Functions of translation type and functorial properties of Segal algebras II

In this paper we investigate functorial properties of the Segal algebra which consists of all functionsf in Wiener's algebra onG with Fourier transform in Wiener's algebra on the dual group . Especially may serve as a very large and natural domain for Poisson's formula. Moreover, there is introduced a Segal algebraE ₀(G) containing as a subspace, but still eachfE ₀(S) satisfies Poisson's formula.     

An algorithmic approach to Hermite-Birkhoff-interpolation

Summary This paper deals with an algorithmic approach to the Hermite-Birkhoff-(HB)interpolation problem. More precisely, we will show that Newton's classical formula for interpolation by algebraic polynomials naturally extends to HB-interpolation. Hence almost all reasons which make Newton's method superior to just solving the system of linear equations associated with the interpolation problem may be repeated. Let us emphasize just two: Newton's formula being a biorthogonal expansion has a well known permanence property when the system of interpolation conditions grows. From Newton's formula by an elementary argument due to Cauchy an important representation of the interpolation error can be derived. All of the above extends to HB-interpolation with respect to canonical complete ebyev-systems and naturally associated differential operators [7]. A numerical example is given.     

Chiral separation of halogenated amino acids by ligand-exchange capillary electrophoresis

The chiral separation of halogenated amino acids by ligand-exchange CE is described. Halogenated amino acids attracted increasing interest in recent years because of their physiological activities. Different chiral selectors, as there are L-4-hydroxyproline, L-histidine, and N-alkyl derivatives of L-4-hydroxyproline in form of their copper(II) complexes, are compared for their chiral recognition ability for halogenated amino acids. The influence of various parameters, such as selector concentration, pH, organic modifier, and field strength, on the resolution was investigated. All halogenated amino acids investigated were baseline-separated under optimized conditions.     

Noniterative biexponential fluorescence lifetime imaging in the investigation of cellular metabolism by means of NAD(P)H autofluorescence.

The cofactors NADH and NADPH, hereafter NAD(P)H [NAD(P)= nicotinamide adenine dinucleotide (phosphate)], belong to the principal endogenous indicators of energetic cellular metabolism. Since the metabolic activity of cells is given by the ratio between the concentrations of free and protein-bound NAD(P)H, the development of autofluorescence techniques which accurately measure the modifications to this ratio is particularly significant. Hitherto the methods applied in the monitoring of cellular metabolism have provided either imprecise results, due to interference of the NAD(P)H signal by perturbing factors, or they have required a complicated internal calibration. We employ biexponential fluorescence lifetime imaging (FLIM) in order to discriminate between the free and protein-bound NAD(P)H without any previous calibration. Thus, we have obtained directly, and for the first time, a high-resolution map of cellular metabolism, that is, an image of the contribution of the protein-bound NAD(P)H to the cumulative NAD(P)H fluorescence signal. Moreover, we demonstrate that protein-NAD(P)H complexes characterised by different fluorescence lifetimes are not uniformly distributed all over the cell, as assumed until now, but are concentrated in certain cellular regions. The different fluorescence lifetimes indicate either different protein-NAD(P)H complexes or different bond strengths between NAD(P)H and the protein in these complexes. Since an important aspect in biological applications is to monitor the dynamics of the relevant processes (such as cellular metabolism), rapid dynamical techniques, for example, rapid biexponential fluorescence lifetime imaging, are needed. Furthermore, it is necessary to reduce the evaluation effort as much as possible. Most of the evaluation techniques in multiexponential FLIM are time-expensive iterative methods. The few exceptions are connected with a loss of information, for example, global analysis; or a loss in accuracy, for example, the rapid evaluation technique (RLD). We implement for the first time in FLIM a noniterative, nonrestrictive method originally developed by Prony for approximations of multiexponential decays. The accuracy of this method is verified in biexponential FLIM experiments in time-domain on mixtures of two chromophores both in homogenous and in heterogeneous media. The resulting fluorescence lifetimes agree (within error margins) with the lifetimes of the pure substances determined in monoexponential FLIM experiments. The rapidity of our evaluation method as compared to iterative pixel-by-pixel methods is evidenced by a reduction of the evaluation time by more than one order of magnitude. Furthermore, the applicability of this method for the biosciences is demonstrated in the investigation of cellular metabolism by means of NAD(P)H endogenous fluorescence.     

