On solvability of linear differential equations in ${\Bbb R}^{\Bbb N}$

We construct $x^0$ in ${\Bbb R}^{\Bbb N}$ and a row-finite matrix $T=\{T_{i,j}(t)\}_{i,j\in\N}$ of polynomials of one real variable $t$ such that the Cauchy problem $\dot x(t)=T_tx(t)$, $x(0)=x^0$ in the Fr\'echet space $\R^\N$ has no solutions. We also construct a row-finite matrix $A=\{A_{i,j}(t)\}_{i,j\in\N}$ of $C^\infty(\R)$ functions such that the Cauchy problem $\dot x(t)=A_tx(t)$, $x(0)=x^0$ in ${\Bbb R}^{\Bbb N}$ has no solutions for any $x^0\in{\Bbb R}^{\Bbb N}\setminus\{0\}$. We provide some sufficient condition of solvability and of unique solvability for linear ordinary differential equations $\dot x(t)=T_tx(t)$ with matrix elements $T_{i,j}(t)$ analytically dependent on $t$.

Comment on "Electron collisional excitation of argon-like Ni XI using the Breit-Pauli R-matrix method" [Eur. Phys. J. D 42, 235-241 (2007)] - Electron impact excitation of Ni XI

In a recent paper, Verma et al. [Eur. Phys. J. D 42, 235 (2007)] have reported results for energy levels, radiative rates, collision strengths, and effective collision strengths for transitions among the lowest 17 levels of the (1s(2)2s(2)2p(6))3s(2)3p(6), 3s(2)3p(5)3d and 3s3p(6)3d configurations of Ni XI. They adopted the CIV3 and R-matrix codes for the generation of wavefunctions and the scattering process, respectively. In this paper, through two independent calculations performed with the fully relativistic DARC (along with GRASP) and FAC codes, we demonstrate that their results are unreliable. New data are presented and their accuracy is assessed.

2-D R-matrix propagation: A large scale electron scattering simulation dominated by the multiplication of dynamically changing matrices

We examine the computational aspects of propagating a global R-matrix, R, across sub-regions in a 2-D plane. This problem originates in the large scale simulation of electron collisions with atoms and ions at intermediate energies. The propagation is dominated by matrix multiplications which are complicated because of the dynamic nature of R, which changes the designations of its rows and columns and grows in size as the propagation proceeds. The use of PBLAS to solve this problem on distributed memory HPC machines is the main focus of the paper.

The Portugal coastal counter current off NW Spain: new insights on its biogeochemical variability

Time series of wind-stress data, AVHRR and SeaWiFS satellite images, and in situ data from seven cruises are used to assemble a coherent picture of the hydrographic variability of the seas off the Northwest Iberian Peninsula from the onset (September-October) to the cessation (February-May) of the Portugal coastal counter current (PCCC). During this period the chemistry and the biology of the shelf, slope and ocean waters between 40degrees and 43degreesN have previously been undersampled. Novel information extracted from these observations relate to: