Baker-Campbell-Hausdorff relations for finite-dimensional lie algebras

A method is proposed for disentangling exponentials of operators that belong to finite-dimensional Lie algebras. A straightforward matrix representation is combined with a widely used parameter-differentiation method, giving rise to a simpler and more systematic procedure. The SU(1, 1), SU(2) and double photon algebras are explicitly considered as illustrative examples.Work partly supported by Fundación Antochas Project No. 1108911 and by the USA-Argentina Cooperative Research Project NSF INT-8802247 and CONICET No. 163/88.     

Computer Use and Visualization in Students' Construction of Reflection and Rotation Concepts

The effects of a dynamic instructional environment (based on use of The Geometer's Sketchpad, N. Jackiw, 1991 , in a computer lab) and visualization on eighth-grade students' (N= 241) construction of the concepts of reflection and rotation were investigated. Also investigated were the effects of the environment on students' two- and three-dimensional visualization. After controlling for initial differences, it was concluded that students experiencing the dynamic environment significantly outperformed students experiencing a traditional environment on content measures of the concepts of reflection and rotation, as well as on measures of two-dimensional visualization. The students' environment did not significantly affect their three-dimensional visualization.     

Synthesis, isolation, and characterization of an organometallic triiodopalladium(IV) complex. Quantitative and regioselective synthesis of two C-I reductive elimination products

Iodine and the pincer complex [Pd(O,N,C-L)I], where L is the monoanionic ligand resulting from deprotonation of the acetyl group of the dimethylmonoketal of 2,6-diacetylpyridine, are in equilibrium at low temperatures with the palladium(IV) complex [Pd(O,N,C-L)I(3)], which can be isolated at -40 °C and characterized by (1)H NMR spectroscopy and X-ray diffraction studies, in spite of its great instability. When the same reaction is carried out at room temperature, a quantitative reductive elimination process occurs, giving L-I, which in the presence of water affords L'-I, resulting from hydrolysis of L-I.     

Synthesis, structural characterization of benzimidazole-functionalized Ni(II) and Hg(II) N-heterocyclic carbene complexes and their applications as efficient catalysts for Friedel-Crafts alkylations

[Ni(L₁)₂](PF₆)₂ (3a, L₁ = 3-(1-ethyl-1H-benzimidazol-2-yl)methyl)-1-((6-methylpyridin-2-yl)methyl)imidazolyl-idene), [Ni(L₂)₂(CH₃CN)](PF₆)₂ (3b, L₂ = 3-(1-ethyl-1H-benzimidazol-2-yl)methyl)-1-((6-methylpyridin-2-yl)-methyl)benzimidazolylidene), and [Hg(L₁)₂(CH₃CN)₂](PF₆)₂ (4) have been successfully prepared and fully characterized by NMR, ESI-MS spectroscopy, and X-ray diffraction analysis. The nickel complexes reveal a square-planar structure with two carbene ligands and benzimidazole groups at the cis configuration. The nickel complex 3b has been proved to be a highly efficient catalyst for Friedel-Crafts alkylation of indoles with β-nitrostyrenes at room temperature in moderate-to-excellent yields. The crystal packing structure of 4 shows that double-stranded 1D supramolecular chains are formed by inter-chain benzimidazole rings and pyridine rings face-to-face π-π stacking interactions.     

Diffusion–reaction of aluminum and oxygen in thermally grown Al2O3 oxide layers

The diffusion–reaction of aluminum (Al) and oxygen (O), to form thermally grown oxide (TGO) layers in thermal barrier coatings (TBCs), is studied through an analytical model. A nonsymmetrical radial basis function approach is used to numerically solve the mass balance equations that predict the TGO growth. Correct boundary conditions for the Al and O reactions are laid out using scaling arguments. The Damköhler number shows that the O–Al reaction is several orders of magnitude faster than diffusion. In addition, a comparison between aluminum and oxygen diffusivities indicates that TGO growth is governed by aluminum diffusion. The results are compared with experimental measurements on air plasma spray-deposited TBCs treated at 1,373 K with exposure times ranging from 1 to 1700 hours. We found that, for several time decades, the thickness of the thermally grown layer has power law dependence of time with an exponent of ½, following the diffusion control mechanism. At later times, however, the presence of other oxides and additional kinetics modify the diffusive exponent.     

Effective Iodine Capture Behavior by a Censer-shaped Macrocycle in Vapor Phase and Aqueous Solution

Iodine capture is of great significance for disposal of the hazardous radioactive iodine. CTX[P(O)Ph] , one kind of censer-shaped macrocycle cyclotrixylohydroquinoylene ( CTX ) derivatives, was applied as an efficient iodine adsorbent. It showed satisfactory iodine adsorption capacity in vapor phase and could be reused without obvious adsorption capacity loss. Besides, the adsorbent could also uptake iodine in water. Fortunately, two iodine loading CTX[P(O)Ph] crystal structures were obtained under different conditions to explore the mechanism of iodine adsorption. This work provides a relatively rare example of iodine adsorption by macrocycle. It is promising that the results with crystal information might be meaningful for exploring and designing new kinds of iodine adsorbents.     

A 3.3 Å-Resolution Structure of Hyperthermophilic Respiratory Complex III Reveals the Mechanism of Its Thermal Stability

Respiratory chain complexes convert energy by coupling electron flow to transmembrane proton translocation. Owing to a lack of atomic structures of cytochrome bc₁ complex (Complex III) from thermophilic bacteria, little is known about the adaptations of this macromolecular machine to hyperthermophilic environments. In this study, we purified the cytochrome bc₁ complex of Aquifex aeolicus, one of the most extreme thermophilic bacteria known, and determined its structure with and without an inhibitor at 3.3 Å resolution. Several residues unique for thermophilic bacteria were detected that provide additional stabilization for the structure. An extra transmembrane helix at the N-terminus of cyt. c₁ was found to greatly enhance the interaction between cyt. b and cyt. c₁, and to bind a phospholipid molecule to stabilize the complex in the membrane. These results provide the structural basis for the hyperstability of the cytochrome bc₁ complex in an extreme thermal environment.     

Insight into the binary mixture of ethyl lactate+acetonitrile from density,speed of sound and refractive index measurements

Density, sound velocity and refractive index of ethyl lactate + acetonitrile mixtures were measured at five temperatures from 283.15 to 323.15 K. Excess molar volumes, partial molar volumes, thermal expansion coefficients, isentropic compressibility and molar refraction values were calculated. It is concluded that deviations from ideality in this system should be assigned to the ability of the smaller acetonitrile molecules to occupy free volume space of ethyl lactate.     

Transport Properties of Random Walks on Scale-Free/Regular-Lattice Hybrid Networks

We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds (F) and across network shortcuts (f). For fast shortcuts (f/F≫1) and low shortcut densities, traversal time data collapse onto a universal curve, while a crossover behavior that can be related to the percolation threshold of the scale-free network component is identified at higher shortcut densities, in analogy to similar observations reported recently in Newman-Watts small-world networks. Furthermore, we observe that random walk traversal times are larger for networks with a higher degree of inhomogeneity in their shortcut distribution, and we discuss access time distributions as functions of the initial and final node degrees. These findings are relevant, in particular, when considering the optimization of existing information networks by the addition of a small number of fast shortcut connections.