Immanant positivity for Catalan-Stieltjes matrices

We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices. To obtain these sufficient conditions, we construct new planar networks with a recursive nature for Catalan-Stieltjes matrices. As applications, we provide a unified way to produce inequalities for many combinatorial polynomials, such as the Eulerian polynomials, Schröder polynomials, and Narayana polynomials.     

Propagating transverse electric and transverse magnetic modes in liquid crystal-clad planar waveguides

ABSTRACT

In a planar dielectric waveguide, weak confinement of a propagating mode in a high index core leads to a measurable evanescent interaction with the cladding. In this work, we study the effect of a reorientable anisotropic cladding on the behaviour of Transverse Electric (TE) and Transverse Magnetic (TM) mode polarisations using a liquid crystal (LC)-clad waveguide architecture. The polarised evanescent field of a guided mode interacts with a voltage-tunable birefringent LC cladding to deflect an out-coupled beam. Experimental measurements are coupled with a theoretical framework and show good consistency with simulation results. We isolate the effect of mode confinement by changing the thickness of the high index core. Interactions between the LC index ellipsoid and the mode polarisation are probed by changing the initial alignment of the LC. Finally, we examine the difference in deflection between TE and TM modes, which incorporates both a change in mode confinement and a difference in LC index components.     

Isolated square planar metal complexes of carbon

Based on the group theory analysis and quantum chemical calculations within the framework of SW X _α method (in relativistic approximation for core electrons and non-relativistic for valence ones), the existence possibility of square planar complexes [M₄C] and [M₄C]^2? (M = Al, Ga, In, Tl, Sc, and Y) in gas phase has been shown. The extraction of Kt₂[M₄C] square planar complexes of carbon in the crystal state is possible too. A high stability of these complexes, in comparison with usual tetrahedral, is achieved due to the formation of five-and four-center bonds (bonds M-M and M-C).     

On the Rigidity of Polynorbornenes with Dipolar Pendant Groups

A range of polynorbornenes (PNBs) with fused dipolar pendant groups at C‐5,6 positions was synthesized by ring‐opening metathesis polymerization catalyzed by a ruthenium carbene complex (Grubbs I). Photophysical studies, EFISH measurements, and atomic force microscopy images have been used to investigate the structures and morphology of these polymers. These results suggest that the polymers may adopt rigid rod‐like structures. The presence of the double bonds in PNBs appeared to be indispensable for the rigidity of the polymers. Interaction between unsaturated pendant groups may result in coherent alignment leading to a rod‐like structure.     

Enantioselective Oxidation of Sulfides Catalyzed by Chiral MoV and CuII Complexes of Catechol-Appended β-Cyclodextrin Derivatives in Water

The two modified β-cyclodextrin (β-CD) derivatives having catechol-type ligand (2,3- and 3,4-dihydroxy groups on the benzoate ring) were synthesized. The chiral catalytic activity of their Mo^V and Cu^II complexes was examined in the asymmetric oxidation of aromatic sulfides using hydrogen peroxide in water (pH 6.0). The oxidation with the Mo^V complexes of two β-CD derivatives were more accelerated than that with the Cu^II complexes. The sign of the optical rotation of the sulfoxides obtained in the above two cases showed the opposite configuration in the oxidation of the same sulfide. The difference of the enantioselectivity appeared also between the two complexes of the 2,3- and 3,4-dihydroxybenzoate derivatives with the same metal ion. While the use of the Mo^V complexes with the catechol derivatives yielded the sulfoxides with 35–65% ee, the use of the Cu^II complexes gave the products with the␣opposite configuration at 26–52% ee. The chiral induction in the oxidation, observed conversely between the␣catalysts, was reflected on the chiral conformation of the respective metal catalysts, showed in Induced Circular Dichroism (ICD) spectra. The highest optical yield, 65%, was observed in the oxidation of butyl phenyl sulfide using the catalytic amount (0.1 equiv) of the Mo^V complex with mono-6-O-(3,4-dihydroxybenzoyl)-β-CD. The reaction gave predominantly the (S)-sulfoxide in 95% chemical yield.     

