A coupled nonlinear hyperbolic-parabolic system

A boundary initial value problem for a quasi-linear hyperbolic system in one space variable is coupled to a boundary initial value problem for a quasi-linear parabolic equation in two space variables. The coupling occurs through one of the boundary conditions for the hyperbolic system and the source term in the parabolic equation. Such a coupling can arise in the consideration of gas flowing in a porous medium and out of that medium via a pipe. A local existence and uniqueness theorem is demonstrated. The proof involves the method of characteristics, Bernstein's estimates for parabolic partial differential equations, and the contracting mapping theorem.     

A dirichlet problem for an equation of mixed type with a discontinuous coefficient

Summary A Dirichlet problem for an equation of mixed type with a discontinuous coefficient is considered for a rectangle. In one part of the rectangle, Laplace's equation is specified while the wave equation is specified in the other part. The questions of existence, non-existence, uniqueness and non-uniqueness are discussed.     

New upper limit on the total neutrino mass from the 2 degree field galaxy redshift survey

We constrain f(nu) identical with Omega(nu)/Omega(m), the fractional contribution of neutrinos to the total mass density in the Universe, by comparing the power spectrum of fluctuations derived from the 2 Degree Field Galaxy Redshift Survey with power spectra for models with four components: baryons, cold dark matter, massive neutrinos, and a cosmological constant. Adding constraints from independent cosmological probes we find f(nu)<0.13 (at 95% confidence) for a prior of 0.1相似文献   

Solid-state structures of sym-dibenzo-16-crown-5 and its derivatives

Solid-state structures of sym-dibenzo-16-crown-5 (1) and five derivatives with one or two substituents on the three-carbon bridge have been determined. The derivatives with three sp³-hybridized carbons include sym-(propyl)dibenzo-16-crown-5 (4), sym-(pentafluorophenoxy)-dibenzo-16-crown-5 (5), and sym-[di(methoxymethyl)]dibenzo-16-crown-5 (6). Structures of two derivatives with sp²-hybridization of the central carbon (7 and 8) were also determined. Twisting of the three-carbon bridge causes one of the terminal methylene groups to be oriented within the polyether cavity.     

Regiospecific Carboxylation of Certain Methoxylated 2-Tetralones

As a part of an ongoing synthetic program, certain aromatic ringmethoxylated tetralins, bearing synthetically useful functional groups at positions 2 and 3, were required. The literature¹ revealed that treatment of 6-methoxy-2-tetralone with NaH and dimethyl carbonate gave exclusive carbomethoylation at position 1. However, treatment of 2-tetralone and of 5-methoxy-2-tetralone with magnesium methoxy carbonate (“MMC”) followed by esterification with diazomethane was reported² go give the 3-carbomethoxy product (la, lb) exclusively, although in low (12 and 26%, respectively) yield. The use of MMC in regiospecific carboxylation of certain acylic ketones has also been reported³.     

Nanometer-scale wetting of the silicon surface by its equilibrium oxide

Despite the extremely broad technical applications of the Si/SiO2 structure, the equilibrium wetting properties of silicon oxide on silicon are poorly understood. Here, we produce new results in which a solid-state buffer method is used to systematically titrate oxygen activity about the Si/SiO2 coexistence value. The equilibrium morphology at the Si(001) surface over >8 decades of PO2 about coexistence is revealed to be a uniform sub-stoichiometric SiOx film of sub-nanometer thickness, coexisting with secondary island structures which coarsen with annealing time. A new thermodynamic method using chemical potential to stabilize and control surficial oxides in nanoscale devices is suggested.