Lattice simulation of a center symmetric three-dimensional effective theory for SU(2) Yang-Mills

We perform simulations of an effective theory of SU(2) Wilson lines in three dimensions. Our action includes a kinetic term, the one-loop perturbative potential for the Wilson line, a non-perturbative “fuzzy-bag” contribution and spatial gauge fields. We determine the phase diagram of the theory and confirm that, at moderately weak coupling, the non-perturbative term leads to eigenvalue repulsion in a finite region above the deconfining phase transition.     

Isolation of a Novel Polyketide from Neodidymelliopsis sp.

Fungi have become an invaluable source of bioactive natural products, with more than 5 million species of fungi spanning the globe. Fractionation of crude extract of Neodidymelliopsis sp., led to the isolation of a novel polyketide, (2Z)-cillifuranone (1) and five previously reported natural products, (2E)-cillifuranone (2), taiwapyrone (3), xylariolide D (4), pachybasin (5), and N-(5-hydroxypentyl)acetamide (6). It was discovered that (2Z)-cillifuranone (1) was particularly sensitive to ambient temperature and light resulting in isomerisation to (2E)-cillifuranone (2). Structure elucidation of all the natural products were conducted by NMR spectroscopic techniques. The antimicrobial activity of 2, 3, and 5 were evaluated against a variety of bacterial and fungal pathogens. A sodium [1-¹³C] acetate labelling study was conducted on Neodidymelliopsis sp. and confirmed that pachybasin is biosynthesised through the acetate polyketide pathway.     

The numerical evaluation of the error term in a quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight function

A method is derived for the numerical evaluation of the error term arising in a quadrature formula of Clenshaw-Curtis type for functions of the form (1-x²)^{l- \frac12}f(x)(1-x^{2})^{\lambda - \frac{1}{2}}f(x) over the interval [−1,1]. The method is illustrated by an example.     

Doubly diastereoselective conjugate addition of enantiopure lithium amides to enantiopure N-enoyl oxazolidin-2-ones: a mechanistic probe

The doubly diastereoselective conjugate addition of the antipodes of lithium N-benzyl-N-(α-methylbenzyl)amide to a range of enantiopure N-enoyl oxazolidin-2-ones has been used as a mechanistic probe to determine that the reactive conformation is the anti-s-cis form. The β-amino carbonyl products resulting from these conjugate addition reactions are useful templates for further elaboration into an α,β,α-pseudotripeptide.     

The Hydrogen-Bonded Coordination Polymer Tetracesium Bis(5-nitroisophthalate) Heptahydrate

Abstract  

The coordination polymer complex tetracesium bis(5-nitroisophthalate) heptahydrate [Cs₄(C₈H₃NO₆)₂ (H₂O)₇] _n has been synthesized and characterized using single-crystal X-ray diffraction. Crystals are monoclinic, space group P2₁/c, with Z = 4 in a cell with dimensions a = 12.3213(3), b = 6.7557(2), c = 36.2020(9) ?, β = 90.548(2)^o. The complex is based on a repeating unit comprising four independent and different Cs coordination centres, two 6-coordinate, and two 8-coordinate [Cs–O, range 2.959(5)–3.386(5) ?], and seven water molecules, two of which are monodentate and the other five bridging, while all other oxygen atoms in the structure, including those of the nitro groups form inter-Cs bridges. Extensive water O–H···O hydrogen-bonding interactions give a three-dimensional framework. This structure represents the first of an alkali metal compound of 5-nitroisophthalic acid that has been reported.     

A tits alternative for groups that are residually of bounded rank

In this short note a Tits alternative for certain kinds of groups which are residually of rank at mostr is obtained. The main theorem states that ifG is a group that is residually (locally (soluble-by-finite) of rankr), then eitherG is locally (soluble-by-finite) orG contains a non-abelian free subgroup. The third author would like to thank the School of Mathematics at the University of Wales, Cardiff for its hospitality whild part of this work was being done.