) and Dr. G. R. Hennig (BCAC) for helpful discussions.     

Finsler-spacetime tangent bundle

The Levi-Civita connection coefficients of the spacetime tangent bundle, for the case of a Finsler spacetime, are reduced to the form given by Yano and Davies for a generic tangent bundle of a Finsler manifold. A useful expression is also obtained for the Riemann curvature scalar of a Finsler-spacetime tangent bundle.     

Riemann curvature scalar of spacetime tangent bundle

The maximum possible proper acceleration relative to the vacuum determines much of the differential geometric structure of the space-time tangent bundle. By working in an anholonomic basis adapted to the spacetime affine connection, one derives a useful expression for the Riemann curvature scalar of the bundle manifold. The explicit documentation of the proof is important because of the central role of the curvature scalar in the formulation of an action with resulting field equations and associated solutions to physical problems.     

Gaussian quadrature and acceleration of convergence

The aim of this paper is to take up again the study done in previous papers, to the case where the integrand possesses an algebraic singularity within the interval of integration. The singularities or poles close to the interval of integration considered in this paper are only real or purely imaginary. This revised version was published online in August 2006 with corrections to the Cover Date.     

On limiting field strengths in gravitation

We consider through the equivalence principle the existence of maximal and minimal field strengths in gravitation. We explore the consequences for gravitational collapse and for explaining the rotation curve of galaxies without invoking dark matter. Other interesting implications like maximal size of planetary systems are outlined.1. Note that, in our case, such results, both for electromagnetic and gravitational fields, are obtained when torsion is considered [8]: In fact, we have arrived at a minimum radius, for instance, of the electron, starting explicitly frm a modified Poisson's equation when a term containing the spin is incorporated through torsion.     

Multistability in the laser cooling of atomic beams

Summary We describe the interaction of a beam of two-level atoms with multiple laser beams propagating in the opposite direction. The lasers are frequency-chirped in order to remain close to resonance and they continuously decelerate the atoms by radiation pressure. In a deterministic treatment, the average atomic velocity exhibits multistability cycles as a function of the chirping rate. A statistical (Fokker-Planck) treatment shows the corresponding splitting of the atomic velocity distribution into well-separate, quasi-monokinetic bunches of atoms. In the laboratory reference frame, multistability shows up through the increasingly decelerated motion of these atomic bunches. Analytical results are presented, as well as numerical simulations for a beam of cesium atoms, both in the laboratory frame and in the non-inertial frame. The conditions for the observation of multiple cooling with frequency-chirped lasers are discussed. A comparison with standard chirped cooling is outlined. Possible applications are indicated.