Viscous Shock Wave and Boundary Layer Solution to an Inflow Problem for Compressible Viscous Gas

The inflow problem for a one-dimensional compressible viscous gas on the half line (0,+) is investigated. The asymptotic stability on both the viscous shock wave and a superposition of the viscous shock wave and the boundary layer solution is established under some smallness conditions. The proofs are given by an elementary energy method.     

Observation of geometric phases for mixed states using NMR interferometry

Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently fault-tolerant quantum computation. This, however, requires one to deal with geometric phases in the presence of noise and interactions between different physical subsystems. Despite the wealth of literature on the subject of geometric phases very little is known about this very important case. Here we report the first experimental study of geometric phases for mixed quantum states. We show how different they are from the well-understood, noiseless, pure-state case.     

Preparation of epitaxial compositionally graded (Ba1-xSrx)TiO3 thin films with enhanced dielectric properties

Epitaxial compositionally graded (Ba_1-xSr_x)TiO₃ (BST) (0.0x0.25) thin films were deposited on (100) LaAlO₃ substrates by pulsed laser ablation, the substrates having bottom electrodes made of 100-nm-thick conductive La_0.5Sr_0.5CoO₃ (LSCO). Extensive X-ray diffraction, rocking-curve, and -scan studies indicate that the graded films are (100)-oriented and exhibit good in-plane relationships of [010]_BST//[010]_LAO and [001]_BST//[001]_LAO. For the up-graded films with barium concentration (1-x) increasing across the film thickness in the direction from the film/substrate interface to the film surface, the full width at half maximum of the BST film (200) rocking curve and the surface roughness, examined by atomic force microscopy, were larger than those of the down-graded films with barium concentration decreasing from the film/substrate interface to the film surface. The dielectric properties of the graded films, measured using vertical structures, show that at room temperature, the dielectric constant (_r) and dissipation factor (cos) at 100 kHz were 380 and 0.013 for the up-graded films, and 650 and 0.010 for the down-graded films, respectively. The dielectric behavior was enhanced in the down-graded films, which was attributed to the fact that the pure BaTiO₃ layer in the down-graded BST films not only serves as a bottom layer but also acts as an excellent seeding layer for enhancing subsequent film growth, leading to better film crystallinity and larger grain sizes in the down-graded films. The graded BST films undergo a diffuse phase transition, giving a broad, flat capacitance-versus-temperature profile. With such a graded structure, it is possible to build a dielectric thin-film capacitor having a capacitance which has a low temperature dependence over a broad temperature regime. PACS 77.55.+f; 68.55.Jk; 81.15.Fg     

Titanium dipyrrolylmethane derivatives: rapid intermolecular alkyne hydroamination

Alkynes are rapidly hydroaminated by primary amines using titanium dipyrrolylmethane derivatives as catalyst.     

Polymer-directed synthesis of penniform BaWO4 nanostructures in reverse micelles

Novel penniform superstructures of BaWO4 nanowires have been successfully synthesized in catanionic reverse micelles by using a double-hydrophilic block copolymer as the directing agent. This synthetic method is very simple, mild, and controllable, and it provides a novel method for direct solution-growth of hierarchical nanostructures based on inorganic nanowires.     

The Lewis acids catalyzed aza-Diels-Alder reaction of methylenecyclopropanes with imines

[reaction: see text] The methylenecyclopropanes can react with various imines to give the aza-Diels-Alder adducts in good yields in the presence of Lewis acids.     

Fully commutative elements and Kazhdan-Lusztig cells in the finite and affine Coxeter groups

The main goal of the paper is to show that the fully commutative elements in the affine Coxeter group form a union of two-sided cells. Then we completely answer the question of when the fully commutative elements of form or do not form a union of two-sided cells in the case where is either a finite or an affine Coxeter group.

     

Invariant Mean—Value Property and M—Harmonicity in the Unit Ball of R^n

In 1993,Ahern,Flores and Rudin showed that,if f is integrable over the unit ball BC^n of C^n and satisfies∫BC^nfoφdv=f（φ（0)) for every φ∈Aut(BC^n),then f is M-harmonic if and only if n≤11.The present paper is about an analogous question in the context of the unit ball Bn of R^n as well as in the weighted setting.