Topological dynamics of transformations induced on the space of probability measures

LetT be a continuous transformation of a compact metric spaceX. T induces in a natural way a transformationT _M on the spaceM (X) of probability measures onX, and a transformationT _K on the spaceK (X) of closed subsets ofX. This note investigates which of the topological properties ofT∶X→X (like distality, transitivity, mixing property etc. ...) are “inherited” byT _M∶M (X)→M (X) andT _K∶K (X)→K (X).     

Groundstate-calculation for the T-t Jahn-Teller system by an exponential transformation approach

The dynamical T-t Jahn-Teller problem is handled by a canonical exponential transformation exp (- S) H exp (S). The groundstate wavefunction of the diagonal part of H is given in the transformed and original space. Its expectation value for the total Hamiltonian is shown to agree with the exact numerical groundstate results up to intermediate coupling strengths. For strong coupling values the dominant k power still seems to be given correctly. However, in this limiting case exact results can be derived by a second transformation. Both types of transformations lead in a combined form to very accurate groundstate energies, which can be fitted with respect to the given numerical values.     

Occupation dynamics of anE-e Jahn-Teller system

The internal dynamics of a Jahn-Teller system (E-e type) is given. The time-dependent occupation numbers and the energy-transfer between the different uncoupled states are calculated. It is shown that the resonant behaviour of the system, as already known from optical calculations and measurements, manifests itself in the time-dependent occupation probabilities of each single state.     

Dynamical systems under constant organization. III. Cooperative and competitive behavior of hypercycles

Qualitative analysis for a system of differential equations playing an important role in a theory of molecular self-organization.     

Molecular wires acting as coherent quantum ratchets

The effect of laser fields on electron transport through a molecular wire weakly coupled to two leads is investigated. The molecular wire acts as a coherent quantum ratchet if the molecule is composed of periodically arranged, asymmetric chemical groups. This setup presents a quantum rectifier with a finite dc response in the absence of a static bias. The nonlinear current is evaluated in closed form within the Floquet basis of the isolated, driven wire. The current response reveals multiple current reversals together with a nonlinear dependence on the amplitude and the frequency of the laser field. The current saturates for long wires at a nonzero value, while it may change sign upon decreasing its length.     

Resolution of the frozen-charge paradox in stopping of channeled heavy ions

The long-standing problem of the lacking signature of a Barkas effect in the stopping of swift heavy ions under channeling conditions has been analyzed theoretically. The stopping model provides explicit dependences on impact parameter and allows for projectile screening and higher-order Z(1) corrections. The analysis differentiates between principal target shells. A distinct Barkas correction is found in accordance with standard theory. It is less pronounced for channeled than for random stopping because of the dominance of outer target shells. Varying contributions from different target shells to the stopping force may give rise to an inversion of the commonly observed variation with ion energy and charge state of the Barkas correction.     

Bounds on the number of Hadamard designs of even order

A new lower bound on the number of non‐isomorphic Hadamard symmetric designs of even order is proved. The new bound improves the bound on the number of Hadamard designs of order 2n given in [12] by a factor of 8n ? 1 for every odd n > 1, and for every even n such that 4n ? 1 > 7 is a prime. For orders 8, 10, and 12, the number of non‐isomorphic Hadamard designs is shown to be at least 22,478,260, 1.31 × 10¹⁵, and 10²⁷, respectively. For orders 2n = 14, 16, 18 and 20, a lower bound of (4n ? 1)! is proved. It is conjectured that (4n ? 1)! is a lower bound for all orders 2n ≥ 14. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 363‐378, 2001     

Egalitarianism meets ideologies of mathematical education–instances from Norwegian curricula and classrooms

The article starts focusing egalitarianism in a Norwegian curricular context in general and in mathematics education from primary schools to teacher education in particular. It progresses by locating and problematizing some major ideologies in mathematics education such as rationalism, activism, competitivism and ‘autodidactism’ on one hand and egalitarianism on the other. Some results from TIMSS, where Norway differs significantly from other countries, are touched upon and contrasted with episodes from qualitative studies. It is asked, from a general didaktic point of view, whether egalitarian values in mathematics education should be seen as strength or weekness, and the other way round, whether mathematical education contributes to or counterworks egalitarianism in society.