Quantum-limited noise performance of a mode-locked laser diode

Low-noise operation of a 9-GHz hybridly mode-locked laser diode is demonstrated. The integrated timing jitter was 47 fs (10 Hz to 10 MHz) and 86 fs (10 Hz to 4.5 GHz), with a pulse width of 6.7 ps. The noise performance as a function of filter bandwidth and oscillator noise is also addressed.     

The Nevanlinna–Pick problem on the closed unit disk: Minimal norm rational solutions of low degree

For the Nevanlinna–Pick interpolation problem with n$n$ interpolation conditions (interior and boundary), we construct a family of rational solutions of degree at most n−1$n-1$. We also establish necessary and sufficient conditions for the existence and the uniqueness of a solution with the minimally possible H^∞$H^{\infty }$-norm and construct a family of minimal-norm rational solutions of degree at most n−1$n-1$ in the indeterminate case. Finally, we supplement a result of Ruscheweyh and Jones showing that in case the interpolation nodes and the target values are all unimodular, any rational solution of degree at most n−1$n-1$ is necessarily a finite Blaschke product.     

The first pulsar discovered by FAST

<正>To assist with the commissioning [1] of the Five-hundredmeter Aperture Spherical radio Telescope (FAST), we performed a pulsar search, with the primary goal of developing and testing the pulsar data acquisition and processing pipelines. We tested and used three pipelines, two (P1 and P2 hereafter) searched for the periodic signature of pulsars     

Bimodules in crossed products of von Neumann algebras

In this paper, we study bimodules over a von Neumann algebra M   in the context of an inclusion M⊆M_?αG$M\subseteq M{?}_{\alpha }G$, where G is a discrete group acting on a factor M by outer ?-automorphisms. We characterize the M  -bimodules X⊆M_?αG$X\subseteq M{?}_{\alpha }G$ that are closed in the Bures topology in terms of the subsets of G  . We show that this characterization also holds for w^?$w^{?}$-closed bimodules when G has the approximation property (AP  ), a class of groups that includes all amenable and weakly amenable ones. As an application, we prove a version of Mercer's extension theorem for certain w^?$w^{?}$-continuous surjective isometric maps on X.     

Rings whose zero-divisor graphs have positive genus

It is shown that, for a fixed positive integer g, there are finitely many isomorphism classes of rings whose zero-divisor graph has genus g. The proof can then be modified to yield an analogous result for nonorientable genus.     

A classification of orbits admitting a unique invariant measure

We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are $S_{\infty }$-invariant and concentrated on a single isomorphism class must be zero, or one, or continuum. Further, such an isomorphism class admits a unique $S_{\infty }$-invariant probability measure precisely when the structure is highly homogeneous; by a result of Peter J. Cameron, these are the structures that are interdefinable with one of the five reducts of the rational linear order $(\mathbb{Q},<)$.     

C−H Activation of Inert Arenes using a Photochemically Activated Guanidinato-Magnesium(I) Compound

UV irradiation of solutions of a guanidinate coordinated dimagnesium(I) compound, [{(Priso)Mg}₂] 3 (Priso=[(DipN)₂CNPrⁱ₂]⁻, Dip=2,6-diisopropylphenyl), in either benzene, toluene, the three isomers of xylene, or mesitylene, leads to facile activation of an aromatic C−H bond of the solvent in all cases, and formation of aryl/hydride bridged magnesium(II) products, [{(Priso)Mg}₂(μ-H)(μ-Ar)] 4 – 9 . In contrast to similar reactions reported for β-diketiminate coordinated counterparts of 3 , these C−H activations proceed with little regioselectivity, though they are considerably faster. Reaction of 3 with an excess of the pyridine, p-NC₅H₄Bu^t (py^But), gave [(Priso)Mg(py^ButH)(py^But)₂] 10 , presumably via reduction of the pyridine to yield a radical intermediate, [(Priso)Mg(py^But⋅)(py^But)₂] 11 , which then abstracts a proton from the reaction solvent or a reactant. DFT calculations suggest two possible pathways to the observed arene C−H activations. One of these involves photochemical cleavage of the Mg−Mg bond of 3 , generating magnesium(I) doublet radicals, (Priso)Mg⋅. These then doubly reduce the arene substrate to give “Birch-like” products, which subsequently rearrange via C−H activation of the arene. Circumstantial evidence for the photochemical generation of transient magnesium radical species includes the fact that irradiation of a cyclohexane solution of 3 leads to an intramolecular aliphatic C−H activation process and formation of an alkyl-bridged magnesium(II) species, [{Mg(μ-Priso^−H)}₂] 12 . Furthermore, irradiation of a 1 : 1 mixture of 3 and the β-diketiminato dimagnesium(I) compound, [{(^DipNacnac)Mg}₂] (^DipNacnac=[HC(MeCNDip)₂]⁻), effects a “scrambling” reaction, and the near quantitative formation of an unsymmetrical dimagnesium(I) compound, [(Priso)Mg−Mg(^DipNacnac)] 13 . Finally, the EPR spectrum (77 K) of a glassed solution of UV irradiated 3 is dominated by a broad featureless signal, indicating the presence of a doublet radical species.     

