Qualitative features of periodic solutions of KdV

In this paper we prove new qualitative features of solutions of KdV on the circle. The first result says that the Fourier coefficients of a solution of KdV in Sobolev space $H^N,\, N\geq 0$, admit a WKB type expansion up to first order with strongly oscillating phase factors defined in terms of the KdV frequencies. The second result provides estimates for the approximation of such a solution by trigonometric polynomials of sufficiently large degree

Addition theorems and the Drach superintegrable systems

We propose new construction of the polynomial integrals of motion related to the addition theorems. As an example we reconstruct Drach systems and get some new two-dimensional superintegrable Stackel systems with third, fifth and seventh order integrals of motion.Comment: 18 pages, the talk given on the conference "Superintegrable Systems in Classical and Quantum Mechanics", Prague 200

Nekhoroshev theorem for the periodic Toda lattice

The periodic Toda lattice with $N$ sites is globally symplectomorphic to a two parameter family of $N-1$ coupled harmonic oscillators. The action variables fill out the whole positive quadrant of $\R^{N-1}$. We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) all parts of phase space.Comment: 28 page

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

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

Adding cetuximab to capecitabine plus oxaliplatin (XELOX) in first-line treatment of metastatic colorectal cancer: a randomized phase II trial of the Swiss Group for Clinical Cancer Research SAKK

Background: To determine the activity and tolerability of adding cetuximab to the oxaliplatin and capecitabine (XELOX) combination in first-line treatment of metastatic colorectal cancer (MCC). Patients and methods: In a multicenter two-arm phase II trial, patients were randomized to receive oxaliplatin 130 mg/m2 on day 1 and capecitabine 1000 mg/m2 twice daily on days 1-14 every 3 weeks alone or in combination with standard dose cetuximab. Treatment was limited to a maximum of six cycles. Results: Seventy-four patients with good performance status entered the trial. Objective partial response rates after external review and radiological confirmation were 14% and 41% in the XELOX and in the XELOX + Cetuximab arm, respectively. Stable disease has been observed in 62% and 35% of the patients, with 76% disease control in both arms. Cetuximab led to skin rash in 65% of the patients. The median overall survival was 16.5 months for arm A and 20.5 months for arm B. The median time to progression was 5.8 months for arm A and 7.2 months for arm B. Conclusion: Differences in response rates between the treatment arms indicate that cetuximab may improve outcome with XELOX. The correct place of the cetuximab, oxaliplatin and fluoropyrimidine combinations in first-line treatment of MCC has to be assessed in phase III trial

Stress-Induced Premature Senescence Related to Oxidative Stress in the Developmental Programming of Nonalcoholic Fatty Liver Disease in a Rat Model of Intrauterine Growth Restriction.

Metabolic syndrome (MetS) refers to cardiometabolic risk factors, such as visceral obesity, dyslipidemia, hyperglycemia/insulin resistance, arterial hypertension and non-alcoholic fatty liver disease (NAFLD). Individuals born after intrauterine growth restriction (IUGR) are particularly at risk of developing metabolic/hepatic disorders later in life. Oxidative stress and cellular senescence have been associated with MetS and are observed in infants born following IUGR. However, whether these mechanisms could be particularly associated with the development of NAFLD in these individuals is still unknown. IUGR was induced in rats by a maternal low-protein diet during gestation versus. a control (CTRL) diet. In six-month-old offspring, we observed an increased visceral fat mass, glucose intolerance, and hepatic alterations (increased transaminase levels, triglyceride and neutral lipid deposit) in male rats with induced IUGR compared with the CTRL males; no differences were found in females. In IUGR male livers, we identified some markers of stress-induced premature senescence (SIPS) (lipofuscin deposit, increased protein expression of p21 <sup>WAF</sup> , p16 <sup>INK4a</sup> and Acp53, but decreased pRb/Rb ratio, foxo-1 and sirtuin-1 protein and mRNA expression) associated with oxidative stress (higher superoxide anion levels, DNA damages, decreased Cu/Zn SOD, increased catalase protein expression, increased nfe2 and decreased keap1 mRNA expression). Impaired lipogenesis pathways (decreased pAMPK/AMPK ratio, increased pAKT/AKT ratio, SREBP1 and PPARγ protein expression) were also observed in IUGR male livers. At birth, no differences were observed in liver histology, markers of SIPS and oxidative stress between CTRL and IUGR males. These data demonstrate that the livers of IUGR males at adulthood display SIPS and impaired liver structure and function related to oxidative stress and allow the identification of specific therapeutic strategies to limit or prevent adverse consequences of IUGR, particularly metabolic and hepatic disorders

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

Inverse spectral problems for energy-dependent Sturm-Liouville equations

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.Comment: AMS-LaTeX, 28 page

Nuclear Data from AMS & Nuclear Data for AMS -some examples

We summarize some recent cross-section measurements using accelerator mass spectrometry (AMS). AMS represents an ultra-sensitive technique for measuring a limited, but steadily increasing number of longer-lived radionuclides. This method implies a two-st