Linear carbon dioxide in the high-pressure high-temperature crystalline phase IV

High-temperature IR absorption spectra of solid CO2 in phases II and IV were measured in a resistive heated diamond anvil cell up to 30 GPa. The spectral structures of the bending mode, observed in high quality thin crystalline samples, and of the IR lattice phonons, measured for the first time between 80 and 640 K, are discussed using group theory arguments. According to this analysis the claimed bent molecular geometry of CO2 in phase IV can be unambiguously ruled out. Furthermore, the structures of both phases II and IV have been identified, among those so far proposed, as orthorhombic.     

On the birational geometry of

Here we are interested in birational properties of the moduli space of stable maps to the complex projective line. In particular, we determine the class of the canonical divisor in the rational Picard group and we investigate the cones of ample and effective divisors.     

Fast and stable QR eigenvalue algorithms for generalized companion matrices and secular equations

Summary We introduce a class of n×n structured matrices which includes three well-known classes of generalized companion matrices: tridiagonal plus rank-one matrices (comrade matrices), diagonal plus rank-one matrices and arrowhead matrices. Relying on the structure properties of , we show that if A then A=RQ , where A=QR is the QR decomposition of A. This allows one to implement the QR iteration for computing the eigenvalues and the eigenvectors of any A with O(n) arithmetic operations per iteration and with O(n) memory storage. This iteration, applied to generalized companion matrices, provides new O(n²) flops algorithms for computing polynomial zeros and for solving the associated (rational) secular equations. Numerical experiments confirm the effectiveness and the robustness of our approach.The results of this paper were presented at the Workshop on Nonlinear Approximations in Numerical Analysis, June 22 – 25, 2003, Moscow, Russia, at the Workshop on Operator Theory and Applications (IWOTA), June 24 – 27, 2003, Cagliari, Italy, at the Workshop on Numerical Linear Algebra at Universidad Carlos III in Leganes, June 16 – 17, 2003, Leganes, Spain, at the SIAM Conference on Applied Linear Algebra, July 15 – 19, 2003, Williamsburg, VA and in the Technical Report [8]. This work was partially supported by MIUR, grant number 2002014121, and by GNCS-INDAM. This work was supported by NSF Grant CCR 9732206 and PSC CUNY Awards 66406-0033 and 65393-0034.     

Inversion of circulant matrices over

In this paper we consider the problem of inverting an circulant matrix with entries over . We show that the algorithm for inverting circulants, based on the reduction to diagonal form by means of FFT, has some drawbacks when working over . We present three different algorithms which do not use this approach. Our algorithms require different degrees of knowledge of and , and their costs range, roughly, from to operations over . Moreover, for each algorithm we give the cost in terms of bit operations. We also present an algorithm for the inversion of finitely generated bi-infinite Toeplitz matrices. The problems considered in this paper have applications to the theory of linear cellular automata.

     

Isotope analysis in central heavy ion collisions at intermediate energies

Symmetry energy is a key quantity in the study of the equation of state of asymmetric nuclear matter. Heavy ion collisions at low and intermediate energies, performed at Laboratori Nazionali di Legnaro and Laboratori Nazionali del Sud, can be used to extract information on the symmetry energy coefficient C_sym, which is currently poorly known but relevant both for astrophysics and for deeper knowledge of the structure of exotic nuclei.     

High pressure photoinduced ring opening of benzene

The chemical transformation of crystalline benzene into an amorphous solid (a-C:H) was induced at high pressure by employing laser light of suitable wavelengths. The reaction was forced to occur at 16 GPa, well below the pressure value (23 GPa) where the reaction normally occurs. Different laser sources were used to tune the pumping wavelength into the red wing of the first excited singlet state S(1)((1)B(2u)) absorption edge. Here the benzene ring is distorted, presenting a greater flexibility which makes the molecule unstable at high pressure. The selective pumping of the S(1) level, in addition to structural considerations, was of paramount importance to clarify the mechanism of the reaction.     

Experimental study for the feasibility of a crystalline undulator

We present an idea for creation of a crystalline undulator and report its first realization. One face of a silicon crystal was given periodic microscratches (grooves) by means of a diamond blade. The x-ray tests of the crystal deformation due to a given periodic pattern of surface scratches have shown that a sinusoidal-like shape is observed on both the scratched surface and the opposite (unscratched) face of the crystal; that is, a periodic sinusoidal-like deformation goes through the bulk of the crystal. This opens up the possibility for experiments with high-energy particles channeled in a crystalline undulator, a novel compact source of radiation.     

Iteration schemes for the divide-and-conquer eigenvalue solver

Summary. We propose globally convergent iteration schemes for updating the eigenvalues of a symmetric matrix after a rank-1 modification. Such calculations are the core of the divide-and-conquer technique for the symmetric tridiagonal eigenvalue problem. We prove the superlinear convergence right from the start of our schemes which allows us to improve the complexity bounds of [3]. The effectiveness of our algorithms is confirmed by numerical results which are reported and discussed. Received September 22, 1993     

Aromatic polyamides. I. Synthesis and characterization of some aromatic polyamides and their model diamides

The synthesis of some wholly aromatic polyamides based on unsubstituted and chloro- and nitro-substituted diamines by low temperature solution polymerization is described. Poly(1,3-phenylene isophthalamide) and poly(chloro-2,4-phenylene isophthalamide) were selected for further investigation. To study the two polyamides on a systematic basis their model diamides were synthesized. These materials were characterized with respect to chemical structure and purity by elemental analysis, infrared (IR), and nuclear magnetic resonance (NMR) spectroscopic techniques. The usefulness of the model compounds in the interpretation of the polymer spectra is also demonstrated.     

Transport and structural properties of pure and Cr doped Li3VO4

This study deals with the effects of 5 and 10% chromium additions on the transport and structural properties of Li3VO4. The Cr substitution is easily obtained without impurity phases and does not affect the room- and high-temperature host crystal structure, as evidenced by X-ray powder diffraction and micro-Raman analysis. The EPR signals are interpreted in terms of quantified amounts of Cr ions in 5+ and 3+ valence states. Suitable 7Li and 51V MAS NMR spectra simulations agree with the EPR results about the relative amount of Cr5+ and Cr3+ ions substituted in V5+ and Li+ sites, respectively. The Cr3+ presence on Li site, also suggested by Raman results and Rietveld refinements, requires Li vacancies to maintain the charge neutrality. The p-type conductivity, suggested by the positive thermoelectric power coefficients, significantly increases by the cation doping up to an order of magnitude.