An approach to nonstandard quantum mechanics

We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to non-relativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the M{\o}ller wave operators and the S-Matrix

Excessive CEO Pay: Background and Policy Approaches

[Excerpt] During the past several decades, average pay for non-management workers has stagnated, after adjustment for inflation, falling slightly since the early 1970s. In contrast, compensation of top corporate executives has risen dramatically. Supporters of current CEO pay levels argue that executive compensation is determined by normal private market bargaining, that rising pay reflects competition for a limited number of qualified candidates, and that even the richest pay packages are a bargain compared with the billions in shareholder wealth that successful CEOs create. Others, however, cite instances in which executive pay appears to be excessive. Some see a social equity problem in which CEO pay is seen to embody a troublesome rise in income and wealth inequality. Others see excessive pay as a form of shareholder abuse made possible by weak corporate governance structures and a lack of clear, comprehensive disclosure of the various components of executive compensation. This report describes the major legislative and regulatory proposals that have sought to remedy these perceived problems. It will be updated as events warrant

Measured limits to contamination of optical surfaces by elastomers in vacuum

We have monitored the reflectivity of mirrors that were exposed to a fluoroelastomer (3M-Fluorel 2176) and a room-temperature vulcanizing silicone rubber (RTV-615) in vacuum. The 95% confidence limit on the decrease of mirror reflectivities was less than 0.35 ppm/week for Fluorel and <0.29 ppm@week for RTV-615

On the origin dependence of multipole moments in electromagnetism

The standard description of material media in electromagnetism is based on multipoles. It is well known that these moments depend on the point of reference chosen, except for the lowest order. It is shown that this "origin dependence" is not unphysical as has been claimed in the literature but forms only part of the effect of moving the point of reference. When also the complementary part is taken into account then different points of reference lead to different but equivalent descriptions of the same physical reality. This is shown at the microscopic as well as at the macroscopic level. A similar interpretation is valid regarding the "origin dependence" of the reflection coefficients for reflection on a semi infinite medium. We show that the "transformation theory" which has been proposed to remedy this situation (and which is thus not needed) is unphysical since the transformation considered does not leave the boundary conditions invariant.Comment: 14 pages, 0 figure

The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering

We calculate the massive two--loop pure singlet Wilson coefficients for heavy quark production in the unpolarized case analytically in the whole kinematic region and derive the threshold and asymptotic expansions. We also recalculate the corresponding massless two--loop Wilson coefficients. The complete expressions contain iterated integrals with elliptic letters. The contributing alphabets enlarge the Kummer-Poincar\'e letters by a series of square-root valued letters. A new class of iterated integrals, the Kummer-elliptic integrals, are introduced. For the structure functions $F_2$ and $F_L$ we also derive improved asymptotic representations adding power corrections. Numerical results are presented.Comment: 42, pages Latex, 8 Figure

Persistence-driven durotaxis: Generic, directed motility in rigidity gradients

Cells move differently on substrates with different elasticities. In particular, the persistence time of their motion is higher on stiffer substrates. We show that this behavior will result in a net transport of cells directed up a soft-to-stiff gradient. Using simple random walk models with controlled persistence and stochastic simulations, we characterize this propensity to move in terms of the durotactic index measured in experiments. A one-dimensional model captures the essential features of this motion and highlights the competition between diffusive spreading and linear, wavelike propagation. Since the directed motion is rooted in a non-directional change in the behavior of individual cells, the motility is a kinesis rather than a taxis. Persistence-driven durokinesis is generic and may be of use in the design of instructive environments for cells and other motile, mechanosensitive objects.Comment: 5 pages, 4 figure

The O(α2)O(\alpha^2) Initial State QED Corrections to e+e−e^+e^- Annihilation to a Neutral Vector Boson Revisited

We calculate the non-singlet, the pure singlet contribution, and their interference term, at $O(\alpha^2)$ due to electron-pair initial state radiation to $e^+ e^-$ annihilation into a neutral vector boson in a direct analytic computation without any approximation. The correction is represented in terms of iterated incomplete elliptic integrals. Performing the limit $s \gg m_e^2$ we find discrepancies with the earlier results of Ref.~\cite{Berends:1987ab} and confirm results obtained in Ref.~\cite{Blumlein:2011mi} where the effective method of massive operator matrix elements has been used, which works for all but the power corrections in $m^2/s$. In this way, we also confirm the validity of the factorization of massive partons in the Drell-Yan process. We also add non-logarithmic terms at $O(\alpha^2)$ which have not been considered in \cite{Berends:1987ab}. The corrections are of central importance for precision analyzes in $e^+e^-$ annihilation into $\gamma^*/Z^*$ at high luminosity.Comment: 4 pages Latex, 2 Figures, several style file

Development of new molecular markers for phylogeny and molecular identification of arbuscular mycorrhizal fungi (glomeromycota)

The RPB1 gene was analyzed as a possible new nuclear-encoded molecular marker for the Glomeromycota. New Glomus group A-specific primers were designed and successfully tested on several members of this group. No evidence for genetic variability was found within the isolates. Based on the new RPB1 sequences, phylogenetic analyses were performed. The phylum-level phylogeny of the fungi was very well resolved by protein sequence analyses. The Glomeromycota were recovered as a monophyletic group, with the Mortierellales (Zygomycota) as closest relatives. A symbiomycotan clade (Asco-, Basidio and Glomeromycota) was not supported in the RPB1 phylogeny whereas the "Dicaryomycota" (Asco- and Basidiomycota) were supported in the trees. The morphospecies-level RPB1 phylogeny of Glomus group A performed best using nucleotide sequences. Interestingly, Geosiphon pyriformis was determined to be the most deeply-diverging lineage of the Glomeromycota. However, RPB1 sequences of representatives of the remaining families are needed for for a comprehensive phylogeny of glomeromycotan fungi. All members of the Glomeromycota contained an intron at the same location in their RPB1 gene. This sequence region seems to be ideal for molecular species identification using restriction analysis in community studies of the AMF in the future

Movement Matters! Understanding the Developmental Trajectory of Embodied Planning

Human motor skills are exceptional compared to other species, no less than their cognitive skills. In this perspective paper, we suggest that “movement matters!,” implying that motor development is a crucial driving force of cognitive development, much more impactful than previously acknowledged. Thus, we argue that to fully understand and explain developmental changes, it is necessary to consider the interaction of motor and cognitive skills. We exemplify this argument by introducing the concept of “embodied planning,” which takes an embodied cognition perspective on planning development throughout childhood. From this integrated, comprehensive framework, we present a novel climbing paradigm as the ideal testbed to explore the development of embodied planning in childhood and across the lifespan. Finally, we outline future research directions and discuss practical applications of the work on developmental embodied planning for robotics, sports, and education