Discrete Laplace cycles of period four

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of corresponding points form a discrete W-congruence. We derive some properties of discrete Laplace cycles of period four and describe two explicit methods for their construction.     

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Man's Impact on the Global Environment. Assessments and Recommendations for Action. Report of the 'Study of Criterial Environmenta Problems'. (SCEP). MIT Press 1970, 319 pages. Price $2.95.

Field Ion Microscopy K. M. Bowkett and D. A. Smith In the series: Defects in Crystalline Solids. North Holland Publishing Company 1970, 257 pages.     

On Low Temperature Kinetic Theory; Spin Diffusion, Bose Einstein Condensates, Anyons

The paper considers some typical problems for non-linear kinetic models evolving through pair-collisions at temperatures not far from absolute zero, which illustrate specifically quantum behaviours. Based on these—mostly recent—examples, a number of differences between quantum and classical Boltzmann theory is then discussed in more general terms.     

Degradation effects in the extraction of antioxidants from birch bark using water at elevated temperature and pressure

Experiments with birch bark samples have been carried to enable a distinction between extraction and degradation effects during pressurised hot water extraction. Two samples, E80 and E180, contained birch bark extracts obtained after extraction at 80 and 180 °C for up to 45 min, respectively. Two other samples, P80 and P180, were only extracted for 5 min at the two temperatures and were thereafter filtered and hydrothermally treated at 80 and 180 °C, respectively. During the latter treatment, samples were collected at different times to assess the stability of the extracted compounds. An offline DPPH (2,2-diphenyl-1-picrylhydrazyl) assay, as well as a high performance liquid chromatographic separation coupled to an electrochemical detector, were used to determine the antioxidant capacity of the processed samples. The results obtained with the different techniques were compared to assess the yield of the extraction and degradation processes. In addition, an online hyphenated system comprising high performance liquid chromatography coupled to diode-array; electrochemical; and tandem mass spectrometric detection (HPLC-DAD-ECD-MS/MS) was used to study the compositions of the extracts in more detail. The results for the samples processed at 80 °C showed that the extraction reached a steady-state already after 5 min, and that the extracted compounds were stable throughout the entire extraction process. Processing at 180 °C, on the other hand, gave rise to partly degraded extracts with a multitude of peaks in both the diode array and electrochemical detectors, and a higher antioxidant capacity compared to for the extracts obtained at 80 °C. It is concluded that HPLC-DAD-ECD is a more appropriate technique for the determination of antioxidants than the DPPH assay. The mass spectrometric results indicate that one of the extracted antioxidants, catechin, was isomerised to its diastereoisomers; (+)-catechin, (−)-catechin, (+)-epicatechin, and (−)-epicatechin.     

Nanometer interatomic distances in Rydberg Matter clusters confirmed by phase-delay spectroscopy

Recently, rotational spectroscopy in the radio frequency range was used to determine the bond lengths in several types of potassium Rydberg Matter (RM) clusters with high precision (Mol Phy 105: 933–939, 2007). Due to the large bond lengths of a few nm and well-ordered structure of such clusters, it is expected that light scattering can be used to determine their dimensions. A weak carbon dioxide laser beam is introduced collinearly into a tunable RM cavity. When RM is formed, a very pronounced fringe structure with several hundred fringes is observed at the detector as a function of the grating position. These fringes show a phase delay of the carbon dioxide laser light caused by reflections within the RM clusters. The delay lengths derived from the fringe structure give distances between the rows of atoms in the clusters. The excitation level of the most easily observed clusters is n = 5. Clusters with n = 6, 7, and 8 are also commonly detected. The bond distance for n = 5 is found to be 3.804 ± 0.015 nm, while that for n = 6 is 5.525 ± 0.014 nm, in accurate agreement with values from rotational spectroscopy.     

Theoretical prediction of the protein–protein interaction between Arabidopsis thaliana COP1 and UVR8

In plants, ultraviolet-B radiation (280–315 nm) regulates gene expression and plant morphology through the UV RESPONSE LOCUS 8 (UVR8) photoreceptor. The first signaling event after quantal absorbance is the interaction of the UVR8 C-terminus with the E3 ubiquitin ligase CONSTITUTIVELY PHOTOMORPHOGENIC 1 (COP1). The nature of the interaction between these two proteins is hitherto unknown. A protein homology model of the Arabidopsis thaliana COP1 seven-bladed propeller WD40 repeat domain and de novo folds of the C-terminal 27 amino acid (amino acids 397–423) peptide of Arabidopsis UVR8 (UVR8^397?423) is herein reported. Using a theoretical computational docking protocol, the interaction between COP1 and UVR8 was predicted. A core motif was identified in UVR8^397?423 comprising adjacent hydrophobic residues V410 and P411 together with a charged residue D412, homologous to corresponding motifs in other COP1-binding proteins, such as ELONGATED HYPOCOTYL 5 (HY5), cryptochrome 1 (CRY1), and salt tolerance proteins STO/STH. The protein–protein interaction between the COP1 WD40 repeat domain and UVR8^397?423 reveals binding within a region of COP1 overlapping with the binding site for HY5 and the other COP1-interacting proteins. This study provides a framework for understanding docking between UVR8 and COP1, which in turn gives clues for experimental testing of UVR8/COP1 interaction.