Realizing deformations of curves using Lubin-Tate formal groups

Letk be an algebraically closed field of characteristicp>0 andR be a suitable valuation ring of characteristic 0, dominating the Witt vectorsW(k). We show how Lubin-Tate formal groups can be used to lift those orderp ⁿ automorphisms ofk[[Z]] toR[[Z]], which occur as endomorphisms of a formal group overk of suitable height. We apply this result to prove the existence of smooth liftings of galois covers of smooth curves from characteristicp to characteristic 0, provided thep-part of the inertia groups acting on the completion of the local rings at the points of the cover overk arep-power cyclic and determined by an endomorphism of a suitable formal group overk. The author would like to express his thanks to the Max-Planck-Institut für Mathematik, Bonn, for its hospitality and support, where this research was done during a visit from June – September 2001.     

Quad quantum cascade laser spectrometer with dual gas cells for the simultaneous analysis of mainstream and sidestream cigarette smoke

A compact, fast response, infrared spectrometer using four pulsed quantum cascade (QC) lasers has been applied to the analysis of gases in mainstream (MS) and sidestream (SS) cigarette smoke. QC lasers have many advantages over the traditional lead-salt tunable diode lasers, including near room temperature operation with thermoelectric cooling and single mode operation with improved long-term stability. The new instrument uses two 36 m, 0.3 l multiple pass absorption gas cells to obtain a time response of 0.1s for the MS smoke system and 0.4s for the SS smoke system. The concentrations of ammonia, ethylene, nitric oxide, and carbon dioxide for three different reference cigarettes were measured simultaneously in MS and SS smoke. A data rate of 20Hz provides sufficient resolution to determine the concentration profiles during each 2s puff in the MS smoke. Concentration profiles before, during and after the puffs also have been observed for these smoke constituents in SS smoke. Also, simultaneous measurements of CO(2) from a non-dispersive infrared (NDIR) analyzer are obtained for both MS and SS smoke. In addition, during this work, nitrous oxide was detected in both the MS and SS smoke for all reference cigarettes studied.     

Ruthenium-catalyzed enyne cycloisomerizations. Effect of allylic silyl ether on regioselectivity

The ruthenium-catalyzed cycloisomerization of 1,6- and 1,7-enynes substituted in the terminal allylic position with a tert-butyldimethylsilyl ether group emerges as an effective reaction to form unprecedented five- or six-membered rings possessing a geometrically defined enol silane. Straightforward synthetic access to a variety of achiral 1,6- and 1,7-enynes, as well as chiral ones, is presented. Ruthenium catalysts effect efficiently such single-step cycloisomerization at room temperature in acetone under neutral conditions. The cycloisomerization functions with (E) or (Z) 1,2-disubstituted alkenes. Parameters influencing the enol silane geometry are discussed. The level of selectivity depends on the alkyne substitution, the geometry of the double bond, and the nature of the catalyst. Furthermore, examples of stereoinduction are shown and lead to highly substituted carbo- and heterocycles with excellent diastereocontrol.     

Experimental and theoretical characterization of arsenite in water: insights into the coordination environment of As-O

Long-term exposure to arsenic in drinking water has been linked to cancer of the bladder, lungs, skin, kidney, nasal passages, liver, and prostate in humans. It is therefore important to understand the structural aspects of arsenic in water, as hydrated arsenic is most likely the initial form of the metalloid absorbed by cells. We present a detailed experimental and theoretical characterization of the coordination environment of hydrated arsenite. XANES analysis confirms As(III) is a stable redox form of the metalloid in solution. EXAFS analysis indicate, at neutral pH, arsenite has a nearest-neighbor coordination geometry of approximately 3 As-O bonds at an average bond length of 1.77 A, while at basic pH the nearest-neighbor coordination geometry shifts to a single short As-O bond at 1.69 A and two longer As-O bonds at 1.82 A. Long-range ligand scattering is present in all EXAFS samples; however, these data could not be fit with any degree of certainty. There is no XAS detectable interaction between As and antimony, suggesting they are not imported into cells as a multinuclear complex. XAS results were compared to a structural database of arsenite compounds to confirm that a 3 coordinate As-O complex for hydrated arsenite is the predominate species in solution. Finally, quantum chemical studies indicate arsenite in solution is solvated by 3 water molecules. These results indicate As(OH)3 as the most stable structure existing in solution at neutral pH; thus, ionic As transport does not appear to be involved in the cellular uptake process.     

