An ultra-stable referenced interrogation system in the deep ultraviolet for a mercury optical lattice clock

We have developed an ultra-stable source in the deep ultraviolet, suitable to fulfil the interrogation requirements of a future fully-operational lattice clock based on neutral mercury. At the core of the system is a Fabry–Pérot cavity which is highly impervious to temperature and vibrational perturbations. The mirror substrate is made of fused silica in order to exploit the comparatively low thermal noise limits associated with this material. By stabilizing the frequency of a 1062.6 nm Yb-doped fiber laser to the cavity, and including an additional link to LNE-SYRTE’s fountain primary frequency standards via an optical frequency comb, we produce a signal which is both stable at the 10^?15 level in fractional terms and referenced to primary frequency standards. The signal is subsequently amplified and frequency-doubled twice to produce several milliwatts of interrogation signal at 265.6 nm in the deep ultraviolet.     

The Mode Solution of the Wave Equation in Kasner Spacetimes and Redshift

We study the mode solution to the Cauchy problem of the scalar wave equation □φ = 0 in Kasner spacetimes. As a first result, we give the explicit mode solution in axisymmetric Kasner spacetimes, of which flat Kasner spacetimes are special cases. Furthermore, we give the small and large time asymptotics of the modes in general Kasner spacetimes. Generically, the modes in non-flat Kasner spacetimes grow logarithmically for small times, while the modes in flat Kasner spacetimes stay bounded for small times. For large times, however, the modes in general Kasner spacetimes oscillate with a polynomially decreasing amplitude. This gives a notion of large time frequency of the modes, which we use to model the wavelength of light rays in Kasner spacetimes. We show that the redshift one obtains in this way actually coincides with the usual cosmological redshift.     

Synthesis and Surface‐Spectroscopic Characterization of Photoisomerizable glyco‐SAMs on Au(111)

Photoisomerizable glyco‐SAMs (self‐assembled monolayers), utilizing synthetic azobenzene glycoside derivatives were fabricated. The ultimate goal of this project is to assay the influence of the 3D arrangement of sugar ligands on cell adhesion, and eventually make cell adhesion photoswitchable. However, it is a prerequisite for any biological study on the spatial conditions of carbohydrate recognition, that photoisomerization of the surface molecules can be verified. Here, we employed IRRAS and XPS to spectroscopically characterize glyco‐SAMs. In particular and unprecedented to date, we prove reversible E→Z→E isomerization of azobenzene glycoside‐terminated SAMs.     

Synthesis of Oxacyclic Scaffolds via Dual Ruthenium Hydride/Brønsted Acid‐Catalyzed Isomerization/Cyclization of Allylic Ethers

A ruthenium hydride/Brønsted acid‐catalyzed tandem sequence is reported for the synthesis of 1,3,4,9‐tetrahydropyrano[3,4‐b]indoles (THPIs) and related oxacyclic scaffolds. The process was designed on the premise that readily available allylic ethers would undergo sequential isomerization, first to enol ethers (Ru catalysis), then to oxocarbenium ions (Brønsted acid catalysis) amenable to endo cyclization with tethered nucleophiles. This methodology provides not only an attractive alternative to the traditional oxa‐Pictet–Spengler reaction for the synthesis of THPIs, but also convenient access to THPI congeners and other important oxacycles such as acetals.     

Synthesis of a Natural Product‐Like Compound Collection through Oxidative Cleavage and Cyclization of Linear Peptides

Massive efforts in molecular library synthesis have strived for the development of synthesis methodology which systematically delivers natural product‐like compounds of high spatial complexity. Herein, we present a conceptually simple approach that builds on the power of solid‐phase peptide synthesis to assemble precursor peptides (oligomers) designed to undergo oxidative cascade reactions. By harnessing the structural side‐chain diversity and inherent stereochemical features offered by readily available amino acids (monomers), a proof‐of‐concept collection of 54 skeletally and stereochemically diverse compounds was generated, and selected compounds were elaborated into isoform‐selective metalloprotease inhibitors.     

Frequencies and wavelengths from a new, efficient FIR lasing gas: CD2F2

We report for the first time wavelength, relative polarization, and frequency measurements for 47 new cw FIR laser lines in the wavelength region from 120 to 1714 m, all obtained by optically pumping CD₂F₂ with a CO₂ laser. Relative output powers were also measured. For comparison, the 189.8 m line pumped by R_I(34) is nearly five times as efficient as the 118.8 m methyl alcohol line.Contribution of the U.S. Government, not subject to copyright.     

Optimal mortgage loan securitization and the subprime crisis

We analyze the process of mortgage loan securitization that has been a root cause of the current subprime mortgage crisis (SMC). In particular, we solve an optimal securitization problem for banks that has the cash outflow rate for financing a portfolio of mortgage-backed securities (MBSs) and the bank’s investment in MBSs as controls. In our case, the associated Hamilton–Jacobi–Bellman equation (HJBE) has a smooth solution when the optimal controls are computed via a power utility function. Finally, we analyze this optimization problem and its connections with the SMC.     

Iron pentacarbonyl as a precursor for molecule-based magnets: formation of Fe[TCNE](2) (T(c) = 100 K) and Fe[TCNQ](2) (T(c) = 35 K) magnets

The reaction of tetracyanoethylene (TCNE) and 7,7,8,8-tetracyano-p-quinodimethane (TCNQ) with Fe(CO)(5) leads to formation of magnetically ordered materials of Fe[TCNE](2) (T(c) = 100 K) and Fe[TCNQ](2) (T(c) = 35 K) composition, respectively. In contrast, the reaction with 1,2-dichloro-5,6-dicyanobenzoquinone (DDQ) leads to a paramagnetic material.