Optimal boundary holes for the Sobolev trace constant

In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient among functions that vanish in a set contained on the boundary ∂Ω of given boundary measure.We prove existence of extremals for this problem, and analyze some particular cases where information about the location of the optimal boundary set can be given. Moreover, we further study the shape derivative of the Sobolev trace constant under regular perturbations of the boundary set.     

A geometric approach to error estimates for conservation laws posed on a spacetime

We consider a hyperbolic conservation law posed on an (N+1)-dimensional spacetime, whose flux is a field of differential forms of degree N. Generalizing the classical Kuznetsov’s method, we derive an L¹ error estimate which applies to a large class of approximate solutions. In particular, we apply our main theorem and deal with two entropy solutions associated with distinct flux fields, as well as with an entropy solution and an approximate solution. Our framework encompasses, for instance, equations posed on a globally hyperbolic Lorentzian manifold.     

Small Iminocoumarin Derivatives as Red Emitters: From Biological Imaging to Highly Photoluminescent Non‐doped Micro‐ and Nanofibres

The fluorescence properties of four derivatives of 3‐thienyl‐2‐(N‐dicyanovinyl)iminocoumarin, bearing a diethylamino group in the 7‐position or a methoxy group in the 6, 7 and 8 positions, were compared in solution and in the solid state. The 7‐diethylamino derivative was strongly fluorescent in various solvents, with marked solvatochromism. Its fluorescence was quenched by aggregation. In contrast, the methoxy derivatives were only moderately or weakly fluorescent in solution, but two of them were strongly photoluminescent in the crystalline state, owing to favourable molecular packing. The 6‐methoxy derivative even exhibited spectacular crystallization‐enhanced emission, examples of which are particularly rare for this type of dyes. Dyes were tested for biological use. The 7‐diethylamino derivative led to particularly strong fluorescence staining of the cytoplasm of HCT‐116 colon cancer cells. No fading was observed over prolonged illumination by the microscope light beam, but a phototoxic effect was detected. The use of the dyes as red‐emitting materials was also investigated. Using easy‐to‐implement preparation methods, the compounds self‐ assembled to give one‐dimensional nano‐ and microsized particles, including millimeter‐long microfibres that exhibited clear wave‐guiding properties. This study shows the value of these low molecular‐weight molecules for the preparation of new orange and red‐emitting fluorescent materials based on totally pure dye.     

A new class of bicyclic dicationic salts based on the 7-azoniabicyclo[2.2.1]heptane scaffold

A new class of dicationic ionic salts has been developed based on two 7-azoniabicyclo[2.2.1]heptane moieties and a variable spacer. The construction of the 7-azabicyclo[2.2.1]heptane skeleton and introduction of the two- to ten-atom spacer occurred concurrently in a one-pot reaction. Quaternization and subsequent metathesis afforded the dicationic salts consisting of two linked quaternized bicyclic moieties and bis(trifluoromethylsulfonyl)imide or dicyanamide as counterions. These salts are liquids at room temperature if the spacer length was larger than seven atoms. X-ray diffraction analysis revealed a linear conformation of the spacer and RS/SR stereochemistry of the quaternized nitrogens.     

Two-dimensional simulation of linear wave propagation in a suspension of polymeric microcapsules used as ultrasound contrast agents

A generation of tissue-specific stable ultrasound contrast agent (UCA) composed of a polymeric capsule with a perfluorocarbone liquid core has become available. Despite promising uses in clinical practice, the acoustical behavior of such UCA suspensions remains unclear. A simulation code (2-D finite-difference time domain, FDTD) already validated for homogeneous particles [Galaz Haiat, Berti, Taulier, Amman and Urbach, (2010). J. Acoust. Soc. Am. 127, 148-154] is used to model the ultrasound propagation in such UCA suspensions at 50 MHz to investigate the sensitivity of the ultrasonic parameters to physical parameters of UCA. The FDTD simulation code is validated by comparison with results obtained using a shell scatterer model. The attenuation coefficient (respectively, the sound velocity) increases (respectively, decreases) from 4.1 to 58.4 dB/cm (respectively, 1495 to 1428 m/s) when the concentration varies between 1.37 and 79.4 mg/ml, while the backscattered intensity increases non-linearly, showing that a concentration of around 30 mg/ml is sufficient to obtain optimal backscattering intensity. The acoustical parameters vary significantly as a function of the membrane thickness, longitudinal and transverse velocity, indicating that mode conversions in the membrane play an important role in the ultrasonic propagation. The results may be used to help manufacturers to conceive optimal liquid-filled UCA suspensions.     

