Coupled channels approach to the deuteron break-up in the field of a nucleus

The elastic scattering and break-up of the deuteron in the field of a nucleus is formulated in terms of coupled differential equations together with correct boundary conditions. Cross sections for the two processes are given in terms of the scattering coefficients. An approximate treatment of the Coulomb distortion in the break-up channel is suggested.     

Shape change and fast M1 transitions in Kr

A shape transition from a probably asymmetric shape at low excitation to a more axial-symmetric shape above 21/2⁺ has been found in ⁸¹Kr. This shape change and the drastic increase of the M1 transition probabilities above spin 21/2 are attributed to the alignment of two g_9/2 protons.     

Evidence for noncollinearity between surface and bulk magnetization in ultrathin Co films

The magnetization reversal of ultrathin Co films on Cu(001) has been investigated by grazing ion scattering and magneto-optical Kerr effect. Differences in the behavior of surface and bulk magnetization are found and attributed to the reduced coordination and site symmetry at the surface. The reversal behavior of the surface magnetization depends on the chemical surface composition. For pure Co films, the reversal of the bulk magnetization is preceded by a complete reversal of the surface magnetization. A particular magnetic state of the surface is suggested as a precursor for magnetization reversal.     

Folding and unfolding of an elastinlike oligopeptide: "inverse temperature transition," reentrance, and hydrogen-bond dynamics

The temperature-dependent behavior of a solvated oligopeptide, GVG(VPGVG), is investigated. Spectroscopic measurements, thermodynamic measurements, and molecular dynamics simulations find that this elastinlike octapeptide behaves as a two-state system that undergoes an "inverse temperature" folding transition and reentrant unfolding close to the boiling point of water. A molecular picture of these processes is presented, emphasizing changes in the dynamics of hydrogen bonding at the protein/water interface and peptide backbone librational entropy.     

Total and differential cross-sections for the pp\rightarrow pp\eta^\prime reaction near threshold

The -meson production in the reaction has been studied at excess energies of Q = 26.5, 32.5 and 46.6 MeV using the internal beam facility COSY-11 at the cooler synchrotron COSY. The total cross-sections as well as one angular distribution for the highest Q-value are presented. The excitation function of the near-threshold data can be described by a pure s-wave phase space distribution with the inclusion of the proton-proton final-state interaction and Coulomb effects. The obtained angular distribution of the -mesons is also consistent with pure s-wave production.Received: 11 August 2003, Revised: 14 November 2003, Published online: 6 April 2004PACS: 13.60.Le Meson production - 13.75.-n Hadron-induced low- and intermediate-energy reactions and scattering (energy GeV) - 13.85.Lg Total cross-sections - 25.40.-h Nucleon-induced reactions     

Der Zwei-Quadrate-Satz von Fermat - eine Studie zur Heuristik des Beweisens

Dieser Beitrag hat seinen Ursprung in Veranstaltungen zur Heuristik im Rahmen meiner Tätigkeit in der fachdidaktischen Ausbildung von Gymnasiallehrern an der hiesigen RWTH. Mehr und mehr habe ich dabei die Überzeugung gewonnen, dass es notwendig ist, Lehramtskandidaten historische, heuristische und pädagogische Aspekte wichtiger mathematischer Inhalte erfahren zu lassen, die innerhalb der fachlichen Ausbildung nicht oder nicht genügend Berücksichtigung finden können und die aber im Hinblick auf den späteren Beruf wesentlich sind. Es wird hiermit weniger für eine Behandlung des Zwei-Quadrate-Satzes in der Schule - wenngleich sehr erwünscht - plädiert, wohl aber könnte dieses Thema Bestandteil eines fachdidaktischen Seminars oder Proseminars sein. Die Einschränkung im obigen Zitat von Hardy war natürlich eine zusätzliche didaktische Herausforderung. Den Gutachtern danke ich für ihre Ermutigung sowie für zahlreiche Verbesserungsvorschläge und Hinweise auf Unklarheiten und Fehler. Ebenso danke ich Herrn Artmann sehr, der eine frühere Fassung gelesen und konstruktiv kritisiert hat.Einige Grafiken wurden mit der dynamischen Mathematiksoftware GEONExT erzeugt. GEONExT ist unter der Adresse http: //geonext.de frei erhältlich.     

Decomposition Rank of Subhomogeneous C*-Algebras

We analyze the decomposition rank (a notion of covering dimensionfor nuclear C*-algebras introduced by E. Kirchberg and the author)of subhomogeneous C*-algebras. In particular, we show that asubhomogeneous C*-algebra has decomposition rank n if and onlyif it is recursive subhomogeneous of topological dimension n,and that n is determined by the primitive ideal space. As an application, we use recent results of Q. Lin and N. C.Phillips to show the following. Let A be the crossed productC*-algebra coming from a compact smooth manifold and a minimaldiffeomorphism. Then the decomposition rank of A is dominatedby the covering dimension of the underlying manifold. 2000 MathematicsSubject Classification 46L85, 46L35.     

Higher-order energy expansions and spike locations

We consider the following singularly perturbed semilinear elliptic problem: where is a bounded domain in R ^N with smooth boundary , is a small constant and f is some superlinear but subcritical nonlinearity. Associated with (I) is the energy functional defined by where . Ni and Takagi ([29, 30]) proved that for a single boundary spike solution , the following asymptotic expansion holds: where c ₁ > 0 is a generic constant, is the unique local maximum point of and is the boundary mean curvature function at . In this paper, we obtain a higher-order expansion of where c ₂, c ₃ are generic constants and is the scalar curvature at . In particular c ₃ > 0. Some applications of this expansion are given.Received: 14 January 2003, Accepted: 28 July 2003, Published online: 15 October 2003Mathematics Subject Classification (2000): Primary 35B40, 35B45; Secondary 35J25