Reactivity of molybdenum and rhenium hydroxo-carbonyl complexes toward organic electrophiles

The hydroxo compounds [Re(OH)(CO)(3)(N-N)] (N-N=bipy, 2 a; Me(2)-bipy, 2 b) were prepared in a biphasic H(2)O/CH(2)Cl(2) medium by reaction of [Re(OTf)(CO)(3)(N-N)] with KOH. In contrast, when anhydrous CH(2)Cl(2) was used, the binuclear hydroxo-bridged compound [[Re(CO)(3)(bipy)](2)(mu-OH)]OTf (3-OTf) was obtained. Compound [Re(OH)(CO)(3)(Me(2)-bipy)] (2 b) reacted with phenyl acetate or vinyl acetate to afford [Re(OAc)(CO)(3)(Me(2)-bipy)] (4) and phenol or acetaldehyde, respectively. The reactions of [Mo(OH)(eta(3)-C(3)H(4)-Me-2)(CO)(2)(phen)] (1), 2 a, and 2 b toward several unsaturated organic electrophiles were studied. The reaction of 1 with (p-tolyl)isocyanate afforded an adduct of N,N'-di(p-tolyl)urea and the carbonato-bridged compound [[Mo(eta(3)-C(3)H(4)-Me-2)(CO)(2)(phen)](2)(mu-eta(1)(O),eta(1)(O)-CO(3))] (5). In contrast, the reaction of 2 a with phenylisocyanate afforded [Re(OC(O)NHPh)(CO)(3)(bipy)] (6); this results from formal PhNCO insertion into the O-H bond. On the other hand, compounds [Mo[SC(O)NH(p-tolyl)](eta(3)-C(3)H(4)-Me-2)(CO)(2)(phen)] (7), [Re[SC(O)NH(p-tolyl)](CO)(3)(Me(2)-bipy)] (8 a), and [Re[SC(O)NHEt](CO)(3)(Me(2)-bipy)] (8 b) were obtained by reaction of 1 or 2 b with the corresponding alkyl or aryl isothiocyanates. In those cases, RNCS was inserted into the M-O bond. The reactions of 1, 2 a, and 2 b with dimethylacetylenedicarboxylate (DMAD) gave the complexes [Mo[C(OH)-C(CO(2)Me)C(CO(2)Me)-O](eta(3)-C(3)H(4)-Me-2)(CO)(phen)] (9) and [Re[C(OH)C(CO(2)Me)C(CO(2)Me)O](CO)(2)(N-N)] (N-N=bipy, 10 a; Me(2)-bipy, 10 b). The molecules of these compounds contain five-membered metallacycles that are the result of coupling between the hydroxo ligand, DMAD, and one of the CO ligands. The new compounds were characterized by a combination of IR and NMR spectroscopy, and for [[Re(CO)(3)(bipy)(2)(mu-OH)]BF(4) (3-BF(4)), 4, 5, 6, 7, 8 b, 9, and 10 b, also by means of single-crystal X-ray diffraction.     

Noether's Theorem on Surfaces

In this article we prove a version of Noether's Theorem (of Calculus of Variations) which is valid for a general regular (compact) surface. As a special feature, the Lie group of transformations is allowed to act on the Cartesian product of the surface and the functional space. Additionally, we apply the Theorem to a problem in Classical Differential Geometry of surfaces. The given application is actually an example showing how Noether's Theorem can be used to construct invariant properties of the solutions to variational problems defined on surfaces, or equivalently, of the solutions to the associated Euler-Lagrange equations resulting from them.     

Contribution of thermal imaging to fertigation in soilless culture

Thermography is a tool used in many scientific disciplines, including agriculture. This paper describes the application of thermography as a rapid diagnostic method of adequate watering. Two experiments were conducted. In experiment 1, Philodendron erubescens and Anthurium andraeum were transplanted to pots in a greenhouse in Almeria (Spain). The vegetative growth parameters of these plants were measured. In experiment 2, two areas of vegetative cover were established on green walls: one with a combination of aromatic plants and another with ornamental indoor plants. The thermographic images were recorded using a compact infrared camera, which had a spectral infrared range of 7.3–13 μm, microbolometer of 320 × 240 pixels, and the resolution was 0.01 °C at 30 °C. Three irrigation treatments were applied in both experiments, consisting of a control treatment (CT), a deficit irrigation [1/3 less volume, deficient irrigation (DI)] treatment, and an excess irrigation [1/3 greater volume, excess irrigation (EI)] treatment. In both experiments, the sample temperatures were recorded by thermography for each irrigation treatment. In experiment 1, the vegetative growth parameters were greater under CT than under DI or EI. The data of the reference thermographs over the leaves of the potted plants were significantly correlated with the superior growth parameters under the optimal irrigation treatment. A continuous vegetative canopy was formed on both of the green walls in experiment 2, and the average temperatures were correlated with the irrigation treatments in this experiment. The temperatures reflected in the reference thermographs allowed for the determination of the most appropriate irrigation treatment. These results suggest that thermography can be a useful method to provide an early diagnosis of water stress in potted plants and green walls.     

