Ambiguities Appearing in the Study of Time-Dependent Constants of Motion for the One-Dimensional Harmonic Oscillator

A family of time-dependent constants of motionfor the one-dimensional harmonic oscillator is derived.The relation between constants of motion, Lagrangian,and Hamiltonian is described. A well-defined time-dependent Lagrangian (for whichEuler–Lagrange equations and Legendretransformation are fully satisfied) is not uniquelydetermined.     

Thermal Stability of Sol-Gel Hydrotalcites

Sol-Gel Hydrotalcites were synthesized using magnesium ethoxide and variable aluminum sources: aluminum acetilacetonate, aluminum chloride, aluminum nitrate and aluminum sulfate; in all cases, the gelation was done at pH 10. X-ray diffraction studies show that the crystallinity depends on the aluminum precursor used. The crystallinity was found in the order aluminum acetylcetonate>aluminum chloride>aluminum nitrate>aluminum sulfate. The precursor determines the sintering behavior as well.     

Observation of B Meson decays to b1pi and b1K

We present the results of searches for decays of B mesons to final states with a b1 meson and a charged pion or kaon. The data, collected with the BABAR detector at the Stanford Linear Accelerator Center, represent 382x10(6) BB[over ] pairs produced in e+e- annihilation. The results for the branching fractions are, in units of 10(-6), B(B+-->b1(0)pi+)=6.7+/-1.7+/-1.0, B(B+-->b1(0)K+)=9.1+/-1.7+/-1.0, B(B0-->b1(-/+)pi(+/-))=10.9+/-1.2+/-0.9, and B(B0-->b1(-)K+)=7.4+/-1.0+/-1.0, with the assumption that B(b1-->omega pi)=1. We also measure charge and flavor asymmetries A(ch)(B+-->b1(0)pi+)=0.05+/-0.16+/-0.02, Ach(B+-->b1(0)K+)=-0.46+/-0.20+/-0.02, A(ch)(B0-->b1(-/+)pi(+/-))=-0.05+/-0.10+/-0.02, C(B0-->b1(-/+)pi(+/-))=-0.22+/-0.23+/-0.05, DeltaC(B0-->b1(-/+)pi(+/-))=-1.04+/-0.23+/-0.08, and A(ch)(B0-->b1(-)K+)=-0.07+/-0.12+/-0.02. The first error quoted is statistical, and the second systematic.     

Amplitude analysis of the B+/--->phiK*(892)+/- decay

We perform an amplitude analysis of B+/--->phi(1020)K*(892)+/- decay with a sample of about 384 x 10(6) BB[over ] pairs recorded with the BABAR detector. Overall, twelve parameters are measured, including the fractions of longitudinal fL and parity-odd transverse f perpendicular amplitudes, branching fraction, strong phases, and six parameters sensitive to CP violation. We use the dependence on the Kpi invariant mass of the interference between the JP=1(-) and 0+ Kpi components to resolve the discrete ambiguity in the determination of the strong and weak phases. Our measurements of fL=0.49+/-0.05+/-0.03, f perpendicular=0.21+/-0.05+/-0.02, and the strong phases point to the presence of a substantial helicity-plus amplitude from a presently unknown source.     

Modulated Taylor-Couette Flow: Onset of Spiral Modes

The linear stability of the flow between concentric cylinders, with the inner cylinder rotating at a constant angular velocity and the outer cylinder with an angular velocity varying harmonically about a zero mean, is addressed. The bifurcations of the base state are analyzed using Floquet theory, paying particular attention to non-axisymmetric bifurcations which are dominant in significant regions of parameter space. In these regions the spiral modes of the unforced system become parametrically excited and dominant. This is typical behavior of parametrically forced extended systems, where some modes are stabilized, but others are simultaneously excited. The flow structure of the bifurcated states are examined in detail, paying particular attention to the dynamic implications of their symmetries, and in particular how and when subsequent period doublings are inhibited. Received 5 November 2001 and accepted 29 March 2002 Published online: 2 October 2002 RID="*" ID="*" This work was supported by NSF Grants INT-9732637 and CTS-9908599 (U.S.A.) and MCYT Grants PB97-0685 and BFM2001-2350 (Spain). Communicated by H.J.S. Fernando     

A Versatile Strategy to Synthesize Perfluoropolyether‐Based Thermoplastic Fluoropolymers by Alkyne‐Azide Step‐Growth Polymerization

Perfluoropolyether (PFPE)‐based thermoplastic fluoropolymers are synthesized by A₂ + B₂ step‐growth polymerization between PFPE‐diyne and fluorinated diazides. This versatile method allows synthesizing PFPE‐based materials with tunable physicochemical properties depending on the exact nature of the fluorinated segment of the diazide precursor. Semicrystalline or amorphous materials endowed with high thermostability (≈300 °C under air) and low glass transition temperature (≈−100 °C) are obtained, as confirmed by differential scanning calorimetry, thermogravimetry, and rheometry. Step‐growth polymerizations can be copper‐catalyzed but also thermally activated in some cases, thus avoiding the presence of copper residues in the final materials. This strategy opens up new opportunities to easily access PFPE‐based materials on an industrial scale. Furthermore, a plethora of developments can be envisioned (e.g., by adding a third trifunctional component to the formulations for the synthesis of PFPE‐based elastomers).

     

Knapsack problem with probability constraints

This paper is dedicated to a study of different extensions of the classical knapsack problem to the case when different elements of the problem formulation are subject to a degree of uncertainty described by random variables. This brings the knapsack problem into the realm of stochastic programming. Two different model formulations are proposed, based on the introduction of probability constraints. The first one is a static quadratic knapsack with a probability constraint on the capacity of the knapsack. The second one is a two-stage quadratic knapsack model, with recourse, where we introduce a probability constraint on the capacity of the knapsack in the second stage. As far as we know, this is the first time such a constraint has been used in a two-stage model. The solution techniques are based on the semidefinite relaxations. This allows for solving large instances, for which exact methods cannot be used. Numerical experiments on a set of randomly generated instances are discussed below.     

Dynamic nuclear polarization-enhanced solid-state NMR of a 13C-labeled signal peptide bound to lipid-reconstituted Sec translocon

Dynamic nuclear polarization (DNP) has made it possible to record 2D double-quantum-filtered (DQF) solid-state NMR (ssNMR) spectra of a signal peptide bound to a lipid-reconstituted SecYEG translocon complex. The small quantity of peptide in the sample (~40 nmol) normally prohibits multidimensional ssNMR experiments. Such small amounts are not the exception, because for samples involving membrane proteins, most of the limited sample space is occupied by lipids. As a consequence, a conventional 2D DQF ssNMR spectrum with the sample used here would require many weeks if not months of measurement time. With the help of DNP, however, we were able to acquire such a 2D spectrum within 20 h. This development opens up new possibilities for membrane protein studies, particularly in the exploitation of high-resolution spectroscopy and the assignment of individual amino acid signals, in this case for a signal peptide bound to the translocon complex.