Symmetric Functions, Noncommutative Symmetric Functions, and Quasisymmetric Functions

This paper is concerned with two generalizations of the Hopf algebra of symmetric functions that have more or less recently appeared. The Hopf algebra of noncommutative symmetric functions and its dual, the Hopf algebra of quasisymmetric functions. The focus is on the incredibly rich structure of the Hopf algebra of symmetric functions and the question of which structures and properties have good analogues for the noncommutative symmetric functions and/or the quasisymmetric functions. This paper attempts to survey the ongoing investigations in this topic as dictated by the knowledge and interests of its author. There are many open questions that are discussed.     

Compact high-order finite-element method for elliptic transport problems with variable coefficients

We present a new conforming bilinear Petrov-Galerkin finite-element scheme for elliptic transport problems with variable coefficients. This scheme combines a generalized test function and artificial diffusion to achieve O(h⁴) grid-point accuracy on uniform stencils of 3 × 3 in two dimensions without resorting to the extended stencils of high-order elements. The method is compared with upwind and high-order finite-difference schemes and the standard Galerkin finite-element method for representative test problems. © 1994 John Wiley & Sons, Inc.     

Time-dependent density functional theory description of on-site electron repulsion and ligand field effects in the optical spectrum of hexaaquoruthenium(II) in solution

Time-dependent density functional theory (TDDFT) and density functional-based molecular dynamics were used to simulate the finite temperature t(2g)5 e(g) <-- t(2g)6 absorption band of the Ru2+ hexahydrate coordination complex in aqueous solution. The (1)T1 <-- (1)A1 and (1)T2 <-- (1)A1 molecular term splitting of this transition, which is not accounted for by the Kohn-Sham excitation spectrum, is shown to be satisfactorily reproduced by TDDFT at the BLYP/ALDA level of theory. Comparison to the spectrum of the Ru2+ (H2O)6 complex in vacuo computed by similar density functional classical molecular dynamics methods leads to the observation that bulk solvation has a negligible effect on the position and the shape of the absorption profile.     

Fabrication of a glass-implemented microcapillary electrophoresis device with integrated contactless conductivity detection

Glass microdevices for capillary electrophoresis (CE) gained a lot of interest in the development of micrototal analysis systems (microTAS). The fabrication of a microTAS requires integration of sampling, chemical separation and detection systems into a microdevice. The integration of a detection system into a microchannel, however, is hampered by the lack of suitable microfabrication technology. Here, a microfabrication method for integration of insulated microelectrodes inside a leakage-free microchannel in glass is presented. A combination of newly developed technological approaches, such as low-temperature glass-to-glass anodic bonding, channel etching, fabrication of buried metal interconnects, and deposition of thin plasma-enhanced chemical vapour deposition (PECVD) silicon carbide layers, enables the fabrication of a CE microdevice with an integrated contactless conductivity detector. The fabrication method of this CE microdevice with integrated contactless conductivity detector is described in detail. Standard CE separations of three inorganic cations in concentrations down to 5 microM show the viability of the new microCE system.     

Charge shift and triplet state formation in the 9-mesityl-10-methylacridinium cation

The target donor-acceptor compound forms an acridinium-like, locally excited (LE) singlet state on illumination with blue or near-UV light. This LE state undergoes rapid charge transfer from the acridinium ion to the orthogonally sited mesityl group in polar solution. The resultant charge-transfer (CT) state fluoresces in modest yield and decays on the nanosecond time scale. The LE and CT states reside in thermal equilibrium at ambient temperature; decay of both states is weakly activated in fluid solution, but decay of the CT state is activationless in a glassy matrix. Analysis of the fluorescence spectrum allows precise location of the relevant energy levels. Intersystem crossing competes with radiative and nonradiative decay of the CT state such that an acridinium-like, locally excited triplet state is formed in both fluid solution and a glassy matrix. Phosphorescence spectra position the triplet energy well below that of the CT state. The triplet decays via first-order kinetics with a lifetime of ca. 30 micros at room temperature in the absence of oxygen but survives for ca. 5 ms in an ethanol glass at 77 K. The quantum yield for formation of the LE triplet state is 0.38 but increases by a factor of 2.3-fold in the presence of iodomethane. The triplet reacts with molecular oxygen to produce singlet molecular oxygen in high quantum yield. In sharp contradiction to a recent literature report, there is no spectroscopic evidence to indicate the presence of an unusually long-lived CT state.     

