A practical volume algorithm

We present a practical algorithm for computing the volume of a convex body with a target relative accuracy parameter \(\varepsilon >0\). The convex body is given as the intersection of an explicit set of linear inequalities and an ellipsoid. The algorithm is inspired by the volume algorithms in Lovász and Vempala (J Comput Syst Sci 72(2):392–417, 2006) and Cousins and Vempala (SODA, pp. 1215–1228, 2014), but makes significant departures to improve performance, including the use of empirical convergence tests, an adaptive annealing scheme and a new rounding algorithm. We propose a benchmark of test bodies and present a detailed evaluation of our algorithm. Our results indicate that that volume computation and integration might now be practical in moderately high dimension (a few hundred) on commodity hardware.     

Random Copolymers of 1,5-Dioxepan-2-one

ABSTRACT

Copolymers of 1,5-dioxepan-2-one (DXO) and e-caprolactone (?-CL), δ-valerolactone (δ-VL) or L-lactide (LLA) have been synthesized and characterized. High molecular weight copolymers were obtained using stannous-2-ethyl hexanoate as catalyst in bulk. Reactivity ratios for the copolymerization of DXO and δ-VL were determined at 110°C as r_VL=0.5 and r_DXO=2.3. At high conversion, depolymerization of δ-VL occurred, resulting in lower molecular weight and variations in the copolymer composition.

Physical properties, such as crystallinity and melting temperature of the DXO-copolymers proved to be strongly dependent on the choice of comonomer and on the molar composition of the copolymers. DXO appears to be incorporated into the poly-?-caprolactone (PCL) crystals and to some extent into the poly-δ-valerolactone (PVL) crystals, resulting in a more gradual decrease in crystallinity with increasing amount of DXO.     

Synthethesis of 4-alkyl-3,5-diamino-l,2,4,6-thiatriazine l,l-dioxides. Part II

4-Alkyl-l,2,4,6-thiatriazine-l-oxides and dioxides have been prepared using a variety of new methods and their structures determined by ¹³C nmr analysis.     

Enantioselective partial reduction of 2,5-disubstituted pyrroles via a chiral protonation approach

[reaction: see text] The partial reduction of 2,5-pyrrole diester 1 followed by enantioselective protonation in situ to furnish synthetically useful building blocks is described. An enantiomeric excess of up to 74% was achieved using (-)-ephedrine and related analogues as chiral proton sources. The pyrroline product obtained could be recrystallized to give enantiomerically pure material.     

Dynamic covalent chemistry

Dynamic covalent chemistry relates to chemical reactions carried out reversibly under conditions of equilibrium control. The reversible nature of the reactions introduces the prospects of "error checking" and "proof-reading" into synthetic processes where dynamic covalent chemistry operates. Since the formation of products occurs under thermodynamic control, product distributions depend only on the relative stabilities of the final products. In kinetically controlled reactions, however, it is the free energy differences between the transition states leading to the products that determines their relative proportions. Supramolecular chemistry has had a huge impact on synthesis at two levels: one is noncovalent synthesis, or strict self-assembly, and the other is supramolecular assistance to molecular synthesis, also referred to as self-assembly followed by covalent modification. Noncovalent synthesis has given us access to finite supermolecules and infinite supramolecular arrays. Supramolecular assistance to covalent synthesis has been exploited in the construction of more-complex systems, such as interlocked molecular compounds (for example, catenanes and rotaxanes) as well as container molecules (molecular capsules). The appealing prospect of also synthesizing these types of compounds with complex molecular architectures using reversible covalent bond forming chemistry has led to the development of dynamic covalent chemistry. Historically, dynamic covalent chemistry has played a central role in the development of conformational analysis by opening up the possibility to be able to equilibrate configurational isomers, sometimes with base (for example, esters) and sometimes with acid (for example, acetals). These stereochemical "balancing acts" revealed another major advantage that dynamic covalent chemistry offers the chemist, which is not so easily accessible in the kinetically controlled regime: the ability to re-adjust the product distribution of a reaction, even once the initial products have been formed, by changing the reaction's environment (for example, concentration, temperature, presence or absence of a template). This highly transparent, yet tremendously subtle, characteristic of dynamic covalent chemistry has led to key discoveries in polymer chemistry. In this review, some recent examples where dynamic covalent chemistry has been demonstrated are shown to emphasise the basic concepts of this area of science.     

Frequency effects on the conduction electron spin resonance linewidth in aluminium

The CESR linewidth of pure aluminium is shown to have a temperature dependent phonon contribution which is largely frequency independent. A second term in the linewidth is found to be temperature independent but linearly dependent upon frequency giving 0.11 mT per GHz. Finally it is shown that if partial breakdown of motional narrowing occurs it contributes a term proportional to the frequency and not, as expected, to the frequency squared.     

Beta-alpha correlation in the decay of 20Na

We have measured the β-α angular correlation in the allowed positron decay of ²⁰Na to the 7.42 MeV state of ²⁰Ne. The correlation is of the form $\text{1 +}\text{a}\text{cos}\text{θ +}\text{p}\text{cos}{}^2\text{θ}$. We find $\text{p}\text{= ?0.003 ± 0.005}$ in reasonable agreement with expectations based on the conserved vector current theory.