Equidivisible kleene monoids and the Elgot-Mezei theorem

Equidivisible Kleene monoids satisfy the Elgot-Mezei theorem.     

Excited-state processes in first-generation phenyl-cored thiophene dendrimers

First generation dendrimers with three oligothiophene arms (meta-arranged, 3G1-nS) and four arms (ortho- and para-arranged, 4G1-nS) connected to a central phenyl core were investigated spectroscopically in solution. In all dendrimers, on an ultrafast time scale (<10 ps), two "cooling" processes convert the initially generated, "hot" exciton into the geometrically relaxed, "cold" exciton. A decrease in the triplet yield, particularly evident for the 4-arm dendrimers; intersystem crossing rate; and nonradiative triplet decay time with increasing number of bridging thiophene units n all meet with expectations from prior studies on linear oligothiophenes. A relatively fast internal conversion process (>0.6 ns(-1)) is observed in both dendrimer series, possibly due to increased twisting about the phenyl core that reduces the triplet yields considerably with respect to oligothiophenes. An anomalous shifting of the triplet-triplet absorption spectra characterizes the 4G1-nS dendrimers as unique from the 3G1-nS series in terms of the hindrance of torsional motion and confinement of excited states enforced by the arrangement of dendrons.     

Number of Bound States of Schrödinger Operators with Matrix-Valued Potentials

We give a Cwikel–Lieb–Rozenblum type bound on the number of bound states of Schrödinger operators with matrix-valued potentials using the functional integral method of Lieb. This significantly improves the constant in this inequality obtained earlier by Hundertmark.     

Electronic structure analysis of iron(III)-porphyrin complexes by X-ray absorption spectra at the C, N and Fe K-edges.

X-ray absorption near edge structure (XANES) measurements at the C, N, and Fe K absorption edges were performed for iron(III)-tetraphenylporphyrin (FeTPP), iron(III)-tetrakis(p-carboxyphenyl)porphyrin (FeTCPP), and iron(III)-tetrakis(p-sulfonatophenyl)porphyrin (FeTSPP). The spectral shapes differ in the Fe K XANES, but not in C and N K XANES among FeTPP, FeTCPP, and FeTSPP. Crosschecks of XANES data for C, N, and Fe K absorption edges in combination with discrete variational (DV)-Xalpha molecular orbital (MO) calculations indicate that each p-electron-withdrawing group on four meso-phenyl substitutes in an Fe(III)-porphyrin complex brings about a unique electron state through the complex because of the electron-withdrawal strength, itself. Consequently, they affect the positive charge of the center Fe(III) ion.     

High-accuracy surface position sensor based on a two-lens system

Two optical lenses are used to compose a surface position measuring system. A measurand is positioned near the front focal point of the first lens. At the output end of the other lens, a beam splitter is used to split the beam into two paths. One photodetector is positioned before the focal point of the lens in one path and another after the focal point in the other so that the intensities falling onto the two detectors can be adjusted to be equal when the first lens is in focus. This device provides a compact and high-accuracy surface sensor. In this paper, the design and experimental study of the sensor system is described. It is shown that such a sensor embodiment can lead to a resolution of 1 μm.     

Local structure of nitrogen atoms in a porphine ring of mesophenyl substituted porphyrin with an electron-withdrawing group using X-ray photoelectron spectroscopy and X-ray absorption spectroscopy.

This study investigated the protonation of nitrogen atoms in porphyrins with meso-phenyl p-substituted by an electron-withdrawing group using N 1s X-ray photoelectron spectroscopy (XPS), the N K X-ray absorption near-edge structure (XANES), and the discrete variational (DV)-Xalpha molecular orbital (MO) method. Both tetraphenylporphyrin (TPP) and tetrakis(p-sulfonatophenyl)porphyrin (TSPP) have a single structure: the former has two protonated and two non-protonated N atoms in the porphine ring; the latter has four protonated N atoms in the porphine ring. In contrast, a combination of XPS, XANES, and DV-Xalpha MO calculations shows that tetrakis(p-carboxyphenyl)porphyrin (TCPP) has a dual structure: one structure has two protonated and two non-protonated N atoms; the other has four protonated N atoms. Furthermore, this result was also considered based on the protonation constants of N atoms in the porphyrins. The correlation between the strength of electron-withdrawing groups and protonation to N atoms in porphyrins can be described using the spectral patterns of the N 1s XPS and N K XANES spectra.