A priori estimates for the Hill and Dirac operators

Consider the Hill operator $Ty=-y''+q'(t)y$ in $L^2(\R)$, where $q\in L^2(0,1)$ is a 1-periodic real potential. The spectrum of $T$ is is absolutely continuous and consists of bands separated by gaps \g_n,n\ge 1 with length |\g_n|\ge 0. We obtain a priori estimates of the gap lengths, effective masses, action variables for the KDV. For example, if \m_n^\pm are the effective masses associated with the gap \g_n=(\l_n^-,\l_n^+), then |\m_n^-+\m_n^+|\le C|\g_n|^2n^{-4} for some constant $C=C(q)$ and any $n\ge 1$. In order prove these results we use the analysis of a conformal mapping corresponding to quasimomentum of the Hill operator. That makes possible to reformulate the problems for the differential operator as the problems of the conformal mapping theory. Then the proof is based on the analysis of the conformal mapping and the identities. Moreover, we obtain the similar estimates for the Dirac operator

Banking in the Eastern neighbours and Central Asia: Challenges and opportunities

This study examines the opportunities for growth in the banking sector in the ENCA region and discusses the challenges involved in providing an enabling environment for the development of the private sector. The banking sector has a key role to play as faster growth and economic diversification will require more activity in the small corporate and SME sectors.In dieser Studie werden die Wachstumsaussichten für den Bankensektor in den östlichen Nachbarländern und in Zentralasien untersucht und die Schwierigkeiten erörtert, die sich bei der Schaffung eines günstigen Umfelds für die Entwicklung des privaten Sektors ergeben. Der Bankensektor spielt dabei eine Schlüsselrolle, da ein rasches Wachstum und die wirtschaftliche Diversifizierung eine Ausweitung der Finanzierungstätigkeit im KMU-Sektor erfordern

Sensitivity of p-Process Nucleosynthesis to Nuclear Reaction Rates in a 25 Solar Mass Supernova Model

The astrophysical p process, which is responsible for the origin of the proton rich stable nuclei heavier than iron, was investigated using a full nuclear reaction network for a type II supernova explosion when the shock front passes through the O/Ne layer. Calculations were performed with a multi-layer model adopting the seed of a pre-explosion evolution of a 25 solar mass star. The reaction flux was calculated to determine the main reaction path and branching points responsible for synthesizing the proton rich nuclei. In order to investigate the impact of nuclear reaction rates on the predicted p-process abundances, extensive simulations with different sets of collectively and individually modified neutron-, proton-, alpha-capture and photodisintegration rates have been performed. These results are not only relevant to explore the nuclear physics related uncertainties in p-process calculations but are also important for identifying the strategy and planning of future experiments.Comment: 27 pages, 24 figures, accepted for publication in ApJ

Analytic and Reidemeister torsion for representations in finite type Hilbert modules

For a closed Riemannian manifold we extend the definition of analytic and Reidemeister torsion associated to an orthogonal representation of fundamental group on a Hilbert module of finite type over a finite von Neumann algebra. If the representation is of determinant class we prove, generalizing the Cheeger-M\"uller theorem, that the analytic and Reidemeister torsion are equal. In particular, this proves the conjecture that for closed Riemannian manifolds with positive Novikov-Shubin invariants, the L2 analytic and Reidemeister torsions are equal.Comment: 78 pages, AMSTe

Measurement of the Ge 70 (n,γ) cross section up to 300 keV at the CERN n-TOF facility

©2019 American Physical Society.Neutron capture data on intermediate mass nuclei are of key importance to nucleosynthesis in the weak component of the slow neutron capture processes, which occurs in massive stars. The (n,γ) cross section on Ge70, which is mainly produced in the s process, was measured at the neutron time-of-flight facility n-TOF at CERN. Resonance capture kernels were determined up to 40 keV neutron energy and average cross sections up to 300 keV. Stellar cross sections were calculated from kT=5 keV to kT=100 keV and are in very good agreement with a previous measurement by Walter and Beer (1985) and recent evaluations. Average cross sections are in agreement with Walter and Beer (1985) over most of the neutron energy range covered, while they are systematically smaller for neutron energies above 150 keV. We have calculated isotopic abundances produced in s-process environments in a 25 solar mass star for two initial metallicities (below solar and close to solar). While the low metallicity model reproduces best the solar system germanium isotopic abundances, the close to solar model shows a good global match to solar system abundances in the range of mass numbers A=60-80.Peer reviewedFinal Published versio

