Open Sets Avoiding Integral Distances

We study open point sets in Euclidean spaces $\mathbb{R }^d$ R d without a pair of points an integral distance apart. By a result of Furstenberg, Katznelson, and Weiss such sets must be of Lebesgue upper density $0$ 0 . We are interested in how large such sets can be in $d$ d -dimensional volume. We determine the exact values for the maximum volumes of the sets in terms of the number of their connected components and dimension. Here techniques from diophantine approximation, algebra and the theory of convex bodies come into play. Our problem can be viewed as a counterpart to known problems on sets with pairwise rational or integral distances. It possibly opens a new research direction with strong links to topology and measure theory.     

Experimental demonstration of a quantum protocol for byzantine agreement and liar detection

We introduce a new quantum protocol for solving detectable Byzantine agreement (also called detectable broadcast) between three parties, and also for solving the detectable liar detection problem. The protocol is suggested by the properties of a four-qubit entangled state, and the classical part of the protocol is simpler than that of previous proposals. In addition, we present an experimental implementation of the protocol using four-photon entanglement.     

Passively mode-locked Yb:YAG thin-disk laser with pulse energies exceeding 13 microJ by use of an active multipass geometry

We demonstrate the generation of high-energy picosecond pulses directly from a thin-disk laser oscillator by employing a self-imaging active multipass geometry. Stable single-pulse operation has been obtained with an average output power in excess of 50 W, excluding a cw background of 8%, at a repetition rate of 3.8 MHz. Self-starting passive mode locking was accomplished using a semiconductor saturable absorber mirror. The maximum pulse energy was 13.4 microJ at a pulse duration of 1.36 ps with a time-bandwidth product of 0.34. Single-pass external frequency doubling with a conversion efficiency of 60% yielded >28 W of average power at 515 nm.     

Few-boson dynamics in double wells: from single-atom to correlated pair tunneling

We investigate few-boson tunneling in a one-dimensional double well, covering the full crossover from weak interactions to the fermionization limit of strong correlations. Based on exact quantum-dynamical calculations, it is found that the tunneling dynamics of two atoms evolves from Rabi oscillations to correlated pair tunneling as we increase the interaction strength. Near the fermionization limit, fragmented-pair tunneling is observed and analyzed in terms of the population imbalance and two-body correlations. For more atoms, the tunneling dynamics near fermionization is shown to be sensitive to both atom number and initial configuration.     

Volatile organic compounds in head and neck squamous cell carcinoma—An in vitro pilot study

Owing to the lack of specific symptoms, diagnosis of head and neck squamous cell carcinoma (HNSCC) may be delayed. We evaluated volatile organic compounds in tumor samples from patients suffering from HNSCC and tested the hypothesis that there is a characteristic altered composition in the headspace of HNSCC compared with control samples from the same patient with normal squamous epithelium. These results provide the basis for future noninvasive breath analysis in HNSCC. Headspace air of suspected tumor and contralateral control samples in 20 patients were analyzed using ion-mobility spectrometry. Squamous cell carcinoma was diagnosed in 16 patients. In total, we observed 93 different signals in headspace measurements. Squamous cell carcinomas revealed significantly higher levels of volatile cyclohexanol (0.54 ppb_v, 25th to 75th percentiles 0.35–0.86) compared with healthy squamous epithelium (0.24 ppb_v, 25th to 75th percentiles 0.12–0.3; p < 0.001). In conclusion, head and neck squamous cell carcinoma emitted significantly higher levels of volatile cyclohexanol in headspace compared with normal squamous epithelium. These findings form the basis for future breath analysis for diagnosis, therapy control and the follow-up of HNSSC to improve therapy and aftercare.     

