Secret Sharing Schemes with Detection of Cheaters for a General Access Structure

In a secret sharing scheme, some participants can lie about the value of their shares when reconstructing the secret in order to obtain some illicit benefit. We present in this paper two methods to modify any linear secret sharing scheme in order to obtain schemes that are unconditionally secure against that kind of attack. The schemes obtained by the first method are robust, that is, cheaters are detected with high probability even if they know the value of the secret. The second method provides secure schemes, in which cheaters that do not know the secret are detected with high probability. When applied to ideal linear secret sharing schemes, our methods provide robust and secure schemes whose relation between the probability of cheating and the information rate is almost optimal. Besides, those methods make it possible to construct robust and secure schemes for any access structure.     

More compact invariant manifolds appearing in the non-linear coupling of oscillators

Near partially elliptic rest points of generic families of vector fields or transformations, many types of normally hyperbolic invariant compact manifolds can appear, diffeomorphic to intersections of quadrics. To cite this article: M. Chaperon et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

A high-current electron beam ion trap as an on-line charge breeder for the high precision mass measurement TITAN experiment

The precision of atomic mass measurements in a Penning trap is directly proportional to the charge state q of the ion and, hence, can be increased by using highly charged ions (HCI). For this reason, charge breeding with an electron beam ion trap (EBIT) is employed at TRIUMF’s Ion Trap for Atomic and Nuclear science (TITAN) on-line facility in Vancouver, Canada. By bombarding the injected and trapped singly charged ions with an intense beam of electrons, the charge state of the ions is rapidly increased inside the EBIT. To be compatible with the on-line requirements of short-lived isotopes, very high electron beam current densities are needed. The TITAN EBIT includes a 6 Tesla superconducting magnet and is designed to have electron beam currents and energies of up to 5 A and 60 keV, respectively. Once operational at full capacity, most species can be bred into a He-like configuration within tens of ms. Subsequently, the HCI are extracted, pass a Wien filter to reduce isobaric contamination, are cooled, and injected into a precision Penning trap for mass measurement. We will present the first results and current status of the TITAN EBIT, which has recently been moved to TRIUMF after assembly and commissioning at the Max-Planck-Institute (MPI) for Nuclear Physics in Heidelberg, Germany.     

The 1-type of a Waldhausen K-theory spectrum

We give a small functorial algebraic model for the 2-stage Postnikov section of the K-theory spectrum of a Waldhausen category and use our presentation to describe the multiplicative structure with respect to biexact functors.     

A Characterization of Cosmological Time Functions

A characterization of time functions on a spacetime is made by using theMöbius equation. It is shown that a time function characterized in this wayyields past timelike geodesic incompleteness and local Lorentzian warpedproduct decomposition of spacetime, provided that the stress-energy tensoris a fluid. Also, by imposing additional assumptions on the stress-energytensor and global analytic structure of the spacetime, more restrictivedecompositions closer to Robertson–Walker spacetimes are obtained.     

Chromatographic characterization of thermally upgraded products from alternative fuels

An overview is presented of the analytical approaches developed by our research group over the last ten years for analysis of alternative fuel, both biomass and fossil. The alternative fuels are analyzed successively by PLC-8 (preparative liquid chromatography–group-type) fractionation and high resolution gas chromatography. Some of the possibilities for fractionation and characterization of alternative fuels are herein exemplified with sugar cane bagasse pyrolysis products.     

Characterization of high-order harmonic radiation on femtosecond and attosecond time scales

We characterize the temporal structure of high-order harmonic radiation on both the femtosecond and attosecond time scales. The harmonic emission is characterized by mixed-color two-photon ionization with an infrared femtosecond laser using a Mach–Zehnder interferometer where both pump and probe arms travel completely separate paths. In a first experiment, we measure the duration and chirp of individual harmonics. In a second experiment, we resolve, for the first time with this type of setup, the attosecond beating of several harmonics generated under conditions similar to the first experiment. We suggest that the results of both measurements can be combined to determine the full attosecond time structure of the harmonic emission. PACS 32.80.Rm; 42.65.Ky     

Dynamic mechanical analysis

Using dynamic mechanical analysis (DMA) we have studied thermal degradation for a system containing a diglycidyl ether of bisphenol A (DGEBA) and 1,3-bisaminomethylcylohexane (1,3-BAC). The changes of dynamic mechanical properties during thermal degradation indicated a shift of the glass transition temperature (T _g) to higher temperatures and a decrease in the peak value of the dynamic loss factor (tan δ) with an increasing of aging time. The value of dynamic storage modulus (E′) at the rubbery state showed an increase with aging time, whiteE′ at the glassy state only underwent a moderate change with increased thermal degradation. From these results it can be argued that thermal degradation during the stage prior to the onset of the severe degradation involves structural changes in the epoxy system, as further crosslinking and loss of dangling chains in the crosslinked network.