Anticancer agent development: X-ray crystal structure and keto-enol tautomerism of dimethyl 1-hydroxy-6,7-methylenedioxy-4-(3′,4′,5′-trimethoxyphenyl-trans-3,4-dihydronaphthalene-2,3-dicarboxylate

Structural and conformational information obtained from the crystal structure and solution¹H nmr investigations of the title compound are compared. The 4-aryltetralone, C₂₄H₂₄O₁₀, crystallizes as a chloroform solvate in the monoclinic space group, P2₁/n, witha=12.519(4),b=17.938(6),c=12.534(9)Å,=111.90(5)°, and D_calc=1.51 g cm^–3 forZ=4. The data for this compound were collected at –150°C. Least-squares refinement of 2796 observed [F _o5(F _o)] reflections led to the final agreement index ofR=0.062. A threefold static disorder was observed for one of the carboxyl groups. The second carboxyl group participates in an intramolecular hydrogen bond and is thus ordered. The¹H nmr spectrum revealed the title compound to exist as a keto-enol tautomeric mixture in solution. Vicinal hydrogen coupling constant analysis proved reliable in ascertaining B-ring stereochemistry of 2,3-disubstituted-4-aryltetralones.     

The search for organically bonded iron in New Zealand brown coals

Brown coal from two areas in New Zealand was treated with acids (HF and HCl) to remove the clays. Iron was then introduced into the “cleaned” coal by ion exchange. Mössbauer spectra of the untreated coal, the low temperature ash of the coal, “cleaned” coal and ion-exchanged coal were analysed. From these spectra we conclude that a pair of lines with QS～1 mm s^?1 and IS～0.45 mm s^?1 is probably due to organically bonded iron.     

Self-avoiding random walk: A Brownian motion model with local time drift

Summary A natural model for a self-avoiding Brownian motion inR ^d, when specialised and simplified tod=1, becomes the stochastic differential equation , where {L(t, x):t0,xR} is the local time process ofX. ThoughX is not Markovian, an analogue of the Ray-Knight theorem holds for {L(,x):xR}, which allows one to prove in many cases of interest that exists almost surely, and to identify the limit.     

Compatible additive permutations of finite integral bases

Let be an additive permutation of a finite integral base. It is shown that ifB is symmetric, then there is a unique additive permutation ofB which is compatible with in the sense that ^–1 is also an additive permutation; and that, further, ifB is asymmetric, then there is no additive permutation ofB which is compatible with. Thus, in the symmetric case, there are no additively compatible sets (of permutations) forB of size greater than 3. This contrasts with the situation for completely compatible sets (equivalently, additive sequences of permutations) where for certainB compatible sets of size (resp. length) 4 or less are known, but where nothing is known of sets of greater size (resp. length). It is also noted how this result restricts the possibility of a useful multiplication theorem for the additive analogue of perfect systems of difference sets and graceful graphs.     

Stamp collapse in soft lithography

We have studied the so-called roof collapse in soft lithography. Roof collapse is due to the adhesion between the PDMS stamp and substrate, and it may affect the quality of soft lithography. Our analysis accounts for the interactions of multiple punches and the effect of elastic mismatch between the PDMS stamp and substrate. A scaling law among the stamp modulus, punch height and spacing, and work of adhesion between the stamp and substrate is established. Such a scaling law leads to a simple criterion against the unwanted roof collapse. The present study agrees well with the experimental data.