Positive solution to semilinear parabolic equation associated with critical Sobolev exponent

We study the semilinear parabolic equation ${u_{t}- \Delta u = u^{p}, u \geq 0}$ on the whole space R ^N , ${N \geq 3}$ associated with the critical Sobolev exponent p = (N + 2)/(N ? 2). Similarly to the bounded domain case, there is threshold blowup modulus concerning the blowup in finite time. Furthermore, global in time behavior of the threshold solution is prescribed in connection with the energy level, blowup rate, and symmetry.     

Preparation of phenyl‐modified natural rubber in latex stage

Phenyl‐modified natural rubber was prepared in latex stage by bromination of deproteinized natural rubber followed by Suzuki‐Miyaura cross‐coupling reaction. First, the bromination of natural rubber was carried out using N‐bromosuccinimide in latex stage. The bromine atom content increased as amount of N‐bromosuccinimide increased. Second, the allylic bromine atom was replaced with a phenyl group using phenyl boronic acid in the presence of a palladium catalyst, according to the Suzuki‐Miyaura cross‐coupling reaction in latex stage. The resulting products were characterized by nuclear magnetic resonance (NMR) spectroscopy. Signal at 7.13 ppm was assigned to the phenyl group of the product, while signals at 3.98, 4.14, and 4.44 ppm were assigned to the remaining allylic brominated cis‐1,4‐isoprene units. The estimated phenyl group content and the conversion of the Suzuki‐Miyaura cross‐coupling reaction were 1.32 and 23.7 mol%, respectively. Glass transition temperature (T_g) of deproteinized natural rubber increased from ?62°C to ?46.7°C, when the phenyl group was introduced into the rubber.     

Source/drain engineering for MOSFETs with embedded-Si:C technology

Embedded silicon carbon alloy (e-Si:C) technology for source and drain (S/D) is expected to improve nMOSFET drive current. The distribution and activation characteristics of arsenic in Si:C film and the interfacial solid-phase reaction of the Ni/Si:C system were studied with the aim of achieving the maximum improvement of the characteristics of e-Si:C S/D. It was clarified that the active carrier concentration of Si:C decreased with increasing carbon concentration compared to the control Si. There is concern that the low doping activation in Si:C increases series resistance of e-Si:C S/D nMOSFETs and degrades the performance gain expected from the strain effect.     

On Default Priors for Robust Bayesian Estimation with Divergences

This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum γ-divergence estimator is well-known to work well in estimation against heavy contamination. The robust Bayesian methods by using quasi-posterior distributions based on divergences have been also proposed in recent years. In the objective Bayesian framework, the selection of default prior distributions under such quasi-posterior distributions is an important problem. In this study, we provide some properties of reference and moment matching priors under the quasi-posterior distribution based on the γ-divergence. In particular, we show that the proposed priors are approximately robust under the condition on the contamination distribution without assuming any conditions on the contamination ratio. Some simulation studies are also presented.     

Biomimetic Design of a Robustly Stabilized Folded State Enabling Seed-Initiated Supramolecular Polymerization under Microfluidic Mixing**

We have investigated the folding and assembly behavior of a cystine-based dimeric diamide bearing pyrene units and solubilizing alkyl chains. In low-polarity solvents, it forms a 14-membered ring through double intramolecular hydrogen bonds between two diamide units. The spectroscopic studies revealed that the folded state is thermodynamically unstable and eventually transforms into more energetically stable helical supramolecular polymers that show an enhanced chiral excitonic coupling between the transition dipoles of the pyrene units. Importantly, compared to an alanine-based monomeric diamide, the dimeric diamide exhibits a superior kinetic stability in the metastable folded state, as well as an increased thermodynamic stability in the aggregated state. Accordingly, the initiation of supramolecular polymerization can be regulated using a seeding method even under microfluidic mixing conditions. Furthermore, taking advantage of a self-sorting behavior observed in a mixture of l -cysteine- and d -cysteine-based dimeric diamides, a two-step supramolecular polymerization was achieved by stepwise addition of the corresponding seeds.     

Solvation dynamics of coumarin 153 in alcohols confined in silica nanochannels

Solvation dynamics in alcohols confined in silica nanochannels was examined by time-resolved fluorescence spectroscopy using coumarin 153 (C153) as a fluorescent probe. Surfactant-templated mesoporous silica was fabricated inside the pores of an anodic alumina membrane. The surfactant was removed by calcination to give mesoporous silica (Cal-NAM) containing one-dimensional (1D) silica nanochannels (diameter, 3.1 nm) whose inner surface was covered with silanol groups. By treating Cal-NAM with trimethylchlorosilane, trimethylsilyl (TMS) groups were formed on the inner surface of the silica nanochannels (TMS-NAM). Fluorescence dynamic Stokes shifts of C153 were measured in alcohols (ethanol, butanol, hexanol, and decanol) confined in the silica nanochannels of Cal- and TMS-NAMs, and the time-dependent fluorescence decay profiles could be best fitted by a biexponential function. The estimated solvent relaxation times were much larger than those observed in bulk alcohols for both Cal- and TMS-NAMs when ethanol or butanol was used as a solvent, indicating that the mobility of these alcohol molecules was restricted within the silica nanochannels. However, hexanol or decanol in Cal- and TMS-NAMs did not cause a remarkable increase in the solvent relaxation time in contrast to ethanol or butanol. Therefore, it was concluded that a relatively rigid assembly of alcohols (an alcohol chain) was formed within the silica nanochannels by hydrogen bonding interaction and van der Waals force between the surface functional groups of the silica nanochannels and alcohol molecules and by the successive interaction between alcohol molecules when alcohol with a short alkyl chain (ethanol or butanol) was used as a solvent.     

