The additive multiboxes

We introduce the new notion of additive “multibox” for linear logic proof-nets. Thanks to this notion, we define a cut-elimination procedure which associates with every proof-net of multiplicative and additive linear logic a unique cut-free one.     

Stochastic analysis in life office management: applications to large annuity portfolios

The paper deals with the riskiness analysis for a large portfolio of life annuities. By means of the limiting distribution of the present value of the portfolio, in the first part of the paper a model for evaluating the investment and the projection risks is presented. In the second part, with regard to the investment risk's effects, the insolvency risk is measured considering the cumulative probability distribution function of the discounted average cost per policy. Copyright © 2003 John Wiley & Sons, Ltd.     

Polarization splitter based on a square-lattice photonic-crystal fiber

A three-core polarization splitter based on a square-lattice photonic-crystal fiber is presented. The component separates the input field into two orthogonally polarized beams that are coupled to the horizontal and vertical output ports. The splitter has been designed through modal and beam propagation analysis by employing high-performance codes based on the finite-element method. Results obtained for a device length of 20 mm show extinction ratios as low as -23 dB with bandwidths as great as 90 nm.     

<Emphasis Type="Italic">Comment on</Emphasis>¶Low temperature specific heat of blue bronze K <Emphasis Type="Bold">0.30</Emphasis>MoO <Emphasis Type="Bold">3</Emphasis>, by J. Odin,J.C. Lasjaunias,K. Biljaković, K. Hasselbach,and P. Monceau

Eur. Phys. J. B 24, 315 (2001) Here we comment on a recently published paper on the presence of a phason contribution in the low temperature heat capacity data of the charge-density-wave compounds K_0.3MoO₃ and (TaSe₄)₂I. We have shown that the anomaly in the C _P / T ³ data reported by Odin et al. is straightforwardly interpreted in terms of low energy phonon modes resulting from the peculiar topology of these compounds. Received 21 February 2002 Published online 19 July 2002     

An integral equation approach to acoustic cloaking

The paper presents an original boundary integral equation (BIE) formulation for the analysis of the acoustic cloaking of a scatterer. The advantage of such an approach is the lower computational burden, especially when the analysis of a large portion of the hosting domain is required. The partial differential equation governing the propagation inside the cloak is recast in the form of non-homogeneous wave equation, with field sources depending on the mechanical properties of the cloak. The boundary integral formulation is derived using the standard procedure. The boundary element method (BEM) is used to derive the matrix transfer function of the cloak. The latter is applied to the incident field at the cloak's outer boundary to obtain the total field at arbitrary locations in the host. The formulation is applied to the simple case of a radially symmetric cloak embedding a circular obstacle. Numerical results are presented for sound-hard and sound-soft obstacles, including a study of the cloaking efficiency as a function of the frequency.     

How accurate is the cancelation of the first even zonal harmonic of the geopotential in the present and future LAGEOS-based Lense-Thirring tests?

The strategy followed so far in the performed or proposed tests of the general relativistic Lense-Thirring effect in the gravitational field of the Earth with laser-ranged satellites of LAGEOS type relies upon the cancelation of the disturbing huge precessions induced by the first even zonal harmonic coefficient J ₂ of the multipolar expansion of the Newtonian part of the terrestrial gravitational potential by means of suitably designed linear combinations of the nodes Ω of more than one spacecraft. Actually, such a removal does depend on the accuracy with which the coefficients of the combinations adopted can be realistically known. Uncertainties of the order of 2 cm in the semimajor axes a and 0.5 milliarcseconds in the inclinations I of LAGEOS and LAGEOS II, entering the expression of the coefficient c ₁ of the combination of their nodes used so far, yield an uncertainty δc ₁ = 1.30 × 10⁻⁸. It gives an imperfectly canceled J ₂ signal of 10.8 milliarcseconds per year corresponding to 23% of the Lense-Thirring signature. Uncertainties of the order of 10–30 microarcseconds in the inclinations yield δc ₁ = 7.9 × 10⁻⁹ which corresponds to an uncanceled J ₂ signature of 6.5 milliarcseconds per year, i.e. 14% of the Lense-Thirring signal. Concerning a future LAGEOS-LAGEOS II-LARES combination with coefficients k ₁ and k ₂, the same uncertainties in a and the less accurate uncertainties in I as before yield δk ₁ = 1.1 × 10⁻⁸, δk ₂ = 2 × 10⁻⁹; they imply a residual J ₂ combined precession of 14.7 milliarcseconds per year corresponding to 29% of the Lense-Thirring trend. Uncertainties in the inclinations at ≈ 10 microarcseconds level give δk ₁ = 5 × 10⁻⁹, δk ₂ = 2 × 10⁻⁹; the uncanceled J ₂ effect is 7.9 milliarcseconds per year, i.e. 16% of the relativistic effect.