Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups

The Harish-Chandra correlation functions, i.e. integrals over compact groups of invariant monomials with the weight exp tr (X Ω Y Ω ^† ) are computed for the orthogonal and symplectic groups. We proceed in two steps. First, the integral over the compact group is recast into a Gaussian integral over strictly upper triangular complex matrices (with some additional symmetries), supplemented by a summation over the Weyl group. This result follows from the study of loop equations in an associated two-matrix integral and may be viewed as the adequate version of Duistermaat–Heckman’s theorem for our correlation function integrals. Secondly, the Gaussian integration over triangular matrices is carried out and leads to compact determinantal expressions.     

Synergic approach to XAFS analysis for the identification of most probable binding motifs for mononuclear zinc sites in metalloproteins

In the present work a data analysis approach, based on XAFS data, is proposed for the identification of most probable binding motifs of unknown mononuclear zinc sites in metalloproteins. This approach combines multiple‐scattering EXAFS analysis performed within the rigid‐body refinement scheme, non‐muffin‐tin ab initio XANES simulations, average structural information on amino acids and metal binding clusters provided by the Protein Data Bank, and Debye–Waller factor calculations based on density functional theory. The efficiency of the method is tested by using three reference zinc proteins for which the local structure around the metal is already known from protein crystallography. To show the applicability of the present analysis to structures not deposited in the Protein Data Bank, the XAFS spectra of six mononuclear zinc binding sites present in diverse membrane proteins, for which we have previously proposed the coordinating amino acids by applying a similar approach, is also reported. By comparing the Zn K‐edge XAFS features exhibited by these proteins with those pertaining to the reference structures, key spectral characteristics, related to specific binding motifs, are observed. These case studies exemplify the combined data analysis proposed and further support its validity.     

Noise Reduction in Spur Gear Systems

This article lists some tips for reducing gear case noise. With this aim, a static analysis was carried out in order to describe how stresses resulting from meshing gears affect the acoustic emissions. Different parameters were taken into account, such as the friction, material, and lubrication, in order to validate ideas from the literature and to make several comparisons. Furthermore, a coupled Eulerian–Lagrangian (CEL) analysis was performed, which was an innovative way of evaluating the sound pressure level of the aforementioned gears. Different parameters were considered again, such as the friction, lubrication, material, and rotational speed, in order to make different research comparisons. The analytical results agreed with those in the literature, both for the static analysis and CEL analysis—for example, it was shown that changing the material from steel to ductile iron improved the gear noise, while increasing the rotational speed or the friction increased the acoustic emissions. Regarding the CEL analysis, air was considered a perfect gas, but its viscosity or another state equation could have also been taken into account. Therefore, the above allowed us to state that research into these scientific fields will bring about reliable results.     

Logics from ?{￠}\sqrt{^{\prime}} Quasi-MV Algebras

The purpose of the present article is to extend the scope of some investigations about abstract logics arising quite naturally out of Quasi-MV algebras (for short, qMV algebras) also to ?{^￠}\sqrt{^{\prime}} qMV algebras. We will therefore introduce, mutually compare and (in some cases) axiomatise several logics arising out of the variety of ?{^￠}\sqrt{^{\prime}} qMV algebras and out of some important subclasses of such. Subsequently, we will investigate the same logics by resorting to the methods and techniques of abstract algebraic logic.     

Raman scattering of MnOx?CeOx composite catalysts: structural aspects and laser‐heating effects

Composite MnO_x CeO_x catalysts (Mn_at: Ce_at = 1) synthesized via the redox and coprecipitation routes were comparatively characterized by micro‐Raman spectroscopy using a laser irradiation power ranging between 0.6 and 4.2 mW. A quasi‐molecular dispersion of the oxide species determines a major and irreversible structural rearrangement of the redox MnO_x CeO_x system because of severe heating effects for laser power in excess of 0.6 mW. The X‐ray diffraction data of samples calcined in the range of 673 1273 K confirm that the micro‐Raman characterization of the composite MnO_x CeO_x systems requires an adequate minimization of the irradiation power to prevent the strong sintering and restructuring phenomena due to laser‐heating effects. Copyright © 2011 John Wiley & Sons, Ltd.     

Dirac Operators on Quantum Projective Spaces

We construct a family of self-adjoint operators D _N , ${N\in{\mathbb Z}}We construct a family of self-adjoint operators D _N , N ? \mathbb Z{N\in{\mathbb Z}} , which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space \mathbb CP^l_q{{\mathbb C}{\rm P}^{\ell}_q} , for any ℓ ≥ 2 and 0 < q < 1. They provide 0⁺-dimensional equivariant even spectral triples. If ℓ is odd and N=\frac12(l+1){N=\frac{1}{2}(\ell+1)} , the spectral triple is real with KO-dimension 2ℓ mod 8.     

Continuously tunable 1 byte delay in coupled-resonator optical waveguides

A reconfigurable coupled-resonator optical waveguide made of a few directly coupled ring resonators is employed to control the delay of data streams modulated at tens of gigabits per second. A delay of 8 bit lengths (1 optical byte) with a small pulse broadening and 1 dB/bit fractional loss is achieved by using only eight rings. The limiting role of waveguide loss and spurious backreflections is experimentally investigated. The high storage efficiency (1 bit/ring) of the device enables an easy, reliable, hitless, and relatively low-power-consuming management of the delay. A higher storage efficiency is demonstrated to be associated to an unavoidable higher pulse distortion.     

Modular forms and three-loop superstring amplitudes

We study a proposal of D'Hoker and Phong for the chiral superstring measure for genus three. A minor modification of the constraints they impose on certain Siegel modular forms leads to a unique solution. We reduce the problem of finding these modular forms, which depend on an even spin structure, to finding a modular form of weight 8 on a certain subgroup of the modular group. An explicit formula for this form, as a polynomial in the even theta constants, is given. We checked that our result is consistent with the vanishing of the cosmological constant. We also verified a conjecture of D'Hoker and Phong on modular forms in genus 3 and 4 using results of Igusa.     

Temperature effects in ultrasonic Lamb wave structural health monitoring systems

There is a need to better understand the effect of temperature changes on the response of ultrasonic guided-wave pitch-catch systems used for structural health monitoring. A model is proposed to account for all relevant temperature-dependent parameters of a pitch-catch system on an isotropic plate, including the actuator-plate and plate-sensor interactions through shear-lag behavior, the piezoelectric and dielectric permittivity properties of the transducers, and the Lamb wave dispersion properties of the substrate plate. The model is used to predict the S(0) and A(0) response spectra in aluminum plates for the temperature range of -40-+60 degrees C, which accounts for normal aircraft operations. The transducers examined are monolithic PZT-5A [PZT denotes Pb(Zr-Ti)O3] patches and flexible macrofiber composite type P1 patches. The study shows substantial changes in Lamb wave amplitude response caused solely by temperature excursions. It is also shown that, for the transducers considered, the response amplitude changes follow two opposite trends below and above ambient temperature (20 degrees C), respectively. These results can provide a basis for the compensation of temperature effects in guided-wave damage detection systems.