Diffusion of metal complexes inside of silica-surfactant nanochannels within a porous alumina membrane

The present paper describes diffusivities of a series of metal complexes inside of silica-surfactant nanochannels (channel diameter = 3.4 nm), which were formed within a porous alumina membrane by a surfactant-templated method using cetyltrimethylammonium bromide (CTAB) as a template surfactant. The metal complexes used in this study were Fe(CN)6(3-), Ru(NH3)6(3-), ferrocenecarboxylic acid (Fc-COO-), (ferrocenylmethyl)-trimethylammonium (Fc-NMe3+), N,N-(dimethylamminomethyl)ferrocene (Fc-NMe2), and ferrocene methanol (Fc-OH). Apparent diffusion coefficients of these metal complexes were estimated by measuring their mass transports through the silica-surfactant nanochannels. The estimated apparent diffusion coefficients were on the order of 10(-11) cm2 s(-1) for Fe(CN)6(3-) and Ru(NH3)6(3-), and these values were five orders of magnitude smaller than those in a bulk aqueous solution. For the ferrocene derivatives, the apparent diffusion coefficients of charged ferrocene derivatives are almost the same (5.3 x 10(-11) cm2 s(-1) for Fc-COO- and 5.4 x 10(-11) cm2 s(-1) for Fc-NMe3+), whereas neutral ferrocene derivatives (Fc-NMe2 and Fc-OH) show faster diffusion than the charged species. In addition, the apparent diffusion coefficient of Fc-NMe2 (27 x 10(-11) cm2 s(-1)) was about three times larger than that of Fc-OH (10 x 10-11 cm2 s(-1)). The difference in these diffusion coefficients is discussed by considering the mesostructure of the silica-surfactant nanochannels, that is, an ionic interface with cationic head groups of CTA and their counteranions, a hydrophobic interior of the micellar phase, and a silica framework. As a result, it is inferred that the slow diffusivities of the charged metal complexes are due to the electrostatic interaction between the charged species and the ionic interface, whereas less interaction between neutral ferrocenes and the ionic interface causes distribution of metal complexes into the hydrophobic micellar phase, which is a less viscous medium compared to the ionic interface, resulting in the faster diffusivities of the neutral species.     

Anti-Stokes Luminescence in Multi-Resonance-Type Thermally-Activated Delayed Fluorescence Molecules

Photon-upconversion in organic molecular systems is one of the promising technologies for future energy harvesting systems because these systems can generate excitons that possess higher energy than excitation energy. The photon-upconversion caused by absorbing ambient heat as additional energy is particularly interesting because it could ideally provide a light-driving cooling system. However, only a few organic molecular systems have been reported. Here, we report the anti-Stokes photoluminescence (ASPL) derived from hot-band absorption in a series of multi-resonance-type thermally-activated delayed fluorescence (MR-TADF) molecules. The MR-TADF molecules exhibited an anti-Stokes shift of approximately 0.1 eV with a high PL quantum yield in the solution state. The anti-Stokes shift corresponded well to the 1–0 vibration transition from the ground state to the excited singlet state, and we further evaluated a correlation between the activation energy for the ASPL intensity and the TADF process. Our demonstration underlines that MR-TADF molecules have become a novel class of ASPL materials for various future applications, such as light-driving cooling systems.     

Control of wettability of molecularly thin liquid films by nanostructures

The patterning of liquid thin films on solid surfaces is very important in various fields of science and engineering related to surfaces and interfaces. A method of nanometer-scale patterning of a molecularly thin liquid film on a silicon substrate using the lyophobicity of the oxide nanostructures has recently been reported (Fukuzawa, K.; Deguchi, T.; Kawamura, J.; Mitsuya, Y.; Muramatsu, T.; Zhang, H. Appl. Phys. Lett. 2005, 87, 203108). However, the origin of the lyophobicity of the nanostructure with a height of around 1 nm, which was fabricated by probe oxidation, has not yet been clarified. In the present study, the change in thickness of the liquid film on mesa-shaped nanostructures and the wettability for the various combinations of the thickness of the liquid films and the height of ridge-shaped nanostructures were investigated. These revealed that lyophobicity is caused by a lowering of the intermolecular interaction between the liquid and silicon surfaces by the nanostructure and enables the patterning of a liquid film along it. The tendency of the wettability for a given liquid film and nanostructure size can be predicted by estimating the contributions of the intermolecular interaction and capillary pressure. In this method, the height of the nanostructure can control the wettability. These results can provide a novel method of nanoscale patterning of liquid thin films, which will be very useful in creating new functional surfaces.