Quantitative multiplex CARS spectroscopy in congested spectral regions

A novel procedure is developed to describe and reproduce experimental coherent anti-Stokes Raman scattering (CARS) data, with particular emphasis on highly congested spectral regions. The approach, exemplified here with high-quality multiplex CARS data, makes use of spontaneous Raman scattering results. It is shown that the underlying vibrational Raman response can be retrieved from the multiplex CARS spectra, so that the Raman spectrum can be reconstituted, provided an adequate signal-to-noise ratio (SNR) is present in the experimental data and sufficient a priori knowledge of the vibrational resonances involved exists. The conversion of CARS to Raman data permits a quantitative interpretation of CARS spectra. This novel approach is demonstrated for highly congested multiplex CARS spectra of adenosine mono-, di-, and triphosphate (AMP, ADP, and ATP), nicotinamide adenine dinucleotide (NAD+), and small unilamellar vesicles (SUVs) of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC). Quantitative determination of nucleotide concentrations and composition analysis in mixtures is demonstrated.     

A classical point charge model study of system size dependence of oxidation and reorganization free energies in aqueous solution

The response of water to a change of charge of a solvated ion is, to a good approximation, linear for the type of iron-like ions frequently used as a model system in classical force field studies of electron transfer. Free energies for such systems can be directly calculated from average vertical energy gaps. Exploiting this feature, we have computed the free energy and the reorganization energy of the M2+/M3+ and M1+/M2+ oxidations in a series of model systems all containing a single Mn+ ion and an increasing number of simple point charge water molecules. Long-range interactions are taken into account by Ewald summation methods. Our calculations confirm the observation made by Hummer, Pratt, and Garcia (J. Phys. Chem. 1996, 100, 1206) that the finite size correction to the estimate of solvation energy (and hence oxidation free energy) in such a setup is effectively proportional to the inverse third power (1/L3) of the length L of the periodic cell. The finite size correction to the reorganization energy is found to scale with 1/L. These simulation results are analyzed using a periodic generalization of the Born cavity model for solvation, yielding three different estimates of the cavity radius, namely, from the infinite system size extrapolation of oxidation free energy and reorganization energy, and from the slope of the linear dependence of oxidation free energy on 1/L3. The cavity radius for the reorganization energy is found to be significantly larger compared to the radius for the oxidation (solvation) free energy. The radius controlling the 1/L3 dependence of oxidation free energy is found to be comparable to the radius for reorganization. The implication of these results for density functional theory-based ab initio molecular dynamics calculation of redox potentials is discussed.     

Micromolding of solvent resistant microfluidic devices

We demonstrate a rapid fabrication procedure for solvent-resistant microfluidic devices based on the perfluoropolyether (PFPE) SIFEL. We carefully modified the poly-dimethylsiloxane (PDMS) micromolding procedure, such that it can still be executed using the standard facilities for PDMS devices. Most importantly, devices with a thin SIFEL layer for the patterned channels and a PDMS support layer on top offered the best of two worlds in terms of chemical and mechanical stability during fabrication and use. Tests revealed that these devices overcome two important drawbacks of PDMS devices: (i) incompatibility with almost all non-aqueous solvents, and (ii) leaching of oligomer into solution. The potential of our device is shown by performing a relevant organic synthesis reaction with aggressive reactants and solvents. PFPE-PDMS devices will greatly expand the application window of micromolded devices.     

I/O-efficient algorithms for computing planar geometric spanners

We present I/O-efficient algorithms for computing planar Steiner spanners for point sets and sets of polygonal obstacles in the plane.