Greensche Funktionen in der Theorie der Kernmaterie

The aim of this article is the representation of the theory of nuclear matter with the technique of many-body Green functions. We have treated the theory of Green functions thoroughly in the first chapters taking support of the functional method, which offers a convenient approach to the construction of the theory. After treatment of the properties of the exact two-point function and of the effective single-particle potential, preconditions and properties of the approximate solutions are discussed. Results achieved todate are treated in chapter 6. Brueckner theory and allied methods are not further discussed, since these are sufficiently known. The theory of linear response, being important for the semi-phenomenological treatment of real atomic nuclei, is presented in appendix A.     

Conformal mapping by the method of alternating projections

Summary The functional analytic principle of alternating projections is used to construct an iterative method for numerical conformal mapping of the unit disc onto regions with smooth boundaries. The result is a simple method which requires in each iterative step only two complex Fourier transforms. Local convergence can be proved using a theorem of Ostrowski. Convergence is linear. The asymptotic convergence factor is equal to the spectral radius of a certain operator. A version with overrelaxation as well as a discretized version are discussed along the same lines. For regions which are close to the unit disc convergence is fast. For some familiar regions the convergence factors can be calculated explicitly. Finally, the method is compared with Theodorsen's.Dedicated to the memory of Peter Henrici     

Convergence proofs and error estimates for an iterative method for conformal mapping

Summary The iterative method as introduced in [8] and [9] for the determination of the conformal mapping of the unit disc onto a domainG is here described explicitly in terms of the operatorK, which assigns to a periodic functionu its periodic conjugate functionK u. It is shown that whenever the boundary curve ofG is parametrized by a function with Lipschitz continuous derivative then the method converges locally in the Sobolev spaceW of 2-periodic absolutely continuous functions with square integrable derivative. If is in a Hölder classC ²⁺, the order of convergence is at least 1+. If is inC ^l+1+ withl1, 0<<1, then the iteration converges inC ^l+. For analytic boundary curves the convergence takes place in a space of analytic functions.For the numerical implementation of the method the operatorK can be approximated by Wittich's method, which can be applied very effectively using fast Fourier transform. The Sobolev norm of the numerical error can be estimated in terms of the numberN of grid points. It isO(N ^1–l–) if is inC ^l+1+, andO (exp (–N/2)) if is an analytic curve. The number in the latter formula is bounded by logR, whereR is the radius of the largest circle into which can be extended analytically such that'(z)0 for |z|<R. The results of some test calculations are reported.     

Herstellung und Charakterisierung in Membranen von Ionophoren mit Selektivität fü Natrium-Ionen

Preparation of Neutral Sodium-Selective Ionophores and their Characterization in Membrane Electrodes Different ionopbores based on N,N′-dibenzyl-N,N′-diphenyl-1,2-phenylenedioxydiacetamide ( 1 ) have been prepared by substitution of the aromatic ring carrying the ether O-atoms. Substituents of widely different electronegativity (CH₃, CH₃O, CHO, CN NO₂, Br) do not relevantly influence the ion selectivity.     

Three dimensional imaging using secondary ion mass spectrometry and atomic force microscopy

With the breakthroughs in lateral resolution with regards to secondary ion mass spectroscopy in recent years, new areas of research with much promise have opened up to the scientific community. Even though the much improved lateral resolution of 50 nm can effectively deliver more accurate 3D-images, the traditional 3D reconstructions, consisting of compiling previously acquired successive secondary ion mass spectrometry images into a 3D-stack, do not represent the real localized chemical distribution of the sputtered volume. Based on samples initially analyzed on the Cameca NanoSIMS 50 instrument, this paper portrays the advantages of combining the topographical information from atomic force microscopy and the chemical information from secondary ion mass spectrometry. Taking account of the roughness evolution within the analyzed zone, 3D reconstructions become a lot more accurate and allow an easier interpretation of results. On the basis of an Al/Cu sample, a comparison between traditional 3D imaging and corrected 3D reconstructions is given and the advantages of the newly developed 3D imaging method are explained.     

Experiments on the total synthesis of Lysolipin I. Part II. Michael addition of 1,3-cyclohexanedione to quinone acetals

Base-catalyzed reaction of 1,3-cyclohexanedione ( 3 ) with the quinone monoacetals 4 and 7 leads to the polycyclic products 5 and 8 , respectively, and in the case of 4 to variable amounts of dibenzofuranone 6 . The 2-arylcyclohexanedione 9 , on the other hand, is isolated from the reaction of 3 and bisacetal 11 catalyzed by ZnCl₂ (Scheme 2). Treatment of the adduct 8 with (CH₃O)₂SO₂/K₂CO₃ results in cleavage of teh heterocyclic ring by a retro-Michael reaction affording teh liable enone 23 which was further transformed to 24 by selective hydrogenation. The 8-acetoxydibenzofuranone 22 is obtainable from 8 by acid treatment and acetylation (Scheme 4). The reactions of the silylenol ethers 27 and 35 with quinone monoacetals were very complex (Scheme 6). The desired arylcyclohexanone derivatives 28 and 36 were formed in very low yields. Under certain conditions (elevated temperature or strong Lewis acids as catalysts), single-electron transfer or addition to the ene-acetal rather than to the enone function of the quinone monoacetals became predominant. In connection with this study, the sensitive 2-methoxy-p-benzoquinone monoacetals 15 (Scheme 3) and 29 (Scheme 6) have been prepared and characterized.     

Enhanced structure determination of beta-pyrrole and N-substituted porphyrins by desorption chemical ionization mass spectrometry.

The extensive macrocycle—but minimal substituent—fragmentation occurring in the chemical ionization mass spectra of porphyrins when ammonia, rather than hydrogen, is the reagent gas leads to more detailed structure determinations.     

Fast conformal mapping of an ellipse to a simply connected region

The iterative method of Wegmann (1978) for conformal mapping of a region E to a region G is reformulated in terms of a conjugation operator. If the boundary of G is sufficiently smooth, the method converges quadratically in a Sobolev space W. To overcome the crowding an elongated canonical region E should be chosen if the image region G is elongated. For ellipses E the operator of conjugation can be expressed in a very simple way in terms of Fourier series. Numerically, this can be performed very efficiently by fast Fourier transform (FFT).     

Characterization of polyalkylvinyl ether phases by solid-state and suspended-state nuclear magnetic resonance investigations

Pure organic polyalkylvinyl ether phases were synthesized by suspension polymerization using different ratios and compositions of n-butylvinyl ether (C₄VE) and n-octadecylvinyl ether (C₁₈VE) with triethylene glycol divinyl ether or divinylbenzene as crosslinkers, respectively. These phases were investigated by means of solid-state ¹³C cross-polarization magic angle spinning nuclear magnetic resonance (NMR) spectroscopy and ¹H high-resolution magic angle spinning (HR MAS) NMR spectroscopy in suspended-state. A comparison of these two methods showed the substantial advantages of ¹H HR MAS NMR measurements. Structure elucidation was achieved using a 2D H,H-COSY NMR experiment performed under MAS conditions enabling full peak assignment of the ¹H NMR spectra of these phases. The dynamic behavior of the polyalkylvinyl ether phases was determined by employing temperature-dependent measurements of spin–lattice relaxation times (T₁) as well as accumulation of a 2D wide line separation NMR spectrum.