Conditions under which the order of two non-negative Hermitian matrices is preserved when taking integral powers

Let A and B be two n×n non-negative matrices. We write A ? B iff

$\text{u}{}^1\text{(A ? B)u ? 0}$

for all column vectors u in Cⁿ. Here u¹ is the conjugate transpose of u. In this paper are stated equivalent conditions under which A^k ? B^k for all natural numbers k. The result is then generalized to Hermitian operators in a Hilbert space.     

Structural control of the photoluminescence of silole regioisomers and their utility as sensitive regiodiscriminating chemosensors and efficient electroluminescent materials

We synthesized a group of silole regioisomers 1(x,y), whose photoluminescence varied dramatically with its regiostructure. By internally hindering the intramolecular rotation, we succeeded in creating a novel silole (1(3,4)) that is strongly luminescent in solutions and whose fluorescence quantum yield in acetone is as high as 83%. We revealed that 1(3,4) was a sensitive chemosensor capable of optically discriminating nitroaromatic regioisomers of p-, o-, and m-nitroanilines. Against general belief, crystal formation of 1(2,4) blue-shifted its emission color and boosted its emission efficiency. The light-emitting diode based on the crystal of 1(2,4) emitted a strong blue light (464 nm) in a high current efficiency (5.86 cd/A).     

Microstructure and rheology of stimuli-responsive nanocolloidal systems-effect of ionic strength

The effect of ionic strength on the rheological behavior of model pH-responsive nanocolloidal systems consisting of methacrylic acid-ethyl acrylate (MAA-EA) cross-linked with diallyl phthalate (DAP) was examined. Neutralization of acid groups increases the osmotic pressure exerted by counterions trapped in the polymeric network against ions in bulk solution, which is responsible for the swelling and increase in viscosity. Swelling decreases with increasing salt concentration as a result of reduced osmotic pressure inside the microgels, which is attributed to the charge shielding effect of counterions (salt) on the negatively charged carboxylate groups. Electromotive measurements using ion-selective electrodes confirmed that not all the counterions, that is, K+, remain mobile, but a fraction of these ions can penetrate the porous microgel particles to shield the negatively charged carboxylate groups. A consequence of this is that some of the Na+ counterions inside the particles are expelled, thus regaining their translational entropy, and become mobile sodium ions in the bulk solution. We successfully developed a new scaling law that relates the swelling ratio, Q, of microgels as a function of neutralization degree, alpha, cross-linked density, Nx, molar fraction of acidic units, y, and concentration of mobile counterions, CK+ and CNa+, represented as (Nx/c0)(CK+ + CNa+Q + Q2/3 proportional, variant yNxalpha. The new scaling law no longer assumes that all the counterions are trapped inside the microgels. The proportionality reduces to the form Q proportional, variant (yalphaNx)3/2 in the absence of salt, that is, CK+ + CNa+ approximately 0. By combining the results from light scattering and rheological measurements, we are able to correlate the microstructural evolution of the colloidal systems with their bulk rheological behavior.     

Microstructure of un-neutralized hydrophobically modified alkali-soluble emulsion latex in different surfactant solutions

At low pH conditions and in the presence of anionic, cationic, and nonionic surfactants, hydrophobically modified alkali-soluble emulsions (HASE) exhibit pronounced interaction that results in the solubilization of the latex. The interaction between HASE latex and surfactant was studied using various techniques, such as light transmittance, isothermal titration calorimetry, laser light scattering, and electrophoresis. For anionic surfactant, noncooperative hydrophobic binding dominates the interaction at concentrations lower than the critical aggregation concentration (CAC) (C < CAC). However, cooperative hydrophobic binding controls the formation of mixed micelles at high surfactant concentrations (C > or = CAC), where the cloudy solution becomes clear. For cross-linked HASE latex, anionic surfactant binds only noncooperatively to the latex and causes it to swell. For cationic surfactant, electrostatic interaction occurs at very low surfactant concentrations, resulting in phase separation. With further increase in surfactant concentration, noncooperative hydrophobic and cooperative hydrophobic interactions dominate the binding at low and high surfactant concentrations, respectively. For anionic and cationic surfactant systems, the CAC is lower than the critical micelle concentration (CMC) of surfactants in water. In addition, counterion condensation plays an important role during the binding interaction between HASE latex and ionic surfactants. In the case of nonionic surfactants, free surfactant micelles are formed in solution due to their relatively low CMC values, and HASE latexes are directly solubilized into the micellar core of nonionic surfactants.     

