A Wilson group of non-uniformly exponential growth

This Note constructs a finitely generated group W whose word-growth is exponential, but for which the infimum of the growth rates over all finite generating sets is 1 – in other words, of non-uniformly exponential growth.This answers a question by Mikhael Gromov (Structures métriques pour les variétés riemanniennes, in: J. Lafontaine, P. Pansu (Eds.), CEDIC, Paris, 1981).The construction also yields a group of intermediate growth V that locally resembles W in that (by changing the generating set of W) there are isomorphic balls of arbitrarily large radius in V and W's Cayley graphs. To cite this article: L. Bartholdi, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Algebraic Dirichlet-to-Neumann mapping for linear elasticity problems with extreme contrasts in the coefficients

The convergence of iterative based domain decomposition methods is linked with the absorbing boundary conditions defined on the interface between the sub-domains. For linear elasticity problems, the optimal absorbing boundary conditions are associated with non-local Dirichlet-to-Neumann maps. Most of the methods to approximate these non-local maps are based on a continuous analysis. In this paper, an original algebraic technique based on the computation of local Dirichlet-to-Neumann maps is investigated. Numerical experiments are presented for linear elasticity problems with extreme contrasts in the coefficients.     

Sterically controlled reductive oligomerisations of CO by activated magnesium(i) compounds: deltate vs. ethenediolate formation

An extremely bulky, symmetrical three-coordinate magnesium(i) complex, [{(^TCHPNacnac)Mg}₂] (^TCHPNacnac = [{(TCHP)NCMe}₂CH]⁻, TCHP = 2,4,6-tricyclohexylphenyl) has been prepared and shown to have an extremely long Mg–Mg bond (3.021(1) Å) for such a complex. It was shown not to react with either DMAP (4-dimethylaminopyridine) or CO. Three unsymmetrical 1 : 1 DMAP adducts of less bulky Mg–Mg bonded species have been prepared, viz. [(^ArNacnac)Mg–Mg(DMAP)(^ArNacnac)] (^ArNacnac = [(ArNCMe)₂CH]⁻ Ar = 2,6-xylyl (Xyl), mesityl (Mes) or 2,6-diethylphenyl (Dep)), and their reactivity toward CO explored. Like the previously reported bulkier complex, [(^DipNacnac)Mg–Mg(DMAP)(^DipNacnac)] (Dip = 2,6-diisopropylphenyl), [(^DepNacnac)Mg–Mg(DMAP)(^DepNacnac)] reductively trimerises CO to give a rare example of a deltate complex, [{(^DepNacnac)Mg(μ-C₃O₃)Mg(DMAP)(^DepNacnac)}₂]. In contrast, the two smaller adduct complexes react with only two CO molecules, ultimately giving unusual ethenediolate complexes [{(^ArNacnac)Mg{μ-OC(H) C(DMAP^−H)O}Mg(^ArNacnac)}₂] (Ar = Xyl or Mes). DFT calculations show the latter reactions to proceed via reductive dimerizations of CO, and subsequent intramolecular C–H activation of Mg-ligated DMAP by “zig–zag” [C₂O₂]²⁻ fragments of reaction intermediates. Calculations also suggest that magnesium deltate complexes are kinetic products in these reactions, while the magnesium ethenediolates are thermodynamic products. This study shows that subtle changes to the bulk of the reacting 1 : 1 DMAP–magnesium(i) adduct complexes can lead to fine steric control over the products arising from their CO reductive oligomerisations. Furthermore, it is found that the more activated nature of the adduct complexes, relative to their symmetrical, three-coordinate counterparts, [{(^ArNacnac)Mg}₂], likely derives more from the polarisation of the Mg–Mg bonds of the former, than the elongated nature of those bonds.

Subtle changes to the bulk of 1 : 1 adducts of DMAP with magnesium(i) complexes leads to steric control over the products arising from their reductive oligomerisations of carbon monoxide.      

Substitution effects enhancing the lasing ability of organic compounds

Simple calculations can help to predict which derivatives in a series of organic compounds are potential lasing material. In conjugated systems, a necessary condition for lasing is that there is not less than a specific minimum energy difference between a first excited allowed and a second excited forbidden transition. This order of transition and energy spacing can be obtained by judicious substitutions even in molecules that do not meet these conditions. Lasing action in the near UV has been observed in five new compounds.     

The occupation measure of super-Brownian motion conditioned to nonextinction

We study super-Brownian motion inR ^d starting from a nontrivial finite measure and conditioned to nonextinction as defined by Evans. If (Y _t ) _t0 denotes this process, we provide a new approach to the immortal particle representation of (Y _t ) _t0 . We then show that the measureZ onR ^d defined byZ(B)= _o ¹ Y _t (B) dt is almost surely finite on compact sets whend5 and almost surely infinite on every ball whend4.     

