On the uniqueness of smooth,stationary black holes in vacuum

A fundamental conjecture in general relativity asserts that the domain of outer communication of a regular, stationary, four dimensional, vacuum black hole solution is isometrically diffeomorphic to the domain of outer communication of a Kerr black hole. So far the conjecture has been resolved, by combining results of Hawking [17], Carter [4] and Robinson [28], under the additional hypothesis of non-degenerate horizons and real analyticity of the space-time. We develop a new strategy to bypass analyticity based on a tensorial characterization of the Kerr solutions, due to Mars [24], and new geometric Carleman estimates. We prove, under a technical assumption (an identity relating the Ernst potential and the Killing scalar) on the bifurcate sphere of the event horizon, that the domain of outer communication of a smooth, regular, stationary Einstein vacuum spacetime of dimension 4 is locally isometric to the domain of outer communication of a Kerr spacetime.     

A multiplicity result for a special class of gradient-type systems with non-differentiable term

We prove the existence of multiple solutions of certain systems of hemivariational inequalities, using a recent minimax result of B. Ricceri. We apply both our main theorem and the principle of symmetric criticality to obtain multiple solutions of systems of hemivariational inequalities defined on certain Sobolev spaces.     

Diffusion coefficient and shear viscosity of rigid water models

We report the diffusion coefficient and viscosity of popular rigid water models: two non-polarizable ones (SPC/E with three sites, and TIP4P/2005 with four sites) and a polarizable one (Dang-Chang, four sites). We exploit the dependence of the diffusion coefficient on the system size (Yeh and Hummer 2004 J. Phys. Chem. B 108 15873) to obtain the size-independent value. This also provides an estimate of the viscosity of all water models, which we compare to the Green-Kubo result. In all cases, a good agreement is found. The TIP4P/2005 model is in better agreement with the experimental data for both diffusion and viscosity. The SPC/E and Dang-Chang models overestimate the diffusion coefficient and underestimate the viscosity.     

Bifibrations and Weak Factorisation Systems

We review a theorem of A. Roig about Quillen model structures on Grothendieck bifibrations and observe that it contains a gap. We reformulate one of its assumptions in order to validate it. As an application to the new version, we introduce the fibred model structure on the category of small categories enriched in a suitable monoidal model category.     

Carotid plaque high-resolution MRI at 3 T: evaluation of a new imaging score for symptomatic plaque assessment

Purpose

To assess the sensitivity and specificity of intra-plaque hemorrhage (IPH), large lipid-rich necrotic core (LR-NC) and ulceration or cap rupture (UCR) for symptomatic carotid plaque characterization and to evaluate a new imaging score [Hemorrhage, Ulceration or cap rupture, Lipid-rich necrotic Core (HULC) score based on the sum of presence/absence of IPH, UCR and LR-NC; range 0–3] for assessment of recently symptomatic carotid plaques.

Material and methods

Twenty-seven recently symptomatic (< 8 weeks) and 36 asymptomatic patients with a carotid plaque thicker than 2 mm were prospectively imaged on a 3-T magnetic resonance (MR) system using high-resolution, multi-contrast MR sequences. Prior to analysis, all images were reviewed to assess image quality of each sequence. Sensitivity and specificity of IPH, LR-NC, UCR and HULC scores were calculated.

Results

Fifty-one patients were analyzed (26 symptomatic carotids and 67 asymptomatic carotids) after exclusion of studies with poor image quality. Sensitivity and specificity for symptomatic carotid plaque was, respectively, 46.1% and 97% for IPH, 84.6% and 73.1% for UCR and 80.7% and 76.1% for LR-NC. A HULC score of 2 or more showed a sensitivity of 73% and a specificity of 92.5%.

Conclusion

At 3 T, intra-plaque hemorrhage is the most specific criterion to characterize symptomatic carotid plaque. The HULC score offers the best compromise between sensitivity and specificity.     

The Use of Organic Rankine Cycles for Recovering the Heat Lost in the Compression Area of a Cryogenic Air Separation Unit

The use of organic Rankine cycles (ORCs) is a viable solution for the recovery of waste heat. For an air separation unit (ASU) with a production of V˙O2=58300mN3/h operating in Romania, the value of utilization of the heat transferred to the cooling system of the compression area represents 21% of the global system electrical energy input. To recover this thermal energy and transform it into mechanical energy, an ORC system was proposed. To maximize the production of mechanical power, an exergy analysis was performed. Exergy analysis was used to choose the most suitable organic fluid and find the optimum constructive structure of the Rankine cycle. The calculation of the exergy destruction in the key apparatuses of the system allowed investigation into the optimization search procedure. The large exergy destruction in the liquid preheater suggested the decrease in the temperature difference in this part of the evaporator by increasing the inlet temperature of the liquid; and an internal recuperative heat exchanger was used for this purpose. When permitted, the overheating of the vapors also reduced the temperature difference between the heat source and the organic fluid during the heat transfer process. The analysis was comparatively performed for several organic fluids such as R-245fa, R123, n-pentane and R717. The use of ammonia, that offered the possibility of superheating the vapors at the turbine inlet, brought a gain of mechanical power corresponding to 6% economy in the electrical energy input of the global plant.     

