Anionic polymerization with alkaline earth counterion. III. Aging of oligo- and polystyryl-barium and -strontium in THF

The self-deactivation of polystyryl-barium and polystyryl-strontium in tetrahydrofuran (THF) results essentially from protonation by the solvent. The deactivation constant k_d of this reaction is independent of carbanion concentration, length, and functionality of chains. Relations of k_d with temperature are: polystyryl-barium: k_d = 6.25 × 10⁷ exp(-18,900/RT) sec^?1; polystyryl-strontium: k_d = 4.1 × 10⁶ exp(?16,000/RT) sec^?1. The self-deactivation of α,ω-dicarbanionic oligostyryl-barium is a nonrandomlike reaction. Residual living oligomers are left dicarbanionic even if an important deactivation occurs.     

Cation-binding to biomolecules

Ab initio SCF computations indicate that Mg²⁺ should bind essentially to the oxygen atoms of uracil, the remaining part of the base being rather repulsive towards such an interaction. The Coulombic component predominates in the interaction, the essential feature of which may thus be deduced from the study of the molecular electrostatic potential of uracil. These ab initio results contradict an earlier CNDO prediction that the binding of uracil and Mg²⁺ should occur preferentially at the C₅=C₆ double bond of the base. It is shown that the CNDO result is an artifact due to an exaggeration by this method of the charge transfer between the ligand and the cation. The small amount of available experimental data seem in favor of the ab initio results.     

Etudes quantiques sur la conformation de la valinomycine et de ses éléments constitutifs

Quantum mechanical calculations using the PCILO method are performed on the conformational properties of constituents and models of valinomycin. The work is executed in a progressive way and uses the results obtained for model compound of size i (i being the total number of both amino acid and hydroxy acid residues in a model molecule) to study those of size i + 1. Conformational energy maps for compounds of size i = 1 and i = 2 (respectively the “didepsipeptide” and the “tridepsipeptide” models) are obtained. For greater compounds, a minimization procedure is used to localize the energy minima. The results shows that valinomycin can adopt essentially three conformations, two of them involving only C₁₀ like structures in a bracelet-shaped conformation, and the third one a combination of C₁₀ and C₁₃ hydrogen bonded rings. These results agree well with crystallographic studies but are different from some models presented earlier to explain the uncomplexed → complexed transition of valinomycin with ions.     

Synthesis of copolymer brushes endowed with adhesion to stainless steel surfaces and antibacterial properties by controlled nitroxide-mediated radical polymerization

Novel copolymer brushes have been synthesized by a two-step "grafting from" method that consists of the electrografting of poly(2-phenyl-2-(2,2,6,6-tetramethyl-piperidin-1-yloxy)-ethylacrylate) onto stainless steel, followed by the nitroxide-mediated radical polymerization of 2-(dimethylamino ethyl)acrylate and styrene or n-butyl acrylate, initiated from the electrografted polyacrylate chains. The grafted copolymers were quaternized in order to endow them with antibacterial properties. Peeling tests have confirmed the strong adhesion of the grafted copolymer onto the stainless steel substrate. Quartz crystal microbalance experiments have proven that fibrinogen adhesion is lower on the hydrophilic quaternized films compared to the nonionic counterpart. Such quaternized copolymers exhibit significant antibacterial activity against the Gram-positive bacteria S. aureus and the Gram-negative bacteria E. coli.     

Preparation and Absolute Configuration of (−)-(E)-α-trans-Bergamotenone

The synthesis, absolute configuration, and olfactive evaluation of (?)-(E)-α-trans-bergamotenone (= (?)-(1′S,6′R,E)-5-(2′,6′-dimethylbicyclo[3.1.1]hept-2′-en-6′-yl)pent-3-en-2-one; (?)- 1 ), as well as its homologue (?)- 19 are reperted. The previously arbitrarily attributed absolute configuration of 1 and of (?)-α-trans-bergamotene (= (?)-(1 S,6R)-2,6-dimethyl-6-(4-methylpent-3-enyl)bicyclo[3.1. 1]hept-2-ene; (?)- 2 ), together with those of the structurally related aldehydes (?)- 3a,b and alcohols (?)- 4a,b , have been rigorously assigned.     

A modified sinc quadrature rule for functions with poles near the arc of integration

Sinc function approach is used to obtain a quadrature rule for estimating integrals of functions with poles near the are of integration. Special treatment is given to integration over the intervals (–, ), (0, ), and (–1, 1). It is shown that the error of the quadrature rule converges to zero at the rateO(exp(–cN)) asN , whereN is the number of nodes used, and wherec is a positive constant which is independent ofN.     

