Semiclassical calculation of the recurrence spectra of He Rydberg atom in perpendicular electric and magnetic fields

Closed orbit theory is a semiclassical technique for explaining the spectra of Rydberg atoms in external fields. By developing the closed orbit theory from two degrees of freedom to three non-separable degrees of freedom, we calculated the recurrence spectra of He Rydberg atom in perpendicular electric and magnetic fields. The closed orbits in the corresponding classical system have also been obtained. Fourier transformed spectra of He atoms have allowed direct comparison between the resonance peaks and the scaled action values of closed orbits, whereas the nonhydrogenic resonance can be explained in terms of the new orbits created by the core scattering. The semiclassical result is in good agreement with the quantum spectra, which suggests that our method is correct.     

Closed-form solutions of general second order linear recurrences and applications

Two closed-form solutions of a general second order linear recurrence with variable coefficients are established. The first form is combinatorial in nature and is derived through the use of a set which counts the number of elements which are two units apart. The second form is closely related to continued fractions and is derived through the use of continued fraction-like relation. Several applications including a number of verifications of conjectures produced from the Ramanujan Machine are worked out, which illustrate its versatility in this respect.     

两个投影算子的组合的幂等性

研究了两个交换的投影算子P和Q的组合aP+bQ+cPQ(a≠0,b≠0)的幂等性,并给出了它们的值域与核.利用矩阵的CS-分解研究了两个正交投影算子P和Q的组合aP+bQ+cPQ(a≠0,b≠0)的正交幂等性,证明了只有当两个正交投影算子P与Q交换时,aP+bQ+cPQ才有可能是正交幂等的.这些结果刻画了两个投影算子的一些重要特性.     

Impact of drifts in the ASDEX upgrade upper open divertor using SOLPS-ITER

SOLPS-ITER L-mode-like simulations with the full set of currents and drift velocities activated, and fluid neutrals have been carried out to interpret experimental results obtained in AUG. Drifts are critical to quantitatively reproduce the experimental results; however, simulations without drifts can also reproduce some trends qualitatively. The magnitude and dependence of the peak heat flux onto both targets on the upstream collisionality are, in general, in quantitative agreement within uncertainties with infrared thermography measurements in favourable field direction. The onset of power detachment is observed. In unfavourable toroidal field direction, a more symmetrical inner/outer target solution with regards to the power distribution is predicted, in agreement with experimental observations. However, also in unfavourable toroidal field direction, insufficient power is dissipated in the simulations and therefore q_{peak, inn} is overpredicted by up to a factor of 4 and q_{peak, out} by up to a factor of 1.5. The largest contribution to the sources due to radial transport in the energy balance equation is the radial divergence of the energy flux due to V_{E × B}.     

Recurrence of Ancestral Lines and Offspring Trees in Time Stationary Branching Populations

For time stationary Galton- Watson-branching populations on a general type space, the structure of the “individually positive recurrent part” of the system is described: its building blocks consist of finitely many “clans” with positive recurrent trunks. Conditions are given when this nubsystem is void, and when it equals the full system. In addition, positive recurrence on the clan level is characterized. Whereas individual positive recurrence turns out to be a symmetric concept with respect to forward and backward time direction (i. e., with respect to anceatral lines and offspring trees), with individual null recurrence this symmetry can fail even in the absence of branching, i.e., for independently migrating particle systems (Example 13.1). For discrete type spaces a classification of types as to the various individual recurrence concepts (positive, null, forward and backward in time) is proposed and illustrated by a couple of results and examples. For finite type spaces conditiom on the branching dynamics and its mean matrix for the existence of nontrivial equilibria are given.     

Statistical issues in measurement

Measurement theories are traditionally couched in algebraic terms, which makes them unsuitable for statistical testing. A probabilistic recasting of these theories is proposed here. It is observed then that an axiom of probabilistic measurement has typically the form of a logical polynomial, the structure of which induces a particular partition of the parameter space, giving rise to a calss of statistical problems for which the null hypothesis is a union of convex polyhedrons. This is a consequence of the fact that a logical polynomial can always be rewritten in normal form, that is, as a disjunction of conjunctions. A likelihood ratio method is worked out in a couple of exemplary cases. One of these examples provides a test of transitivity, a property which lies at the heart of ordinal measurement.     

On Gauss-Type Quadrature Rules

Some Gauss-type Quadrature rules over [0, 1], which involve values and/or the derivative of the integrand at 0 and/or 1, are investigated. Our work is based on the orthogonal polynomials with respect to linear weight function ω(t): = 1 ? t over [0, 1]. These polynomials are also linked with a class of recently developed “identity-type functions”. Along the lines of Golub's work, the nodes and weights of the quadrature rules are computed from Jacobi-type matrices with simple rational entries. Computational procedures for the derived rules are tested on different integrands. The proposed methods have some advantage over the respective Gauss-type rules with respect to the Gauss weight function ω(t): = 1 over [0, 1].     

Hamel‐isomorphic images of the unit ball

In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ?² and ?. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non‐measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non‐measurable (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Network Dynamics in Elemental Assimilation and Metabolism

Metabolism and physiology frequently follow non-linear rhythmic patterns which are reflected in concepts of homeostasis and circadian rhythms, yet few biomarkers are studied as dynamical systems. For instance, healthy human development depends on the assimilation and metabolism of essential elements, often accompanied by exposures to non-essential elements which may be toxic. In this study, we applied laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) to reconstruct longitudinal exposure profiles of essential and non-essential elements throughout prenatal and early post-natal development. We applied cross-recurrence quantification analysis (CRQA) to characterize dynamics involved in elemental integration, and to construct a graph-theory based analysis of elemental metabolism. Our findings show how exposure to lead, a well-characterized toxicant, perturbs the metabolism of essential elements. In particular, our findings indicate that high levels of lead exposure dysregulate global aspects of metabolic network connectivity. For example, the magnitude of each element’s degree was increased in children exposed to high lead levels. Similarly, high lead exposure yielded discrete effects on specific essential elements, particularly zinc and magnesium, which showed reduced network metrics compared to other elements. In sum, this approach presents a new, systems-based perspective on the dynamics involved in elemental metabolism during critical periods of human development.