Minimal Blow-Up Solutions to the Mass-Critical Inhomogeneous NLS Equation

We consider the mass-critical focusing nonlinear Schrödinger equation in the presence of an external potential, when the nonlinearity is inhomogeneous. We show that if the inhomogeneous factor in front of the nonlinearity is sufficiently flat at a critical point, then there exists a solution which blows up in finite time with the maximal (unstable) rate at this point. In the case where the critical point is a maximum, this solution has minimal mass among the blow-up solutions. As a corollary, we also obtain unstable blow-up solutions of the mass-critical Schrödinger equation on some surfaces. The proof is based on properties of the linearized operator around the ground state, and on a full use of the invariances of the equation with an homogeneous nonlinearity and no potential, via time-dependent modulations.     

Finite Time Extinction by Nonlinear Damping for the Schrödinger Equation

We consider the Schrödinger equation on a compact manifold, in the presence of a nonlinear damping term, which is homogeneous and sublinear. For initial data in the energy space, we construct a weak solution, defined for all positive time, which is shown to be unique. In the one-dimensional case, we show that it becomes zero in finite time. In the two and three-dimensional cases, we prove the same result under the assumption of extra regularity on the initial datum.     

Supervised Domain Adaptation for Automated Semantic Segmentation of the Atrial Cavity

Atrial fibrillation (AF) is the most common cardiac arrhythmia. At present, cardiac ablation is the main treatment procedure for AF. To guide and plan this procedure, it is essential for clinicians to obtain patient-specific 3D geometrical models of the atria. For this, there is an interest in automatic image segmentation algorithms, such as deep learning (DL) methods, as opposed to manual segmentation, an error-prone and time-consuming method. However, to optimize DL algorithms, many annotated examples are required, increasing acquisition costs. The aim of this work is to develop automatic and high-performance computational models for left and right atrium (LA and RA) segmentation from a few labelled MRI volumetric images with a 3D Dual U-Net algorithm. For this, a supervised domain adaptation (SDA) method is introduced to infer knowledge from late gadolinium enhanced (LGE) MRI volumetric training samples (80 LA annotated samples) to a network trained with balanced steady-state free precession (bSSFP) MR images of limited number of annotations (19 RA and LA annotated samples). The resulting knowledge-transferred model SDA outperformed the same network trained from scratch in both RA (Dice equals 0.9160) and LA (Dice equals 0.8813) segmentation tasks.     

Rank Two Integral Representations of the Infinite Dihedral Group

We give an effective classification of the representations of the infinite dihedral group in GL ₂(R) where R is either the valuation ring ?_(p) or the ring of p-adic integers.     

Observation of the semileptonic decays B-->D*tau-nutau and evidence for B-->Dtau-nutau

We present measurements of the semileptonic decays B--->D0tau-nutau, B--->D*0tau-nutau, B0-->D+tau-nutau, and B0-->D*+tau-nutau, which are potentially sensitive to non-standard model amplitudes. The data sample comprises 232x10(6) Upsilon(4S)-->BB decays collected with the BABAR detector. From a combined fit to B- and B0 channels, we obtain the branching fractions B(B-->Dtau-nutau)=(0.86+/-0.24+/-0.11+/-0.06)% and B(B-->D*tau-nutau)=(1.62+/-0.31+/-0.10+/-0.05)% (normalized for the B0), where the uncertainties are statistical, systematic, and normalization-mode-related.     

AlIII‐Catalysed Formation of Poly(limonene)carbonate: DFT Analysis of the Origin of Stereoregularity

Amino‐triphenolate derived Al^III complexes combined with suitable nucleophiles have been investigated as binary catalysts for the coupling of limonene oxide and carbon dioxide to afford alternating polycarbonates. These catalysts are able to produce stereoregular, perfectly alternating trans‐polymers from cis‐limonene oxide, whereas the pure trans isomer and cis/trans mixture give rise to lower degrees of stereoregularity. The best Al^III catalyst shows the potential to mediate the conversion of both stereoisomers of limonene oxide with high conversion levels of up to 71 % under neat conditions, indicating the high degree of robustness and atom‐efficiency of this catalytic process. Computational studies have revealed unique features of the binary catalyst system, among which is the preferred nucleophilic attack on the quaternary carbon centre in the limonene oxide substrate.     

