Symmetric Gibbs measures

We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of finitely many coordinates). The relations we consider are defined by cocycles taking values in groups, including some nonabelian ones. This generalizes (half of) the identification of the invariant ergodic probability measures for the Pascal adic transformation as exactly the Bernoulli measures---a version of de Finetti's Theorem. Generalizing the other half, we characterize the measures on subshifts of finite type that are invariant under both the adic and the shift as the Gibbs measures whose potential functions depend on only a single coordinate. There are connections with and implications for exchangeability, ratio limit theorems for transient Markov chains, interval splitting procedures, `canonical' Gibbs states, and the triviality of remote sigma-fields finer than the usual tail field

Management of International Cooperation of Japanese and German Universities – Historical Background and Actual Experiences –

Cooperation of universities is increasingly needed in order to educate productive and team-oriented young scholars at Western and Far Eastern Universities. The article refers to the historical background of international university-cooperation in Japan and Germany. The tendency from lagging or parallel research to research cooperation on the university level is pointed out by practical cases. Additionally experiences by research-networks of cooperating universities are pointed out, esp. as for economic research. Concerning teaching the reintegration of research and teaching in cooperating universities is exposed. The conclusions emphasize the actual problem and refer to experiences from university cooperation in Japan and Germany.Meiji Restoration; transformation process-phases of university research; effects of international university cooperation; reintegration of academic research and teaching.

Innovative Management in Subcontracting Business in Growing and Stagnating Economies

The worldwide economic recession demonstrates: innovations are needed to increase productivity and competitivity of enterprises, especially of subcontracting companies. The paper compares the subcontracting business at a boom- and recession-phase, mainly in Japan and Germany. For Japan the components of subcontracting systems are exposed by a static and dynamic view. Changes of subcontracting firms from dependent, but stable suppliers of parts and services to extremely dependent subcontractors are shown for Japan. European subcontracting companies are found being less dependent, or even independent, networking suppliers. The worldwide dynamic view demonstrates: innovative management enables SMEs of former LDCs to compete with subcontracting companies of developed countries. The economic recession, yet, endangers the stability of the subcontracting systems worldwide.new combinations of economic resources – types of subcontracting systems – economic recession – pressure to innovate – new risks and opportunities of subcontracting business.

Schnol's theorem and spectral properties of massless Dirac operators with scalar potentials

The spectra of massless Dirac operators are of essential interest e.g. for the electronic properties of graphene, but fundamental questions such as the existence of spectral gaps remain open. We show that the eigenvalues of massless Dirac operators with suitable real-valued potentials lie inside small sets easily characterised in terms of properties of the potentials, and we prove a Schnol'-type theorem relating spectral points to polynomial boundedness of solutions of the Dirac equation. Moreover, we show that, under minimal hypotheses which leave the potential essentially unrestrained in large parts of space, the spectrum of the massless Dirac operator covers the whole real line; in particular, this will be the case if the potential is nearly constant in a sequence of regions.Comment: 18 page

Spherically symmetric Dirac operators with variable mass and potentials infinite at infinity

We study the spectrum of spherically symmetric Dirac operators in three-dimensional space with potentials tending to infinity at infinity under weak regularity assumptions. We prove that purely absolutely continuous spectrum covers the whole real line if the potential dominates the mass, or scalar potential, term. In the situation where the potential and the scalar potential are identical, the positive part of the spectrum is purely discrete; we show that the negative half-line is filled with purely absolutely continuous spectrum in this case.Comment: 16 pages; submitted to Publ. RIM

Spectral stability of the Coulomb-Dirac Hamiltonian with anomalous magnetic moment

We show that the point spectrum of the standard Coulomb-Dirac operator H_0 is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment H_a as the anomaly parameter tends to 0. For negative angular momentum quantum number kappa, this holds for all Coulomb coupling constants c for which H_0 has a distinguished self-adjoint realisation. For positive kappa, however, there are some exceptional values for c, and in general an index shift between the eigenvalues of H_0 and the limits of eigenvalues of H_a appears, accompanied with additional oscillations of the eigenfunctions of H_a very close to the origin

On the resonances and eigenvalues for a 1D half-crystal with localised impurity

We consider the Schr\"odinger operator $H$ on the half-line with a periodic potential $p$ plus a compactly supported potential $q$. For generic $p$, its essential spectrum has an infinite sequence of open gaps. We determine the asymptotics of the resonance counting function and show that, for sufficiently high energy, each non-degenerate gap contains exactly one eigenvalue or antibound state, giving asymptotics for their positions. Conversely, for any potential $q$ and for any sequences (\s_n)_{1}^\iy, \s_n\in \{0,1\}, and (\vk_n)_1^\iy\in \ell^2, \vk_n\ge 0, there exists a potential $p$ such that \vk_n is the length of the $n$-th gap, $n\in\N$, and $H$ has exactly \s_n eigenvalues and 1-\s_n antibound state in each high-energy gap. Moreover, we show that between any two eigenvalues in a gap, there is an odd number of antibound states, and hence deduce an asymptotic lower bound on the number of antibound states in an adiabatic limit.Comment: 25 page

The HELP inequality on trees

We establish analogues of Hardy and Littlewood's integro-differential equation for Schrödinger-type operators on metric and discrete trees, based on a generalised strong limit-point property of the graph Laplacian