Structure and Reactivity of Five- and Six-Ring N,N-, N,O-, and O,O-acetals: A lesson in allylic 1, 3-strain (A1, 3 strain)

The X-ray structures of fifteen 1, 3-imidazolidine, 1, 3-oxazolidine, 1, 3-dioxan-4-one, and hydropyrimidine-4(1H)-one derivatives are described (Table 2) and compared with known structures of similar compounds (Figs. 1–20). The differences between structures containing exocyclic N-acyl groups and those lacking this structural element arise from the A^1,3 effect of the amide moieties. Even t-Bu groups are forced into axial positions of six-ring half-chair or into flag-pole positions of six-ring twist-boat conformers by this effect (Figs. 16–20). In the N-acylated five-membered heterocycles, a combination of ring strain and A^{1, 3} strain leads to strong pyramidalizations of the amide N-atoms (Table 1) such that the acyl groups wind up on one side and the other substituents on the opposite side of the rings (Figs. 4–9 and Scheme 3). Thus, the acyl (protecting!) groups strongly contribute to the steric bias between the two faces of the rings. Observed, at first glance surprizing stereoselectivities of reactions of these heterocycles (Schemes 1 and 2) are interpreted (Scheme 3) as an indirect consequence of the amide A^{1, 3} strain effect. The conclusions drawn are considered relvant for a better understanding of the ever increasing role which amide groups play in stereoselective syntheses.     

A stability test for real polynomials

Summary By the argument principle the number of zeros inside of the unit circle of a real polynomial , can be estimated by the variation of the argument ofp _n (exp(it)) ift varies from 0 to . This variation has its maximal value n iff then distinct zeros of are separated by then–1 distinct zeros of . Now from Sturm sequence techniques in connection with special properties of the Chebyshev polynomials there results a very simple stability test.Dedicated to Professor Dr. Wilhelm Niethammer on his sixtieth birthday (December 2, 1993)     

Pion production in two-body pd collisions

The reactions d(p, π⁺)t and d(p, π^o)³ He are analyzed in terms of the pp → π⁺d sub-process. The exclusion principle induces an additional exchange contribution involving the πd scattering amplitude. Acceptable deuteron and tritron (³H) wave functions which reproduce the charge form factors yield results consistent with experimental angular distributions at 470, 590, 754 and 1192 proton lab. energies. The forward peak is not sensitive to details of the wave functions. Both the direct and exchange form factors develop a zero which is imposed by the dip in the ³He charge form factor. The associated interference pattern governs the backward cross section.     

Multipion production in photon-photon collisions

The magnitudes of the matrix elements for γγ→2π⁺2π^?, γγ→π⁺π^?2π⁰, γγ→2π⁺2π^?π⁰, γγ→2π⁺2π^?2π⁰, γγ→3π⁺3π^?3π⁺ and γγ→3π⁺3π^?π⁰are deduced from experimental data as a function of the invariant massW of the system (from 1.0 to 3.0 GeV). It is shown that the data are consistent with a universal energy dependence of the reduced channel amplitudes. A statistical model is shown to describe the peaks in the energy dependence of multipion production in γγ collisions quite well without introducing explicit intermediate resonances.     

Zur Struktur von Quadraturformeln

Summary Usually the errorR _n (j) of a quadrature formula is estimated with the aid of theL ₁-norm of the Peano kernel. It is shown that this term may be estimated rather sharp using the norm Q _n of the quadrature rule. Then it follows that formulas with non-negative weights are favourable also in the sense of minimizing theL ₁-norm of the kernel. A remainder term of the typeR _n (f)=cf⁽ⁿ⁺¹⁾ () is possible iff the kernel is definite. In the case of an interpolatory formula this definiteness is usually shown by an application of the so-called V-method. We determine the optimal formulas in the sense of this method. Then we analyse the influence of the structure of the mesh on the norm of a formula. We find that on an equidistant mesh withm nodes there exists a rule with a small norm if the order is not greater than .     

Development and validation of a high-performance thin-layer chromatography assay for the analysis of tacrolimus ointments

JPC – Journal of Planar Chromatography – Modern TLC - A simple and rapid high-performance thin-layer chromatography (HPTLC) assay was developed and validated for the quantification of...     

Potent algicides based on the cyanobacterial alkaloid nostocarboline

[structure: see text] Nostocarboline and seven derivatives were prepared and displayed minimal inhibitory concentration (MIC) values >or=100 nM against the growth of Microcystis aeruginosa PCC 7806, Synechococcus PCC 6911, and Kirchneriella contorta SAG 11.81, probably via the inhibition of photosynthesis. The natural product hybrid nostocarboline/ciprofloxacin displayed additional antibacterial activity against several Gram-negative bacteria (MICs >or=0.7 microM). Nostocarboline can thus be considered a potent, selective, readily available, natural algicide.     

Die Finsler'schen Arbeiten zur Grundlegung der Mathematik

Ohne Zusammenfassung