Equivalence of quotient Hilbert modules-II

For any open, connected and bounded set , let be a natural function algebra consisting of functions holomorphic on . Let be a Hilbert module over the algebra and let be the submodule of functions vanishing to order on a hypersurface . Recently the authors have obtained an explicit complete set of unitary invariants for the quotient module in the case of . In this paper, we relate these invariants to familiar notions from complex geometry. We also find a complete set of unitary invariants for the general case. We discuss many concrete examples in this setting. As an application of our equivalence results, we characterise certain homogeneous Hilbert modules over the bi-disc algebra.

     

Superconductivity in non-stoichiometric and tin-substituted La2CuO4: preparation, characterization, Mössbauer and microwave-absorption studies

Two samples of non-stoichiometric La₂CuO₄ were synthesized, one with La/Cu<2, and the other with 10% Sn substituting Cu. They were investigated by X-ray diffraction, Mössbauer spectroscopy, and microwave-absorption techniques. The microwave-absorption data indicated that they were both superconducting, with the transition temperatures T_c of 40.5 and 41.5 K, the one doped with Sn possessing the higher T_c. The Mössbauer spectra revealed that there exist two kinds of Sn(IV) atoms disordered with Cu. Their isomer shift, δ=−0.244(4) mm/s, is in agreement with Sn(IV) coordinated by oxygen. One site was characterized by a single Mössbauer line, being associated with a weakly distorted environment, wherein the Sn, coordinated more symmetrically, is surrounded by four Cu²⁺ ions. On the other hand, the other site, characterized by a Mössbauer doublet exhibited a quadrupole splitting Δ=1.07(2) mm/s, being associated with a highly distorted coordination, explained to be due to Sn occupying two adjacent cationic sites. To our knowledge, such a substitution for copper ions not resulting in a decrease of T_c has not been reported previously.     

Atomic scale imaging and spectroscopy of a CuO(2) plane at the surface of Bi(2)Sr(2)CaCu(2)O(8+delta)

We have used a scanning tunneling microscope to demonstrate that a single CuO2 plane can form a stable and atomically ordered layer at the surface of Bi(2)Sr(2)CaCu(2)O(8+delta). In contrast to previous studies on high-T(c) surfaces, the CuO2-terminated surface exhibits a strongly suppressed tunneling conductance at low voltages. We consider a number of different explanations for this phenomena and propose that it may be caused by how the orbital symmetry of the CuO2 plane's electronic states affects the tunneling process.     

Structure and stability of Σ3 grain boundaries in face centered cubic metals

Σ3 grain boundaries form as a result of either growth twinning or deformation twinning in face centered cubic (fcc) metals and play a crucial role in determining the mechanical and electrical properties and microstructural stability. We studied the structure and stability of Σ3 grain boundaries (GBs) in fcc metals by using topological analysis and atomistic simulations. Atomistic simulations were performed for Cu and Al with empirical interatomic potentials to reveal the influence of stacking fault energy on the morphology of the twinned grains. Three sets of tilt Σ3 GBs were studied with respect to the tilt axis parallel to ?111?, ?112?, and ?110?, respectively. We showed that Σ3{111} and Σ3{112} GBs are thermodynamically stable and the others will dissociate into terraced interfaces regardless of the stacking fault energy. The morphology of the nano-twinned grains in Cu is predicted from the above analysis and found to match with experiments.     

Some monothetic subsemigroups of S(ℝ)

In this note we verify a conjecture of Magill [3] about orders of “steplike” functions. These functions turn out to be useful in producing a finite subsemigroup of S(ℝ) of any given order.     

Betterment in EDXRF analytical results for compositional characterization of mixed uranium thorium oxide samples with bead specimens compared with pressed pellet specimens

A comparative study on the energy dispersive X‐ray fluorescence analytical results of uranium determinations, in uranium and uranium–thorium mixed oxides, using specimens in the form of fused beads and pressed pellets, has been made. It was observed that in case of fusion bead specimens, the intensity of the analyte lines was approximately 1.6 times of that observed in pellet specimens under identical instrumental conditions. In case of uranium oxide samples, the analytical results with bead specimens were slightly better compared with the pellet specimens. However, in case of the uranium–thorium oxide mixtures, the average precision obtained with bead specimen was significantly better (1%, 1 s) in comparison with that achieved using pellet specimens (7%, 1 s). This difference may be due to the hardness of thorium oxide compared with uranium oxide, which affects the homogeneity of the pellet specimens prepared. In fusion bead method of sample preparation, even highly refractory material like ThO₂ forms uniform glass beads. Addition of internal standard further improves the analytical results, with reduction in the percent deviation of energy dispersive X‐ray fluorescence results from the expected values to 3% from 7% compared with that obtained using without internal standard. The fusion bead method of sample preparation will be very useful for characterization of sintered (U,Th)O₂ pellets, which are highly refractory and difficult to dissolve. Copyright © 2016 John Wiley & Sons, Ltd.     

