Unusual nonoctahedral geometry with molybdenum oxoimido complexes containing η2-pyrazolate ligands

The preparation and oxygen-atom-transfer (OAT) reactivity of oxoimido complexes [MoO(N-t-Bu)(t-Bu(2)-4-Rpz)(2)] [where R = H (1), Br (2), and Me (3); t-Bu(2)pz = 3,5-di-tert-butylpyrazolate] are reported. The reaction of the potassium salt of the respective pyrazolate ligands and the molybdenum oxoimido precursor, [MoO(N-t-Bu)Cl(2)(dme)] (dme = dimethoxyethane), in toluene afforded complexes 1-3 in good yields. The complexes were fully characterized by (1)H and (13)C NMR and IR spectroscopy, mass spectrometry, elemental analysis, and single-crystal X-ray crystallography. The solid-state structures reveal that, in each case, the molybdenum center is coordinated by one oxo, one N-t-Bu group, and two sterically demanding pyrazolate ligands via their two adjacent nitrogen atoms in an η(2) fashion. Coordination around the metal center is severely distorted from octahedral and might be seen as closely approaching a distorted trigonal-prismatic geometry, which is relevant to the active site of dimethyl sulfoxide reductase in its oxidized form. The potential utility of all of the complexes 1-3 for OAT reactivity toward PMe(3) at room temperature is examined, and plausible mechanistic pathways are explored by density functional theory calculations. Furthermore, the complexes reported here open a new and convenient entry into mixed oxoimidomolybdenum complexes.     

Unexpected acidity enhancement triggered by AlH3 association to phosphines

The complexes formed by the interaction between a series of phosphines R-PH(2) (R = H, CH(3), c-C(3)H(5), C(6)H(5)) and AlH(3) have been investigated through the use of high-level G4 ab initio calculations. These very stable complexes behave as much stronger acids than the isolated phosphines. This dramatic acidity enhancement, which can be as high as 174 kJ mol(-1), results from a much greater stabilization of the anionic deprotonated species with respect to the neutral one, upon AlH(3) association. This effect depends quantitatively on the nature of the substituent R and is smaller for R = C(6)H(5) because of the conjugation of the P lone pair with the aromatic system. More unexpectedly, however, the phosphine-alane complexes, RPH(2):AlH(3), are more acidic than the corresponding phosphine-borane RPH(2):BH(3) analogues. This unexpected result is due to the enhanced stability of the anionic deprotonated species for complexes involving AlH(3), because the delocalization of the newly created P lone pair with the P-Al bonding density is more favorable when the Lewis acid is aluminum trihydride than when it is borane.     

Substituent effects on the thermochemistry of thiophenes. a theoretical (G3(MP2)//B3LYP and G3) study

Very good linear correlations between experimental and calculated enthalpies of formation in the gas phase (G3(MP2)//B3LYP and G3) for 48 thiophene derivatives have been obtained. These correlations permit a correction of the calculated enthalpies of formation in order to estimate more reliable "experimental" values for the enthalpies of formation of substituted thiophenes, check the reliability of experimental measurements, and also predict the enthalpies of formation of new thiophenes that are not available in the literature. Moreover, the difference between the enthalpies of formation of isomeric thiophenes with the same substituent in positions 2 and 3 of the ring has been analyzed. Likewise, a comparison of the substituent effect in the thiophene and benzene rings has been established.     

Comment on “Heteroclinic orbits in Chen circuit with time delay” [Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 3058–3066]

The authors claim in the abstract of the referenced paper that Existence of Shil’nikov type of heteroclinic orbit in Chen circuit with direct time delay feedback is proved using the undetermined coefficient method. As a result, Shil’nikov criterion guarantees that the circuit has Smale horseshoes and the circuit demonstrates chaos in a rigorous analytical sense. Unfortunately, we show in this comment that their demonstration is incorrect.     