赤潮生消过程中的水体固有光学性质分析

在珠江口海域海洋光学浮标实验中获取一次聚生角毛藻赤潮生消过程的水体光学数据和相应的生化数据.利用该数据,分析了赤潮生消过程中水体光谱吸收和后向散射等光学性质的时间序列变化.研究发现,在赤潮生消过程中,浮游植物色素、非藻类颗粒物以及黄色物质等水体组分吸收变化显著,赤潮爆发期各组分光谱吸收增强并达到最大值,赤潮消亡期各组分...     

Polyimide polymer glass-free capillary columns for gas chromatography

Polymeric polyimide capillary tubing, both uncoated and coated with stationary phases of two polarities, is explored for use as capillary columns for gas chromatography (GC). These glass-free polyimide columns are flexible and their small winding diameter of less than a cm around a solid support makes them compatible for potential use in portable GC instruments. Polyimide columns with dimensions of 0.32 mm i.d. × 3 m are cleaned, annealed at 300°C, and coated using the static method with phenylmethylsilicone (PMS). Separations of volatile organics are investigated isothermally on duplicate sets of polyimide columns by GC with a flame ionization detector using split injection. Unlike the uncoated ones, the coated polyimide columns successfully separate Grob test mix classes of alkanes, amines, and fatty acid methyl esters. The relative standard deviations for retention time and peak area are 0.5 and 2.5 , respectively. With the 3 m PMS-coated column connected to a retention gap to permit operation at its optimum flow rate of 30 cm/s, a plate count of 3200 or plate height of 1 mm is possible. Lack of retention and tailing peaks are evident for the polyimide polymer capillary columns as compared to that of a 3 m commercial cross-linked PMS fused silica capillary. However, headspace analyses of an aromatic hydrocarbon mix and a Clearcoat automotive paint sample are viable applications on the PMS polyimide polymer column.     

Rational multistep synthesis of a novel polyfunctionalized benzo[d]thiazole and its thiazolo[5,4-b]pyridine analogue

Reliable synthetic routes were studied for an access to a novel polyfunctionalized 6-amino-2-cyanobenzo[d]thiazole-5-carboxylate ester (1) and its analogue 5-amino-2-cyanothiazolo[5,4-b]pyridine-6-carboxylate ester (2). Both compounds 1 and 2 are functionalized as molecular bricks for the synthesis of innovative molecular systems. Part of the chemistry performed in this study was achieved under microwave irradiation.     

Age-related decline in cognitive control: the role of fluid intelligence and processing speed

Background

Research on cognitive control suggests an age-related decline in proactive control abilities whereas reactive control seems to remain intact. However, the reason of the differential age effect on cognitive control efficiency is still unclear. This study investigated the potential influence of fluid intelligence and processing speed on the selective age-related decline in proactive control. Eighty young and 80 healthy older adults were included in this study. The participants were submitted to a working memory recognition paradigm, assessing proactive and reactive cognitive control by manipulating the interference level across items.

Results

Repeated measures ANOVAs and hierarchical linear regressions indicated that the ability to appropriately use cognitive control processes during aging seems to be at least partially affected by the amount of available cognitive resources (assessed by fluid intelligence and processing speed abilities).

Conclusions

This study highlights the potential role of cognitive resources on the selective age-related decline in proactive control, suggesting the importance of a more exhaustive approach considering the confounding variables during cognitive control assessment.