Note on generalised connections and affine bundles

We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of affineness of a generalised connection.Comment: 17 page

Acrylamide Production Using Encapsulated Nitrile Hydratase from \u3cem\u3ePseudonocardia thermophila\u3c/em\u3e in a Sol–gel Matrix

The cobalt-type nitrile hydratase from Pseudonocardia thermophila JCM 3095 (PtNHase) was successfully encapsulated in tetramethyl orthosilicate sol–gel matrices to produce a PtNHase:sol–gel biomaterial. The PtNHase:sol–gel biomaterial catalyzed the conversion of 600 mM acrylonitrile to acrylamide in 60 min at 35 °C with a yields of \u3e90%. Treatment of the biomaterial with proteases confirmed that the catalytic activity is due to the encapsulated enzyme and not surface bound NHase. The biomaterial retained 50% of its activity after being used for a total of 13 consecutive reactions for the conversion of acrylonitrile to acrylamide. The thermostability and long-term storage of the PtNHase:sol–gel are substantially improved compared to the soluble NHase. Additionally, the biomaterial is significantly more stable at high concentrations of methanol (50% and 70%, v/v) as a co-solvent for the hydration of acrylonitrile than native PtNHase. These data indicate that PtNHase:sol–gel biomaterials can be used to develop new synthetic avenues involving nitriles as starting materials given that the conversion of the nitrile moiety to the corresponding amide occurs under mild temperature and pH conditions

The Nature of the Secondary Star in the Black Hole X-Ray Transient V616 Mon (=A0620-00)

We have used NIRSPEC on Keck II to obtain $K$-band spectroscopy of the low mass X-ray binary V616 Mon (= A0620$-$00). V616 Mon is the proto-typical soft x-ray transient containing a black hole primary. As such it is important to constrain the masses of the binary components. The modeling of the infrared observations of ellipsoidal variations in this system lead to a derived mass of 11.0 M_{\sun} for the black hole. The validity of this derivation has been called into question due to the possiblity that the secondary star's spectral energy distribution is contaminated by accretion disk emission (acting to dilute the variations). Our new $K$-band spectrum of V616 Mon reveals a late-type K dwarf secondary star, but one that has very weak $^{\rm 12}$CO absorption features. Comparison of V616 Mon with SS Cyg leads us to estimate that the accretion disk supplies only a small amount of $K$-band flux, and the ellipsoidal variations are not seriously contaminated. If true, the derived orbital inclination of V616 Mon is not greatly altered, and the mass of the black hole remains large. A preliminary stellar atmosphere model for the $K$-band spectrum of V616 Mon reveals that the carbon abundance is approximately 50% of the solar value. We conclude that the secondary star in V616 Mon has either suffered serious contamination from the accretion of supernova ejecta that created the black hole primary, or it is the stripped remains of a formerly more massive secondary star, one in which the CNO cycle had been active.Comment: 20 pages, 5 figure

Remarks on Bootstrap Percolation in Metric Networks

We examine bootstrap percolation in d-dimensional, directed metric graphs in the context of recent measurements of firing dynamics in 2D neuronal cultures. There are two regimes, depending on the graph size N. Large metric graphs are ignited by the occurrence of critical nuclei, which initially occupy an infinitesimal fraction, f_* -> 0, of the graph and then explode throughout a finite fraction. Smaller metric graphs are effectively random in the sense that their ignition requires the initial ignition of a finite, unlocalized fraction of the graph, f_* >0. The crossover between the two regimes is at a size N_* which scales exponentially with the connectivity range \lambda like_* \sim \exp\lambda^d. The neuronal cultures are finite metric graphs of size N \simeq 10^5-10^6, which, for the parameters of the experiment, is effectively random since N<< N_*. This explains the seeming contradiction in the observed finite f_* in these cultures. Finally, we discuss the dynamics of the firing front

Time-Energy coherent states and adiabatic scattering

Coherent states in the time-energy plane provide a natural basis to study adiabatic scattering. We relate the (diagonal) matrix elements of the scattering matrix in this basis with the frozen on-shell scattering data. We describe an exactly solvable model, and show that the error in the frozen data cannot be estimated by the Wigner time delay alone. We introduce the notion of energy shift, a conjugate of Wigner time delay, and show that for incoming state $\rho(H_0)$ the energy shift determines the outgoing state.Comment: 11 pages, 1 figur

The Texas Petawatt Laser And Current Experiments

The Texas Petawatt Laser is operational with experimental campaigns executed in both F/40 and F3 target chambers. Recent improvements have resulted in intensities of >2x10(21) W/cm(2) on target. Experimental highlights include, accelerated electron energies of >2 GeV, DD fusion ion temperatures >25 keV and isochorically heated solids to 10-50 eV.Physic