On the theory of collective motion in nuclei. III. From Hamiltonian dynamics to vortex-free fluidity

It is assumed that the Hamiltonian for collective motion in nuclei is invariant under the orthogonal group O(n, $\text{R}$). For degenerate orbits in phase space it is shown that the classical Hamiltonian equations reduce to the equations of a vortex-free fluid with a velocity field determined by independent equations of motion.     

Control of continuous sedimentation of ideal suspensions as an initial and boundary value problem

We present the control of continuous sedimentation in an ideal thickener as an initial and boundary value problem and construct the entropy solution.     

Induced product representations of extended Cuntz algebras

Let _H be the extended Cuntz algebra over the Hilbert space H. Since its zero grade part _H⁰ is the C^*-inductive limit of B(H^r), we look for some family of representations on an inductive limit of H^r as r. When such construction is shaped according to the structure of _H⁰, von Neumanns notion of a reference sequence of unit vectors for Hilbert infinite tensor products emerges; after a further Rieffel induction step, a class IPR[H] of representations of _H arises. For any two such representations, we describe explicitly their associated intertwiners. Any two representations in IPR[H] are either disjoint or unitarily equivalent. Actions of the group by translation on sequences of unit vectors are involved, as well as the ideals of .     

The p-chain Spectral Sequence

We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah–Hirzebruch-type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum and Connes and Farrell and Jones to compute algebraic K- and L-groups of group rings and topological K-groups of reduced group C*-algebras.     

Wiener path integrals and the fundamental solution for the Heisenberg Laplacian

In this paper, we present an explicit calculation of the heat kernel, fundamental solution and Schwartz kernel of the resolvent for the Heisenberg Laplacian using Wiener path integrals and their realizations via the Trotter product formula. This also gives another derivation of mehler’s formula.     

CAS-supported multiple representations in elementary linear algebra

Usually the Gaussian algorithm (GA) is presented at school as a method of solving a given system of linear equations by reducing it to a “triangular form”. In contrast to this technically oriented view, I will demonstrate a CAS-supported learning environment which includes a visual representation of GA and an activity-oriented «Gauss-game». This game stresses the concept of elementary matrices and leads directly to a partial, implementation of GA in the form of a «semi-automatic” functional CAS-program. These multiple representation of GA tries to take into consideration the research results on mental representations, to design rich variations of student activities and thereby to lead leading to webbeb concepts around GA. The CAS MuPAD is used.     

Some Characterizations of Ergodic Probability Measures

Let P be a Markov kernel defined on a measurable space (X, ??). A P-ergodic probability is an extreme point of the family of all P-invariant probability measures on ??. Several characterizations of P-ergodic probabilities are given. In particular, for the special case of a topological space X both P-ergodic Baire probabilities and P-ergodic Borel probabilities with additional regularity properties are characterized.     

13C solid state NMR investigation of structural relaxation of the polymer backbone in poly (ethylmethacrylate)

Geometry and time scale of structural relaxation of poly(n-alkylmethacrylates) above the glass transition is studied by temperature dependent one- and two-dimensional 13C-NMR spectroscopy. The geometry of the isotropization of the polymer backbone as deduced from detailed analysis of spectral line shapes is identified as random angular jumps. Analysis of echo decays confirms that at a given temperature this isotropization can adequately be described with a single correlation time. The results are discussed in terms of conformational memory and local structure recently identified in these polymeric glasses.