The structure of the unit group of the group algebra $\mathbb{F}_{2^k } A_4 $

The structure of the unit group of the group algebra of the group A4 over any finite field of characteristic 2 is established in terms of split extensions of cyclic groups.     

Quantum theory of cavity-assisted sideband cooling of mechanical motion

We present a quantum-mechanical theory of the cooling of a cantilever coupled via radiation pressure to an illuminated optical cavity. Applying the quantum noise approach to the fluctuations of the radiation pressure force, we derive the optomechanical cooling rate and the minimum achievable phonon number. We find that reaching the quantum limit of arbitrarily small phonon numbers requires going into the good-cavity (resolved phonon sideband) regime where the cavity linewidth is much smaller than the mechanical frequency and the corresponding cavity detuning. This is in contrast to the common assumption that the mechanical frequency and the cavity detuning should be comparable to the cavity damping.     

Surface conductivity of biological macromolecules measured by nanopipette dielectrophoresis

We report the measurement of the surface conductivity of biological macromolecules by dielectrophoretic trapping at the tip of a glass nanopipet. We find that the threshold voltage for trapping is a function of salt concentration and can be directly linked to the effective conductivity of the biomolecule and its solvation shell. The surface conductivities obtained for 20-mer single-stranded DNA, 40-mer double-stranded DNA, and yellow fluorescent protein are 7.9+/-1.9 nS, 5.3+/-0.7 nS, and 21.5+/-1.6 nS, respectively.     

Structurally Tunable 3‐Cyanoformazanate Boron Difluoride Dyes

The straightforward synthesis of a series of 3‐cyanoformazanate boron difluoride dyes is reported. Phenyl, 4‐methoxyphenyl and 4‐cyanophenyl N‐substituted derivatives were isolated and characterized by single‐crystal X‐ray crystallography, cyclic voltammetry, and UV/Vis spectroscopy. The compounds were demonstrated to possess tunable, substituent‐dependent absorption, emission, and electrochemical properties, which were rationalized through electronic structure calculations.     

Comparative Studies of Thermally Induced Homolytic CarbonCarbon Bond Cleavage Reactions of Strained Dicarba[2]ferrocenophanes and Their Ring‐Opened Oligomers and Polymers

Reactivity studies of dicarba[2]ferrocenophanes and also their corresponding ring‐opened oligomers and polymers have been conducted in order to provide mechanistic insight into the processes that occur under the conditions of their thermal ring‐opening polymerisation (ROP) (300 °C). Thermolysis of dicarba[2]ferrocenophane rac‐[Fe(η⁵‐C₅H₄)₂(CHPh)₂] (rac‐ 14 ; 300 °C, 1 h) does not lead to thermal ROP. To investigate this system further, rac‐ 14 was heated in the presence of an excess of cyclopentadienyl anion, to mimic the postulated propagating sites for thermally polymerisable analogues. This afforded acyclic [(η⁵‐C₅H₅)Fe(η⁵‐C₅H₄)‐CH₂Ph] ( 17 ) through cleavage of both a Fe?Cp bond and also the C?C bond derived from the dicarba bridge. Evidence supporting a potential homolytic C?C bond cleavage pathway that occurs in the absence of ring‐strain was provided through thermolysis of an acyclic analogue of rac‐ 14 , namely [(η⁵‐C₅H₅)Fe(η⁵‐C₅H₄)(CHPh)₂‐C₅H₅] ( 15 ; 300 °C, 1 h), which also afforded ferrocene derivative 17 . This reactivity pathway appears general for post‐ROP species bearing phenyl substituents on adjacent carbons, and consequently was also observed during the thermolysis of linear polyferrocenylethylene [Fe(η⁵‐C₅H₄)₂(CHPh)₂]_n ( 16 ; 300 °C, 1 h), which was prepared by photocontrolled ROP of rac‐ 14 at 5 °C. This afforded ferrocene derivative [Fe(η⁵‐C₅H₄CH₂Ph)₂] ( 23 ) through selective cleavage of the ?H(Ph)C?C(Ph)H? bonds in the dicarba linkers. These processes appear to be facilitated by the presence of bulky, radical‐stabilising phenyl substituents on each carbon of the linker, as demonstrated through the contrasting thermal properties of unsubstituted linear trimer [(η⁵‐C₅H₅)Fe(η⁵‐C₅H₄)(CH₂)₂(η⁵‐C₅H₄)Fe(η⁵‐C₅H₄)(CH₂)₂(η⁵‐C₅H₄)Fe(η⁵‐C₅H₅)] ( 29 ) with a ?H₂C?CH₂? spacer, which proved significantly more stable under analogous conditions. Evidence for the radical intermediates formed through C?C bond cleavage was detected through high‐resolution mass spectrometric analysis of co‐thermolysis reactions involving rac‐ 14 and 15 (300 °C, 1 h), which indicated the presence of higher molecular weight species, postulated to be formed through cross‐coupling of these intermediates.     

Formation and emission of tetraalkylammonium salt molecular ions sputtered from a gelatin matrix

A gelatin matrix was simultaneously doped with nine equimolar, homologous, tetraalkylammonium salts ranging in mass from 210 to 700 Da. Bombardment of the sample with kiloelectronvolt ions resulted in a nonidentical distribution of relative cation intensities with a maximum at m/z 242 for samples with a total salt concentration of 0.004 g of salt/g of gelatin. A rapid increase in relative intensities with increasing mass is observed for the low mass salts and is believed to be linked to changes in the ionization efficiencies. The changes in ionization efficiencies are likely related to decreasing coulombic attractive forces between the organic cation and the counterion. Disappearance cross-sections, determined from decay curves, indicate that sputter-induced damage increases with increasing mass of the cation. Fragment-to-intact cation ratios also suggest that damage accumulates fastest in the heaviest salts. These observations indicate that desorption yields of the organic salts in a gelatin matrix decrease with increasing mass. In addition, suppression of lower mass tetraalkylammonium salt intact cation intensities was observed for salt-in-gelatin concentrations greater than 10⁻³ g/g.     

Best cooperative partner selection and input resource reallocation using DEA

Reallocation of input resources (RIR) is a process by which certain decision making units (DMUs) reallocate resources among themselves; a process that occurs frequently in many enterprises. In this paper, a new data envelopment analysis (DEA) approach is developed to select the best cooperative partner DMU. Context-dependent DEA is used to identify the different levels of best-practice frontiers. Two DEA-based models are established for two cooperative scenarios, namely, resources pooling only and best-practice sharing. A cooperative method is applied to determine how to reallocate the input resources, and Shapley value is used to estimate the revenue changes that the various DMUs should expect after RIR. Two different situations with different objectives are considered. One objective is to maximize total revenue for the partnership, while the other is to maximize the Shapley value. The proposed approaches are illustrated with two examples.     

Anti-symplectic involutions with lagrangian fixed loci and their quotients

We study the lagrangian embedding as a fixed point set of anti-symplectic involution on a symplectic 4-manifold . Suppose the fixed loci of are the disjoint union of smooth Riemann surfaces ; then each component becomes a lagrangian submanifold. Furthermore, if one of the components is a Riemann surface of genus , then its quotient has vanishing Seiberg-Witten invariants. We will discuss some examples which allow an anti-symplectic involution with lagrangian fixed loci.