Analysis of nitrosamines in water by automated SPE and isotope dilution GC/HRMS Occurrence in the different steps of a drinking water treatment plant, and in chlorinated samples from a reservoir and a sewage treatment plant effluent

A method based on automated solid-phase extraction (SPE) and isotope dilution gas chromatography/high resolution mass spectrometry (GC/HRMS) has been developed for the analysis of nine nitrosamines in water samples. The combination of automated SPE and GC/HRMS for the analysis of nitrosamines has not been reported previously. The method shows as advantages the selectivity and sensitivity of GC/HRMS analysis and the high efficiency of automated SPE with coconut charcoal EPA 521 cartridges. Low method detection limits (MDLs) were achieved, along with a greater facility of the procedure and less dependance on the operator with regard to the methods based on manual SPE. Quality requirements for isotope dilution-based methods were accomplished for most analysed nitrosamines, regarding to trueness (80–120%), method precision (<15%) and MDLs (0.08–1.7 ng/L).Nineteen water samples (16 samples from a drinking water treatment plant {DWTP}, 2 chlorinated samples from a sewage treatment plant {STP} effluent, and 1 chlorinated sample from a reservoir) were analysed. Concentrations of nitrosamines in the STP effluent were 309.4 and 730.2 ng/L, being higher when higher doses of chlorine were applied. N-Nitrosodimethylamine (NDMA) and N-nitrosodiethylamine (NDEA) were the main compounds identified in the STP effluent, and NDEA was detected above 200 ng/L, regulatory level for NDMA in effluents stated in Ontario (Canada). Lower concentrations of nitrosamines were found in the reservoir (20.3 ng/L) and in the DWTP samples (n.d. −28.6 ng/L). NDMA and NDEA were respectively found in the reservoir and in treated and highly chlorinated DWTP samples at concentrations above 10 ng/L (guide value established in different countries). The highest concentrations of nitrosamines were found after chlorination and ozonation processes (ozonated, treated and highly chlorinated water) in DWTP samples.     

1,2,4-triazolium-cation-based energetic salts

3,4,5-Triamino-1,2,4-triazole (guanazine, 1) can be readily methylated with methyl iodide yielding methylguanazinium iodide (2). Salts containing the novel methylguanazinium cation with energetic anions were synthesised by metathesis reactions with silver azide (3), silver nitrate (4), silver perchlorate (5), sodium 5,5'-azotetrazolate (6), silver 5-nitrotetrazolate (7) and silver dinitramide (8), yielding a new family of heterocycle-based salts, which were fully characterised by analytical (mass spectrometry and elemental analysis) and spectroscopic methods (IR, Raman and NMR). In addition, the molecular structures of all compounds were confirmed by X-ray analysis, revealing extensive hydrogen-bonding in the solid state and densities between 1.399 (3) and 1.669 g cm(-3) (5). The hydrogen-bonded ring motifs are discussed in the formalism of graph-set analysis for hydrogen-bond patterns and compared to each other. Preliminary sensitivity testing of the crystalline compounds indicate surprisingly low sensitivities to both friction and impact, the highest friction and shock sensitivity being found for the perchlorate (5, 220 N) and the dinitramide (8, 20 J) salts, respectively. In addition, DSC analysis was used to assess the thermal stabilities of the compounds: 3-6 melt above 200 degrees C with concomitant decomposition, whereas 7 and 8 have clearly defined melting points at 162 and 129 degrees C, respectively, and with decomposition occurring about 30 degrees C above the melting point. Lastly all compounds have positive calculated heats of formation between 336 (4) and 4070 kJ kg(-1) (6) and calculated detonation velocities in the range between 8330 (7) and 8922 m s(-1) (6) making them of interest as new highly energetic materials with low sensitivity.