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.

The importance of hydrogen's potential-energy surface and the strength of the forming R-H bond in surface hydrogenation reactions

An understanding of surface hydrogenation reactivity is a prevailing issue in chemistry and vital to the rational design of future catalysts. In this density-functional theory study, we address hydrogenation reactivity by examining the reaction pathways for N+H -> NH and NH+H -> NH2 over the close-packed surfaces of the 4d transition metals from Zr-Pd. It is found that the minimum-energy reaction pathway is dictated by the ease with which H can relocate between hollow-site and top-site adsorption geometries. A transition state where H is close to a top site reduces the instability associated with bond sharing of metal atoms by H and N (NH) (bonding competition). However, if the energy difference between hollow-site and top-site adsorption energies (Delta E-H) is large this type of transition state is unfavorable. Thus we have determined that hydrogenation reactivity is primarily controlled by the potential-energy surface of H on the metal, which is approximated by Delta E-H, and that the strength of N (NH) chemisorption energy is of less importance. Delta E-H has also enabled us to make predictions regarding the structure sensitivity of these reactions. Furthermore, we have found that the degree of bonding competition at the transition state is responsible for the trend in reaction barriers (E-a) across the transition series. When this effect is quantified a very good linear correlation is found with E-a. In addition, we find that when considering a particular type of reaction pathway, a good linear correlation is found between the destabilizing effects of bonding competition at the transition state and the strength of the forming N-H (HN-H) bond. (c) 2006 American Institute of Physics.

The stereoselective coordination chemistry of the helicating ligand N,N '-bis(-2,2 '-dipyridyl-5-yl)carbonyl-(S/R,S/R)-1,2-diphenylethylenediamine

Enantiomerically pure N,N'-bis(-2,2'-dipyridyl-5-yl)carbonyl-(S/R,S/R)-1,2-diphenylethylenediamine has been synthesised by linking two 2,2'-bipyridine units by (R,R)- and (S,S)-1,2-diphenylethylenediamine. The ligands possess a hindered rotation between the bipyridine chromophores, which are held together by intramolecular hydrogen bonds. ES mass spectroscopy confirmed that reaction with Fe(II), Co(III) and Cd(II) afforded dinuclear complexes. CD spectroscopy implied that enantiopure ligands conferred helicity to the metals centre giving a dominant triple helicate diastereoisomer (with the RR isomer giving a P helicate). H-1 NMR spectroscopy of the cadmium complex confirmed the presence of a single diastereoisomer. (C) 2003 Elsevier B.V. All rights reserved.

Ultrafast Laser-Driven Excitation Dynamics in Ne: An Ab Initio Time-Dependent R-Matrix Approach

An attosecond pump-probe scheme that combines the use of a free-electron laser pulse with an ultrashort pulse is applied in order to explore the ultrafast excitation dynamics in Ne. We describe the multielectron dynamics using a new nonperturbative time-dependent R-matrix theory. This theory enables the interaction of ultrashort light fields with multielectron atoms and atomic ions to be determined from first principles. By probing the emission of an inner 2s electron from Ne we are also able to study the bound state population dynamics during the free-electron laser pulse.

Electron impact excitation collision strengths for neon-like Ni XIX calculated using the relativistic R-matrix method

In a recent paper [Pramana - J. Phys. 64, 129 (2005)] results have been presented for electron impact excitation collision strengths for transitions among the fine-structure levels of the 2s(2)2p(6) and 2s(2)2p(5)3s configurations of Ni XIX. In this paper we demonstrate through an independent calculation with the relativistic R-matrix code that those results are unreliable and the conclusions drawn are invalid.

Time-dependent R -matrix theory for ultrafast atomic processes

We describe an ab initio nonperturbative time-dependent R-matrix theory for ultrafast atomic processes. This theory enables investigations of the interaction of few-femtosecond and -attosecond pulse lasers with complex multielectron atoms and atomic ions. A derivation and analysis of the basic equations are given, which propagate the atomic wave function in the presence of the laser field forward in time in the internal and external R-matrix regions. To verify the accuracy of the approach, we investigate two-photon ionization of Ne irradiated by an intense laser pulse and compare current results with those obtained using the R-matrix Floquet method and an alternative time-dependent method. We also verify the capability of the current approach by applying it to the study of two-dimensional momentum distributions of electrons ejected from Ne due to irradiation by a sequence of 2 as light pulses in the presence of a 780 nm laser field.

2DRMP: A suite of two-dimensional R-matrix propagation codes

The R-matrix method has proved to be a remarkably stable, robust and efficient technique for solving the close-coupling equations that arise in electron and photon collisions with atoms, ions and molecules. During the last thirty-four years a series of related R-matrix program packages have been published periodically in CPC. These packages are primarily concerned with low-energy scattering where the incident energy is insufficient to ionize the target. In this paper we describe previous term2DRMP,next term a suite of two-dimensional R-matrix propagation programs aimed at creating virtual experiments on high performance and grid architectures to enable the study of electron scattering from H-like atoms and ions at intermediate energies.

HBrowse: a GRACE tool for browsing R-matrix H-files

An H-file is used to convey information from the inner-region to the outer-region in R-matrix computations. HBrowse is a workstation tool for displaying a graphical abstraction of a local or remote R-matrix H-file. While it is published as a stand-alone tool for post-processing the output from R-matrix inner-region computations it also forms part of the Graphical R-matrix Atomic Collision Environment (GRACE), HBrowse is written in C and OSF/Motif for the UNIX operating system. (C) 2000 Elsevier Science B.V. All rights reserved.

ISO-SWS observations of CO2 and H2O in R cassiopeiae

We present ISO-SWS spectra of the O-rich Mira variable R Gas, showing CO2 in absorption and emission, and H2O in absorption. The CO2 absorption feature is the 01(1)0 - 00(0)0 ro-vibrationaI band at 14.97 mu m. The emission features are the 10(0)0-01(1)0 and 11(1)0 - 02(2)0 re-vibrational transitions at 13.87 and 13.48 mu m respectively. The water absorption spectrum shows the nu(1) and nu(3) re-vibrational bands in the 2.75 - 3 mu m region. Using LTE models, we derive physical parameters for the features. We find the CO2 emission temperature to be similar to 1100 K. We discuss the nature of the CO2 feature at 15 mu m and show that it can be modeled as an emission/absorption band by deviating front thermal equilibrium for the population of the 01(1)0 vibrational level. The H2O absorption spectrum is shown to arise from gas at different temperatures, but can be fit reasonably well with two components at T = 950 K and T = 250 K. The CO2 emission and hut H2O absorption temperatures an similar, suggesting chat these features probe the same region of the inner envelope. We discuss the inner envelope chemistry using molecular equilibrium calculations and recent modeling work by Duari et al. (1999), and find our observations consistent with the results.

Averroes y las cosas justas por naturaleza

En su comentario a la Ética a Nicómaco, Averroes se ocupó del pasaje donde Aristóteles distingue entre las cosas que son justas por naturaleza y aquéllas que lo son en virtud de la ley (V, 7 1134b18-1135a5). Su comentario es particularmente breve, pero plantea algunas dificultades importantes, como su alusión a un derecho naturale legale, que, según Leo Strauss, vendría a ser simplemente un derecho positivo de aceptación general. En este artículo se busca caracterizar lo justo natural y lo justo positivo en el comentario de Averroes y mostrar el alcance de la variación de los criterios propios de la justicia positiva.