Inverse problems for Sturm-Liouville equations with boundary conditions linearly dependent on the spectral parameter from partial information

[[abstract]]Abstract.In this paper, we study the inverse spectral problems for Sturm–Liouville equations with boundary conditions linearly dependent on the spectral parameter and show that the potential of such problem can be uniquely determined from partial information on the potential and parts of two spectra, or alternatively, from partial information on the potential and a subset of pairs of eigenvalues and the normalization constants of the corresponding eigenvalues.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[booktype]]電子版[[countrycodes]]DE

A quadratic upper bound on the size of a synchronizing word in one-cluster automata

International audienceČerný’s conjecture asserts the existence of a synchronizing word of length at most (n-1)² for any synchronized n-state deterministic automaton. We prove a quadratic upper bound on the length of a synchronizing word for any synchronized n-state deterministic automaton satisfying the following additional property: there is a letter a such that for any pair of states p, q, one has p·a^r=q·a^s for some integers r, s (for a state p and a word w, we denote by p·w the state reached from p by the path labeled w). As a consequence, we show that for any finite synchronized prefix code with an n-state decoder, there is a synchronizing word of length O(n²). This applies in particular to Huffman codes

Fusion Energy-Production from a Deuterium-Tritium Plasma in the Jet Tokamak

The paper describes a series of experiments in the Joint European Torus (JET), culminating in the first tokamak discharges in deuterium-tritium fuelled mixtures. The experiments were undertaken within limits imposed by restrictions on vessel activation and tritium usage. The objectives were: (i) to produce more than one megawatt of fusion power in a controlled way; (ii) to validate transport codes and provide a basis for accurately predicting the performance of deuterium-tritium plasma from measurements made in deuterium plasmas; (iii) to determine tritium retention in the torus systems and to establish the effectiveness of discharge cleaning techniques for tritium removal; (iv) to demonstrate the technology related to tritium usage; and (v) to establish safe procedures for handling tritium in compliance with the regulatory requirements. A single-null X-point magnetic configuration, diverted onto the upper carbon target, with reversed toroidal magnetic field was chosen. Deuterium plasmas were heated by high power, long duration deuterium neutral beams from fourteen sources and fuelled also by up to two neutral beam sources injecting tritium. The results from three of these high performance hot ion H-mode discharges are described: a high performance pure deuterium discharge; a deuterium-tritium discharge with a 1% mixture of tritium fed to one neutral beam source; and a deuterium-tritium discharge with 100% tritium fed to two neutral beam sources. The TRANSP code was used to check the internal consistency of the measured data and to determine the origin of the measured neutron fluxes. In the best deuterium-tritium discharge, the tritium concentration was about 11% at the time of peak performance, when the total neutron emission rate was 6.0 x 10(17) neutrons/s. The integrated total neutron yield over the high power phase, which lasted about 2 s, was 7.2 x 10(17) neutrons, with an accuracy of +/- 7%. The actual fusion amplification factor, Q(DT), was about 0.15. With an optimum tritium concentration, this pulse would have produced a fusion power of almost-equal-to 5 MW and a nominal Q(DT) almost-equal-to 0.46. The same extrapolation for the pure deuterium discharge would have given almost-equal-to 11 MW and a nominal Q(DT) = 1.14, so that the total fusion power (neutrons and alpha-particles) would have exceeded the total losses in the equivalent deuterium-tritium discharge in these transient conditions. Techniques for introducing, tracking, monitoring and recovering tritium were demonstrated to be highly effective: essentially all of the tritium introduced into the neutral beam system and, so far, about two thirds of that introduced into the torus have been recovered