Aromatic Heterocycles Used as Terminal Groups of Calamitic Liquid Crystals

Three series of compounds 1 ‐ 21 were prepared by using 2‐, 3‐, and 4‐pyridinemethanol as terminal group of calamitic liquid crystals. These compounds have some similarities in their phase behavior. They all exhibit SmA phase. A tilt smectic phase, SmC, will be formed when their flexible alkoxy chain is longer than hexoxy group. The profound difference between them is that the compounds 15 ‐ 17 possess a short temperature range of N phase. The compounds 3 and 6 have the widest SmA phase, up to 94 °C, and SmC phase, up to 46 °C, respectively.     

Electrodeposition of copper on a Pt(111) electrode in sulfuric acid containing poly(ethylene glycol) and chloride ions as probed by in situ STM

This study employed real-time in situ STM imaging to examine the adsorption of PEG molecules on Pt(111) modified by a monolayer of copper adatoms and the subsequent bulk Cu deposition in 1 M H(2)SO(4) + 1 mM CuSO(4)+ 1 mM KCl + 88 μM PEG. At the end of Cu underpotential deposition (~0.35 V vs Ag/AgCl), a highly ordered Pt(111)-(√3 × √7)-Cu + HSO(4)(-) structure was observed in 1 M H(2)SO(4) + 1 mM CuSO(4). This adlattice restructured upon the introduction of poly(ethylene glycol) (PEG, molecular weight 200) and chloride anions. At the onset potential for bulk Cu deposition (~0 V), a Pt(111)-(√3 × √3)R30°-Cu + Cl(-) structure was imaged with a tunneling current of 0.5 nA and a bias voltage of 100 mV. Lowering the tunneling current to 0.2 nA yielded a (4 × 4) structure, presumably because of adsorbed PEG200 molecules. The subsequent nucleation and deposition processes of Cu in solution containing PEG and Cl(-) were examined, revealing the nucleation of 2- to 3-nm-wide CuCl clusters on an atomically smooth Pt(111) surface at overpotentials of less than 50 mV. With larger overpotential (η > 150 mV), Cu deposition seemed to bypass the production of CuCl species, leading to layered Cu deposition, starting preferentially at step defects, followed by lateral growth to cover the entire Pt electrode surface. These processes were observed with both PEG200 and 4000, although the former tended to produce more CuCl nanoclusters. Raising [H(2)SO(4)] to 1 M substantiates the suppressing effect of PEG on Cu deposition. This STM study provided atomic- or molecular-level insight into the effect of PEG additives on the deposition of Cu.     

Low‐loss aluminium nitride thin film for mid‐infrared microphotonics

Mid‐infrared (mid‐IR) microphotonic devices including (i) straight/bent waveguides and (ii) Y‐junction beam splitters are developed on thin films of CMOS‐compatible sputter deposited aluminum nitride (AlN)‐on‐silicon. An optical loss of 0.83 dB/cm at λ = 2.5 µm is achieved. In addition, an efficient mid‐IR 50:50 beam splitter is demonstrated over 200 nm spectral bandwidth along with a <2% power difference between adjacent channels. With the inherent advantage of an ultra‐wide transparent window (ultraviolent to mid‐IR), our AlN mid‐IR platform can enable broadband optical networks on a chip.     

On the uniqueness problem of differential equations in normed spaces †

Simple direct proofs of some recent results by Kalla, Conde, and Hubbell for a generalized elliptic type integral [Appl. Anal., 22 (1986), pp. 273-287] are presented. Furthermore, a new single term asymptotic approximation for this function is derived, which is superior to the two term approximation given by these authors     

Computationally efficient learning of multivariate <Emphasis Type="Italic">t</Emphasis> mixture models with missing information

A finite mixture model using the multivariate t distribution has been well recognized as a robust extension of Gaussian mixtures. This paper presents an efficient PX-EM algorithm for supervised learning of multivariate t mixture models in the presence of missing values. To simplify the development of new theoretic results and facilitate the implementation of the PX-EM algorithm, two auxiliary indicator matrices are incorporated into the model and shown to be effective. The proposed methodology is a flexible mixture analyzer that allows practitioners to handle real-world multivariate data sets with complex missing patterns in a more efficient manner. The performance of computational aspects is investigated through a simulation study and the procedure is also applied to the analysis of real data with varying proportions of synthetic missing values.     

Global attractor of a coupled finite difference reaction diffusion system with delays

In the study of asymptotic behavior of solutions for reaction diffusion systems, an important concern is to determine whether and when the system has a global attractor which attracts all positive time-dependent solutions. The aim of this paper is to investigate the global attraction problem for a finite difference system which is a discrete approximation of a coupled system of two reaction diffusion equations with time delays. Sufficient conditions are obtained to ensure the existence and global attraction of a positive solution of the corresponding steady-state system. Applications are given to three types of Lotka-Volterra reaction diffusion models, where time-delays may appear in the opposing species.     

The field distributions and dispersion characteristics in chiroferrite central-loaded waveguide

The field distributions and dispersion characteristics of hybrid modes in circular chiro ferrite central-loaded waveguide are investigated numerically in this paper. Especially, the effects of constitutive parameters of chiro ferrite material on the propagation behaviour of hybrid modes are examined in detail, and some novel features are pointed out. The results show that, as reciprocal chiral and gyrotropic media, nonreciprocal chiroferrite materials have potential applications for the design of microwave, millimeter wave and integrated optical devices.     

A further remark on the logarithmic derivatives of a square matrix

It is well-known that the logarithmic derivativeμ[A] of a square matrixA has its value no less than the maximum real partp of the eigenvalues ofA and there exist matricesA such thatμ[A] >p with respect to any norm inCⁿ. The purpose of this note is to show thatμ[A] can be made equal top for some operator norm inCⁿ if and only if those eigenvalues ofA with maximum real part are simple roots of the minimal polynomials forA.     

An iterative method for radiative transfer is a slab with specularly reflecting boundary

The purpose of this paper is to present an iterative scheme for solving the radiative-transfer equation in a scattering, absorbing and emitting slab with specularly reflecting boundary. The medium under consideration is anisotropic, nonhomogeneous and azimuthally unsymmetric, and the boundary surface can be either transparent or reflecting. A novelty of this scheme is that it leads to an explicit recursion formula for the determination of the solution as well as an error estimate for the iterations. The recursion formula involves straightforward integrations of a well-behaved function and can be used to calculate numerical results by using a computer. It is shown that the sequence of iterations from the recursion formula converges uniformly to a unique positive solution of the problem, so that this method also gives an existence and uniqueness theorem.