Quasi-optimal range searching in spaces of finite VC-dimension

The range-searching problems that allow efficient partition trees are characterized as those defined by range spaces of finite Vapnik-Chervonenkis dimension. More generally, these problems are shown to be the only ones that admit linear-size solutions with sublinear query time in the arithmetic model. The proof rests on a characterization of spanning trees with a low stabbing number. We use probabilistic arguments to treat the general case, but we are able to use geometric techniques to handle the most common range-searching problems, such as simplex and spherical range search. We prove that any set ofn points inE ^d admits a spanning tree which cannot be cut by any hyperplane (or hypersphere) through more than roughlyn ^1–1/d edges. This result yields quasi-optimal solutions to simplex range searching in the arithmetic model of computation. We also look at polygon, disk, and tetrahedron range searching on a random access machine. Givenn points inE ², we derive a data structure of sizeO(n logn) for counting how many points fall inside a query convexk-gon (for arbitrary values ofk). The query time isO(kn logn). Ifk is fixed once and for all (as in triangular range searching), then the storage requirement drops toO(n). We also describe anO(n logn)-size data structure for counting how many points fall inside a query circle inO(n log² n) query time. Finally, we present anO(n logn)-size data structure for counting how many points fall inside a query tetrahedron in 3-space inO(n ^2/3 log² n) query time. All the algorithms are optimal within polylogarithmic factors. In all cases, the preprocessing can be done in polynomial time. Furthermore, the algorithms can also handle reporting within the same complexity (adding the size of the output as a linear term to the query time).Portions of this work have appeared in preliminary form in Partition trees for triangle counting and other range searching problems (E. Welzl),Proc. 4th Ann. ACM Symp. Comput. Geom. (1988), 23–33, and Tight Bounds on the Stabbing Number of Spanning Trees in Euclidean Space (B. Chazelle), Comput. Sci. Techn. Rep. No. CS-TR-155-88, Princeton University, 1988. Bernard Chazelle acknowledges the National Science Foundation for supporting this research in part under Grant CCR-8700917. Emo Welzl acknowledges the Deutsche Forschungsgemeinschaft for supporting this research in part under Grant We 1265/1-1.     

Lattice instantons in the large dimension limit

We give a lattice construction of the discretizations of the topologically nontrivial maps S ^2n–1S ⁿ . For n=1, 2, 4, 8, these are the Hopf maps. The construction, based on Barnes-Wall lattices, Reed-Muller error-correcting codes, and Hadamard matrices, generalizes to n=2 ⁱ for i any integer. Manton's result for the cases n=2 and 4 (i.e., the monopole and instanton) are included. We argue that discrete harmonic analysis will be exact in the infinite dimension limit.Work supported in part by the DOE contract #DE-ACO2-87ER-40325.B.Department of Energy Outstanding Junior Investigator supported in part by DOE contract number DE-FGO5-85ER-40226.     

Normal modes of a model radiating system

In order to gain insight into normal modes of realistic radiating systems, we study the simple model problem of a finite string and a semi-infinite string coupled by a spring. As expected there is a family of modes which are basically the modes of the finite string slowly damped by the radiation of energy to infinity on the semi-infinite string. But we also study another family of modes, found by Dyson in a different model problem, which are strongly damped modes of the semi-infinite string itself. These may be analogous to the modes of black holes, and they are likely to be present in relativistic stars as well. The question of whether the instability in these modes which Dyson found is present in realistic stars remains open.     

Dérivés C-Glycosyliques XXXII. Synthèse de dérivés spiro-C-glycosylidéniques par cyclisation nucléophile. Communication préliminaire

C -Glycosylic derivatives XXXII. Synthesis of spiro-C -glycosylidenic derivatives via nucleophilic cyclization. On treatment with compounds bearing two nucleophilic groups as ethylenediamine, o-phenylenediamine or their monooxa or monothia analogues, 1,2:5, 6-di-O-isopropylidene-α-D -ribo-hexofuranos-3-ulose gave with excellent yields the corresponding spiro-C-glycosylidenic derivative; for example, when using o-phenylenediamine, a spirobenzimidazoline ( 5 ) was obtained. The latter compound underwent, on oxidation, a ring expansion to a morpholinobenzimidazole ( 8 ). Spirobenzodiazepines, spirobenzooxazepines and spirobenzothiazepines were formed when applying the same type of cyclization reaction to 3-C-acetylmethylene-3-deoxy-1,2:5,6-di-O-isopropylidene-α-D -ribo- and α-D -xylo-hexofuranoses.