Validation of gamma-ray true coincidence summing effects modeled by the Monte Carlo code MCNP-CP

When radionuclides decay by cascading photons, the accuracy of the measured nuclide activity may be affected by true coincidence summing effects. The effects can be quantified by Monte Carlo simulations that can handle correlated γ-and X-ray emissions from a radionuclide. Analysis techniques are also available commercially to correct for the effects due to cascading γ-rays. The MCNP-CP code was used to compute the effects in high purity germanium detectors for several commonly used nuclides and geometries and the results were compared to measurements and an analysis technique. Excellent agreement in true coincidence summing corrections predicted by MCNP-CP and the analysis technique was obtained. In addition, the X-ray true coincidence summing effects were evaluated.     

Generation and stereoselective transformations of 3-phenylcyclopropene

A convenient and inexpensive approach to the generation of 3-phenylcyclopropenes is described. Reaction of these compounds with a range of dienophiles and dipolarophiles led to the stereoselective formation of [4+2]- and [3+2]-cycloadducts, which were exclusively exo-3-phenyl-cis-1,2-disubstituted cyclopropanes. Efficient trapping of 1-lithio-3-phenylcyclopropene with different electrophiles is also discussed. Ab initio calculations suggest that the lowest energy conformation of 3-phenylcyclopropene has the plane of the benzene ring perpendicular to the cyclopropene π-bond but with a low rotation barrier.     

La3Ni2O6: a new double T'-type nickelate with infinite Ni1+/2+O2 layers

New mixed-valent, Ni1+/Ni2+, metastable nickelate, La3Ni2O6, was synthesized by low-temperature reduction of La3Ni2O7 with CaH2. The crystal structure of La3Ni2O6 (space group: I4/mmm, a = 3.9686(1) A and c = 19.3154(6) A) was determined from powder neutron diffraction data by Rietveld analysis. The structure can be described as an intergrowth of LaO2 fluorite and double infinite layer (LaNiO2)2 blocks and represents the n = 2 homologue of the T'-type series Lan+1NinO2n+2. Such double T'-type structural arrangement has never been observed before. The 3d9/3d8 electronic configuration of Ni1+/Ni2+ and the presence of NiO2 infinite layers resemble electronic and structural features of the superconducting cuprates. X-ray absorption spectroscopy supports the 1+/2+ oxidation state and planar coordination of Ni in agreement with the structure determination.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

Correlation Analysis of the Alternating Step Generator

The alternating step generator is a well-known keystream generator consisting of two stop/go clocked LFSRs, LFSR₁ and LFSR₂, whose clocks are controlled by another LFSR, LFSR₃, which is clocked regularly. A probabilistic analysis of this generator is conducted which shows that the posterior probabilites of individual bits of the first derivatives of the regularly clocked LFSR₁ and LFSR₂ sequences, when conditioned on a given segment of the first derivative of the keystream sequence, can be computed efficiently in a number of probabilistic models of interest. The expected values of these probabilities, for a random keystream sequence, are derived by an approximate theoretical analysis and are also verified by systematic computer experiments. It is pointed out that these posterior probabilities can be enhanced in a resynchronization scenario and thus used for a low-complexity fast correlation attack on the two LFSRs. More generally, it is argued that even without resynchronization these probabilities may be significantly different from one half for fast correlation attacks based on iterative decoding algorithms to be successful, although with incresead complexity. A related method for computing the posterior probabilities of individual bits of the LFSR₃ sequence, when conditioned on both the keystream sequence and the LFSR₁ and LFSR₂ sequences, is also developed. As these posterior probabilities are much more different from one half, they can be used for a low-complexity fast correlation attack on LFSR₃, provided that the initial states of LFSR₁ and LFSR₂ are previously reconstructed.     

Bayesian networks for discrete multivariate data: an algebraic approach to inference

In this paper we demonstrate how Gröbner bases and other algebraic techniques can be used to explore the geometry of the probability space of Bayesian networks with hidden variables. These techniques employ a parametrisation of Bayesian network by moments rather than conditional probabilities. We show that whilst Gröbner bases help to explain the local geometry of these spaces a complimentary analysis, modelling the positivity of probabilities, enhances and completes the geometrical picture. We report some recent geometrical results in this area and discuss a possible general methodology for the analyses of such problems.     

An application of convergence acceleration techniques to a class of two-point boundary value problems on a semi-infinite domain

For boundary value problems posed on unbounded domains it is often appropriate to impose a boundary condition at infinity. For certain classes of boundary value problem obvious numerical difficulties can be avoided by truncating the unbounded domain and solving a sequence of finite domain problems instead. We introduce a novel technique which is straightforward to implement and which exploits information contained in this sequence in order to extrapolate to the unbounded case. The technique introduces a new and interesting application of a variety of convergence acceleration algorithms.     

Oxetane ethers are formed reversibly in the lithium-catalyzed Friedel–Crafts alkylation of phenols with oxetanols: Synthesis of dihydrobenzofurans,diaryloxetanes, and oxetane ethers

Studies on the mechanism and intermediate products in the Friedel–Crafts reaction between oxetanols and phenols are presented. The formation of O-alkylated intermediates is identified using ¹H NMR spectroscopy, in a reversible formation of the kinetic oxetane ether products. An interesting relationship between the electronic nature of the nucleophile and the degree of O-alkylation is uncovered. For phenols substituted with an electron withdrawing group such as CN, oxetane ethers are the only products isolated regardless of reaction time. Increasing the electron rich nature of the phenol leads to an increased proportion of the thermodynamic C-alkylated Friedel–Crafts products after just 1?h and as the sole product/s after extended reaction times. These studies have enabled a more complete catalytic cycle to be proposed. Using the same lithium catalyst and carefully selected reaction times, several examples of oxetane ethers are successfully isolated as novel bioisosteres for ester groups.