Polarized Debye Sheath in Degenerate Plasmas

The force on a charged dust grain in a plasma due to polarization of thermal ions and degenerate electrons around the grain is derived in the limits of weakly relativistic and ultra-relativistic degeneracy of electrons. It is found that in both these cases, the magnitude of the polarization force is enhanced compared to that in classical plasmas. The influence of this force on dust-acoustic(DA) modes is examined and discussed. It is shown that the DA wave frequency in degenerate plasmas is significantly reduced compared to the classical DA mode.     

Enhanced field emission from pulsed laser deposited nanocrystalline ZnO thin films on Re and W

Nanocrystalline ZnO thin films have been deposited on rhenium and tungsten pointed and flat substrates by pulsed laser deposition method. An emission current of 1 nA with an onset voltage of 120 V was observed repeatedly and maximum current density ∼1.3 A/cm² and 9.3 mA/cm² has been drawn from ZnO/Re and ZnO/W pointed emitters at an applied voltage of 12.8 and 14 kV, respectively. In case of planar emitters (ZnO deposited on flat substrates), the onset field required to draw 1 nA emission current is observed to be 0.87 and 1.2 V/μm for ZnO/Re and ZnO/W planar emitters, respectively. The Fowler–Nordheim plots of both the emitters show nonlinear behaviour, typical for a semiconducting field emitter. The field enhancement factor β is estimated to be ∼2.15×10⁵ cm⁻¹ and 2.16×10⁵ cm⁻¹ for pointed and 3.2×10⁴ and 1.74×10⁴ for planar ZnO/Re and ZnO/W emitters, respectively. The high value of β factor suggests that the emission is from the nanometric features of the emitter surface. The emission current–time plots exhibit good stability of emission current over a period of more than three hours. The post field emission surface morphology studies show no significant deterioration of the emitter surface indicating that the ZnO thin film has a very strong adherence to both the substrates and exhibits a remarkable structural stability against high-field-induced mechanical stresses and ion bombardment. The results reveal that PLD offers unprecedented advantages in fabricating the ZnO field emitters for practical applications in field-emission-based electron sources.     

Dielectric, thermal and optical study of an unusually shaped liquid crystal

Dielectric measurements have been carried out for the determination of real and imaginary parts of the permittivity of a newly synthesized, unusually shaped liquid crystal. The sample has been investigated in the frequency range from 100 Hz to 10 MHz within a temperature range 80-130 °C. The dielectric measurements in the smectic A phase indicate a Cole-Cole type of dispersion, and the activation energy was found to be 5.5 meV by using the Arrhenius plot of relaxation time. In addition to this, thermal and optical transmittance studies have also been conducted in the above mentioned temperature range, and the temperature dependence of these parameters has been discussed in detail. The phase transition temperature obtained from a differential scanning calorimetry (DSC) study matches within 2 °C that was obtained from an optical transmittance study. The dielectric and optical behavior of the unusually shaped liquid crystal has been explained on the basis of a proposed theoretical model in which a sample possesses two different conformers having induced polarizations in opposite directions.     

Metabolite assignment of ultrafiltered synovial fluid extracted from knee joints of reactive arthritis patients using high resolution NMR spectroscopy

Currently, there are no reliable biomarkers available that can aid early differential diagnosis of reactive arthritis (ReA) from other inflammatory joint diseases. Metabolic profiling of synovial fluid (SF)—obtained from joints affected in ReA—holds great promise in this regard and will further aid monitoring treatment and improving our understanding about disease mechanism. As a first step in this direction, we report here the metabolite specific assignment of ¹H and ¹³C resonances detected in the NMR spectra of SF samples extracted from human patients with established ReA. The metabolite characterization has been carried out on both normal and ultrafiltered (deproteinized) SF samples of eight ReA patients (n = 8) using high-resolution (800 MHz) ¹H and ¹H─¹³C NMR spectroscopy methods such as one-dimensional ¹H CPMG and two-dimensional J-resolved¹H NMR and homonuclear ¹H─¹H TOCSY and heteronuclear¹H─¹³C HSQC correlation spectra. Compared with normal SF samples, several distinctive ¹H NMR signals were identified and assigned to metabolites in the ¹H NMR spectra of ultrafiltered SF samples. Overall, we assigned 53 metabolites in normal filtered SF and 64 metabolites in filtered pooled SF sample compared with nonfiltered SF samples for which only 48 metabolites (including lipid/membrane metabolites as well) have been identified. The established NMR characterization of SF metabolites will serve to guide future metabolomics studies aiming to identify/evaluate the SF-based metabolic biomarkers of diagnostic/prognostic potential or seeking biochemical insights into disease mechanisms in a clinical perspective.