Anthocyanins Formulated with Carboxymethyl Starch for Gastric and Intestinal Delivery

Anthocyanins obtained from jambolan have been used as active agents in different carboxymethyl starch-based tablet formulations and their release profiles evaluated in simulated gastric fluids (SGF) and simulated intestinal (SIF) fluids. Structural analysis highlighted a strong interaction between anthocyanins and carboxymethyl starch, evidenced by scanning electron microscopy and infrared analysis. Tablet dissolution behavior varied according to the pH of the media, being controlled by the swelling and/or erosion of the polymeric matrix. Various formulations for immediate, fast, and sustained release of anthocyanins for 30 min, 2 h and 12 h of dissolution have been developed. It was found that monolithic carboxymethyl starch tablets loaded with powdered jambolan extract efficiently afforded the complete delivery (100% of anthocyanins) to different sites of the simulated gastrointestinal tract and ensured the stability of these pigments, which maintained their antioxidant activity.     

Comparative Study of Useful Compounds Extracted from Lophanthus anisatus by Green Extraction

Essential oils were obtained from different parts of Agastache foeniculum (Lophanthus anisatus) plants by means of extraction: green extraction using hydro-distillation (HD) and bio-solvent distillation, BiAD, discontinuous distillation, and supercritical fluid extraction, in two stages: (1) with CO₂, and (2) with CO₂ and ethanol co-solvent. The extraction yields were determined. The yield values varied for different parts of the plant, as well as the method of extraction. Thus, they had the values of 0.62 ± 0.020 and 0.92 ± 0.015 g/100 g for the samples from the whole aerial plant, 0.75 ± 0.008 and 1.06 ± 0.005 g/100 g for the samples of leaves, and 1.22 ± 0.011 and 1.60 ± 0.049 g/100 g for the samples of flowers for HD and BiAD, respectively. The yield values for supercritical fluid extraction were of 0.94 ± 0.010 and 0.32 ± 0.007 g/100 g for the samples of whole aerial plant, 0.9 ± 0.010 and 1.14 ± 0.008 g/100 g for the samples of leaves, and 1.94 ± 0.030 and 0.57 ± 0.003 g/100 g for the samples of flowers, in the first and second stages, respectively. The main components of Lophanthus anisatus were identified as: estragon, limonene, eugenol, chavicol, benzaldehyde, and pentanol. The essential oil from Agatache foeniculum has antimicrobial effects against Staphylococcus aureus, the Escherichia coli and Pseudomonas aeruginosa. Acclimatization of Lophantus anisatus in Romania gives it special qualities by concentrating components such as: estragole over 93%, limonene over 8%, especially in flowers; and chavicol over 14%, estragole over 30%, eugenol and derivatives (methoxy eugenol, methyl eugenol, etc.) over 30% and phenyl ether alcohol over 20% in leaves. As a result of the research carried out, it was proven that Lophanthus anisatus can be used as a medicinal plant for many diseases, it can be used as a spice and preservative for various foods, etc.     

Synthesis,Characterisation, and in vitro Cytotoxic Activity of Dithiocarbamato Glycoconjugate Half-Sandwich Ruthenium and Osmium Complexes

The synthesis by transmetallation and in-depth characterisation by IR spectroscopy of five half-sandwich ruthenium and osmium dithiocarbamato isonipecotamide glycoconjugate complexes are presented herein. The evaluation of their in vitro cytotoxicity and of the zinc precursors’ in vitro cytotoxicity towards ovarian cancer (A2780 and A2780cisR) and normal prostate (PNT2) cells is reported. While the cytotoxicity of the compounds is rather limited, some selectivity is observed.     

Dual action of Impurities in Crystal Growth from Solutions

A dual action of impurities becomes evidently in growth kinetic of prismatic faces of KDP. At higher supersaturation two-dimensional nucleation mechanism due to impurities prevails. At smaller supersaturation the blocking effect of the steps created by the dislocation mechanism of growth become efficient. The limit of the “dead” growth zone depending on the impurity's concentration and the solution pH is a result of this last effect and agrees with the Cabrera-Vermilyea mechanism.