Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.     

Relaxation processes in glasses of the Ge-As-S system

The internal friction in Ge _x As_{40 ? x} S₆₀ glasses is investigated in the temperature range 100 K-T _g at infralow frequencies (10^?3?10^?1 Hz). It is shown that the concentration dependence of the internal friction of these materials changes as a result of the transformation of the dominant kinetic unit in dissipative processes of the relaxation and nonrelaxation types. It is established tha the change in the mechanism of internal friction in the Ge _x As_{40 ? x} S₆₀ glasses leads to a jump in the activation energy of the α relaxation and to a local minimum in the frequency factor τ₀.     

Category with a natural cone

Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given. We point out that the main results of this paper were already stated in [3], and the purpose of this article is to give full details of the foregoing.     

Annealing effect on soft magnetic properties and magnetoimpedance of Finemet Fe73.5Si13.5B9Nb3Au1 alloy

Effect of annealing on the soft magnetic properties of Fe_73.5Si_13.5B₉Nb₃Au₁ amorphous ribbon has been investigated by means of structure examination, magnetoimpedance ratio (MIR) and incremental permeability ratio (PR) spectra measured in the frequency range of 1–10 MHz at a fixed current of 10 mA X-ray diffraction analysis showed that the as-cast sample was amorphous and it became nanocrystalline under a proper heat treatment. When annealing amorphous alloy at 530 °C for 30, 60, 90 min, soft magnetic properties have been improved drastically. Among the samples investigated, the sample annealed at 530 °C for 90 min showed the softest magnetic behavior. The MIR and PR curves revealed the desirable changes in anisotropy field depending upon annealing.     

The statement and numerical solution of an optimization problem in X-ray tomography

A nonclassical problem is considered for the transport equation with coefficients depending on the energy of radiation. The task is to find the discontinuity surfaces for the coefficients of the equation from measurements of the radiation flux leaving the medium. For this tomography problem, an optimization problem is stated and numerically analyzed. The latter consists in determining the radiation energy that ensures the best reconstruction of the unknown medium. A simplified optimization problem is solved analytically.     

Properties of<Emphasis Type="Italic">B</Emphasis><Subscript>c</Subscript> meson

The mass spectrum ofcb meson is investigated with an effective quark-antiquark potential of the form -α_c/r +Ar ^νwith ν varying from 0.5 to 2.0. TheS andP-wave masses, pseudoscalar decay constant, weak decay partial widths in spectator model and the lifetime ofB _cmeson are computed. The properties calculated here are found to be in good agreement with other theoretical and experimental values at potential index,ν = 1     

The LPCTrap experiment: measurement of the β–ν angular correlation in 6He using a transparent Paul trap

We report on the status of the LPCTrap experiment, devoted to measure the β–ν angular correlation in the pure Gamow–Teller decay of ⁶He. This measurement is motivated by the search for the presence of tensor type contributions to the weak interaction. The ⁶He ions are confined in a novel transparent Paul trap. The β particles and the recoil ions are detected in coincidence to deduce the angular correlation parameter. The commissioning run performed in 2005 has given the proof of principle of this experiment. Up to 10⁵ coincidences were recorded during a second run in 2006.