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991.
Reaction of a solution of CuSO(4) and S,S'-diphenylsulfimide, Ph(2)SNH 1, with sodium salts of trimesic acid (H(3)tma) in MeOH gives the 2-D coordination network [Cu(3)(Ph(2)SNH)(6)(tma)(2)] in which each trimesate is bound to three copper centres. Addition of other solvents to the reaction mixture causes a change in the shape of the network. By this route, three forms have been prepared and characterised by X-ray crystallography. These include the known honeycomb, 2, and brick-wall, 3, motifs and a herringbone, 4, arrangement which is novel for transition metal-containing trimesate complexes. Key to the supramolecular isomerism observed is the ability of 1 to facilitate structural isomerism at copper(II) centres. In contrast to 2 in which the copper centres are square planar, 4 is analogous to an inter-allogon, with both planar and tetrahedral copper centres. Also prepared is a related complex which is composed of discrete units of three copper centres. These are further linked into a 2-D network by hydrogen bonds. 相似文献
992.
The facile and efficient conversion of a tert-butyl protecting group to an acetyl protecting group for thiols by catalytic amounts of bromine in acetyl chloride and the presence of acetic acid has been developed. The fairly mild reaction conditions are of particular interest for new protecting group strategies for sulfur functionalised target structures. 相似文献
993.
A procedure is described that greatly simplifies the use of an oxazaborolidine catalyst derived from (1R,2S) cis-1-amino-indan-2-ol. This B-OMe catalyst has been employed in the asymmetric reduction of a number of structurally diverse prochiral ketones, in particular the reduction of alpha-amino acetophenone and its derivatives. A method for reducing the effective catalyst loading by "in situ recycling" is also presented. [structure: see text] 相似文献
994.
[reaction: see text] New anionic oxygen to alpha- and beta-vinyl carbamoyl migration reactions, 17a and 26a-c --> 18 and 30a-c, proceed under LDA-mediated conditions leading stereoselectively to highly substituted stilbenes bearing electron-donating and -withdrawing substituents. Compounds 17a and 26a-c are prepared by combination of efficient, directed ortho metalation, Sonogashira, and Suzuki-Miyaura cross-coupling procedures. 相似文献
995.
In this paper we consider random perturbations of dynamical systems and diffusion processes with a first integral. We calculate, under some assumptions, the limiting behavior of the slow component of the perturbed system in an appropriate time scale for a general class of perturbations. The phase space of the slow motion is a graph defined by the first integral. This is a natural generalization of the results concerning random perturbations of Hamiltonian systems. Considering diffusion processes as the unperturbed system allows to study the multidimensional case and leads to a new effect: the limiting slow motion can spend non-zero time at some points of the graph. In particular, such delay at the vertices leads to more general gluing conditions. Our approach allows one to obtain new results on singular perturbations of PDEs.
Mathematics Subject Classification (2001): 60H10; 34C29; 35B20 相似文献
996.
Stockman MI 《Physical review letters》2004,93(13):137404
We predict theoretically that surface plasmon polaritons propagating toward the tip of a tapered plasmonic waveguide are slowed down and asymptotically stopped when they tend to the tip, never actually reaching it (the travel time to the tip is logarithmically divergent). This phenomenon causes accumulation of energy and giant local fields at the tip. There are various prospective applications in nano-optics and nanotechnology. 相似文献
997.
We investigate the structure of Kellendonks tiling semigroup in the case of
1-dimensional tilings. 相似文献
998.
Mark Watkins. 《Mathematics of Computation》2004,73(246):907-938
The classical class number problem of Gauss asks for a classification of all imaginary quadratic fields with a given class number . The first complete results were for by Heegner, Baker, and Stark. After the work of Goldfeld and Gross-Zagier, the task was a finite decision problem for any . Indeed, after Oesterlé handled , in 1985 Serre wrote, ``No doubt the same method will work for other small class numbers, up to 100, say.' However, more than ten years later, after doing , Wagner remarked that the case seemed impregnable. We complete the classification for all , an improvement of four powers of 2 (arguably the most difficult case) over the previous best results. The main theoretical technique is a modification of the Goldfeld-Oesterlé work, which used an elliptic curve -function with an order 3 zero at the central critical point, to instead consider Dirichlet -functions with low-height zeros near the real line (though the former is still required in our proof). This is numerically much superior to the previous method, which relied on work of Montgomery-Weinberger. Our method is still quite computer-intensive, but we are able to keep the time needed for the computation down to about seven months. In all cases, we find that there is no abnormally large ``exceptional modulus' of small class number, which agrees with the prediction of the Generalised Riemann Hypothesis.
999.
In his 1961 paper, Marcel Golay showed how the search for pairs of binary sequences of length with complementary autocorrelation is at worst a problem. Andres, in his 1977 master's thesis, developed an algorithm which reduced this to a search and investigated lengths up to 58 for existence of pairs. In this paper, we describe refinements to this algorithm, enabling a search at length 82. We find no new pairs at the outstanding lengths 74 and 82. In extending the theory of composition, we are able to obtain a closed formula for the number of pairs of length generated by a primitive pair of length . Combining this with the results of searches at all allowable lengths up to 100, we identify five primitive pairs. All others pairs of lengths less than 100 may be derived using the methods outlined.
1000.
Alexander Litvak Alain Pajor Mark Rudelson Nicole Tomczak-Jaegermann Roman Vershynin 《Comptes Rendus Mathematique》2004,339(1):33-38
Let be the space equipped with a norm 6·6 whose unit ball has a bounded volume ratio with respect to the Euclidean unit ball. Let Γ be any random N×n matrix with N>n, whose entries are independent random variables satisfying some moment assumptions. We show that with high probability Γ is a good isomorphism from the n-dimensional Euclidean space onto its image in : there exist α,β>0 such that for all , . This solves a conjecture of Schechtman on random embeddings of ?2n into ?1N. To cite this article: A. Litvak et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献