On the capacity of sets of divergence associated with the spherical partial integral operator

In this article, we study the pointwise convergence of the spherical partial integral operator when it is applied to functions with a certain amount of smoothness. In particular, for , , , we prove that -quasieverywhere on , where is such that almost everywhere. A weaker version of this result in the range as well as some related localisation principles are also obtained. For and , we construct a function such that diverges everywhere.

     

On the modular curves

Let denote an elliptic curve over and the modular curve classifying the elliptic curves over such that the representations of in the 7-torsion points of and of are symplectically isomorphic. In case is given by a Weierstraß equation such that the invariant is a square, we exhibit here nontrivial points of . From this we deduce an infinite family of curves for which has at least four nontrivial points.

     

High pass filter with above IC integrated SrTiO3 high K MIM capacitors

This paper describes realization and characterization of SrTiO₃ (STO) high K MIM capacitors above BiCMOS integrated circuit (IC). These capacitances are connected to IC and are used as coupling capacitors in order to realize a high pass filter. Surface capacitance achieved is 10 nF/mm² with capacitance value of 1.2 nF. The process for STO MIM fabrication does not exceed 400 °C, which is compatible with interconnections. Typical K and dielectric losses values obtained are, respectively 110% and 2%. Yield obtained reaches 83% for capacitors. A functional high pass filter using these STO capacitors was realized in this study. It exhibits a cut-off frequency at 6.5 kHz and a constant gain at higher frequencies of −1.3 dB.     

Effects of temperature on the relaxation to equilibrium and stationary nonequilibrium states of some Langevin systems

We investigate the effects of temperature on the properties of the time relaxation to equilibrium and nonequilibrium steady states of correlation functions of some Langevin harmonic systems. We consider commonly used dissipative and conservative Langevin dynamics, and show that the time relaxation rate depends on the temperature in the case of thermal reservoirs at different temperatures connected to the system, but it does not happen in the case of relaxation to equilibrium, i.e., if all the heat bath are at the same temperature. Our formalism maps the initial stochastic problem on a noncanonical quantum field theory, and the calculations of the relaxation rates are based on a perturbative analysis. We argue to show the reliability of the perturbative computation.     

Reduced expression of <Emphasis Type="Italic">TAC1</Emphasis>, <Emphasis Type="Italic">PENK</Emphasis> and <Emphasis Type="Italic">SOCS2</Emphasis> in <Emphasis Type="Italic">Hcrtr-2</Emphasis> mutated narcoleptic dog brain

Background  

Narcolepsy causes dramatic behavioral alterations in both humans and dogs, with excessive sleepiness and cataplexy triggered by emotional stimuli. Deficiencies in the hypocretin system are well established as the origin of the condition; both from studies in humans who lack the hypocretin ligand (HCRT) and in dogs with a mutation in hypocretin receptor 2 (HCRTR2). However, little is known about molecular alterations downstream of the hypocretin signals.     

Desorption electrospray ionization mass spectrometry: direct toxicological screening and analysis of illicit Ecstasy tablets

Desorption electrospray ionization mass spectrometry (DESI-MS) was used as a simple and rapid way to analyze drug tablets and powders without sample preparation. Experiments were performed with a home-made DESI source coupled to a triple-quadrupole linear-ion trap (QqQ(LIT)) mass spectrometer. Twenty-one commercial drugs as well as some illicit Ecstasy tablets and powders were analyzed. MS spectra almost exclusively showed the protonated or deprotonated ion of the drug after directing the pneumatically assisted electrospray onto the tablet's surface. With some tablets, inhomogeneity of the surface resulted in different spectra depending on the spot analyzed, thus showing that DESI could be used for imaging. Directly triggered MS/MS spectra were used for confirmatory analysis, with analysis times often below 10 s per tablet. For illicit Ecstasy tablets, DESI-MS, GC/MS and LC/MS analyses provided similar qualitative results for the main analytes. With MS/MS spectra library comparison or exact mass measurements, this technique could become very powerful for the rapid analysis of unknown tablets and shows the great potential of desorption techniques as an alternative to solution-based analysis.     

Zeros of Dedekind zeta functions in the critical strip

In this paper, we describe a computation which established the GRH to height (resp. ) for cubic number fields (resp. quartic number fields) with small discriminant. We use a method due to E. Friedman for computing values of Dedekind zeta functions, we take care of accumulated roundoff error to obtain results which are mathematically rigorous, and we generalize Turing's criterion to prove that there is no zero off the critical line. We finally give results concerning the GRH for cubic and quartic fields, tables of low zeros for number fields of degree and , and statistics about the smallest zero of a number field.

     

Direct Trifluoromethylation of Alcohols Using a Hypervalent Iodosulfoximine Reagent

The direct trifluoromethylation of a variety of aliphatic alcohols using a hypervalent iodosulfoximine reagent afforded the corresponding ethers in moderate to good yields (14–72 %). Primary, secondary, and even tertiary alcohols, including examples derived from natural products, underwent this transformation in the presence of catalytic amounts of zinc bis(triflimide). Typical reaction conditions involved a neat mixture of 6.0 equivalents of the alcohol with 1.0 equivalent of the reagent, with the majority of reactions complete within 2 h with 2.5 mol % of the Lewis acid catalyst. Furthermore, experimental evidence was provided that the C−O bond-forming process occurred via the coordination of the alcohol to the iodine atom and subsequent reductive elimination.     

Nafion as cosurfactant: solubilization of nafion in water in the presence of Pluronics

Incorporation of Nafion to aqueous solutions of Pluronics adversely impacts micellization due to extensive Nafion/copolymer interactions. Light scattering and zeta potential measurements provide evidence for the formation of sizable and stable Nafion/copolymer complexes, in expense of the neat copolymer micelles. At high copolymer concentrations, the overall interaction diagram of Nafion/copolymer reflects the competitive action of the release of packing constraints due to micellar destabilization induced by Nafion on one hand and the gelator nature of the Nafion on the other. Measurements using a quartz crystal microbalance (QCM-D) show that aqueous solutions of Pluronics (even at very low concentration) can dissolve the Nafion coating on the crystal resonator, while typical low molecular weight ionic surfactants fail to induce similar effects. These studies demonstrate that complexation with this class of copolymers is a facile route to impart dispersibility to Nafion in aqueous environments that otherwise can be achieved through tedious and harsh treatments.