The Synthesis of Dibenzo[3n]crown-n by Novel Methods and their Cation Binding Studied by Fluorescence Spectroscopy. Part IV

The dibenzo[3n]crown-n were synthesised from1,2-bis(o-hydroxyphenoxy)ethane obtained from 1,2-bis(o-formylphenoxy)ethane via Bayer-Willigeroxidations with H₂O₂/CH₃COOH in good yields. The cyclic condensation of 1,2-bis(o-hydroxyphenoxy)ethanewith dichlorides, and ditosylates of polyethylene glycols in DMF/Me₂CO₃ gave the macrocyclesdibenzo[15]crown-5, dibenzo[18]crown-6, dibenzo[21]crown-7 anddibenzo[24]crown-8. The structures were identified using IR, mass, ¹H and ¹³C NMR spectroscopy. Therecognition of the molecules for the cations, Li⁺, Na⁺, K⁺, Rb⁺ and Zn²⁺were conducted quantitatively with steady state fluorescencespectroscopy. The 1:1 association constants in acetonitrileshowed a good relation of the appropriate size of the macrocyclic ether towards the fitting cationradii. Namely, dibenzo[15]crown-5 was the best for Li⁺ binding and more than 100 times better thanNa⁺ and K⁺. Dibenzo[21]crown-7 was excellent for Rb⁺ binding while K⁺ is 100 timesless preferred. The largest crown ether studied, dibenzo[24]crown-8, exhibited the order of binding power,Rb⁺ > K⁺ > Na⁺. Zn²⁺ displayed, however, a marked binding with only dibenzo[18]crown-6.p>     

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Nuclear acoustic resonance in metals

A comprehensive quantum theoretical treatment of nuclear acoustic resonance (NAR) in metals is presented for the first time. Basic equations describing the NAR-absorption and NAR-dispersion are derived from the sound induced perturbation Hamiltonian Ih(t) by applying a generalized form of the Kubo susceptibility. It is shown that in metals, where a sound wave may induce nuclear magnetic dipole and nuclear electric quadrupole transitions simultaneously, the appearance of interference terms enables one to determine not only the absolute values but also the signs of the gradient-elastic tensor components. Explicit expressions are displayed for the dipolar, quadrupolar and interference contributions to the generalized NAR susceptibility in cubic metals. As an example the derivative of the expected⁹³Nb NAR-absorption line (|m|=1) is calculated for different signs of the gradient elastic tensor componentS ₄₄.     

A note on the hilbertfunction of a one-dimensional Cohen-Macaulay ring

In this note we give examples of one-dimensional noetherian local integral domains with the property that the number of generators of the square of the maximal ideal is less than the embedding dimension. On the other hand we show that if \((R,m)\) is a local one-dimensional Cohen-Macaulay ring, then \((m^n )\) for all n such that μ \((m^n )\) < m(R). Here μ denotes the minimal number of generators of an ideal and m(R) the multiplicity of R. A similar statement was conjectured by D. Sally in [5], Our main result 2.1 generalizes Prop. 2.6. in [6].     

Non-destructive measurement of the mobility in semiconductors by means of the microwave Faraday effect

The paper describes the measurement of the electron mobility in semiconducting plates placed between two cylindrical antennas with diameterd–0·75 ₀ by means of the microwave Faraday effect. This system enables (i) to measure the Faraday rotation in semiconducting plates of arbitrary transverse dimensions, greater or at least equal to the diameter of dielectric antennas, (ii) to evaluate the unknown value of the charge carrier mobility from the measured rotation in an unbounded solid state plasma slab approximation. The measurement of the Faraday rotation in n-type Ge plates are reported. The comparison of the experimental data with the theory shows good agreement.     

über die Striktionslinien von einparametrigen Scharen linearer Räume

A generalisation of a ruled surface in n-dimensional euclidean space may be generated by euclidean motion of a s-plane A_s. For this one-parametric family {A_s} the curve of striction is defined and the following theorems are proved:

1. The generators A_s are parallel along the curve of striction, i.e. the multivectors representing A_s form a parallel vector field along the curve of striction.
2. If the curve of striction is geodesic on {A_s}, it is also an isogonal trajectory of the family of generators {A_s}.