A novel and effective method has been developed for the synthesis of 9H-pyrrolo[1,2-a]indoles by treatment of 3-substituted-4,6-dimethoxyindoles with chalcones in the presence of hydrochloric acid. 相似文献
Consider a combinatorial identity that can be proved by induction. In this paper, we describe a general method for translating the inductive proof into a recursive bijection. Furthermore, we will demonstrate that the resulting recursive bijection can often be defined in a direct, non-recursive way. Thus, the translation method often results in a bijective proof of the identity that helps illuminate the underlying combinatorial structures. This paper has two main parts: First, we describe the translation method and the accompanying Maple code; and second, we give a few examples of how the method has been used to discover new bijections. 相似文献
In the setting of adjoint pairs of operators we consider the question: to what extent does the Weyl M-function see the same singularities as the resolvent of a certain restriction AB of the maximal operator? We obtain results showing that it is possible to describe explicitly certain spaces and such that the resolvent bordered by projections onto these subspaces is analytic everywhere that the M-function is analytic. We present three examples – one involving a Hain-Lüst type operator, one involving a perturbed Friedrichs
operator and one involving a simple ordinary differential operators on a half line – which together indicate that the abstract
results are probably best possible.
James Hinchcliffe and Serguei Naboko wish to thank the British EPSRC for financial support under grant EP/C008324/1 “Spectral
Problems on Families of Domains and Operator M-functions”. Serguei Naboko wishes to thank the Russian RFBR for grant 06-01-00219. All authors wish to thank INTAS for financial
support under INTAS Project No. 051000008-7883. The authors wish to thank the referee for many helpful comments. 相似文献
The spin wave dispersion in NiBr2 has been studied by medium and long wavelength inelastic neutron scattering in the [1 1 0], [1 0 0] and [0 0 1] directions at 4.2 and 30 K, i.e. in the incommensurate helical and collinear antiferromagnetic phases. The values of the intralayer Heisenberg exchange constant Jij and XY anisotropy constant D at 4.2(30) K are J01 0.379(1)(0.379(1)), J02 0.0036(50)(0.0036(50)), J03 - 0.105(5) (?0.105(5)), J′ - 0.0423(50)(?0.389(50))D 0.0364(50)(0.0290(50)), where J′; is the interlayer exchange constant. In fitting the 4.2 K data account is taken of the co-existence of three equivalent domains and of intensity arising from and where is the wavevector of the helix. In the low frequency region of the dispersion curve such peaks are resolved. The results reinforce the hypothesis that in zero-field the commensurate-incommensurate phase transition is driven by fluctuations. 相似文献
A dramatic source temperature effect is observed in the low collision energy collision-induced dissociation spectra of molecular ions derived via 70 eV electron bombardment of 2-pentanone and via charge exchange. The observation cannot simply be attibuted to the increased thermal energy of the 2-pentanone molecular ions. A number of factors appear to contribute to the observed results, (i) the increase, with temperature, in the ratio of the concentration of enol to keto neutral molecules, (ii) temperature effects on the Franck-Condon factors which control the yields and internal energies of the keto and enol molecular ions, (iii) differences in the relative stabilities of the keto and enol molecular ions, (iv) temperature effects on the equilibrium between the isomeric molecular ions. This last item is probably most important, with the concentration of being most significant. These data highlight the role that ion source temperature can play as a variable in elucidating ion structure problems. 相似文献
We report quantitative MALDI-TOF measurements for polydimethylsiloxane (PDMS) of two different molecular weights using the relative ratio of the signal intensities of integrated oligomer distributions for these two molecular weight distributions. By reporting the ratio of intensities of the integrals of two oligomer distributions, we assume that the ionization and desorption efficiencies, crystallization conditions and other factors affecting intensity are similar. Poly(methyl methacrylate) (PMMA-33,000) was mixed with PDMS samples to show whether the presence of another material might affect the desorption efficiency. Quantitative values for the number-average molecular weight (Mn), weight-average molecular weight (Mw) and polydispersities (D) were calculated using the oligomer distributions. The results show a linear relationship between the analyte concentrations and the signal intensities in the range from 1,000 Da to 10,000 Da, and the desorption efficiency of these two PDMS materials was the same even in the presence of PMMA. 相似文献
[reaction: see text] A highly convergent synthesis of the angiogenesis inhibitor luminacin D has been achieved in 13 linear steps (19 steps total, 5.3% overall yield) utilizing a samarium(II) iodide-mediated mixed tandem aldol/Evans-Tishchenko reaction to construct the carbohydrate precursor. The modular synthetic design will allow derivatization at key positions necessary for biochemical mode of action studies. 相似文献