Synthese und Reaktionen 8-gliedriger Heterocyclen aus 3-Dimethylamino-2,2-dimethyl-2H-azirin und Saccharin bzw. Phthalimid

Synthesis and Reactions of 8-membered Heterocycles from 3-Dimethylamino-2,2-dimethyl-2H-azirine and Saccharin or Phthalimide 3-Dimethylamino-2,2-dimethyl-2H-azirine ( 1 ) reacts at 0-20° with the NH-acidic compounds saccharin ( 2 ) and phthalimide ( 8 ) to give the 8-membered heterocycles 3-dimethylamino-4,4-dimethyl-5,6-dihydro-4 H-1,2,5-benzothiadiazocin-6-one-1,1-dioxide ( 3a ) and 4-dimethylamino-3,3-dimethyl-1,2,3,6-tetrahydro-2,5-benzodiazocin-1,6-dione ( 9 ), respectively. The structure of 3a has been established by X-ray (chap. 2). A possible mechanism for the formation of 3a and 9 is given in Schemes 1 and 4. Reduction of 3a with sodium borohydride yields the 2-sulfamoylbenzamide derivative 4 (Scheme 2); in methanolic solution 3a undergoes a rearrangement to give the methyl 2-sulfamoyl-benzoate 5 . The mechanism for this reaction as suggested in Scheme 2 involves a ring contraction/ring opening sequence. Again a ring contraction is postulated to explain the formation of the 4H-imidazole derivative 7 during thermolysis of 3a at 180° (Scheme 3). The 2,5-benzodiazocine derivative 9 rearranges in alcoholic solvents to 2-(5′-dimethylamino-4′,4′-dimethyl-4′H-imidazol-2′-yl) benzoates ( 10 , 11 ), in water to the corresponding benzoic acid 12 , and in alcoholic solutions containing dimethylamine or pyrrolidine to the benzamides 13 and 14 , respectively (Scheme 5). The reaction with amines takes place only in very polar solvents like alcohols or formamide, but not in acetonitrile. Possible mechanisms of these rearrangements are given in Scheme 5. Sodium borohydride reduction of 9 in 2-propanol yields 2-(5′-dimethylamino-4′,4′-dimethyl-4′H-imidazol-2′-yl)benzyl alcohol ( 15 , Scheme 6) which is easily converted to the O-acetate 16 . Hydrolysis of 15 with 3N HCl at 50° leads to an imidazolinone derivative 17a or 17b , whereas hydrolysis with 1N NaOH yields a mixture of phthalide ( 18 ) and 2-hydroxymethyl-benzoic acid ( 19 , Scheme 6). The zwitterionic compound 20 (Scheme 7) results from the hydrolysis of the phthalimide-adduct 9 or the esters 11 and 12 . Interestingly, compound 9 is thermally converted to the amide 13 and N-(1′-carbamoyl-1′-methylethyl)phthalimide ( 21 , Scheme 7) whose structure has been established by an independent synthesis starting with phthalic anhydride and 2-amino-isobutyric acid. However, the reaction mechanism is not clear at this stage.     

Star discrepancy estimates for digital (t, m, 2)-nets and digital (t, 2) -sequences over Z2

Summary We prove upper bounds on the star discrepancy of digital (t, m, 2)-nets and (t, 2)-sequences over Z₂. The main tool is a decomposition lemma for digital (t, m, 2)-nets, which states that every digital (t, m, 2)-net is just the union of 2^tdigitally shifted digital (0, m - t, 2)-nets. Using this result we generalize upper bounds on the star discrepancy of digital (0, m, 2) -nets and (0, 2) -sequences.     

A review of nanowire growth promoted by alloys and non-alloying elements with emphasis on Au-assisted III–V nanowires

Seed particles of elements or compounds which may or may not form alloys are now used extensively in promoting well-controlled nanowire growth. The technology has evolved following the well-known Vapour–Liquid–Solid (VLS) model which was developed over 40 years ago. This model indicates that a liquid alloy is formed from the seed particle and the growth precursor(s), resulting in crystal growth by precipitation from a supersaturated solution. The enhanced growth rate compared to the bulk growth from the vapour is typically attributed to preferential decomposition of precursor materials at or near the particle surface. Recently, however, there has been much interest in further developing this model, which was developed for Au-assisted Si whiskers (with diameter on the micrometre scale), in order to generally describe particle-assisted growth on the nanoscale using a variety of materials and growth systems. This review discusses the current understanding of particle-assisted nanowire growth. The aim is first to give an overview of the historical development of the model, with a discussion of potential growth mechanisms. In particular, the enhancement of growth rate in one dimension due to preferential deposition at the particle–wire interface will be discussed. Then, the particular example of III–V nanowires grown by metal–organic vapour phase epitaxy using Au particles will be revised, with details of the various growth processes involved in this system. The aim of this review is not to provide a conclusive answer to the question of why nanowires grow from seed particle alloys, but to describe the progress made towards this goal of a unified theory of growth, and to clarify the current standing of the question.     

A remark on the glueball-gluon coupling

The QCD trace anomaly motivates the consideration of a low energy glueball-gluon coupling . We point out that this should constitute the leading kinetic term for the gluons at low energies. Anti-screening of the gluons by the glueball then induces a classical Coulomb potential of color charges which increases at large distances and motivates the inclusion of a corresponding term in the inter-quark potential. Received: 16 March 1999 / Published online: 20 May 1999     

Robust optimization using computer experiments

During metamodel-based optimization three types of implicit errors are typically made. The first error is the simulation-model error, which is defined by the difference between reality and the computer model. The second error is the metamodel error, which is defined by the difference between the computer model and the metamodel. The third is the implementation error. This paper presents new ideas on how to cope with these errors during optimization, in such a way that the final solution is robust with respect to these errors. We apply the robust counterpart theory of Ben-Tal and Nemirovsky to the most frequently used metamodels: linear regression and Kriging models. The methods proposed are applied to the design of two parts of the TV tube. The simulation-model errors receive little attention in the literature, while in practice these errors may have a significant impact due to propagation of such errors.     

A family of dynamic finite difference schemes for large-eddy simulation

A family of dynamic low-dispersive finite difference schemes for large-eddy simulation is developed. The dynamic schemes are constructed by combining Taylor series expansions on two different grid resolutions. The schemes are optimized dynamically during the simulation according to the flow physics and dispersion errors are minimized through the real-time adaption of the dynamic coefficient. In case of DNS-resolution, the dynamic schemes reduce to the standard Taylor-based finite difference schemes with formal asymptotic order of accuracy. When going to LES-resolution, the schemes seamlessly adapt to dispersion-relation preserving schemes. The schemes are tested for large-eddy simulation of Burgers’ equation and numerical errors are investigated as well as their interaction with the subgrid model. Very good results are obtained.     

Synthesis of a new pair of fluorescence resonance energy transfer donor and acceptor dyes and its use in a protease assay

A new, efficient and very robust fluorescence resonance energy transfer (FRET) system, which can be measured in a normal as well as in a time-resolved mode, was developed and its feasibility demonstrated in a protease assay format.