Selective extraction and elution of weak bases by in-line solid-phase extraction capillary electrophoresis using a pH step gradient and a weak cation-exchange monolith

A polymer monolith bearing weak cation-exchange functionality was prepared for the purpose of demonstrating pH-selective extraction and elution in in-line solid-phase extraction-capillary electrophoresis (SPE-CE) utilising a model set of cationic analytes, namely imidazole, lutidine and 3-phenylpropanamine. Optimization of the electrolyte conditions for efficient elution of the adsorbed analytes using a moving pH boundary required that the capillary and monolith be filled with 44 mM sodium acetate at high pH (pH 6) and a low pH electrolyte of 3 mM sodium acetate pH 3 was placed in the electrolyte vials. This combination allowed the adsorbed analytes to be simultaneously eluted and focused into narrow bands, with peak widths of the eluted analytes having a baseline width of 1.2 s immediately after the monolith. Using these optimum elution conditions, the versatility of the SPE-CE approach was demonstrated by removing unwanted adsorbed components after extraction with a wash at a different pH and also by selecting a pH at which only some of the model weak bases were ionised. The analytical performance of the approach was evaluated and the relative standard deviation for peak heights, peak area and migration times were in the ranges of 1.4-5.3, 1.2-3.3 and 0.4-1.2% respectively. Analytes exhibited linear calibrations with r(2) values ranging from 0.996 to 0.999 over two orders of magnitude. Analyte pre-concentration provided excellent sensitivity, and limits of detection for the analyte used in this study were in the range 8.0-30 ng ml(-1), which was an enhancement of 63 when compared to normal hydrodynamic injection occupying 1.3% of the capillary of these bases in water.     

Identification of inorganic ions in post‐blast explosive residues using portable CE instrumentation and capacitively coupled contactless conductivity detection

Novel CE methods have been developed on portable instrumentation adapted to accommodate a capacitively coupled contactless conductivity detector for the separation and sensitive detection of inorganic anions and cations in post‐blast explosive residues from homemade inorganic explosive devices. The methods presented combine sensitivity and speed of analysis for the wide range of inorganic ions used in this study. Separate methods were employed for the separation of anions and cations. The anion separation method utilised a low conductivity 70 mM Tris/70 mM CHES aqueous electrolyte (pH 8.6) with a 90 cm capillary coated with hexadimethrine bromide to reverse the EOF. Fifteen anions could be baseline separated in 7 min with detection limits in the range 27–240 μg/L. A selection of ten anions deemed most important in this application could be separated in 45 s on a shorter capillary (30.6 cm) using the same electrolyte. The cation separation method was performed on a 73 cm length of fused‐silica capillary using an electrolyte system composed of 10 mM histidine and 50 mM acetic acid, at pH 4.2. The addition of the complexants, 1 mM hydroxyisobutyric acid and 0.7 mM 18‐crown‐6 ether, enhanced selectivity and allowed the separation of eleven inorganic cations in under 7 min with detection limits in the range 31–240 μg/L. The developed methods were successfully field tested on post‐blast residues obtained from the controlled detonation of homemade explosive devices. Results were verified using ion chromatographic analyses of the same samples.     

Synthesis of Novel C/D Ring Modified Bile Acids

Bile acid receptors have been identified as important targets for the development of new therapeutics to treat various metabolic and inflammatory diseases. The synthesis of new bile acid analogues can help elucidate structure–activity relationships and define compounds that activate these receptors selectively. Towards this, access to large quantities of a chenodeoxycholic acid derivative bearing a C-12 methyl and a C-13 to C-14 double bond provided an interesting scaffold to investigate the chemical manipulation of the C/D ring junction in bile acids. The reactivity of this alkene substrate with various zinc carbenoid species showed that those generated using the Furukawa methodology achieved selective α-cyclopropanation, whereas those generated using the Shi methodology reacted in an unexpected manner giving rise to a rearranged skeleton whereby the C ring has undergone contraction to form a novel spiro–furan ring system. Further derivatization of the cyclopropanated steroid included O-7 oxidation and epimerization to afford new bile acid derivatives for biological evaluation.