Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Parametric harmonic-to-fundamental ratio contrast echocardiography: a novel approach to identification and accurate measurement of left ventricular area under variable levels of ultrasound signal attenuation

Objectives

We introduced a harmonic-to-fundamental ratio (HFR) of the radiofrequency (RF) signals that reduces confounding effects of attenuation. We studied whether HFR analysis of RF signals received from contrast microbubbles allows accurate measurement of the left ventricular (LV) cavity area under varying levels of attenuation.

Background

Attenuation is a fundamental problem in ultrasound imaging and limits the use of clinical echocardiography.

Methods

RF data from short axis systolic and diastolic scans were obtained from 14 open-chest dogs following left-atrial bolus of Optison. Attenuation was induced by interposed silicone pads calibrated to induce 7 dB or 14 dB reductions of the backscattered RF signal. RF images were reconstructed from the RF signals, HFR values calculated for each image pixel for 0 dB, 7 dB and 14 dB attenuation conditions, and LV area obtained by summation of “LV cavity pixels”. A reference LV cavity area was obtained from endocardial border tracings in enhanced scans by experts.

Results

Correlation of the HFR-defined and reference areas at systole was R = 0.95, R = 0.94, and R = 0.91 for 0 dB, 7 dB and 14 dB levels of attenuation, respectively, and at diastole was R = 0.95 for 0 dB, 7 dB and 14 dB levels of attenuation. The mean difference from both systolic and diastolic values was <1.45 cm² (i.e. negligible) in all attenuation settings.

Conclusion

Our novel HFR method supports precise measurement of the LV cavity area in contrast images with simulated high attenuation of ultrasound signals.     

Radial oscillations of neutron stars in strong magnetic fields

The eigen frequencies of radial pulsations of neutron stars are calculated in a strong magnetic field. At low densities we use the magnetic BPS equation of state (EOS) similar to that obtained by Lai and Shapiro while at high densities the EOS obtained from the relativistic nuclear mean field theory is taken and extended to include strong magnetic field. It is found that magnetized neutron stars support higher maximum mass whereas the effect of magnetic field on radial stability for observed neutron star masses is minimal.     

Experimental investigations of relaxation times of gel electrolytes during polymerization by MR methods

In this article, the properties of gel electrolytes based on the NaClO₄ inorganic salt are described. For electrolytes with various concentrations of inorganic salts, relaxation times T ₁ and T ₂ were measured by means of MR techniques at regular intervals during the polymerization. To measure relaxation time T ₁, the inversion recovery (IR) technique was used. The measurement of relaxation time T ₂ was performed using the spin–echo (SE) technique. The reduction of relaxation times during the polymerization, namely, T ₁ from the value of 5.5 to 1.7 ms and T ₂ from the value of 5.5 to 1 ms, indicates a change in the internal structure of the gels and a change in their chemical composition. The waveforms measured will contribute to further studies of gel electrolytes aimed at increasing their electrical conductivity and establishing the influence of water molecules on the conductivity.     

Self-focusing by Ostwald ripening: a strategy for layer-by-layer epitaxial growth on upconverting nanocrystals

We demonstrate a novel epitaxial layer-by-layer growth on upconverting NaYF(4) nanocrystals (NCs) utilizing Ostwald ripening dynamics tunable both in thickness and composition. Injection of small sacrificial NCs (SNCs) as shell precursors into larger core NCs results in the rapid dissolution of the SNCs and their deposition onto the larger core NCs to yield core-shell structured NCs. Exploiting this NC size dependent dissolution/growth, the shell thickness can be controlled either by manipulating the number of SNCs injected or by successive injection of SNCs. In either of these approaches, the NCs self-focus from an initial bimodal distribution to a unimodal distribution (σ <5%) of core-shell NCs. The successive injection approach facilitates layer-by-layer epitaxial growth without the need for tedious multiple reactions for generating tunable shell thickness, and does not require any control over the injection rate of the SNCs, as is the case for shell growth by precursor injection.     

Formation and dispersion of CO<Subscript>2</Subscript> after combustion in closed area

This study deals with the formation of carbon dioxide (CO₂) after combustion process and dispersion in a closed area. The formation and dispersion of CO₂ were numerically simulated and validated by experiment. Ethanol (C₂H₅OH) was chosen as a fuel for the combustion process. Numerical simulations were carried out by using Reynolds averaged Navier–Stokes (RANS) approach with k-ε and k-ω turbulent models. The combustion process was simulated using two methods. Species transport with chemical reactions was the first method, and the second method was the nonpremix combustion model based on the mixture fraction theory. There were done some sensitivity studies on the influence of the time step size and a resolution of computational grid. Results from numerical simulations were validated by experimental measurements, where the CO₂ concentration was measured by the non-dispersive infrared (NDIR) sensor at four points.     

Pharmacological Potential and Chemical Composition of Crocus sativus Leaf Extracts

Crocus sativus L. (saffron) has been traditionally used as a food coloring or flavoring agent, but recent research has shown its potent pharmacological activity to tackle several health-related conditions. Crocus sp. leaves, and petals are the by-products of saffron production and are not usually used in the medicine or food industries. The present study was designed to determine the chemical composition of the water and ethanolic extracts of C. sativus leaves and test their cytotoxic activity against melanoma (IGR39) and triple-negative breast cancer (MDA-MB-231) cell lines by MTT assay. We also determined their anti-allergic, anti-inflammatory, and anti-viral activities. HPLC fingerprint analysis showed the presence of 16 compounds, including hydroxycinnamic acids, xanthones, flavonoids, and isoflavonoids, which could contribute to the extracts’ biological activities. For the first time, compounds such as tectoridin, iristectorigenin B, nigricin, and irigenin were identified in Crocus leaf extracts. The results showed that mangiferin (up to 2 mg/g dry weight) and isoorientin (8.5 mg/g dry weight) were the major active ingredients in the leaf extracts. The ethanolic extract reduced the viability of IGR39 and MDA-MB-231 cancer cells with EC₅₀ = 410 ± 100 and 330 ± 40 µg/mL, respectively. It was more active than the aqueous extract. Kaempferol and quercetin were identified as the most active compounds. Our results showed that Crocus leaves contain secondary metabolites with potent cytotoxic and antioxidant activities.