Relation between structure and enthalpy for stacking interactions of aromatic molecules

An approximately linear correlation has been found between the enthalpy of complexation and the area of overlap of the chromophores using published structural and thermodynamical data on the self- and hetero-association of aromatic molecules measured under similar solution conditions. This finding is consistent with the assumption that short-range van-der-Waals forces dominate over other contributions to the enthalpy of stacking of aromatic molecules. It provides a ‘model-independent’ approach for a priori estimation of the enthalpy of aromatic–aromatic stacking interactions from knowledge of the structural properties or vice versa.     

Raman spectra of fluid nitrogen: intermolecular torques and orientational correlation times

A comparison is made between the rotovibrational Raman bands of fluid nitrogen at room temperature in the 180–355 amagat density range and the corresponding pure rotational bands reported previously. Accurate moment values are derived from the Raman spectra, accounting for the response of the entire experimental apparatus, after subtraction of the unwanted isotope band and of the leaking polarized Q branch. Correlation times are also calculated for both rotovibrational and pure rotational spectra accounting for the finite instrumental slitwidth.

Intermolecular torques and orientational correlation times derived from the two spectra are in good agreement for almost the entire available density range. Small discrepancies, particularly evident in the low density correlation times, are discussed and related to the rotation-vibration interaction. Intermolecular correlations are found to be negligible.     

The maximum number of columns in supersaturated designs with

Cheng and Tang [Biometrika, 88 (2001), pp. 1169–1174] derived an upper bound on the maximum number of columns that can be accommodated in a two‐symbol supersaturated design (SSD) for a given number of rows () and a maximum in absolute value correlation between any two columns (). In particular, they proved that for (mod ) and . However, the only known SSD satisfying this upper bound is when . By utilizing a computer search, we prove that for , and . These results are obtained by proving the nonexistence of certain resolvable incomplete blocks designs. The combinatorial properties of the RIBDs are used to reduce the search space. Our results improve the lower bound for SSDs with rows and columns, for , and . Finally, we show that a skew‐type Hadamard matrix of order can be used to construct an SSD with rows and columns that proves . Hence, we establish for and for all (mod ) such that . Our result also implies that when is a prime power and (mod ). We conjecture that for all and (mod ), where is the maximum number of equiangular lines in with pairwise angle .     

Heuristic approaches for support vector machines with the ramp loss

Recently, Support Vector Machines with the ramp loss (RLM) have attracted attention from the computational point of view. In this technical note, we propose two heuristics, the first one based on solving the continuous relaxation of a Mixed Integer Nonlinear formulation of the RLM and the second one based on the training of an SVM classifier on a reduced dataset identified by an integer linear problem. Our computational results illustrate the ability of our heuristics to handle datasets of much larger size than those previously addressed in the literature.     

Surface Properties of Anatase TiO2 Nanowire Films Grown from a Fluoride‐Containing Solution

Controlling the surface chemistry of nucleating seeds during wet‐chemical synthesis allows for the preparation of morphologically well‐defined nanostructures. Synthesis conditions play a key role in the surface properties, which directly affect the functional properties of the material. Therefore, it is important to establish post‐synthesis treatments to facilitate the optimization of surface properties with respect to a specific application, without losing the morphological peculiarity of the nanostructure. We studied the surface properties of highly crystalline and porous anatase TiO₂ nanowire (NW) electrodes, grown by chemical‐bath deposition in fluoride‐containing solutions, using a combined electrochemical and spectroscopic approach. As‐deposited films showed low capacity for catechol adsorption and a poor photoelectrocatalytic activity for water oxidation. Mild thermal annealing at 200 °C resulted in a significant improvement of the electrode photoelectrocatalytic activity, whereas the bulk properties of the NWs (crystal structure, band‐gap energy) remained unchanged. Enhancement of the functional properties of the material is discussed on the basis of adsorption capacity and electronic properties. The temperature‐induced decrease of recombination centers, along with the concomitant increase of adsorption and reaction sites upon thermal annealing are called to be responsible for such improved performance.