Rothe's method to strongly damped wave equations

A strongly damped wave equation is studied as an abstract differential equation in a Banach space. Existence and uniqueness of a strong solution is established with the help of Rothe's method.     

On the space of quadruples of quinary alternating forms

We discuss some aspects of the invariant theory and arithmetic of the prehomogeneous vector space of quadruples of quinary alternating forms. In particular, we complete the explicit construction of all prehomogeneous covariants of this space and give the rational classification of maximal singular orbits.     

Possible new interactions of neutrino and the KATRIN experiment

We analyse the possible role of new interactions of neutrino in the forthcoming tritium beta decay experiment KATRIN aimed at detecting the neutrino mass with the sensitivity of 0.3–0.2 eV. It is shown that under certain circumstances the standard procedure of data analysis would have to be modified by the introduction of an extra parameter describing the strength of the new interactions. Our model simulations show that the modified procedure may improve the quality of the fit compared with the standard case. Ignoring the possibility of new interactions may lead to a systematic error in the neutrino mass determination.     

Existence, stability and structure of a hexagonal phase doped with nanoparticles

We describe and study by small-angle X-ray scattering (SAXS) a new type of hybrid system. It is composed of a swollen lyotropic hexagonal phase into the cylinders of which solid magnetic particles of nanometric size have been incorporated. It has been found to be stable for volume fractions of particles up to 2% provided the cylinders are sufficiently large. A unidimensionnal magnetic liquid is thus realized. The structural properties of this colloidal assembly have been investigated by SAXS, and the specific features of the scattering spectra are analysed and interpreted. One of the remarkable results is the evidence of depletion interactions between the particles and the inner walls of the cylinders inside which particles are located. Received: 4 September 1997 / Revised: 14 October 1997 / Accepted: 19 November 1997     

Some functional inequalities and their Baire category properties

Summary In the paper we consider, from a topological point of view, the set of all continuous functionsf:I I for which the unique continuous solution:I – [0, ) of(f(x)) (x, (x)) and(x, (x)) (f(x)) (x, (x)), respectively, is the zero function. We obtain also some corollaries on the qualitative theory of the functional equation(f(x)) = g(x, (x)). No assumption on the iterative behaviour off is imposed.     

The Wiener-Hopf method for systems of pseudodifferential equations with an application to crack problems

The aim of this paper is to develop the Wiener-Hopf method for systems of pseudo-differential equations with non-constant coefficients and to apply it to the describtion of the asymptotic behaviour of solutions to boundary integral equations for crack problems when a crack occurs in a linear anisotropic elastic medium. The method was suggested in [15] for scalar pseudo-differential equations with constant coefficients and applied in [7] to the crack problems in the isotropic case. The existence and a-priori smoothness of solutions for the anisotropic case has been proved in [11, 12], while the isotropic case has been treated earlier in [7, 25, 41, 50]. Our results improve even those for the isotropic case obtained in [7, 50]. Asymptotic estimates for the behaviour of solutions in the anisotropic case have been obtained in [28] by a different method.In memoriam, dedicated to Professor Dr. V.D. Kupradze on the occasion of the 90th anniversary of his birthThis work was carried out during the first author's visit in Stuttgart in 1992 and supported by the DFG priority research programme Boundary Element Methods within the guest-programme We-659/19-2.     

A sandwich theorem and Hyers—Ulam stability of affine functions

It is shown that two real functionsf andg, defined on a real intervalI, satisfy the inequalitiesf(x + (1 – )y) g(x) + (1 – )g(y) andg(x + (1 – )y) f(x) + (1 – )f(y) for allx, y I and [0, 1], iff there exists an affine functionh: I such thatf h g. As a consequence we obtain a stability result of Hyers—Ulam type for affine functions.     

NMR Spectral Assignment of Per-substituted Key-Intermediates of β-Cyclodextrin and Implications in the Structures of the Derivatives

The compounds, 6-per-O-(t-butyldimethylsilyl)--cyclodextrin(1), 2,3-per-O-benzyl-6-per-O-(t-butyldimethylsilyl)--cyclodextrin(2), 2,3-per-O-benzyl--cyclodextrin (3),2,3,6-per-O-benzyl--cyclodextrin (4),2,3,6-per-O-benzoyl--cyclodextrin (5), are used as keyintermediates in the synthesis of selectively substituted -CD derivatives. Simple and assignable ¹H and ¹³C NMR spectra (chemical shifts and coupling constants) were obtained for compounds1–4 indicating C₇ symmetry, ⁴C₁ glucose conformation and major arrangement of H6, H6' atoms at the primary side. The derivative 5, however, gave very broad peaksat room temperature. The peaks could partially be assigned at 270 K, but the broadening was still present at 220 K. This implies that there exist several conformers of similar energyand C₁ symmetry that continuously interchange, since there is not a single type of stabilizing interaction thatpredominates. We attributed this phenomenon to the presence of the carbonyl group, which probablydisfavors - stacking and induces random arrangements of the aromatic rings.