A Partial Proof of Bertrand's Theorem

In this paper, we provide a thorough proof of most of Bertrand's Theorem. Using Arnold's book "Mathematical methods of classical mechanics" as a backbone and calculus methods demonstrated by Jovanović in his article "A note on the proof of Bertrand's theorem," we show that for masses in a central field with bounded orbits, closed orbits are restricted to central forces obeying a power law. This paper covers a subset of all possible power laws, leading to the conclusion that only Newton's Law of gravitation and Hooke's Law provide closed, bounded orbits.Key Words: Mathematics, Calculus, Physics, Classical Mechanics, Two-Body Proble

Neutron Capture Cross Sections for the Weak s Process

In past decades a lot of progress has been made towards understanding the main s-process component that takes place in thermally pulsing Asymptotic Giant Branch (AGB) stars. During this process about half of the heavy elements, mainly between 90<=A<=209 are synthesized. Improvements were made in stellar modeling as well as in measuring relevant nuclear data for a better description of the main s process. The weak s process, which contributes to the production of lighter nuclei in the mass range 56<=A<=90 operates in massive stars (M>=8Msolar) and is much less understood. A better characterization of the weak s component would help disentangle the various contributions to element production in this region. For this purpose, a series of measurements of neutron-capture cross sections have been performed on medium-mass nuclei at the 3.7-MV Van de Graaff accelerator at FZK using the activation method. Also, neutron captures on abundant light elements with A<56 play an important role for s-process nucleosynthesis, since they act as neutron poisons and affect the stellar neutron balance. New results are presented for the (n,g) cross sections of 41K and 45Sc, and revisions are reported for a number of cross sections based on improved spectroscopic information

Trans-rectal ultrasound-coupled near-infrared optical tomography of the prostate. Part I: Simulation

We investigate the feasibility of trans-rectal optical tomography of the prostate using an endo-rectal near-infrared (NIR) applicator that is to be integrated with a trans-rectal ultrasound (TRUS) probe. Integration with TRUS ensures accurate endo-rectal positioning of the NIR applicator and the utility of using TRUS spatial prior information to guide NIR image reconstruction. The prostate NIR image reconstruction is challenging even with the use of spatial prior owing to the anatomic complexity of the imaging domain. A hierarchical reconstruction algorithm is developed that implements cascaded initial-guesses for nested domains. This hierarchical image reconstruction method is then applied to evaluating a number of NIR applicator designs for integration with a sagittal TRUS transducer. A NIR applicator configuration feasible for instrumentation development is proposed that contains one linear array of optodes on each lateral side of the sagittal TRUS transducer. The performance of this NIR applicator is characterized for the recovery of single tumor mimicking lesion as well as dual targets in the prostate. The results suggest a strong feasibility of transrectal prostate imaging by use of the endo-rectal NIR/US probe.Electrical and Computer Engineerin

EUV spectra of highly-charged ions W54+^{54+}-W63+^{63+} relevant to ITER diagnostics

We report the first measurements and detailed analysis of extreme ultraviolet (EUV) spectra (4 nm to 20 nm) of highly-charged tungsten ions W$^{54+}$ to W$^{63+}$ obtained with an electron beam ion trap (EBIT). Collisional-radiative modelling is used to identify strong electric-dipole and magnetic-dipole transitions in all ionization stages. These lines can be used for impurity transport studies and temperature diagnostics in fusion reactors, such as ITER. Identifications of prominent lines from several W ions were confirmed by measurement of isoelectronic EUV spectra of Hf, Ta, and Au. We also discuss the importance of charge exchange recombination for correct description of ionization balance in the EBIT plasma.Comment: 11 pages, 4 figure

The s Process: Nuclear Physics, Stellar Models, Observations

Nucleosynthesis in the s process takes place in the He burning layers of low mass AGB stars and during the He and C burning phases of massive stars. The s process contributes about half of the element abundances between Cu and Bi in solar system material. Depending on stellar mass and metallicity the resulting s-abundance patterns exhibit characteristic features, which provide comprehensive information for our understanding of the stellar life cycle and for the chemical evolution of galaxies. The rapidly growing body of detailed abundance observations, in particular for AGB and post-AGB stars, for objects in binary systems, and for the very faint metal-poor population represents exciting challenges and constraints for stellar model calculations. Based on updated and improved nuclear physics data for the s-process reaction network, current models are aiming at ab initio solution for the stellar physics related to convection and mixing processes. Progress in the intimately related areas of observations, nuclear and atomic physics, and stellar modeling is reviewed and the corresponding interplay is illustrated by the general abundance patterns of the elements beyond iron and by the effect of sensitive branching points along the s-process path. The strong variations of the s-process efficiency with metallicity bear also interesting consequences for Galactic chemical evolution.Comment: 53 pages, 20 figures, 3 tables; Reviews of Modern Physics, accepte

Endocrine resistance in breast cancer: new roles for ErbB3 and ErbB4

Endocrine resistance is a major limitation to the successful treatment of estrogen receptor-positive (ER+) breast cancer, and the EGFR (epidermal growth factor receptor) and ErbB-2 receptor tyrosine kinases are involved in this process. A recent study now implicates the other two ErbB family members, ErbB-3 and -4. Exposure of ER+ breast cancer cells to the pure antiestrogen, fulvestrant, increased levels of ErbB-3 or ErbB-4 and sensitivity to the growth-stimulatory effects of heregulin ݱ, a potent ligand for these receptors. Thus, the initial growth-inhibitory effects of fulvestrant appear compromised by cellular plasticity that allows rapid compensatory growth stimulation via ErbB-3/4. Further evaluation of pan-ErbB receptor inhibitors in endocrine-resistant disease appears warranted

State-resolved valence shell photoionization of Be-like ions: experiment and theory

High-resolution photoionization experiments were carried out using beams of Be-like C$^{2+}$, N$^{3+}$, and O$^{4+}$ ions with roughly equal populations of the $^1$S ground-state and the $^3$P$^o$ manifold of metastable components. The energy scales of the experiments are calibrated with uncertainties of 1 to 10 meV depending on photon energy. Resolving powers beyond 20,000 were reached allowing for the separation of contributions from the individual metastable $^3$P$^o_0$, $^3$P$^o_1$, and $^3$P$^o_2$ states. The measured data compare favourably with semi-relativistic Breit-Pauli R-matrixComment: 23 figures and 3 table

A layering model for superconductivity in the borocarbides

We propose a superlattice model to describe superconductivity in layered materials, such as the borocarbide families with the chemical formul\ae\ $RT_2$B$_2$C and $RT$BC, with $R$ being (essentially) a rare earth, and $T$ a transition metal. We assume a single band in which electrons feel a local attractive interaction (negative Hubbard-$U$) on sites representing the $T$B layers, while U=0 on sites representing the $R$C layers; the multi-band structure is taken into account minimally through a band offset $\epsilon$. The one-dimensional model is studied numerically through the calculation of the charge gap, the Drude weight, and of the pairing correlation function. A comparison with the available information on the nature of the electronic ground state (metallic or superconducting) indicates that the model provides a systematic parametrization of the whole borocarbide family.Comment: 4 figure

Performance-based financing as a health system reform : mapping the key dimensions for monitoring and evaluation

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