Isolated singularities of some semilinear elliptic equations

Let Ω be an open subset of $\text{R}{}^{\mathrm{<mi\; mathvariant="italic"\; is="true">N</mi>}}$, N ? 3, containing 0. We consider the solutions of ?Δu(x) + g(u(x)) = f(x) in Ω-{0}, where g is nondecreasing and f is bounded and we study the possible singularities at 0: when u(x) = o(|x|^{1 ? N}) we prove that u is isotropic near 0 and show that either it is a C¹ function in Ω (removable singularity) or |x|^{N ? 2}u(x) → c, c ≠ 0 (weak singularity) or |x|^{N ? 2} |u(x) |→ + ∞ (strong singularity). We also characterize the g's for which solutions with a weak singularity exist and improve a previous removability result of H. Brézis and L. Véron (Arch. Rational Mech. Anal.23 (1979), 153–166).     

Synthesis of sydnonimine derivatives as potential trypanocidal agents

N‐(p‐Nitrophenoxy)carbonyl‐3‐morpholino‐sydnonimine (NCMS) has been prepared from 3‐morpholinosydnonimine hydrochloride. Using the Griess assay and the superoxide‐mediated reduction of ferricytochrome c, the nitric oxide (NO?) and superoxide anion (O₂?^‐) ‐ releasing properties in phosphate buffer pH 7.4 of this novel peroxynitrite donor was studied and compared with the known 3‐morpholino‐sydnonimine (SIN‐1). From compound NCMS, a series of N‐substituted sydnonimine derivatives were easily prepared that contain purine or melaminophenyl groups which specify a recognition by a trypanosomal purine transporter. The ability of these new sydnonimines to inhibit the uptake of [2³H]adenosine on Trypanosoma equiperdum was studied.     

Mutagenesis Mediated by Triple Helix–Forming Oligonucleotides Conjugated to Psoralen: Effects of Linker Arm Length and Sequence Context

Targeted mutagenesis and gene knock-out can be mediated by triple helix-forming oligonucleotides (TFO) linked to mutagenic agents, such as psoralen. However, this strategy is limited by the availability of homopurine/ homopyrimidine stretches at or near the target site because such sequences are required for high-affinity triplex formation. To overcome this limitation, we have tested TFO conjugated to psoralen via linker arms of lengths varying from 2 to 86 bonds, thereby designed to deliver the psoralen at varying distances from the third strand binding site present at the 3'end of the supFG1 mutation reporter gene. Following triplex formation and UVA irradiation, mutations were detected using an SV40-based shuttle vector assay in human cells. The frequency and distribution of mutations depended on the length of the linker arm. Precise targeting was observed only for linker arms of length 2 and 6, which also yielded the highest mutation frequencies (3 and 14%, respectively). Psoralen–TFO with longer tethers yielded mutations at multiple sites, with the maximum distance from the triplex site limited by the linker length but with the distribution within that range influenced by the propensity for psoralen intercalation at A:T base-pair-rich sites. Thus, gene modification can be extended beyond the site of third strand binding but with a decrease in the precision of the targeting.     

Hydrous ferric oxide: evaluation of Cd-HFO surface complexation models combining Cd(K) EXAFS data,potentiometric titration results,and surface site structures identified from mineralogical knowledge

The surface properties of ferrihydrite were studied by combining wet chemical data, Cd(K) EXAFS data, and a surface structure and protonation model of the ferrihydrite surface. Acid-base titration experiments and Cd(II)-ferrihydrite sorption experiments were performed within 3<-log[H(+)]<10.5 and 0.5<[Cd(t)]<12 mM in 0.3 M NaClO(4) at 25 degrees C, where [Cd(t)] refers to total Cd concentration. Measurements at -5.5triple bond Fe-OH(-1/2),logk((int))=-8.29, assuming the existence of a unique intrinsic microscopic constant, logk((int)), and consequently the existence of a single significant type of acid-base reactive functional groups. The surface structure model indicates that these groups are terminal water groups. The Cd(II) data were modeled assuming the existence of a single reactive site. The model fits the data set at low Cd(II) concentration and up to 50% surface coverage. At high coverage more Cd(II) ions than predicted are adsorbed, which is indicative of the existence of a second type of site of lower affinity. This agrees with the surface structure and protonation model developed, which indicates comparable concentrations of high- and low-affinity sites. The model further shows that for each class of low- and high-affinity sites there exists a variety of corresponding Cd surface complex structure, depending on the model crystal faces on which the complexes develop. Generally, high-affinity surface structures have surface coordinations of 3 and 4, as compared to 1 and 2 for low-affinity surface structures.