Which n-Venn Diagrams Can Be Drawn with Convex k-Gons?

We establish a new lower bound for the number of sides required for the component curves of simple Venn diagrams made from polygons. Specifically, for any n-Venn diagram of convex k-gons, we prove that k ≥ (2ⁿ - 2 - n) / (n (n - 2)). In the process we prove that Venn diagrams of seven curves, simple or not, cannot be formed from triangles. We then give an example achieving the new lower bound of a (simple, symmetric) Venn diagram of seven convex quadrilaterals. Previously Grunbaum had constructed a symmetric 7-Venn diagram of non-convex 5-gons ["Venn Diagrams II", Geombinatorics 2:25-31, 1992].     

Reynolds number invariance of the structure inclination angle in wall turbulence

Cross correlations of the fluctuating wall-shear stress and the streamwise velocity in the logarithmic region of turbulent boundary layers are reported over 3 orders of magnitude change in Reynolds number. These results are obtained using hot-film and hot-wire anemometry in a wind tunnel facility, and sonic anemometers and a purpose-built wall-shear stress sensor in the near-neutral atmospheric surface layer on the salt flats of Utah's western desert. The direct measurement of fluctuating wall-shear stress in the atmospheric surface layer has not been available before. Structure inclination angles are inferred from the cross correlation results and are found to be invariant over the large range of Reynolds number. The findings justify the prior use of low Reynolds number experiments for obtaining structure angles for near-wall models in the large-eddy simulation of atmospheric surface layer flows.     

Photoelectron Spectroscopy and Theoretical Studies of PCSe−, AsCS−, AsCSe−, and NCSe−: Insights into the Electronic Structures of the Whole Family of ECX− Anions (E=N,P, As; X=O,S, Se)

The newly synthesized phosphorus‐ and arsenic‐containing analogues of the thio‐ and seleno‐cyanate anions, PCSe^?, AsCS^?, and AsCSe^?, as well as the known ion NCSe^? were investigated in the gas phase by negative‐ion photoelectron spectroscopy (NIPES), velocity‐map imaging (VMI) spectroscopy, and quantum‐chemical computations. The electron affinities (EA), spin–orbit (SO) splittings, and “symmetric”/“asymmetric” stretching frequencies of the neutral radicals ECX^. (E=N, P, As; X=S, Se), generated by electron detachment from the corresponding anions, were obtained from the spectra. The calculated EAs, SO splittings, and vibrational frequencies are in excellent agreement with the experimental measurements. These newly obtained values, when combined with those previously determined for the lighter analogues, show interesting trends on descending the pnictogen and chalcogen series. These trends are rationalized based on electronegativity arguments, the electron distributions in the HOMOs, and NBO/NRT analyses.     

Photoelectron Spectroscopy and Theoretical Studies of PCSe−, AsCS−, AsCSe−, and NCSe−: Insights into the Electronic Structures of the Whole Family of ECX− Anions (E=N,P, As; X=O,S, Se)

The newly synthesized phosphorus‐ and arsenic‐containing analogues of the thio‐ and seleno‐cyanate anions, PCSe^?, AsCS^?, and AsCSe^?, as well as the known ion NCSe^? were investigated in the gas phase by negative‐ion photoelectron spectroscopy (NIPES), velocity‐map imaging (VMI) spectroscopy, and quantum‐chemical computations. The electron affinities (EA), spin–orbit (SO) splittings, and “symmetric”/“asymmetric” stretching frequencies of the neutral radicals ECX^. (E=N, P, As; X=S, Se), generated by electron detachment from the corresponding anions, were obtained from the spectra. The calculated EAs, SO splittings, and vibrational frequencies are in excellent agreement with the experimental measurements. These newly obtained values, when combined with those previously determined for the lighter analogues, show interesting trends on descending the pnictogen and chalcogen series. These trends are rationalized based on electronegativity arguments, the electron distributions in the HOMOs, and NBO/NRT analyses.     

Flaxseed Increases Animal Lifespan and Reduces Ovarian Cancer Severity by Toxically Augmenting One-Carbon Metabolism

We used an LC-MS/MS metabolomics approach to investigate one-carbon metabolism in the plasma of flaxseed-fed White Leghorn laying hens (aged 3.5 years). In our study, dietary flaxseed (via the activity of a vitamin B6 antagonist known as “1-amino d-proline”) induced at least 15-fold elevated plasma cystathionine. Surprisingly, plasma homocysteine (Hcy) was stable in flaxseed-fed hens despite such highly elevated cystathionine. To explain stable Hcy, our data suggest accelerated Hcy remethylation via BHMT and MS-B12. Also supporting accelerated Hcy remethylation, we observed elevated S-adenosylmethionine (SAM), an elevated SAM:SAH ratio, and elevated methylthioadenosine (MTA), in flaxseed-fed hens. These results suggest that flaxseed increases SAM biosynthesis and possibly increases polyamine biosynthesis. The following endpoint phenotypes were observed in hens consuming flaxseed: decreased physiological aging, increased empirical lifespan, 9–14% reduced body mass, and improved liver function. Overall, we suggest that flaxseed can protect women from ovarian tumor metastasis by decreasing omental adiposity. We also propose that flaxseed protects cancer patients from cancer-associated cachexia by enhancing liver function.     

IR detection of H atoms produced by IR multiphoton dissociation

Hydrogen atoms produced by irradiation of alkenes with a focused CO₂ TEA laser react with Cl₂, forming vibrationally excited HCl, from which IR emission can be monitored. The application of this experimental technique to the study of H- atom reactions is discussed.     

RHF and two-configuration SCF calculations are inappropriate for conjugated diradicals

Restricted Hartee Fock (RHF) and two-configuration self-consistent field (TCSCF) calculations provide qualitatively correct molecular orbitals for the two open-shell electrons in diradicals. Nevertheless, these calculations fail to give correct relative energies and in some cases they even lead to incorrect geometries. Examples of these failures are given for both singlet and triplet states of some conjugated diradicals. In several cases these failures are related to the “doublet instability problem” in RHF calculations on radicals. It is argued that unrestricted Hartee-Fock (UHF) calculations on triplet states are more likely that RHF to provide accurate geometries.     

Vibrattonal excitation of molecules by collisions with “hot” hydrogen atoms from laser photolysis

Excimer laser (ArF) photolysis of diatomic and triatomic hydrides produces hydrogen atoms with translational energies in excess of 15000 cm^?1 per atom. Subsequent collisions of these “hot” atoms with CO₂ and N₂O produces vibrationally excited molecules which can be detected by their characteristic infrared emission.     

Mass spectra of boron compounds

The infrared and Raman spectra of six compounds (trimethylsiloxyethylene, (CH₃)₃SiOCHCH₂, methoxytrimethylsilane, (CH₃)₃SiOCH₃, and their deuterated derivatives: (CD₃)₃SiOCHCH₂, (CH₃)₃SiOCDCD₂, (CD₃)₃SiOCH₃, (CH₃)₃SiOCD₃ have been analysed.The majority of the bands observed have been assigned, in particular those due to ν(SiO).The study of the vinyl compounds shows that the enoxysilane exists in two conformers, the major being the gauche and the minor the s-cis one.