Special values of anticyclotomic L-functions modulo λ

The purpose of this article is to generalize some results of Vatsal on the special values of Rankin–Selberg L-functions in an anticyclotomic \({\mathbb{Z}_{p}}\) -extension. Let g be a cuspidal Hilbert modular newform of parallel weight \({(2,\ldots,2)}\) and level \({\mathcal{N}}\) over a totally real field F, and let K/F be a totally imaginary quadratic extension of relative discriminant \({\mathcal{D}}\) . We study the l-adic valuation of the special values \({L(g,\chi,\frac{1}{2})}\) as \({\chi}\) varies over the ring class characters of K of \({\mathcal{P}}\) -power conductor, for some fixed prime ideal \({\mathcal{P}}\) . We prove our results under the only assumption that the prime to \({\mathcal{P}}\) part of \({\mathcal{N}}\) is relatively prime to \({\mathcal{D}}\) .     

Determining Hilbert modular forms by central values of Rankin–Selberg convolutions: the weight aspect

The purpose of this paper is to prove that a primitive Hilbert cusp form \(\mathbf{g}\) is uniquely determined by the central values of the Rankin–Selberg L-functions \(L(\mathbf{f}\otimes \mathbf{g}, \frac{1}{2})\), where \(\mathbf{f}\) runs through all primitive Hilbert cusp forms of weight \(k\) for infinitely many weight vectors \(k\). This result is a generalization of the work of Ganguly et al. (Math Ann 345:843–857, 2009) to the setting of totally real number fields, and it is a weight aspect analogue of our previous work (Hamieh and Tanabe in Trans Am Math Soc, arXiv:1609.07209, 2016).     

Determination des Transitions Vitreuses et Locales de PMMA/Al2O3 Par des Methodes Thermiques et Chromatographiques

Differential thermal analysis (DTA) technique was used to determine the glass transition temperatures of polymethyl methacrylate (PMMA). When PMMA was adsorbed on α-alumina, DTA could not use to obtain the glass transition temperatures of the system PMMA/α-Al₂O₃. Inverse gas chromatography at infinite dilution proved to be an excellent technique to highlight glass transitions and local transitions of PMMA adsorbed on α-Al₂O₃, at various covered surface fractions.     

Quantum entanglement in a finite temperature interacting electron gas

The entanglement between two electrons in a degenerate electron gas is studied as a function of their separation and of temperature. It is found that interaction leads to a suppression of the entanglement distance.     

New approach to characterise physicochemical properties of solid substrates by inverse gas chromatography at infinite dilution. I. Some new methods to determine the surface areas of some molecules adsorbed on solid surfaces

This study was divided into three different parts that tried to give a new contribution to determine and quantify more precisely the superficial properties of solid substrates (polymers and/or oxides) obtained by inverse gas chromatography (IGC) at infinite dilution. It criticised certain of the classical methods and relationships used to determine some physico-chemical properties of a solid and gave new methods and equations that can be more precise and more realistic. Part I developed some new methods to determine the surface areas of some molecules adsorbed on solids. A theoretical calculation of surface areas of molecules adsorbed on solid substrates was proposed by using some theoretical models. Two new methods to determine the surface areas of polar molecules were developed. The first one consists of the determination of surface areas by coupling two classical methods, the dynamic contact angle and IGC techniques. The second new and general method, using the IGC technique, assumes that the specific interactions between a polar molecule and a solid proposed by Papirer and Schultz are the same. A new equation was obtained to determine the surface areas of polar molecules.     

Dewetting as an investigative tool for studying properties of thin polymer films

Employing mass conservation, time-resolved dewetting experiments of thin polymer films allow to determine in real time the dynamic contact angle and the slippage length. Moreover, based on a systematic variation of interfacial properties of a polymer brush, dewetting makes it possible to calculate the force it needs to extract a single polymer chain from its own melt. In the visco-elastic regime close to the glass transition, the temperature and molecular weight dependence of the relaxation time of residual stresses resulting from film preparation by spin-coating can be obtained from the evolution of the shape of the dewetting rim. The presented examples demonstrate that dewetting represents a powerful approach for a sensitive characterization of rheological, frictional and interfacial properties of thin polymer films.     

Effect of Support on Metathesis of n‐Decane: Drastic Improvement in Alkane Metathesis with WMe5 Linked to Silica–Alumina

[WMe₆] ( 1 ) supported on the surface of SiO₂–Al₂O₃₍₅₀₀₎ ( 2 ) has been extensively characterized by solid‐state NMR spectroscopy, elemental analysis, and gas quantification, which clearly reveal the formation of a mixture of monopodal and bipodal species with the migration of methyl from W to Al. The supported species SiO₂–Al₂O₃₍₅₀₀₎ ( 2 ) transformed at 120 °C into two types of carbynic centers, one of which is cationic and the other neutral. These species are very efficient for the metathesis of n‐decane. Comparison with already‐synthesized neutral bipodal tungsten indicates that the high increase in activity is due to the cationic character of the grafted tungsten.     

Effect of spacer insertion in a commonly used dithienosilole/benzothiadiazole-based low band gap copolymer for polymer solar cells

Dithienosilole-benzothiadiazole based low bandgap copolymers remain promising material for organic photovoltaics. A new copolymer, poly[(4,4′-dioctyldithieno[3,2-b:2′,3′-d]silole-2,6-diyl)-alt-{4,7-bis[2-(3-hexyl)thienyl]-2,1,3-benzothiadiazole-5,5′-diyl}] (PDTSDTBT) was designed by introducing a thiophene spacer bearing a hexyl chain at β-position in the main backbone and compared to its analog poly[(4,4′-dioctyldithieno[3,2-b:2′,3′-d]silole-2,6-diyl)-alt-(2,1,3-benzothiadiazole-4,7-diyl)] (PDTSBT). In PDTSDTBT, linear alkyl chains on silicon were chosen due to facile and cheap access and the inserted 3-hexylthiophene units were chosen to increase solubility and molar mass, a weak point with PDTSBT. The two parameters are important to optimize photovoltaic performances. To compare characteristics, PDTSDTBT of molar masses greater than, and equal to a sample of PDTSBT, were prepared. Pd-catalyzed Stille cross-coupling reactions in a micro-wave reactor to promote an efficient copolymerisations. A strong absorption ranging from 370 nm to 800 nm and a good thermal stability were observed. PDTSDTBT showed better solubility and higher degree of crystallinity. Facile synthesis of high molar masses meant that higher efficiencies, around 40% greater, could be obtained with PDTSDTBT. The polymer was demonstrated to be susceptible to improvement through the use of device-additives. For example, under initial optimisations using PDTSDTBT:PC₆₀BM blend at a ratio of 1:1 delivered a power conversion efficiency of 2.13% with J_SC = 7.73 (mA/cm²), under AM 1.5 (100 mW/cm²) illumination.     

Scattering effects on the performance of carbon nanotube field effect transistor in a compact model

Carbon nanotube field-effect transistors (CNTFET) are being extensively studied as possible successors to CMOS. Device simulators have been developed to estimate their performance in sub-10-nm and device structures have been fabricated. In this work, a new compact model of single-walled semiconducting CNTFET is proposed implementing the calculation of energy conduction sub-band minima and the treatment of scattering effects through energy shift in CNTFET. The developed model has been used to simulate I-V characteristics using VHDL-AMS simulator.