Solution Regularity in Optimal Control via Subgradient Analysis of the Value Function

Lipschitz regularity for solutions to nonsmooth problems in the calculus of variations is considered, where we allow for extended-real-valued Lagrangians. Conditions for regularity are given in terms of subdifferentiability properties of the value function. In particular, it is shown that there exists a Lipschitz minimizer as long as the limiting subgradient of the value function is nonempty at the point in question. The results improve upon previous results in the literature, even in the case of finite Lagrangians.     

Measurement of storage time, estimation of ion number and study of absorption line profile in a Paul trap

Europium (Eu⁺) ions were confined in a Paul trap and detected by non-destructive method. Storage time of Eu⁺ ions achieved in vacuum was improved by orders of magnitude employing buffer gas cooling. The experimentally detected signal was fitted to the ion response signal and the total number of ions trapped was estimated. It is found that the peak signal amplitude as well as the product of FWHM and the peak signal amplitude is proportional to the total number of trapped ions. The trapped ion secular frequency was swept at different rates and its effect on the absorption line profile was studied both experimentally and theoretically.     

Arithmetic on superelliptic curves

This paper is concerned with algorithms for computing in the divisor class group of a nonsingular plane curve of the form which has only one point at infinity. Divisors are represented as ideals, and an ideal reduction algorithm based on lattice reduction is given. We obtain a unique representative for each divisor class and the algorithms for addition and reduction of divisors run in polynomial time. An algorithm is also given for solving the discrete logarithm problem when the curve is defined over a finite field.

     

Polarisation parameters in neutral pion photoproduction

The polarisation parameters Σ, P and T have been measured for the process γp→π⁰p in the photon energy range 1300–2100 MeV and c.m. angles between 30° and 110°, in an experiment with a polarised beam and polarised target. The results are compared with a recent theoretical analysis which fits data from threshold to 16 GeV. The new data are in general agreement with the analysis, but with some significant discrepancies in detail.     

Line frequency expressions for triply degenerate fundamentals of spherical top molecules appropriate for large angular momentum

For states of high angular momentum we obtain expressions for the transition frequencies in the triply degenerate fundamental of a “heavy” spherical top, that are accurate to spectroscopic resolution, without tedious calculation of octahedral (or tetrahedral) vector coupling coefficients or diagonalization of matrices. Our calculations are based upon the physical assumption that as the molecule rotates with larger angular momentum it behaves like a symmetric top with the coupled pure rotational angular momentum quantized along either the four- or threefold body-fixed axes. We find that the approximate calculation which involves only 3-J symbols quite accurately reproduces the result of a complete diagonalization of the Hamiltonian, so that for all but the most accurate saturated absorption spectra theoretical analysis may be carried out without reference to the octahedral (or tetrahedral) subgroup of the rotation group.     

Zwitterionic macrocyclic metal sulfate extractants containing 3-dialkylaminomethylsalicylaldimine units

10,25-Di-tert-alkyl-14,21-dimethyl-3,6,14,21-tetraazatricyclo[21.3.1.18,12]octacosa-1(27),2,6,8,10,12(28),23,25-octaene-27,28-diol macrocycles form Ni(II) and Cu(II) complexes in which the metal cation and the sulfate anion are bound in separated sites in a zwitterionic form of the ligand. The nonyl-substituted macrocycle shows a higher affinity for SO(4)(2-) and a lower binding strength for Cu(2+) than open chain analogues, the pH-dependences for which fall in ranges which allow loading of CuSO(4) at pH approximately 4 and easy stripping to recycle the ligand. X-Ray structure determinations of the Cu(II) and Ni(II) sulfate complexes of the tert-butyl substituted ligand suggest that the de-tuning of M(2+)-binding results from a distortion from planarity of the "salen" N(2)O(2)(2-) donor set imposed by the incorporation of the hexamethylene strap in the ligand and reveal that the sulfate is bound as a hydrate in a 2:2:2:2, ligand-M(2+)-SO(4)(2-)-H(2)O, assembly.     

Coherent dynamics of the localized vibrational modes of hydrogen in CaF2

We report the observation of giant quantum coherence effects in the localized modes of ionized hydrogen in synthetic fluorite. Infrared free induction decay experiments on the substitutional H- center show dramatic modulations at negative delay times due to interference between multiple vibrational levels. Spectrally resolving the degenerate four wave mixing signal allows unambiguous assignments of the participating vibrational states. The dependence of the signal intensity upon the delay path between the exciting free electron laser pulses can be accounted for in terms of the resonant third order polarization with a common dephasing time for the excited states.