Emanation thermal analysis study of a sol-gel precursor for silica-titania waveguides

Emanation Thermal Analysis (ETA) was demonstrated as a tool for the characterization of microstructure changes of a sol-gel precursor for silica-titania layers deposited on the glass plate to be used as planar waveguides. Temperature ranges of 280-330 and 380-500°C, respectively, in which the densification of the layers took place, were determined by ETA under in situ conditions of the sample heating. Results of thermogravimetry were compared with the ETA data. This revised version was published online in August 2006 with corrections to the Cover Date.     

Study of temperature transitions in solid poly(oxymethylene) by thermal analysis methods

Poly(oxymethylene)s with different molecular mass and chemical structure were studied using DSC, dynamic mechanical relaxation, thermomechanical analysis, and thermogravimetry.Molecular mobilities of two types were found in the amorphous phase of poly(oxymethylene). Unconstrained chains of poly(oxymethylene) soften at –70°C and then amorphous chains with different restraints from the crystalline phase are successively activated in a wide temperature interval.Dedicated to Professor Bernhard Wunderlich on the occasion of his 65th birthdayThis work has been supported by DuPont Company     

Using three major criteria to evaluate aromaticity of five-member C-containing rings and their Si-, N-, and P-substituted aromatic heterocyclics

In this paper, we used bond-length equalization, aromatic stabilization energies (ASE) and nucleus-independent chemical shifts (NICS), calculated with (density functional theory) B3LYP levels at the 6-311+G^** basis set, to evaluate the aromaticity of a set of 38 five-member planar π-electron aromatic systems: sila-, aza- and phospha- derivatives and their parent systems. The result revealed statistically significant correlations among the above three criteria, and the order of aromaticity of the whole set was: Aza- derivatives rings > Phospha- derivatives rings > Sila- derivatives rings > Carbon-containing rings; NICS(0.6) and NICS(0.8) had the same results in evaluating the order of aromaticity in our case.     

Fracture mechanisms in rigid core-shell particle modified high performance epoxies

The fracture mechanisms of a high performance epoxy system modified with two types of preformed rigid core-shell particles (RCSP) were investigated. The use of the preformed RCSP anables the control of the dispersion of the toughener phase in the epoxy, which, in turn, allows the mechanical properties of the modified epoxy to be optimized. The toughening effect via the RCSP modification is found to be as good as that via the core-shell rubber modification. The moduli andT _g of these RCSP-modified epoxies are virtually unaltered via the RCSP modification, when compared with the neat epoxy resin equivalent. The toughening mechanisms in these toughened systems appear to be predominantly crack deflection, crack bifurcation, and microcracking. Approaches for effective toughening of high performance polymers via rigid polymers are discussed.     

Rigid-body dynamics in the isothermal-isobaric ensemble: a test on the accuracy and computational efficiency

We have developed a time-reversible rigid-body (rRB) molecular dynamics algorithm in the isothermal-isobaric (NPT) ensemble. The algorithm is an extension of rigid-body dynamics [Matubayasi and Nakahara, J Chem Phys 1999, 110, 3291] to the NPT ensemble on the basis of non-Hamiltonian statistical mechanics [Martyna, G. J. et al., J Chem Phys 1994, 101, 4177]. A series of MD simulations of water as well as fully hydrated lipid bilayer systems have been undertaken to investigate the accuracy and efficiency of the algorithm. The rRB algorithm was shown to be superior to the state-of-the-art constraint-dynamics algorithm SHAKE/RATTLE/ROLL, with respect to computational efficiency. However, it was revealed that both algorithms produced accurate trajectories of molecules in the NPT as well as NVT ensembles, as long as a reasonably short time step was used. A couple of multiple time-step (MTS) integration schemes were also examined. The advantage of the rRB algorithm for computational efficiency increased when the MD simulation was carried out using MTS on parallel processing computer systems; total computer time for MTS-MD of a lipid bilayer using 64 processors was reduced by about 40% using rRB instead of SHAKE/RATTLE/ROLL.