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Random orders on
invariant under permutations are called exchangeable. The compact and convex set of all random total orders is shown to be a Bauer simplex whose set of extreme points, the socalled totally ordered paintbox processes, is homeomorphically parametrized by almost uniform distributions on the unit interval, i.e. by probability measures w on [0, 1] whose distribution functions are w-almost surely the identity. 相似文献
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Cesare Gennari Chiara Longari Stefano Ressel Barbara Salom Antonia Mielgo 《European journal of organic chemistry》1998,1998(6):945-959
Chiral vinylogous amino sulfonic acids (vs-amino acids) were synthesized starting from either L- or D-α-amino acids via N-Boc–α-amino aldehydes. Wittig-Horner reaction with methyl (or ethyl) diethylphosphoryl methanesulfonate and nBuLi gave the corresponding α,β-unsaturated sulfonates in high yield and complete (E) stereoselectivity. Cleavage of the methyl (ethyl) ester was effected by treatment of the sulfonates with nBu4NI in refluxing acetone. Treatment of the nBu4N+ sulfonate salts with SO2Cl2-PPh3-CH2Cl2gave the corresponding sulfonyl chlorides as stable chromato-graphable compounds. The synthetic sequence proved successful not only starting from α-amino acids carrying unfunctionalized side-chains (Ala, Val, Phe, Leu, Pro), but also with functionalized α-amino acids (Ser, Tyr, Gln) provided that the side chains were suitably protected. The sulfonyl chlorides were coupled with the amine salts to give vs-dipeptides. Amine hydrochlorides were prepared from N-Boc derivatives by treatment with HCl in methanol or ethyl acetate. The process was further iterated to give vs-tripeptides and vs-tetrapeptides. The above procedure was also used to synthesize “mixed” peptides, which incorporate both proteinogenic α-amino acids and vs-amino acids. Proteinogenic α-amino acids were incorporated at both the C-terminal and the N-terminal position. 相似文献
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Cesare Gennari Chiara Longari Stefano Ressel Barbara Salom Umberto Piarulli Simona Ceccarelli Antonia Mielgo 《European journal of organic chemistry》1998,1998(11):2437-2449
Chiral vinylogous sulfonamidopeptides (vs-peptides) were synthesized on TentaGel resin employing (S)- and (R)-N-Boc-vinylogous sulfonyl chlorides 2a–i as building blocks. Glycine and two different photocleavable molecules were used as linkers, and the corresponding cleavage conditions were optimized. According to preliminary studies in solution and on solid phase, three libraries were synthesized with the “split-mix synthesis” method. Taking advantage of the acidic character of the sulfonamides (RSO2–NHR: pKa = 10-11), mild conditions were developed to alkylate the sulfonamide nitrogen atom so as to reduce the acidity of the monomers and of the oligomers and increase their in vivo bioavailability. This synthetic methodology was employed to increase the diversity in a library of di-N-alkylated vs-dipeptides 26 . The electron-withdrawing capability of the sulfonamido group pointed to the use of vinylogous sulfonamidopeptides as Michael acceptors. The sodium enolate of dimethyl malonate was used as nucleophile to obtain N-Boc-γ-lactams 35 in moderate yields and good diastereoselectivity. 相似文献
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Sumpf B. Hülsewede R. Erbert G. Dzionk C. Fricke J. Knauer A. Pittroff W. Ressel P. Sebastian J. Tränkle G. 《Optical and Quantum Electronics》2003,35(4-5):521-532
High brightness tapered laser diodes with different resonator geometries were fabricated and analysed. The devices consist of an index-guided straight section and a gain-guided tapered section. Lasers with a total length L = 2 and 4 mm and different length of the ridge waveguide L RW (500 μm ≤ L RW ≤ 1250 μm for L = 2 mm and 500 μm ≤ L RW ≤ 2000 μm for L = 4 mm) were processed to study the influence of the straight section on the spatial mode filtering. The power–voltage–current-characteristics, the beam waist, the far field, and the beam propagation factor M 2 were measured. From the experiments, it can be stated that the lasers with a small L RW reach higher output powers compared to those with larger L RW. Concerning the beam quality the length L RW should exceed a minimal value to guarantee efficient spatial mode filtering. Devices optimised concerning maximum output power and excellent beam quality reach a beam propagation factor smaller than 2.1 at an output power P = 2 W. 相似文献
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P of all partitions of {1,2,3,...}, or rather its distribution. There is a natural compact metrizable topology on P taking care of measurability questions. With respect to the maximum operation P becomes an abelian semigroup, and our first theorem characterizes random partitions as normalized positive definite functions on the subsemigroup of partitions "with finite support". We then present a new proof of Kingman's theorem stating that the exchangeable random partitions form a simplex whose extreme points are the so-called "paint-box distributions". An interesting moment problem which is still open arises in this connection. 相似文献