Inconsistency in the application of the adiabatic theorem

The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic if the change in eigenstate is significant, regardless of how closely the evolution satisfies the requirements of the adiabatic theorem. We also introduce an example of a two-level system with an exactly solvable evolution to demonstrate the inapplicability of the adiabatic approximation for a particular slowly varying Hamiltonian.     

Effects of hypothermia on ischaemic depolarisation in brain : a comparison of responses in rat and gerbil

The latency of development of ischaemic depolarization (LID) has been used to compare the relative effects of different levels of hypothermia on ischaemic responses in brains of rat and gerbil, using a model with imposed complete cessation of cerebral blood flow (CBF=0). At temperatures reducing from 37 degrees C to 20 degrees C, the LIDs were consistently shorter in the gerbil than in the rat. For example, at 37 degrees C the LID in the gerbil was 0.71+/- 01.2 min, and in the rat, 1.37 +/- 0.02 min respectively (P<0.01), whilst at 20 degrees C, the values were 5.48 +/- 0.25 min and 7.30 +/- 0.76 min (P<0.01). However, the relative effects of hypothermia on each species were similar (by linear regression with slopes of -0.29 and -0.35 min/degree C in the two species). There may be underlying differences in brain biophysics or structure between species, but in spite of this, applied hypothermia still imposes a similar depression on the development of ischaemic damage. Both models may thus be used in studies of brain hypothermia as long as the intrinsic differences are appreciated.     

In vivo human retinal imaging by ultrahigh-speed spectral domain optical coherence tomography

An ultrahigh-speed spectral domain optical coherence tomography (SD-OCT) system is presented that achieves acquisition rates of 29,300 depth profiles/s. The sensitivity of SD-OCT and time domain OCT (TD-OCT) are experimentally compared, demonstrating a 21.7-dB improvement of SD-OCT over TD-OCT. In vivo images of the human retina are presented, demonstrating the ability to acquire high-quality structural images with an axial resolution of 6 microm at ultrahigh speed and with an ocular exposure level of less than 600 microW.     

Microwave activation in ionic liquids induces high temperature-high speed electrochemical processes

Self-focusing of intense microwave radiation at the tip of a 25 microm diameter platinum disk microelectrode immersed into the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate (BMIM(+)PF(6)(-)) containing 1 mM ferrocene causes dramatically (two orders of magnitude) enhanced voltammetric current signals and temperatures in excess of 600 K (at the electrode surface)--extreme conditions sufficient for condensed phase pyrolysis processes to occur.     

Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography

A signal-to-noise ratio (SNR) analysis is presented for optical coherence tomography (OCT) signals in which time-domain performance is compared with that of the spectral domain. A significant SNR gain of several hundredfold is found for acquisition in the spectral domain. The SNR benefit is demonstrated experimentally in a hybrid time-domain-spectral-domain OCT system.     

Gene expression in response to low temperatures in mammalian cells: a review of current ideas

This review was undertaken to identify responses of mammalian cells to cold temperatures, such as might be encountered in therapeutic procedures where body temperatures are lowered, in preservation of cells and organs, and in cryopreservation. In general, cold elicits a range of stress responses through identified signaling pathways, which may determine the survival or otherwise of the cells. Under conditions of mild hypothermia, there is evidence for responses which reflect an ordered acclimation to the new environment, whilst deep cooling invokes a more generalised stress response.