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.

     

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.     

Surface segregation of polypeptide-based block copolymer micelles: An approach to engineer nanostructured and stimuli responsive surfaces

We describe the surface segregation of polypeptide-based block copolymer micelles to produce stimuli-responsive nanostructures at the polymer blend/air interface. Such structures were obtained by simultaneous surface migration and self assembly at the surface of diblock copolymer/homopolymer blends. We employed blends composed of homopolymer (PS) and an amphiphilic block copolymer polystyrene-b-poly(l-glutamic acid) (PS-b-PGA). The surface was functionalized based on the preferential segregation to the polymer blend/air interface of the hydrophilic PGA block of the diblock copolymer upon annealing to water vapor. The surface migration of the diblock copolymer to the interface was demonstrated both by XPS and contact angle measurements. As a consequence, the PGA interfacial attraction leads to a large surface excess on diblock copolymer which in turn, through macrophase and microphase separation, produced separated domains at the surface with regions composed either of homo or block copolymer. Herein we demonstrate that the use of asymmetric diblock copolymers with a higher content in PS lead to spherical micellar assemblies randomly distributed at the surface. As observed by AFM imaging the blend composition, i.e. the amount of block copolymer within the blend influences the density of micelles at the surface. Finally, when exposed to water, the pH affects the surface morphology. The PGA segments are collapsed at low pH values and extended at pH values above 4.8, thus inducing variations on the topography of the films at the nanometer scale.     

Synthesis of polynorbornene‐poly(tert‐butyl acrylate) nanoparticles with original morphologies by tandem ROMP and ATRP in microemulsion

Composite latex particles based on homopolymers and graft‐copolymers composed of polynorbornene (PNB) and poly(tert‐butyl acrylate) (PtBA) were synthesized in microemulsion conditions by simultaneous combination of two distinct methods of polymerization: Ring‐opening metathesis polymerization (ROMP) and atom transfer radical polymerization (ATRP). Only one commercial compound (first generation Grubbs catalyst) was used to initiate the ROMP of norbornene (NB) and activate the ATRP of tert‐butyl acrylate (tBA). Well‐defined nanoparticles with hydrodynamic diameters smaller than 50 nm were prepared with original morphologies depending on the monomer compositions, the type of combination (polymer blend or graft‐copolymer), and the conditions of microemulsion polymerizations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

A short and efficient synthesis of the NMDA glycine site antagonist: (3R,4R)-3-amino-1-hydroxy-4-methyl pyrrolidin-2-one (L-687,414)

A short and efficient synthesis of the NMDA glycine site antagonist: (3R,4R)-3-amino-1-hydroxy-4-methyl pyrrolidin-2-one (L-687,414) is described.