A first low‐resolution difference Fourier map of phosphorus in a membrane protein from near‐edge anomalous diffraction

Crystal diffraction of three membrane proteins (cytochrome bc₁ complex, sarcoplasmic reticulum Ca²⁺ ATPase, ADP‐ATP carrier) and of one nucleoprotein complex (leucyl tRNA synthetase bound to tRNAleu, leuRS:tRNAleu) was tested at wavelengths near the X‐ray K‐absorption edge of phosphorus using a new set‐up for soft X‐ray diffraction at the beamline ID01 of the ESRF. The best result was obtained from crystals of Ca²⁺ ATPase [adenosin‐5′‐(β,γ‐methylene) triphosphate complex] which diffracted out to 7 Å resolution. Data were recorded at a wavelength at which the real resonant scattering factor of phosphorus reaches the extreme value of ?20 electron units. The positions of the four triphosphates of the monoclinic unit cell of the ATPase have been obtained from a difference Fourier synthesis based on a limited set of anomalous diffraction data.     

Effect of Nd3+ concentration on CW and pulsed performance of fiber-coupled diode laser pumped Nd:YVO4 laser at 1064 nm

The effect of Nd³⁺ concentration on the CW and Q-switched laser performances at 1064 nm from Nd: YVO₄ has been studied under diode laser pumping in identical laser configuration. The Nd³⁺ concentrations used were 1, 2 and 3 at.% in YVO₄ crystals. Under the CW operations we have compared the thermal lensing effect, slope efficiencies and also the beam quality at the fourth-order degeneracy configuration. Q-switching was done with the help of an acousto-optic modulator and we have compared the pulses obtained from Nd: YVO₄ laser with different doping concentration. It was found that the 1 at.%-doped crystal is the best, offering highest optical-to-optical conversion efficiency (55%), lowest fractional heat load (24%), highest pulse energy (80 μJ) and shortest pulse width (20 ns). It was also found that there was not much difference in performances for 2 and 3 at.%-doped crystals both in CW and Q-switched configurations.     

Preconditioned Iterative Methods for Scattered Data Interpolation

The scattered data interpolation problem in two space dimensions is formulated as a partial differential equation with interpolating side conditions. The system is discretized by the Morley finite element space. The focus of this paper is to study preconditioned iterative methods for the corresponding discrete systems. We introduce block diagonal preconditioners, where a multigrid operator is used for the differential equation part of the system, while we propose an operator constructed from thin plate radial basis functions for the equations corresponding to the interpolation conditions. The effect of the preconditioners are documented by numerical experiments.     

Intramolecular hydrogen bonding. Spectroscopic and theoretical studies of vibrational transitions in dibenzoylmethane enol

The vibrational structure of the title compound (DBM) was investigated by FTIR spectroscopy in liquid solutions, by FTIR linear dichroism (LD) measurements, and by Raman spectroscopy. The results were supported by the application of theoretical model calculations and analyzed with particular attention to the possible origin of the broad, very strong, and irregularly shaped absorbance band observed in the 1700–1400 cm⁻¹ region. The orientation factors derived from the observed LD data indicate that rotational dynamics of the phenyl groups do not contribute significantly to the broadening of the band. The position of the two sharp Evans transmission windows near 1580 and 1500 cm⁻¹ is unaffected by deuteration of the reactive protons in DBM. The transmissions coincide with prominent peaks in the Raman spectrum and can be assigned to combinations of phenylic modes (9a, 18a) with low IR intensity, but large Raman scattering activity.     

A test complex for Gorensteinness

Let be a commutative noetherian ring with a dualizing complex. By recent work of Iyengar and Krause (2006), the difference between the category of acyclic complexes and its subcategory of totally acyclic complexes measures how far is from being Gorenstein. In particular, is Gorenstein if and only if every acyclic complex is totally acyclic.

In this note we exhibit a specific acyclic complex with the property that it is totally acyclic if and only if is Gorenstein.

     

Finite elements for symmetric tensors in three dimensions

We construct finite element subspaces of the space of symmetric tensors with square-integrable divergence on a three-dimensional domain. These spaces can be used to approximate the stress field in the classical Hellinger-Reissner mixed formulation of the elasticty equations, when standard discontinuous finite element spaces are used to approximate the displacement field. These finite element spaces are defined with respect to an arbitrary simplicial triangulation of the domain, and there is one for each positive value of the polynomial degree used for the displacements. For each degree, these provide a stable finite element discretization. The construction of the spaces is closely tied to discretizations of the elasticity complex and can be viewed as the three-dimensional analogue of the triangular element family for plane elasticity previously proposed by Arnold and Winther.

     

Finite Gorenstein representation type implies simple singularity

Let R be a commutative noetherian local ring and consider the set of isomorphism classes of indecomposable totally reflexive R-modules. We prove that if this set is finite, then either it has exactly one element, represented by the rank 1 free module, or R is Gorenstein and an isolated singularity (if R is complete, then it is even a simple hypersurface singularity). The crux of our proof is to argue that if the residue field has a totally reflexive cover, then R is Gorenstein or every totally reflexive R-module is free.     

Working group report: Heavy-ion physics and quark-gluon plasma

This is the report of Heavy Ion Physics and Quark-Gluon Plasma at WHEPP-09 which was part of Working Group-4. Discussion and work on some aspects of quark-gluon plasma believed to have created in heavy-ion collisions and in early Universe are reported.     

Mixed finite element methods for linear elasticity with weakly imposed symmetry

In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a modified form of the Hellinger-Reissner variational principle that only weakly imposes the symmetry condition on the stresses. Although this approach has been previously used by a number of authors, a key new ingredient here is a constructive derivation of the elasticity complex starting from the de Rham complex. By mimicking this construction in the discrete case, we derive new mixed finite elements for elasticity in a systematic manner from known discretizations of the de Rham complex. These elements appear to be simpler than the ones previously derived. For example, we construct stable discretizations which use only piecewise linear elements to approximate the stress field and piecewise constant functions to approximate the displacement field.