Angle criteria for frame sequences and frames containing a Riesz basis

We obtain a condition implying that the union of two frame sequences is also a frame sequence. Christensen found a condition for this in terms of orthogonal projections. We phrase our condition by use of the angle between closed subspaces. Also a lower bound formula is obtained. We then apply the results to find conditions for a frame containing a Riesz basis to be a Riesz frame.     

Stereoelectronic Aspects of the Anomeric Effect in Fluoromethylamine

High-level ab initio calculations have been made for fluoromethylamine to study structural and energetic effects of the relative orientation of the N lone pair to the C? F bond. The anti-conformer (N lone pair anti-planar to the C? F bond) corresponds to the global energy minimum. It has the longest C? F distance, the shortest C? N distance, and is 7.5 kcal·mol^?1 more stable than the related perpendicular conformation (lone pair perpendicular to the C? F bond). The syn-conformation also shows hallmarks of the anomeric effect: long C? F bond, short C? N bond, and energetic stability when allowance is made for the two pairs of eclipsed hydrogens. The transition state for N inversion is close to the syn-structure; rotation about the C? N bond is strongly coupled with this inversion process. Small bond distance changes of ca. 0.02 Å between parallel and perpendicular conformations are associated with dissociation energy differences of ca. 30 kcal·mol^?1. Various criteria for assessing the strength of the anomeric effect are discussed.     

Synthesis, optical and electroanalytical characterizations of a thiacalix[4](N-phenylazacrown-5)ether-BODIPY ionophore

Novel fluorogenic 1,3-alt thiacalix[4](N-phenylazacrown-5)ether ionophore has been synthesized by conjugation of the N-phenyl group with borondipyrromethene (BODIPY) fluorophore moiety. The ionophore exhibits pronounced off-on type fluorescent responses to some transition metal ions, in particular to Cu²⁺. In a PVC membrane electrode, distinct Ag⁺ selectivity was observed in potentiometric transduction.     

Microdeformation behavior in nanotemplated epoxy thermosets: A study with in situ tensile deformation technique in transmission electron microscopy

Microdeformation behavior in nanostructured block copolymer‐toughened epoxy resins, or templated epoxy thermosets, was studied using an in situ tensile deformation technique performed directly in a transmission electron microscope. The observed microdeformation modes were found to correlate well with the macroscopic mechanical properties of the materials. In the order of decreasing macroscopic fracture toughness, the microdeformation modes were observed to change from large uniform plastic deformation over an extensive area, to localized plastic deformation bands, to little plastic deformation observed in the most brittle material. A similar trend was also observed when samples of the same material were tested at different temperatures, reflecting changes in the deformation mechanism as a function of temperature. Structural defects were observed in nanotoughening phases when plastic deformation was observed. The implication of the observed microdeformation modes to the macroscopic toughening mechanisms is discussed in the context of the micromorphology of the nanometer sized toughening phases and parameters of the epoxy matrix chemistry such as bromination, molecular weight, and interfacial miscibility. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 393–406, 2009     

Numerical simulations of droplet formation in a cross‐junction microchannel by the lattice Boltzmann method

An immiscible liquid–liquid multiphase flow in a cross‐junction microchannel was numerically studied using the lattice Boltzmann method. An improved, immiscible lattice BGK model was proposed by introducing surface tension force based on the continuum surface force (CSF) method. Recoloring step was replaced by the anti‐diffusion scheme in the mixed region to reduce the side‐effect and control the thickness of the interface. The present method was tested by the simulation of a static bubble. Laplace's law and spurious velocities were examined. The results show that our model is more advantageous for simulations of immiscible fluids than the existing immiscible lattice BGK models. Computational results of multiphase flow in a cross‐junction microchannel were obtained and analyzed based on dimensionless numbers. It is found that the flow pattern is decided mostly by the capillary number at a small inlet flux. However, at the same capillary number, a large inlet flux will lead to much smaller droplet generation. For this case, the flow is determined by both the capillary number and the Weber number. Copyright © 2007 John Wiley & Sons, Ltd.     

A Geometric Level-Set Formulation of a Plasma-Sheath Interface

In this paper, we present a new geometric level-set formulation of a plasma-sheath interface arising in plasma physics. We formally derive the explicit dynamics of the interface from the Euler-Poisson equations and study the local-time evolution of the interface and sheath in some special cases.     

ANALYSIS OF THE LOCALIZATION OF DAMAGE AND THE COMPLETE STRESS-STRAIN RELATION FOR MESOSCOPIC HETEROGENEOUS ROCK UNDER UNIAXIAL TENSILE LOADING

The mechanical behavior of rock under uniaxial tensile loading is different from that of rock under compressive loads. A micromechanics-based model was proposed for mesoscopic heterogeneous brittle rock undergoing irreversible changes of their microscopic structures due to microcrack growth. The complete stress-strain relation including linear elasticity, nonlinear hardening, rapid stress drop and strain softening was obtained. The influence of all microcracks with different sizes and orientations were introduced into the constitutive relation by using the probability density function describing the distribution of orientations and the probability density function describing the distribution of sizes. The influence of Weibull distribution describing the distribution of orientations and Rayleigh function describing the distribution of sizes on the constitutive relation were researched. Theoretical predictions have shown to be consistent with the experimental results.     

Direct synthesis of Te/Bi2Te3 nanocomposite powders by a polyol process

Research on Chemical Intermediates - Tellurium nanotube-based bismuth telluride (Te/Bi2Te3) nanocomposite powders have been synthesized by the polyol process using Bi (NO3)3, TeCl4 as the metal...     

Fabrication of hollow and mesoporous germania microspheres by templating against plasma-treated polystyrene microspheres

The surfaces of monodisperse polystyrene (PS) colloids have been modified with hydroxyl groups by means of plasma treatment technique. By templating against these surface-modified PS colloids, the germania coating PS composite microspheres were prepared via a sol–gel process. After removal of PS cores, the resulting composite microspheres converted into hollow germania microspheres with mesoporous structure. The shell thickness of these hollow spheres can be controlled by varying the concentration of germania precursor. BET results indicated that the hollow germania microspheres shell exhibits slightly broader pore size distribution than that of corresponding composite one owing to the swelling effects of the PS core during the etching process. In addition, the as-prepared germania exhibits amorphous phase which can be converted into crystalline phase by calcination treatment. It is worthy to noting that this fabrication protocol demonstrated a facile, low-cost and environment-benign way for fabricating hollow germania structures by templating method. Moreover, this protocol is not limit to germania; it also could be used to create the other hollow inorganic oxides spheres.