Graded Nilpotent Algebras and Eggert's Conjecture

A group G is (l,m,n)-generated if it is a quotient group of the triangle group T(l,m,n) = (x,y,z|x ^l= y ^m= z ⁿ= xyz= 1). In [8] the problem is posed to find all possible (l,m,n)-generations for the non-abelian finite simple groups. In this paper we partially answer this question for the Janko group J ₃. We find all (2, 3, t)-generations as well as (2, 2,2,p)-generations, p a prime, for J ₃     

Singularities and semistable degenerations for symplectic topology

We overview our work [7], [8], [9], [10], [11], [6] defining and studying normal crossings varieties and subvarieties in symplectic topology. This work answers a question of Gromov on the feasibility of introducing singular (sub)varieties into symplectic topology in the case of normal crossings singularities. It also provides a necessary and sufficient condition for smoothing normal crossings symplectic varieties. In addition, we explain some connections with other areas of mathematics and discuss a few directions for further research.     

Comparison of connective tissue invaded by Lewis lung carcinoma to healthy connective tissue by means of micro‐Raman spectroscopy

We have measured the micro‐Raman spectra of mouse tissues invaded by Lewis lung carcinoma (LLC). We have also carried out categorical principal component analysis (CATPCA) on the acquired spectra. The results indicate that the tumor tissues can be well discriminated from normal tissues by the first two principal components extracted from the spectra. Furthermore, we have found that the concentrations of nucleic acids and lipids/fatty acids in the tumor are considerably higher than those in the normal tissue, whereas the collagen concentration is lower. These differences can be detected and characterized by Raman images using the 788 cm⁻¹ DNA/RNA band and the 1301 cm⁻¹ lipid/fatty acid band. Copyright © 2009 John Wiley & Sons, Ltd.     

Symplectic homology of Lefschetz fibrations and Floer homology of the monodromy map

We construct a spectral sequence converging to symplectic homology of a Lefschetz fibration whose E ¹ page is related to Floer homology of the monodromy symplectomorphism and its iterates. We use this to show the existence of fixed points of certain symplectomorphisms.     

Role of poloidal E × B drift in divertor heat transport in DIII-D

Simulations for DIII-D high confinement mode plasmas with the multifluid code UEDGE show a strong role of poloidal E × B drifts on divertor heat transport, challenging the paradigm of conduction-limited scrape-off layer (SOL) transport. While simulations with reduced drift magnitude are well aligned with the assumption that electron heat conduction dominates the SOL heat transport, simulations with drifts predict that the poloidal convective E × B heat transport dominates over electron heat conduction in both attached and detached conditions. As poloidal E × B flow propagates across magnetic field lines, poloidal transport with shallow magnetic pitch angles can reach values that are of the same order as would be provided by sonic flows parallel to the field lines. These flows can lead to strong convection-dominated divertor heat transport, increasing the poloidal volume of radiative power front, consistent with previous measurements at DIII-D. Due to these convective flows, the Lengyel integral approach, assuming zero convective fraction, is expected to provide a pessimistic estimate for the radiative capability of impurities in the divertor. For the DIII-D simulations shown here, the Lengyel integral approach underestimates the radiated power by a factor of 6, indicating that, for reliable DIII-D divertor power exhaust predictions, full two-dimensional (2D) calculations, including drifts, would be necessary.     

Microscale Fracture Toughness of Bismuth Doped Copper Bicrystals Using Double Edge Notched Microtensile Tests

The availability of focused ion beam (FIB) milling, nanoindentation, and microelectromechanical systems (MEMS) based test platforms has enabled small-scale mechanical testing to become an increasingly popular approach for measuring material properties. While great emphasis has been placed on measuring plastic properties at the micro- and nanoscale [1, 2], an area that has received significantly less consideration is the measurement of fracture toughness. A technique for performing small-scale, in situ fracture toughness tests using double edge notched tensile (DENT) specimens has been developed and used to measure a nearly 40 % reduction in toughness associated with the addition of Bi to the grain boundary of a Cu bicrystal. That Bi embrittles Cu grain boundaries is well known [3–10], however, as shown herein, the DENT technique offers certain advantages over existing boundary fracture tests, especially when used with ductile materials.     

Application of Fragment Screening and Merging to the Discovery of Inhibitors of the Mycobacterium tuberculosis Cytochrome P450 CYP121

Pieces of the puzzle: The first fragment-based approach was used to target cytochrome?P450 enzymes (CYPs) for drug development. The experiments provide new insights into the binding site of the essential Mycobacterium tuberculosis CYP121 enzyme, and resulted in a promising novel lead compound based on fragment merging.     

Raman spectroscopy of dipyrrins: nonresonant,resonant and surface‐enhanced cross‐sections and enhancement factors

Detailed studies of the mechanism of surface‐enhanced (resonance) Raman spectroscopy (SE(R)RS), and its applications, place a number of demands on the properties of SERS scatterers. With large Raman cross‐sections, versatile synthetic chemistry and complete lack of fluorescence, free dipyrrins meet these demands but the Raman and SE(R)RS spectroscopy of free dipyrrins is largely unknown. The first study of the Raman spectroscopy of free dipyrrins is therefore presented in this work. The nonresonant Raman, resonant Raman and surface‐enhanced Raman spectra of a typical meso aryl‐substituted‐dipyrrin are reported. Absolute differential cross‐sections are obtained for excitation wavelengths in the near infrared and visible region, in solution phase and for dipyrrin adsorbed on the surface of silver nanoparticles. Raman enhancement factors for SERRS and resonance Raman are calculated from the observed differential cross‐sections. The magnitudes of the resonantly enhanced cross‐sections are similar to those recently reported for strong SERS dyes such as Rhodamine 6G and Crystal Violet. Free dipyrrins offer the advantages of existing SERS dyes but without the drawback of strong fluorescence. Free dipyrrins should therefore find applications in all areas of Raman spectroscopy including fundamental studies of the mechanisms of SERS and bioanalytical and environmental applications. Copyright © 2011 John Wiley & Sons, Ltd.     

Atomic absorption with ultracold atoms

Recent advances in laser-atom cooling techniques and diode-laser technology now allow one to conduct an idealised atomic absorption experiment comprising a sample of ultracold, quasi-stationary absorbing atoms and a source of near-monochromatic resonant light. Under such conditions, the atomic absorption coefficient at line centre is independent of the oscillator strength of the atomic resonance line. This offers the prospect of ‘oscillator-strength-free’ atomic absorption spectroscopy in which the absorption signal is equally large for both strong and weak (closed) transitions of the same wavelength and in which absolute atomic absorption could be performed without knowledge of the oscillator strength. Moreover, the resolution and sensitivity for a given atom density are greatly enhanced, typically by approximately three orders of magnitude (and even more for weak transitions), compared with conventional flame or graphite-furnace atomic absorption. We describe an atomic absorption experiment based on samples of ultracold, laser-cooled caesium atoms and a narrow-bandwidth diode laser source that approximates the idealised conditions for oscillator-strength-free atomic absorption. The absorption measurements are used to determine the number density and temperature (approx. 6 μK) of the sample of ultracold atoms. Some of the technical obstacles that would have to be overcome before samples of ultracold atoms and diode laser sources could be used in analytical atomic absorption spectroscopy are discussed.