Angustilodine,an Unusual Pentacyclic Indole Alkaloid from Alstonia

Two new indole alkaloids, angustilodine ( 1 ), with an unprecedented pentacyclic carbon skeleton, and angustilocine ( 2 ), belonging to the seco‐angustilobine‐B group of alkaloids, were obtained from the leaf extract of the Malayan species Alstonia angustiloba, and their structures were established by spectroscopic analysis.     

Preparation and Characterizations of TiO2/Organically Modified Silane Composite Materials Produced by the Sol-Gel Method

TiO₂/organically modified silane (ORMOSIL) composite materials produced by the sol-gel method were studied for optical waveguide applications. High optical quality waveguiding films on different substrates, including silicon, gallium arsenide, silica/silicon substrates, and microscope glass slides, were prepared from high titanium content (0.2 molar) ÿ-glycidoxypropyltrimethoxysilane at low temperature. Scanning electron microscopy (SEM), atomic force microscopy (AFM), differential thermal analysis (DTA), thermal gravimetric analysis (TGA), Fourier transform infrared spectroscopy (FT-IR) and X-ray photoelectron spectroscopy (XPS) have been used to investigate the optical and structural properties of the composite films. The TGA/DTA results showed that the organic compounds in the film would tend to decompose in the temperature range from 200°C to 500°C. SEM and AFM results showed that a dense and porous-free composite material film could be obtained at the heat treatment temperature of 100°C. It was also shown that ORMOSIL is integrated in the glass, providing low shrinkage and high cracking resistance. The propagation loss properties of the composite films were also investigated. About 1.1 dB/cm propagation loss of the planar waveguide film was obtained at the wavelength of 633 nm.     

Dielectrophoretic assembly of nanowires

Nanowire (NW) assembly is currently of great interest, partly because NWs are considered as a fundamental component in the fabrication of a variety of devices. A powerful method has been developed to model the assembly of NWs. The three-dimensional dielectrophoretic (DEP) assembly of NWs across opposing electrodes is, for the first time, comprehensively studied using this new method. It is found that the DEP force reaches a maximum when the ratio of gap size to NW length is in the range 0.85-1.0. Both the magnitude and sign of the DEP torque on each NW varies with this ratio, and also with the orientation angle and the geometry and configuration of the electrode. The simulation of the dynamic assembly of individual and bundled NWs agrees with experiment. This method is of sufficient power that it will be of direct use in modeling DEP-based assembly and thus the manufacturing of nanoelectronic devices.     

On the Distributions of Two Classes of Multiple Dependent Aggregate Claims

In this paper we examine two classes of correlated aggregate claims distributions, with univariate claim counts and multivariate claim sizes. Firstly, we extend the results of Hesselager [ASTIN Bulletin, 24： 19-32（1994）] and Wang ＆ Sobrero＇s [ASTIN Bulletin, 24：161-166 （1994）] concerning recursions for compound distributions to a multivariate situation where each claim event generates a random vector. Then we give a multivariate continuous version of recursive algorithm for calculating a family of compound distribution. Especially, to some extent, we obtain a continuous version of the corresponding results in Sundt [ASTIN Bulletin, 29：29-45 （1999）] and Ambagaspitiya [Insurance： Mathematics and Economics, 24：301-308 （1999）]. Finally, we give an example and show how to use the algorithm for aggregate claim distribution of first class to compute recursively the compound distribution.     

Flexible piecewise approximations based on partition of unity

In this paper, we study a flexible piecewise approximation technique based on the use of the idea of the partition of unity. The approximations are piecewisely defined, globally smooth up to any order, enjoy polynomial reproducing conditions, and satisfy nodal interpolation conditions for function values and derivatives of any order. We present various properties of the approximations, that are desirable properties for optimal order convergence in solving boundary value problems. AMS subject classification 65N30, 65D05Weimin Han: Corresponding author. The work of this author was partially supported by NSF under grant DMS-0106781.Wing Kam Liu: The work of this author was supported by NSF.     

A time-series risk model with constant interest for dependent classes of business

In this paper, we propose a discrete-time model with dependent classes of business using a time-series approach. Specifically, premiums and claims of all classes are supposed to satisfy a multivariate first-order autoregressive time-series model. A constant interest rate is also included in the model. A Lundberg-type inequality for the ruin probability is deduced. We also give an example with constant premiums and two classes of claims for which an expression as well as an exponential bound for the ruin probability is given. A simulation study is provided to help understanding the model.