Isomeric pyrazolo­[3,4-d]­pyrimidine-based mol­ecules: disappearance of dimerization due to interchanged substitutions

In 5-benzyl-1,7-di­methyl-4,5,6,7-tetra­hydro-1H-pyrazolo­[3,4-d]­pyrimidine-4,6-dione, C₁₄H₁₄N₄O₂, which crystallizes in space group P, weak intermolecular C—H⋯O hydrogen bonds generate dimers. The isomeric compound 1-benzyl-5,7-di­methyl-4,5,6,7-tetra­hydro-1H-pyrazolo­[3,4-d]­pyrimidine-4,6-dione, C₁₄H₁₄N₄O₂, crystallizes in space group P2₁/n, and shows no such dimerization. Instead, it exhibits C—H⋯π interactions with the phenyl ring. In both structures, the mol­ecules are linked by aromatic π–π-stacking interactions.     

The minimum forcing number of perfect matchings in the hypercube

Let $M$ be a perfect matching in a graph. A subset $S$ of $M$ is said to be a forcing set of $M$, if $M$ is the only perfect matching in the graph that contains $S$. The minimum size of a forcing set of $M$ is called the forcing number of $M$. Pachter and Kim (1998) conjectured that the forcing number of every perfect matching in the $n$-dimensional hypercube is $2^{n?2}$, for all $n\ge 2$. This was revised by Riddle (2002), who conjectured that it is at least $2^{n?2}$, and proved it for all even $n$. We show that the revised conjecture holds for all $n\ge 2$. The proof is based on simple linear algebra.     

Uranium in ground water of Rajnandgaon District of Central India

The present study highlights uranium levels, associated health effects, and physicochemical properties of ground water samples collected from Rajnandgaon District of Chhattisgarh State, Central India. Uranium concentrations of ground water samples are found to exceed than 30 µg/L (United States Environmental Protection Agency and World Health Organisation recommended limit) at two villages in summer and at one village in winter while it is found higher than 60 µg/L (Atomic Energy Regulatory Board, Department of Atomic Energy, India recommended limit) at only one village in summer. Correlation analysis between uranium and physicochemical parameters suggest that Ca²⁺ ion and total alkalinity play an important role in uranium contamination of ground water.

     

Fluorine plasma treatment of bare and nitrilotris(methylene)triphosphonic acid (NP) protected aluminum: an XPS and ToF‐SIMS study

Nitrilotris(methylene)triphosphonic acid (NP) is a technologically important molecule that has been used for years as a corrosion inhibitor and/or adhesion promoter on aluminum and other metal surfaces. However, to the best of our knowledge, the detailed surface characterization of NP adsorbed on aluminum, or on any other surface, has not been reported. Herein, we report an X‐ray photoelectron spectroscopy and time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) analysis of a series of untreated and NP‐coated aluminum substrates that were exposed to the downstream products of a fluoroalkane + oxygen plasma for different amounts of time (from 0 to 20 s). As indicated by P 2p, N 1s, Al 2p, O 1s, and F 1s narrow scans, even a 4‐s plasma treatment significantly damages the NP protective layer and converts the native aluminum oxide into aluminum oxyfluoride. Heat treatment of the fluorine plasma‐treated samples in the air substantially converts the aluminum oxyfluoride back to aluminum oxide, while similar heating under vacuum results in little change to the materials. A slow loss of fluorine from the samples occurs over the course of weeks when they are stored in the air. A ToF‐SIMS analysis reveals sets of signals that are consistent with no surface treatment, NP treatment, or fluorine plasma treatment. A principal component analysis of the negative ion ToF‐SIMS spectra from the samples shows the expected differentiation of the samples. Copyright © 2014 John Wiley & Sons, Ltd.     

Enhanced intravenous transgene expression in mouse lung using cyclic-head cationic lipids

Herein, we report enhanced intravenous mouse lung transfection using novel cyclic-head-group analogs of usually open-head cationic transfection lipids. Design and synthesis of the new cyclic-head lipid N,N-di-n-tetradecyl-3,4-dihydroxy-pyrrolidinium chloride (lipid 1) and its higher alkyl-chain analogs (lipids 2-4) and relative in vitro and in vivo gene transfer efficacies of cyclic-head lipids 1-4 to their corresponding open-head analogs [lipid 5, namely N,N-di-n-tetradecyl-N,N-(2-hydroxyethyl)ammonium chloride and its higher alkyl-chain analogs, lipids 6-8] have been described. In stark contrast to comparable in vitro transfection efficacies of both the cyclic- and open-head lipids, lipids 1-4 with cyclic heads were found to be significantly more efficient (by 5- to 11-fold) in transfecting mouse lung than their corresponding open-head analogs (5-8) upon intravenous administration. The cyclic-head lipid 3 with di-stearyl hydrophobic tail was found to be the most promising for future applications.     

Circumference, chromatic number and online coloring

Erd?s conjectured that if G is a triangle free graph of chromatic number at least k≥3, then it contains an odd cycle of length at least k ^2?o(1) [13,15]. Nothing better than a linear bound ([3], Problem 5.1.55 in [16]) was so far known. We make progress on this conjecture by showing that G contains an odd cycle of length at least Ω(k log logk). Erd?s’ conjecture is known to hold for graphs with girth at least five. We show that if a graph with girth four is C ₅ free, then Erd?s’ conjecture holds. When the number of vertices is not too large we can prove better bounds on χ. We also give bounds on the chromatic number of graphs with at most r cycles of length 1 mod k, or at most s cycles of length 2 mod k, or no cycles of length 3 mod k. Our techniques essentially consist of using a depth first search tree to decompose the graph into ordered paths, which are then fed to an online coloring algorithm. Using this technique we give simple proofs of some old results, and also obtain several other results. We also obtain a lower bound on the number of colors which an online coloring algorithm needs to use to color triangle free graphs.