Range of the screened coulomb interaction in electrolytes and double layer problems

It is shown that the range of the Coulomb interaction in unsymmetric electrolytes at large distances is determined not by the Debye screening length, but by a rather more complicated function of the density, which is evaluated explicitly.     

Stimulus-dependent spatial patterns of response in SI cortex

Background  

Recently we reported that vibrotactile flutter stimulation of a skin locus at different amplitudes evokes an optical response confined to the same local region of the primary somatosensory cortex (SI), where its overall magnitude varies proportionally to the flutter amplitude. In this report, we characterize the impact of the flutter amplitude on the spatial patterns of activity evoked within the responding SI region.     

Synthesis of the carbocyclic skeleton of abyssomicins C and D

[reaction: see text] Intramolecular Diels-Alder substrate trienyl methylenebutenolide 5 was prepared in six steps by coupling 3-methoxy-4-methylenebutenolide (6) with trienone keto aldehyde 7. Heating 5 in CHCl(3) for 2 d at 70 degrees C afforded 80% of a single Diels-Alder adduct 4 with the complete carbon skeleton of abyssomicin C. Addition of thiophenoxide to the enone double bond of 4 followed by an intramolecular Michael addition afforded 15 with the abyssomicin D carbon skeleton.     

Electrochemistry in ultrahigh vacuum: underpotential deposition of Al on polycrystalline W and Au from room temperature AlCl(3)/1-ethyl-3-methylimidazolium chloride melts

The voltammetric characteristics of polycrystalline Au and W electrodes cleaned (thermal annealing at 1100 K) and characterized (Auger electron spectroscopy) in ultrahigh vacuum (UHV) have been examined in ultrapure AlCl(3)/1-ethyl-3-methylimidazolium chloride (EtMeImCl) melts in UHV. These experiments were performed using a custom-designed transfer system that allows for the all-Al electrochemical cell to be filled with EtMeImCl in an auxiliary UHV chamber and later transferred under UHV to the main UHV chamber that houses the Auger electron spectrometer. The results obtained for the underpotential (UPD) and bulk deposition of Al on Au were found to be very similar to those reported in the literature for measurements carried out under 1 atm of an inert gas in a glovebox. For the far more reactive W surfaces, voltammetric features ascribed to the stripping of underpotential-deposited Al could be observed following a single scan from 1.0 V vs Al(3+)/Al to a potential negative enough for bulk deposition of Al to ensue. This behavior is unlike that reported in the literature for experiments performed in a glovebox, which required either extensive potential cycling in the Al bulk deposition and stripping region or excursions to potentials positive enough for chlorine evolution to ensue for Al UPD features to be clearly discerned. These observations open new prospects for fundamental electrochemical studies of well-characterized, highly reactive metals, including single crystals, in a variety of low vapor pressure ionic liquids.     

Schrödinger Operators with Few Bound States

We show that whole-line Schrödinger operators with finitely many bound states have no embedded singular spectrum. In contradistinction, we show that embedded singular spectrum is possible even when the bound states approach the essential spectrum exponentially fast. We also prove the following result for one- and two-dimensional Schrödinger operators, H, with bounded positive ground states: Given a potential V, if both H±V are bounded from below by the ground-state energy of H, then V≡0.D. D. was supported in part by NSF grant DMS–0227289.R. K. was supported in part by NSF grant DMS–0401277.B. S. was supported in part by NSF grant DMS–0140592.     

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.     

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.