A high resolution VLT/FLAMES study of individual stars in the centre of the Fornax dwarf spheroidal galaxy

For the first time we show the detailed late-stage chemical evolution history of small nearby dwarf spheroidal galaxy in the Local Group. We present the results of a high resolution (R$\sim$20000) FLAMES/GIRAFFE abundance study at ESO/VLT of 81 photometrically selected red giant branch stars in the central 25$'$ of the Fornax dwarf spheroidal galaxy. We present abundances of \alfe\ (Mg, Si, Ca and Ti), iron-peak elements (Fe, Ni and Cr) and heavy elements (Y, Ba, La, Nd and Eu). Our sample was randomly selected, and is clearly dominated by the younger and more metal rich component of Fornax which represents the major fraction of stars in the central region. This means that the majority of our stars are 1$-$4 Gyr old, and thus represent the end phase of chemical evolution in this system. Our sample of stars has unusually low [$\alpha$/Fe], [Ni/Fe] and [Na/Fe] compared to the Milky Way stellar populations at the same [Fe/H]. The particularly important role of stellar winds from low metallicity AGB stars in the creation of s-process elements is clearly seen from the high [Ba/Y]. Furthermore, we present evidence for an s-process contribution to Eu.Comment: 40 pages, 20 figures, accepted for publication in A&

A simple blood test expedites the diagnosis of GLUT1 deficiency syndrome

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Wild redfronted lemurs (Eulemur rufifrons) use social information to learn new foraging techniques

Recent research has claimed that traditions are not a unique feature of human culture, but that they can be found in animal societies as well. However, the origins of traditions in animals studied in the wild are still poorly understood. To contribute comparative data to begin filling this gap, we conducted a social diffusion experiment with four groups of wild redfronted lemurs (Eulemur rufifrons). We used a ‘two-option’ feeding box, where these Malagasy primates could either pull or push a door to get access to a fruit reward to study whether and how these two behavioural traits spread through the groups. During a pre-training phase, two groups were presented with boxes in which one technique was blocked, whereas two groups were presented with unblocked boxes. During a subsequent unconstrained phase, all four groups were confronted with unblocked boxes. Nearly half of the study animals were able to learn the new feeding skill and individuals who observed others needed fewer unsuccessful task manipulations until their first successful action. Animals in the two groups with pre-training also discovered the corresponding alternative technique but preferred the seeded technique. Interestingly, animals in the two groups without pre-training discovered both techniques, and one group developed a group preference for one technique whereas the other did not. In all groups, some animals also scrounged food rewards. In conclusion, redfronted lemurs appear to use social information in acquiring a novel task, and animals in at least in one group without training developed a group preference for one technique, indicating that they have the potential to develop behavioural traditions and conformity

Epilepsy in Dcx Knockout Mice Associated with Discrete Lamination Defects and Enhanced Excitability in the Hippocampus

Patients with Doublecortin (DCX) mutations have severe cortical malformations associated with mental retardation and epilepsy. Dcx knockout (KO) mice show no major isocortical abnormalities, but have discrete hippocampal defects. We questioned the functional consequences of these defects and report here that Dcx KO mice are hyperactive and exhibit spontaneous convulsive seizures. Changes in neuropeptide Y and calbindin expression, consistent with seizure occurrence, were detected in a large proportion of KO animals, and convulsants, including kainate and pentylenetetrazole, also induced seizures more readily in KO mice. We show that the dysplastic CA3 region in KO hippocampal slices generates sharp wave-like activities and possesses a lower threshold for epileptiform events. Video-EEG monitoring also demonstrated that spontaneous seizures were initiated in the hippocampus. Similarly, seizures in human patients mutated for DCX can show a primary involvement of the temporal lobe. In conclusion, seizures in Dcx KO mice are likely to be due to abnormal synaptic transmission involving heterotopic cells in the hippocampus and these mice may therefore provide a useful model to further study how lamination defects underlie the genesis of epileptiform activities