Bipartite 2‐Factorizations of Complete Multipartite Graphs

It is shown that if K is any regular complete multipartite graph of even degree, and F is any bipartite 2‐factor of K, then there exists a factorization of K into F; except that there is no factorization of K_{6, 6} into F when F is the union of two disjoint 6‐cycles.     

Separation and characterization of aggregated species of amyloid-beta peptides

We have investigated the use of isoelectric focusing and immunodetection for the separation of low molecular weight species of amyloid-beta (Aβ) peptides from their aggregates. From solutions of Aβ_1–40 or Aβ_1–42 monomeric peptides, low molecular weight material appeared at a pI value of ca. 5, while the presence of aggregates was detected as bands, observed at a pI of 6–6.5. The formation of Aβ aggregates (protofibrils) was verified by a sandwich ELISA, employing the protofibril conformation-selective antibody mAb158. In order to study the aggregation behavior when using a mixture of the monomers, we utilized the IEF separation combined with Western blot using two polyclonal antisera, selective for Aβ_1–40 and Aβ_1–42, respectively. We conclude that both monomers were incorporated in the aggregates. In a further study of the mixed aggregates, we used the protofibril conformation-selective antibody mAb158 for immunoprecipitation, followed by nanoelectrospray mass spectrometry (IP-MS). This showed that the Aβ_1–42 peptide is incorporated in the aggregate in a significantly larger proportion than its relative presence in the original monomer composition. IP-MS with mAb158 was also performed, and compared to IP-MS with the Aβ-selective antibody mAb1C3, where a monomeric Aβ_1–16 peptide was added to the protofibril preparation. Aβ_1–16 is known for its poor aggregation propensity, and acted therefore as a selectivity marker. The results obtained confirmed the protofibril conformation selectivity of mAb158.     

Singlet energy transfer in porphyrin-based donor-bridge-acceptor systems: interaction between bridge length and bridge energy

Singlet excitation energy transfer is governed by two donor-acceptor interactions, the Coulombic and exchange interactions giving rise to the F?rster and Dexter mechanisms, respectively, for singlet energy transfer. In transfer between colliding molecules or between a donor (D) and acceptor (A) connected in donor-bridge-acceptor (D-B-A) system by an inert spacer (B), the distinction between these two mechanisms is quite clear. However, in D-B-A systems connected by a pi-conjugated bridge, the exchange interaction between the donor and acceptor is mediated by the virtual low-lying excited states (unoccupied orbitals) of that bridge and, as a consequence, becomes much more long-range in character. Thus, the clear distinction to the Coulombic mechanism is lost. This so-called superexchange mechanism for singlet energy transfer has been shown to make a significant contribution to the energy transfer rates in several D-B-A systems, and its D-A distance as well as D-B energy gap dependencies have been studied. We here demonstrate that in a series of oligo-p-phenyleneethynylene (OPE) bridged porphyrin-based D-B-A systems with varying D-A distances the F?rster and through-bond (superexchange) mechanisms both make considerable contributions to the observed singlet energy transfer rates. The donor is either a zinc porphyrin or a zinc porphyrin with a pyridine ligand, and the acceptor is a free base porphyrin. By comparison to a homologous series where only the D-B energy gaps varies, a separation between the two energy transfer mechanisms was possible and, moreover, an interplay between distance and energy gap dependencies was noted. The distance dependence was shown to be approximately exponential with an attenuation factor beta=0.20 A-1. If the effect of the varying D-B energy gaps in the OPE series was taken into account, a slightly higher beta-value was obtained. Ground-state absorption, steady-state, and time-resolved emission spectroscopy were used. The experimental study is accompanied by time-dependent density functional theory (TD-DFT) calculations of the electronic coupling, and the experimental and theoretical results are in excellent qualitative agreement (same distance dependence).     

Femtosecond coherent anti-Stokes Raman-scattering polarization beat spectroscopy of I2-Xe complex in solid krypton

Time-resolved coherent anti-Stokes Raman-scattering (CARS) measurements are carried out to study the interaction between xenon atom and iodine molecule in a solid krypton matrix. Interference between the CARS polarizations of the "free" and complexed iodine molecules is observed, while the quantum beats of the complex are not detected due to low concentration. Vibrational analysis based on the polarization beats yields accurate molecular constants for the I2-Xe complex. The harmonic frequency of the I2-Xe complex is found to be redshifted by 0.90 cm-1 when compared to the free I2, whereas the anharmonicity is approximately the same. The dephasing rate of the complex is found to be somewhat higher than that of the free iodine molecule in solid Kr, showing that the complexation affects dephasing, although not dramatically. Molecular dynamics simulations are carried out to find the conformation of the complex, and wave packet simulations are used to reproduce the CARS signal to confirm the assignments of the observed beatings as quantum and polarization beats. The results show that the polarization beats are a useful tool for investigating weak interactions in condensed phase.     

The local structure of protonated water from x-ray absorption and density functional theory

We present a combined x-ray absorption spectroscopy/computational study of water in hydrochloric acid (HCl) solutions of varying concentration to address the structure and bonding of excess protons and their effect on the hydrogen bonding network in liquid water. Intensity variations and energy shifts indicate changes in the hydrogen bonding structure in water as well as the local structure of the protonated complex as a function of the concentration of protons. In particular, in highly acidic solutions we find a dominance of the Eigen form, H(3)O(+), while the proton is less localized to a specific water under less acidic conditions.     

Properties of superhydrophobic paper treated with rapid expansion of supercritical CO<Subscript>2</Subscript> containing a crystallizing wax

Paper samples were rendered superhydrophobic with Alkyl Ketene Dimer using (1) Airblasting with cryo ground micro particles, (2) crystallizing from organic solvents and (3) spraying with Rapid Expansion of Supercritical Solutions (RESS) technique. The papers were characterized using Scanning Electron Microscopy, contact angle to water measurements and X-ray Photoelectron Spectroscopy (XPS). Advancing contact angles were in the region of 150°–160° and receding contact angles were in the region of 110°–130°. Diagrams showing the drop base diameter vs. the contact angle when water is pumped into, and then withdrawn from, a sessile drop show that a stick slip pattern is present in the advancing phase for a non coated internally sized paper. Papers rendered superhydrophobic with the RESS technique showed a much less pronounced stick slip pattern in the advancing phase but still a stick slip pattern in the receding phase.     

Chlorine interactions with water ice studied by molecular beam techniques

The kinetics of chlorine interactions with ice at temperatures between 103 and 165 K have been studied using molecular beam techniques. The Cl(2) trapping probability is found to be unity at thermal incident energies, and trapping is followed by rapid desorption. The residence time on the surface is less than 25 microg at temperatures above 135 K and approaches 1 s around 100 K. Rate constants for desorption are determined for temperatures below 135 K. The desorption kinetics follow the Arrhenius equation, and activation energies of 0.24 +/- 0.03 and 0.31 +/- 0.01 eV, with corresponding preexponential factors of 10(12.08+/-1.19) and 10(16.52+/-0.38) s(-1), are determined. At least two different Cl(2) binding sites are concluded to exist on the ice surface. The observed activation energies are likely to be the Cl(2)-ice binding energies for these states, and the Cl(2)-surface interactions are concluded to be stronger than earlier theoretical estimates. The surface coverage of Cl(2) on ice under stratospheric conditions is estimated to be negligible, in agreement with earlier work.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.