Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems

We give here some negative results in Sturm-Liouville inverse theory, meaning that we cannot approach any of the potentials with $m+1$ integrable derivatives on $\mathbb{R}^+$ by an $\omega$-parametric analytic family better than order of $(\omega\ln\omega)^{-(m+1)}$. Next, we prove an estimation of the eigenvalues and characteristic values of a Sturm-Liouville operator and some properties of the solution of a certain integral equation. This allows us to deduce from [Henkin-Novikova] some positive results about the best reconstruction formula by giving an almost optimal formula of order of $\omega^{-m}$.Comment: 40 page

Additive Nonparametric Reconstruction of Dynamical Systems from Time Series

We present a nonparametric way to retrieve a system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long term predictions. We demonstrate the potential of our approach for a modified chaotic Chua oscillator.Comment: accepted for Phys. Rev. E, Rapid Com

Self-attraction effect and correction on three absolute gravimeters

The perturbations of the gravitational field due to the mass distribution of an absolute gravimeter have been studied. The so called Self Attraction Effect (SAE) is crucial for the measurement accuracy, especially for the International Comparisons, and for the uncertainty budget evaluation. Three instruments have been analysed: MPG-2, FG5-238 and IMPG-02. The SAE has been calculated using a numerical method based on FEM simulation. The observed effect has been treated as an additional vertical gravity gradient. The correction (SAC) to be applied to the computed g value has been associated with the specific height level, where the measurement result is typically reported. The magnitude of the obtained corrections is of order 1E-8 m/s2.Comment: 14 pages, 8 figures, submitted to Metrologi

REMOVABLE SETS FOR LIPSCHITZ HARMONIC FUNCTIONS ON CARNOT GROUPS

Abstract. Let G be a Carnot group with homogeneous dimension Q ≥ 3 and let L be a sub-Laplacian on G. We prove that the critical dimension for removable sets of Lipschitz L-harmonic functions is (Q − 1). Moreover we construct self-similar sets with positive and finite H Q−1 measure which are removable. 1

On the problems of creating a nuclear-optical frequency standard based on 229Th

The most probable candidate for the role of a nuclear optical standard is the 8.338-eV isomer of the 229mTh isotope of the thorium nucleus. Ways of using the resonance properties of the electron shell as an optical resonator to create laser-nuclear technologies necessary for the optical pumping of nuclear isomers and other manipulations of atomic nuclei leading to the creation of a next-generation frequency standard and nuclear-optical clocks based on them are discussed. Deep relations between the physics of resonance electron-nuclear interactions and the true solution of the thorium puzzle are shown. The article discusses important principles of resonant optical pumping, such as the presence of a finite width in the intermediate electronic state, and others that are usually overlooked with a fatal result for the experiment. The wide application of the various physics of these processes will predetermine a revolutionary leap in the development of new laser-nuclear technologies.Comment: 9 pages, 3 figures, submitted to the Proceedings of KVNO-202

CCM – IAG Strategy for Metrology in Absolute Gravimetry: Role of CCM and IAG

The President of the Consultative Committee for Mass and related quantities (CCM) and the President of the International Association of Geodesy (IAG) Commission 2 «Gravity Field» met on March 21, 2013 with the objective to better coordinate the work at the level of both organizations. It was decided to prepare a common strategic document to be used by their respective Working Groups (WG), Sub-commission (SC) and Joint Working Groups (JWG) to clarify future activities and to develop an action plan.The main objective is to define and to harmonize the activities in order to ensure traceability to the SI for gravity measurements at the highest level for metrology and geodesy with-in the framework of the CIPM Mutual Recognition Arrangement (CIPM MRA