Proofs and surfaces

A formal sequent system dealing with Menelaus' configurations is introduced in this paper. The axiomatic sequents of the system stem from 2-cycles of Δ-complexes. The Euclidean and projective interpretations of the sequents are defined and a soundness result is proved. This system is decidable and its provable sequents deliver incidence results. A cyclic operad structure tied to this system is presented by generators and relations.     

Cellular Chain Complex of Small Covers with Integer Coefficients and Its Application

Let Pⁿ be a simple n-polytope with a Z²-characteristic function λ. And h is a Morse function over Pⁿ. Then the small cover Mⁿ(λ) corresponding to the pair (Pⁿ, λ) has a cell structure given by h. From this cell structure we can derive a cellular chain complex of Mⁿ(λ) with integer coefficients. In this paper, firstly, we discuss the highest dimensional boundary morphism ∂_n of this cellular chain complex and get that ∂_n=0 or 2 by a natural way. And then, from the well-known result that the submanifold corresponding to (F, λ_F) is naturally a small cover with dimension k, where F is any k-face of Pⁿ and λ_F is the restriction of λ on F, we get that ∂_k=0 or ±2 for 0 ≤ k < n. Finally, by using the definition of inherited characteristic function which is the restriction of λ on the faces of Pⁿ, we get a way to calculate the homology groups of Mⁿ(λ). Applying our result to a 3-small cover we have that the homology groups of any 3-small cover is torsion-free or has only 2-torsion.     

Elliptic system with some singular nonlinearity

We investigate multiplicity of solutions for elliptic systems with singular non-linearities. We obtain a theorem which shows that elliptic systems with some singular non-linearities have infinitely many solutions. We get this result by using the variational method, critical point theory and homology theory.     

Q‐DockLHM: Low‐resolution refinement for ligand comparative modeling

The success of ligand docking calculations typically depends on the quality of the receptor structure. Given improvements in protein structure prediction approaches, approximate protein models now can be routinely obtained for the majority of gene products in a given proteome. Structure‐based virtual screening of large combinatorial libraries of lead candidates against theoretically modeled receptor structures requires fast and reliable docking techniques capable of dealing with structural inaccuracies in protein models. Here, we present Q‐Dock^LHM, a method for low‐resolution refinement of binding poses provided by FINDSITE^LHM, a ligand homology modeling approach. We compare its performance to that of classical ligand docking approaches in ligand docking against a representative set of experimental (both holo and apo) as well as theoretically modeled receptor structures. Docking benchmarks reveal that unlike all‐atom docking, Q‐Dock^LHM exhibits the desired tolerance to the receptor's structure deformation. Our results suggest that the use of an evolution‐based approach to ligand homology modeling followed by fast low‐resolution refinement is capable of achieving satisfactory performance in ligand‐binding pose prediction with promising applicability to proteome‐scale applications. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Pesticides in water and the performance of the liquid-phase microextraction based techniques. A review

The control of pesticides in surface, drinking and groundwater is nowadays a real necessity. In the European Community, their concentration must comply with the established parametric and environmental quality standards (EQSs). Regarding the new legislation, this article updates the information concerning the monitoring of pesticides and the technical specifications for their measurement in water samples where ultra-sensitive analytical methods are required. For some compounds, like pesticides, there is still a need to improve the performance of the existing methods. High sensitive techniques like gas chromatography tandem mass spectrometry (GC–MS/MS) and liquid chromatography coupled with mass spectrometry (LC–MS) have been developed. However, for most of the substances present at trace and ultra-trace levels the extraction and preconcentration steps are so far essential for their detection. Advances at a micro scale have been made and different types of microextractions are being developed. Liquid-phase microextraction (LPME) is an example. The study of this technique has increased in the last years and some innovations have been recently reported for pesticides water analysis. This article reviews the new developed LPME-based techniques and compares its performance with the analytical specifications established for pesticides water monitoring. The results show that LPME-based techniques can be a promising tool to improve the nowadays performance of methods used in pesticides water control.     

Exposure to persistent organic pollutants as potential risk factors for developing diabetes

Persistent organic pollutants(POPs),such as dioxins,polychlorinated biphenyls(PCBs) ,and organochlorine pesticides(OCPs),which are synthetic chemicals or by-products with an intrinsic resistance to natural degradation processes,are released into the environment,resulting in the widespread dispersal and accumulation in the environment,as well as in human and ecological food chains.Due to their ubiquity in the environment and lipophilic properties,there is emerging concern over the potential risks of human ex...     

Leibniz and Hochschild homology

We construct and study the map from Leibniz homology HL_?(𝔥) of an abelian extension 𝔥 of a simple real Lie algebra 𝔤 to the Hochschild homology HH_??1(U(𝔥)) of the universal envelopping algebra U(𝔥). To calculate some homology groups, we use the Hochschild-Serre spectral sequences and Pirashvili spectral sequences. The result shows what part of the non-commutative Leibniz theory is detected by classical Hochschild homology, which is of interest today in string theory.     

一个自入射Koszul代数的Hochschild同调与循环同调

代数的Hochschild同调群与其对应的Gabriel箭图的循环圈有着紧密的联系.本文基于Furuya构造的一个四点自入射Koszul代数的极小投射双模分解,用组合的方法计算了该代数的Hochschild同调空间的维数,并用循环圈的语言给出该代数的Hochschild同调空间的一组k-基.进一步,当基础域k的特征为零时,我们也得到了该代数的循环同调群的维数.     

Bioperads and hopf bialgebras in cobordism theory

A construction of Dyer-Lashof operations for cobordisms of topological spaces is presented. Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 270–279, February, 1999.     

Rapid Dihydrogen Cleavage by Persistent Nitroxide Radicals under Frustrated Lewis Pair Conditions

Persistent radicals undergo hydrogen atom abstraction reactions with a great variety of substrates, but not with dihydrogen. It has now been found that the TEMPO radical splits dihydrogen under mild conditions in the presence of the strong bulky B(C₆F₅)₃ boron Lewis acid. The reaction is thought to proceed by a typical frustrated Lewis pair mechanism with the TEMPO radical acting as the active Lewis base. The reaction was analyzed by DFT, which indicates that no significant spin density on the hydrogen atoms is accumulated along the H₂ splitting reaction path.