Scaling properties of ℤ k- 1 actions on the circle

We derive universal scaling properties for ^k–1 actions on the circle whose generators have rotation numbers algebraic of degreek. As fork=2 these properties can be explained for arbitraryk in terms of a renormalization group transformation. It has at least one trivial fixed point corresponding to an action whose generators are pure rotations. The spectrum of the linearized transformation in this fixed point is analyzed completely. The fixed point is hyperbolic with a (k–1)-dimensional unstable manifold. In the casek=2 the known results are therefore recovered.     

Transversal designs associated with frobenius groups

To any Frobenius group G (of degree s, with Frobenius complement of order k) we associate an (s,k) -transversal design (G) which admits G as a point-regular collineation group. (G) is in fact also a dual translation net and furthermore admits a flag-regular collineation group. Also, (G) has two orthogonal resolutions. Conversely, we will characterize the Frobenius groups among the point-regular collineation groups of resolvable transversal designs. We also exhibit two further classes of flag-regular transversal designs. Finally, we completely determine the possible parameters of TD's constructed as above.Dedicated to Professor R. Artzy on the occasion of his 70th birthday     

On bounded time-dependent perturbations of operator cosine functions

In this note it is shown that the Cauchy problem associated with the infinitesimal generatorA of a strongly continuous operator cosine function remains uniformly well-posed under bounded time-dependent perturbations ofA.     

Periodische operatorwertige Cosinusfunktionen

In dieser Note werden stark stetige periodische Cosinusfunktionen mit Werten im Bereich der stetigen linearen Operatoren auf einem Banachraum untersucht. Dabei ergänzen und präzisieren wir die Untersuchungen von E. Giusti. Insbesondere wird ein durchsichtiger und vollständiger Beweis eines Satzes von Giusti über die Charakterisierung periodischer Cosinusfunktionen mit Hilfe von Spektraleigenschaften ihres infinitesimalen Erzeugers angegeben.     

Codes Based on Complete Graphs

We consider the problem of embedding the even graphical code based on the complete graph onn vertices into a shortening of a Hamming code of length 2^m-1, wherem = h(n) should be as small as possible. As it turns out, this problem is equivalent to the existence problem for optimal codes with minimum distance 5, and optimal embeddings can always be realized as graphical codes based onK _n. As a consequence, we are able to determineh(n) exactly for alln of the form 2 ^k + 1 and to narrow down the possibilities in general to two or three conceivable values.Dedicated to Hanfried Lenz on the occasion of his 80th birthdayThe research for this note was done while the first author was visiting the University of Waterloo and the University of Rome, respectively. He thanks his colleagues there for their hospitality and also acknowledges the financial support of the Consiglio Nazionale delle Ricerche (Italy). The third author acknowledges the support of the National Science and Engineering Research Council of Canada given under grant #0GP0009258.     

Analysis of electroweak precision data and prospects for future improvements

We update our previous work on an analysis of the electroweak data by including new and partly preliminary data available up to the 1996 summer conferences. The new results on the partial decay widths into and hadrons now offer a consistent interpretation of all data in the minimal standard model. The value extracted for the strong interaction coupling constant agrees well with determinations in other areas. New constraints on the universal parameters , and are obtained from the updated measurements. No signal of new physics is found in the , , analysis once the SM contributions with GeV and those of not a too heavy Higgs boson are accounted for. The naive QCD-like technicolor model is now ruled out at the 99% CL even for the minimal model with . In the absence of a significant new physics effect in the electroweak observables, constraints on masses of the top quark, , and Higgs boson, , are derived as a function of and the QED effective coupling . The preferred range of depends rather strongly on the actual value of : for , while for at 95% CL. Prospects due to forthcoming improved measurements of asymmetries, the mass of the weak boson , and are discussed. Anticipating uncertainties of 0.00020 for , 20 MeV for , and 2 GeV for , the new physics contributions to the , , parameters will be constrained more severely, and, within the SM, the logarithm of the Higgs mass can be constrained to about . The better constraints on , , and on within the minimal SM should be accompanied with matching precision in . Received: 18 June 1997     

Atomistic Simulations of Integranular Fracture in Symmetric-Tilt Grain Boundaries

Fracture experiments on symmetric-tilt grain boundaries in Cu are interpreted using the Peierls-Nabarro continuum model of dislocation nucleation as a starting point. Good agreement is found only when the continuum model is modified according to the results of atomistic simulations. The same experiments are also reproduced by direct Molecular Dynamics simulations of fracture propagation and dislocation emission from a microcrack placed in the interface plane of the symmetric-tilt (221)(221) grain boundary in fcc Cu. Direction-dependent fracture response is observed, namely the microcrack advancing by brittle fracture along the [11 ] direction and being blunted by dislocation emission along the opposite [ 4] direction. Moreover, the simulations allow us to establish important differences with respect to the continuum-model predictions due to the shielding of the stress field at the crack-tip and to the presence of the residual stress at the interface.     

Spectroscopic and atomic force microscopy investigations of hybrid materials composed of fullerenes and 3-aminopropyltrimethoxysilane

Fullerene based materials may open a new horizon in many fields of science. In this study we fabricated thin films of the hybrid materials formed as a result of interactions between C₆₀ fullerenes and 3-aminopropyltrimethoxysilane (APTMS). The deposition technique was a combination of spin-coating and evaporation methods. Interactions within the films were investigated by means of X-ray photoelectron spectroscopy and near edge X-ray absorption fine structure spectroscopy (NEXAFS). Surface morphology was measured by atomic force microscopy (AFM). We found that there are strong chemical reactions between the nucleophilic nitrogen atoms from APTMS and electrophilic fullerene molecules. Results of NEXAFS investigations suggest that due to direct interactions between APTMS and C₆₀ the electronic structure of the fullerene molecules changes while at the same time AFM proved that the C₆₀ molecule diameter is not altered.