On the Security of Two Public Key Cryptosystems Using Non-Abelian Groups

The security of two public key encryption schemes relying on the hardness of different computational problems in non-abelian groups is investigated. First, an attack on a conceptual public key scheme based on Grigorchuk groups is presented. We show that from the public data one can easily derive an “equivalent” secret key that allows the decryption of arbitrary messages encrypted under the public key. Hereafter, a security problem in another conceptual public key scheme based on non-abelian groups is pointed out. We show that in the present form the BMW scheme is vulnerable to an attack, which can recover large parts of the private subgroup chain from the public key.     

Bayesian analysis of finite mixture models of distributions from exponential families

This paper deals with the Bayesian analysis of finite mixture models with a fixed number of component distributions from natural exponential families with quadratic variance function (NEF-QVF). A unified Bayesian framework addressing the two main difficulties in this context is presented, i.e., the prior distribution choice and the parameter unidentifiability problem. In order to deal with the first issue, conjugate prior distributions are used. An algorithm to calculate the parameters in the prior distribution to obtain the least informative one into the class of conjugate distributions is developed. Regarding the second issue, a general algorithm to solve the label-switching problem is presented. These techniques are easily applied in practice as it is shown with an illustrative example.     

Hyperfine interaction of ZrO2 — Tetragonal phase

The quadrupole hyperfine interaction of the tetragonal phase of the zirconium oxide has been measured at 1523 K using the time-differential perturbed angular correlation technique. The electric field gradient at zirconium sites was determined to beV _zz =(17.5±0.4)·10¹⁷ Vcm⁻² and axially symmetric.     

TDPAC investigation on thermally related HfF4.3H2O and HfO2

The hyperfine quadrupole interaction of HfF₄.3H₂O at Hf sites is investigated from 14 to 820 K. No transitions have been found. After the complete dehydration of this compound at 393 K, chemical reactions take place which give rise to hafnium oxifluorides and metastable forms of hafnium oxide. Heating treatments at increasing temperatures make HfO₂ turn into its monoclinic phase.     

Tranversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near L2 in the restricted three-body problem

The restricted three-body problem is considered for values of the Jacobi constant C near the value C₂ associated to the Euler critical point L₂. A Lyapunov family of periodic orbits near L₂, the so-called family (c), is born for C = C₂ and exists for values of C less than C₂. These periodic orbits are hyperbolic. The corresponding invariant manifolds meet transversally along homoclinic orbits. In this paper the variation of the transversality is analyzed as a function of the Jacobi constant C and of the mass parameter μ. Asymptotical expressions of the invariant manifolds for C ? C₂ and μ ? 0 are found. Several numerical experiments provide accurate information for the manifolds and a good agreement is found with the asymptotical expressions. Symbolic dynamic techniques are used to show the existence of a large class of motions. In particular the existence of orbits passing in a random way (in a given sense) from the region near one primary to the region near the other is proved.     

Hochauflösende29Si-Festkörper-NMR-Spektroskopie: Einfluß des Si-O-Si-Bindungswinkels auf die isotrope chemische Verschiebung von t- und h-Y2Si2O7

Starting from high-resolution solid-state²⁹Si NMR spectra of two modifications of Y₂Si₂O₇ with different Si-O-Si bond angles it was verified that increasing bond angles cause high-field isotropic²⁹Si chemical shifts.

     

A method for measuring the proportion of different plane orientations in metal supported catalysts by gas chemisorption

A method is presented, which allows us to calculate the percentage of metal surface atoms with different coordination numbers, on metal supported catalysts. This method is based on gas-metal stoichiometry values reported for the chemisorption of H₂, O₂ and CO on well defined monocrystals, and on gas chemisorption measurements on metal supported catalysts. It has here been applied to a series of Pd/SiO₂ catalysts.     

Molecular orbital theory and tunnelling currents

Summary The parameters appearing in an effective tight-binding Hamiltonian are shown to be simply related to the tunnelling currents and the overlap between the different orbitals of the constituent atoms. Different systems are considered and the results show that our approach applies both to molecular and condensed-matter systems.

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Riassunto Si mostra che i parametri presenti in una hamiltoniana efficace a legame forte sono correlati semplicemente alle correnti di tunnel e alla sovrapposizione tra i diversi orbitali degli atomi costituenti. Si considerano diversi sistemi e i risultati mostrano che il nostro approccio si applica sia a sistemi molecolari che di materia condensata.

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Резюме ПоказЫвается, что параметрЫ, появляющиеср в эффективном Гамильтониане в приближении силъной связи, связнЫ с туннелънЫми токами и перекрЫтием между разяичнЫми орбиталями составляюших атомов. Рассматриваются различнЫе системЫ. ПолученнЫе результатЫ показЫвают, что наш подход применим к молекулярнЫм системам и к конденсироваииому веществу.