Roots of Dehn twists

Margalit and Schleimer found examples of roots of the Dehn twist t _C about a nonseparating curve C in a closed orientable surface, that is, homeomorphisms h such that h ⁿ   =  t _C in the mapping class group. Our main theorem gives elementary number-theoretic conditions that describe the n for which an n ^th root of t _C exists, given the genus of the surface. Among its applications, we show that n must be odd, that the Margalit-Schleimer roots achieve the maximum value of n among the roots for a given genus, and that for a given odd n, n ^th roots exist for all genera greater than (n − 2)(n − 1)/2. We also describe all n ^th roots having n greater than or equal to the genus.     

Evidence for α-helices in the gas phase: a case study using Melittin from honey bee venom

Gas phase methodologies are increasingly used to study the structure of proteins and peptides. A challenge to the mass spectrometrist is to preserve the structure of the system of interest intact and unaltered from solution into the gas phase. Small peptides are very flexible and can present a number of conformations in solution. In this work we examine Melittin a 26 amino acid peptide that forms the active component of honey bee venom. Melittin is haemolytic and has been shown to form an α-helical tetrameric structure by X-ray crystallography [M. Gribskov et al., The RCSB Protein Data Bank, 1990] and to be helical in high concentrations of methanol. Here we use ion mobility mass spectrometry, molecular dynamics and gas-phase HDX to probe its structure in the gas phase and specifically interrogate whether the helical form can be preserved. All low energy calculated structures possess some helicity. In our experiments we examine the peptide following nano-ESI from solutions with varying methanol content. Ion mobility gives collision cross sections (CCS) that compare well with values found from molecular modelling and from other reported structures, but with inconclusive results regarding the effect of solvent. There is only a slight increase in CCS with charge, showing minimal coloumbically driven unfolding. HDX supports preservation of some helical content into the gas phase and again shows little difference in the exchange rates of species sprayed from different solvents. The [M + 3H](3+) species has two exchanging populations both of which exhibit faster exchange rates than observed for the [M + 2H](2+) species. One interpretation for these results is that the time spent being analysed is sufficient for this peptide to form a helix in the 'ultimate' hydrophobic environment of a vacuum.     

Digital asymmetric waveform isolation (DAWI) in a digital linear ion trap

Traditionally, in a quadrupole mass filter, ion isolation is achieved by scanning the rf and DC voltages with a fixed ratio. In this paper, we describe an innovative procedure implemented in a digitally driven linear ion trap termed digital asymmetric waveform isolation (DAWI) in which ion isolation is obtained by manipulation of the duty cycle of the rectangular waveforms. Variation of the waveform duty cycle allows introduction of a precisely defined DC quadrupole component into the main trapping field of the quadrupole ion filter. The DAWI method is completely controlled at software level and does not require any hardware modification.     

Projective modules and Hilbert spaces with a Nevanlinna-Pick kernel

In this paper we solve a mapping problem for a particular class of Hilbert modules over an algebra multipliers of a diagonal Nevanlinna-Pick (NP) kernel. In this case, the regular representation provides a multiplier norm which induces the topology on the algebra. In particular, we show that, in an appropriate category, a certain class of Hilbert modules are projective. In addition, we establish a commutant lifting theorem for diagonal NP kernels.

     

Ersatz Commutant Lifting with Test Functions

This note presents a commutant lifting theorem (CLT) with initial data a finite set of (test) functions and a compatible reproducing kernel k on a set X. This covers the CLT of Ball, Li, Timotin, and Trent [9] for the polydisc, but in general no analyticity is required, rather statements and proofs use the language and techniques of reproducing kernel Hilbert spaces. Uniqueness of the de Branges–Rovnyak construction like found in Agler [1] and Ambrozie, Englis, and Müller [5] and an abstract Beurling Theorem in the present context are of independent interest. Received: October 12, 2006. Accepted: May 8, 2007.     

Regularity of prime ideals

Mathematische Zeitschrift - We answer several natural questions which arise from a recent paper of McCullough and Peeva providing counterexamples to the Eisenbud–Goto Regularity Conjecture....     

Implosion of solid liner for compression of field reversedconfiguration

The design and first successful demonstration of an imploding solid liner with height to diameter ratio, radial convergence, and uniformity suitable for compressing a field reversed configuration is discussed. Radiographs indicated a very symmetric implosion with no instability growth, with ~13x radial compression of the inner liner surface prior to impacting a central measurement unit. The implosion kinetic energy was 1.5 megajoules, 34% of the capacitor stored energy of 4.4 megajoules