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.

Utilisation of ionic liquid solvents for the synthesis of Lily-of-the-Valley fragrance {beta-Lilial (R); 3-(4-t-butylphenyl)-2-methylpropanal}

The Heck arylation of 2-methylprop-2-en- I -ol in ionic liquids and organic solvents is reported using a range of homogeneous and heterogeneous palladium catalysts. Higher activity is observed in the ionic liquid media compared with N-methyl pyrrolidinone and under solventless conditions. The ionic liquid-catalyst system may be recycled easily with little loss in activity, although significant palladium leaching from the heterogeneous catalyst was observed. In the case of Trans-bis(2,3-dihydro-3-methylbenzothiazole-2-ylidene)diiodopalladium (11) reported to be highly active for this transformation, significant induction petiods were observed indicating that nanoparticles may be responsible for the catalysis. Using the ionic liquid Heck reaction, a recyclable synthesis for the fragrance beta-Lilial((R)) has been developed. (c) 2004 Elsevier B.V. All rights reserved.

Synthesis of 3-(4-tert-butylphenyl)-2-propen-1-one, a precursor to Lilial (R), via an aldol condensation in an ionic liquid

An efficient synthesis of a precursor to Lilial(R), based on an aldol condensation in an ionic liquid, is described, utilising piperidine as the base catalyst. The yields obtained with this methodology are significantly increased in comparison with those reported in organic solvents to date. In the ionic liquid, the self-aldol condensation of propanal is suppressed and leads to an increased selectivity with respect to the cross-aldol condensation product without the need to use an excess of 4-tert-butylbenzaldehyde to obtain high selectivities.