Variable neighborhood search with ejection chains for the antibandwidth problem

In this paper, we address the optimization problem arising in some practical applications in which we want to maximize the minimum difference between the labels of adjacent elements. For example, in the context of location models, the elements can represent sensitive facilities or chemicals and their labels locations, and the objective is to locate (label) them in a way that avoids placing some of them too close together (since it can be risky). This optimization problem is referred to as the antibandwidth maximization problem (AMP) and, modeled in terms of graphs, consists of labeling the vertices with different integers or labels such that the minimum difference between the labels of adjacent vertices is maximized. This optimization problem is the dual of the well-known bandwidth problem and it is also known as the separation problem or directly as the dual bandwidth problem. In this paper, we first review the previous methods for the AMP and then propose a heuristic algorithm based on the variable neighborhood search methodology to obtain high quality solutions. One of our neighborhoods implements ejection chains which have been successfully applied in the context of tabu search. Our extensive experimentation with 236 previously reported instances shows that the proposed procedure outperforms existing methods in terms of solution quality.     

Two-sex Branching Models with Random Control on the Number of Progenitor Couples

In this paper we introduce a class of two-sex branching models where, in each generation, a random control on the number of progenitor couples in the population is considered. For such a class, several probabilistic results are established. Also assuming offspring probability distribution belonging to the bivariate power series family, Bayes estimators for the mean vector and the covariance matrix of the offspring distribution are proposed. A computational method to determine highest posterior density credibility sets is stated. As illustration, a simulated example is provided.     

Weak crossed biproducts and weak projections

In this paper, we present the general theory and universal properties of weak crossed biproducts. We prove that every weak projection of weak bialgebras induces one of these weak crossed structures. Finally, we compute explicitly the weak crossed biproduct associated with a groupoid that admits an exact factorization.     

A mathematical model and a numerical model for hyperbolic mass transport in compressible flows

A number of contributions have been made during the last decades to model pure-diffusive transport problems by using the so-called hyperbolic diffusion equations. These equations are used for both mass and heat transport. The hyperbolic diffusion equations are obtained by substituting the classic constitutive equation (Fick’s and Fourier’s law, respectively), by a more general differential equation, due to Cattaneo (C R Acad Sci Ser I Math 247:431–433, 1958). In some applications the use of a parabolic model for diffusive processes is assumed to be accurate enough in spite of predicting an infinite speed of propagation (Cattaneo, C R Acad Sci Ser I Math 247:431–433, 1958). However, the use of a wave-like equation that predicts a finite velocity of propagation is necessary in many other calculations. The studies of heat or mass transport with finite velocity of propagation have been traditionally limited to pure-diffusive situations. However, the authors have recently proposed a generalization of Cattaneo’s law that can also be used in convective-diffusive problems (Gómez, Technical Report (in Spanish), University of A Coruña, 2003; Gómez et al., in An alternative formulation for the advective-diffusive transport problem. 7th Congress on computational methods in engineering. Lisbon, Portugal, 2004a; Gómez et al., in On the intrinsic instability of the advection–diffusion equation. Proc. of the 4th European congress on computational methods in applied sciences and engineering (CDROM). Jyväskylä, Finland, 2004b) (see also Christov and Jordan, Phys Rev Lett 94:4301–4304, 2005). This constitutive equation has been applied to engineering problems in the context of mass transport within an incompressible fluid (Gómez et al., Comput Methods Appl Mech Eng, doi: 10.1016/j.cma.2006.09.016, 2006). In this paper we extend the model to compressible flow problems. A discontinuous Galerkin method is also proposed to numerically solve the equations. Finally, we present some examples to test out the performance of the numerical and the mathematical model.     

An Experimental Evaluation of a Scatter Search for the Linear Ordering Problem

Scatter search is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear global optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, such as in generating surrogate constraints, scatter search uses strategies for combining solution vectors that have proved effective in a variety of problem settings. In this paper, we present a scatter search implementation designed to find high quality solutions for the NP-hard linear ordering problem, which has a significant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input-output tables in economics. Our implementation incorporates innovative mechanisms to combine solutions and to create a balance between quality and diversification in the reference set. We also use a tracking process that generates solution statistics disclosing the nature of combinations and the ranks of antecedent solutions that produced the best final solutions. Extensive computational experiments with more than 300 instances establishes the effectiveness of our procedure in relation to approaches previously identified to be best.