Soret effect of nonionic surfactants in water studied by different transient grating setups

We studied the thermal diffusion behavior of the nonionic surfactant solutions C 12E 6/water and C 12E 5/water at different concentrations and temperatures using thermal diffusion forced Rayleigh scattering (TDFRS). Two different types of TDFRS setups have been applied. In the classical TDFRS, we use an argon laser to write the optical grating into the sample by using a small amount of ionic dye to convert the optical grating into a temperature grating. In the other setup, called IR-TDFRS, we use an infrared laser as the writing beam, which utilizes the water absorption band to convert the optical grating into a temperature grating. The measurements by IR-TDFRS show a one-mode signal for all concentrations and temperatures, while the signal in the classical TDFRS consists of two modes for higher temperatures and lower surfactant concentrations (Ning, H.; et al. J. Phys. Chem. B 2006, 110, 10746). We find good agreement between the Soret coefficient determined in the IR-TDFRS and the one derived from the first fast mode in the previous studies. The Soret coefficient of the nonionic solutions is positive and enhanced at the critical point. In general, the Soret coefficient of the micelles tends to increase with temperature. We found that the presence of the second mode observed in the classical TDFRS is related to the addition of the ionic dye, but even with the ionic dye it is not possible to observe a second mode in the IR-TDFRS. The origin of the second mode is discussed in terms of charged micelles and an inhomogenous dye distribution in the temperature gradient.     

Information transfer in calix[4]arenes: influence of upper rim substitution on alkaline metal complexation at the lower rim

Novel calix[4]arene amides have been synthesized and their interaction with alkaline cations has been evaluated through extracting aqueous solutions of Li-, Na- and K-picrates with solutions of calix[4]arene amides in CH₂Cl₂. Electron-withdrawing groups on the upper rim of the calix[4]arene scaffold were found to have a negative effect on the absolute amount of metal ions extracted. The decreased extraction ability is accompanied by a higher selectivity towards sodium cations.     

Cover Picture: Supramolecular Self-Assembly as a Tool To Preserve the Electronic Purity of Perylene Diimide Chromophores (Angew. Chem. Int. Ed. 12/2023)

Organic semiconductors are promising for efficient, printable optoelectronics. However, strong excited-state quenching due to uncontrolled aggregation limits their use in devices. We report on the self-assembly of a supramolecular pseudo-cube formed from six perylene diimides (PDIs). The rigid, shape-persistent cage sets the distance and orientation of the PDIs and suppresses intramolecular rotations and vibrations, leading to non-aggregated, monomer-like properties in solution and the solid state, in contrast to the fast fluorescence quenching in the free ligand. The stabilized excited state and electronic purity in the cage enables the observation of delayed fluorescence due to a bright excited multimer, acting as excited-state reservoir in a rare case of benign inter-chromophore interactions in the cage. We show that self-assembly provides a powerful tool for retaining and controlling the electronic properties of chromophores, and to bring molecular electronics devices within reach.     

Application of thin titanium/titanium oxide layers deposited on gold for infrared reflection absorption spectroscopy: structural studies of lipid bilayers

Ultrathin titanium layers when deposited on the surface of gold can be successfully applied for infrared reflection absorption spectroscopy (IRRAS) investigations. It was shown that the reflectivity, the phase shift, and the mean square electric field of the p- and s-polarized IR radiation in up to 20 nm thick titanium layers covered with a 3-4 nm thick layer of native oxide are comparable to those of the air/gold interface. The surface selection rule is fulfilled. Thus, qualitative and quantitative analysis of 1,2-dimyristoyl- sn-glycero-3-phosphocholine (DMPC) bilayers transferred in liquid expanded (LE) and liquid condensed (LC) states can be performed. Differences are found in the hydration state and molecular arrangement of the two investigated bilayers. In the DMPC bilayer in the LE state, the C-N bond in the positively charged choline moiety is inclined by approximately 70 degrees toward the surface of the negatively charged titanium substrate. In the phosphate moiety, the in-plane vector of the O-P-O group makes a small angle of approximately 15 degrees to the surface normal. This open structure of the lipid molecule corresponds to the B crystal structure of the DMPC molecule and provides space for strong hydration of the polar headgroup. In the DMPC bilayer in the LC state, the intermolecular distances are reduced; the C-N bond of the choline group makes a smaller angle to the surface normal, and the in-plane vector of the O-P-O group in the phosphate moiety displays a larger tilt. The degree of hydration is reduced. The arrangement of the polar headgroup region corresponds to the A crystal structure of the DMPC molecule.