Synthesis, characterization, reactivity and catalytic activity of oxidovanadium(IV), oxidovanadium(V) and dioxidovanadium(V) complexes of benzimidazole modified ligands

The reaction between [V(IV)O(acac)(2)] and the ONN donor Schiff base obtained by the condensation of pyridoxal and 2-aminoethylbenzimidazole (Hpydx-aebmz, I) or 2-aminomethylbenzimidazole (Hpydx-ambmz, II) in equimolar amounts results in the formation of [V(IV)O(acac)(pydx-aebmz)] 1 and [V(IV)O(acac)(pydx-ambmz)] 2, respectively. The aerobic oxidation of the methanolic solution of 1 yielded [V(V)O(2)(pydx-aebmz)] 3 and its reaction with aqueous H(2)O(2) gave the oxidoperoxidovanadium(v) complex, [V(V)O(O(2))(pydx-aebmz)] 4. The formation of 4 in solution is also established by titrations of methanolic solutions of 1 with H(2)O(2). By titrating solutions of 3 and of 4 with aqueous H(2)O(2) several distinct V(V)-pydx-aebmz species also containing the peroxido ligand are detected. The full geometry optimization of all species envisaged was done using DFT methods for suitable model complexes. The (51)V NMR chemical shifts (δ(V)) have also been calculated, the theoretical data being used to support assignments of the experimental chemical shifts. The (51)V hyperfine coupling constants are calculated for 1, the obtained values being in good agreement with the experimental EPR data. Reaction between the V(IV)O(2+) exchanged zeolite-Y and Hpydx-aebmz and Hpydx-ambmz in refluxing methanol, followed by aerial oxidation results in the formation of the encapsulated V(V)O(2)-complexes, abbreviated herein as [V(V)O(2)(pydx-aebmz)]-Y 5 and [V(V)O(2)(pydx-ambmz)]-Y 6. The molecular structure of 1, determined by single crystal X-ray diffraction, confirms its distorted octahedral geometry with the ONN binding mode of the tridentate ligand, with one acetylacetonato group remaining bound to the V(IV)O-centre. Oxidation of styrene is investigated using some of these complexes as catalyst precursors with H(2)O(2) as oxidant. Under optimised reaction conditions for the conversion of styrene in acetonitrile, a maximum of 68% conversion of styrene (with [V(V)O(2)(pydx-aebmz)]-Y) and 65% (with [V(V)O(2)(pydx-ambmz)]-Y) is achieved in 6 h of reaction time. The selectivity of the various products is similar for both catalysts and follows the order: benzaldehyde (ca. 55%) > 1-phenylethane-1,2-diol > benzoic acid > styrene oxide > phenyl acetaldehyde. Speciation of the systems and plausible intermediates involved in the catalytic oxidation processes are established by UV-Vis, EPR, (51)V NMR and DFT studies. Both non-radical (Sharpless) and radical mechanisms of the olefin oxidations were theoretically studied, and the radical pathway was found to be even more favorable than the Sharpless mechanism.     

Exact algorithms for the traveling salesman problem with draft limits

This paper deals with the Traveling Salesman Problem (TSP) with Draft Limits (TSPDL), which is a variant of the well-known TSP in the context of maritime transportation. In this recently proposed problem, draft limits are imposed due to restrictions on the port infrastructures. Exact algorithms based on three mathematical formulations are proposed and their performance compared through extensive computational experiments. Optimal solutions are reported for open instances of benchmark problems available in the literature.     

On the existence of polyanalytic functions

We give a sharp estimate for the codimension of the poly‐Bergman space in the poly‐Bergman space over the punctured domain. It is established the behaviour at the infinity point of polyanalytic Bergman functions on the complement of closed disks. In the main result of the paper, we prove that for and the j‐polyanalytic Bergman space over the domain U is trivial precisely when the complement of U has at most one point and at most two points or three points lying in a circle, respectively. We point out the differences between the domains over which the Bergman space and the non‐analytic poly‐Bergman space are trivial.     

Density and spectrum of minimal submanifolds in space forms

Let \(\varphi : M^m \rightarrow N^n\) be a minimal, proper immersion in an ambient space suitably close to a space form \(\mathbb {N}^n_k\) of curvature \(-k\le 0\). In this paper, we are interested in the relation between the density function \(\Theta (r)\) of M and the spectrum of its Laplace–Beltrami operator. In particular, we prove that if \(\Theta (r)\) has subexponential growth (when \(k<0\)) or sub-polynomial growth (\(k=0\)) along a sequence, then the spectrum of \(M^m\) is the same as that of the space form \(\mathbb {N}^m_k\). Notably, the result applies to Anderson’s (smooth) solutions of Plateau’s problem at infinity on the hyperbolic space, independently of their boundary regularity. We also give a simple condition on the second fundamental form that ensures M to have finite density. In particular, we show that minimal submanifolds with finite total curvature in the hyperbolic space also have finite density.     

Determination of Cd levels in smoke condensate of Brazilian and Paraguayan cigarettes by Thermospray Flame Furnace Atomic Absorption Spectrometry (TS-FF-AAS)

In this study, the concentrations of Cd in smoke condensate of Paraguayan and Brazilian full flavor normal size cigarettes were determined. A “fishtail” chimney was used to confine and direct cigarette smoke to an impaction trap followed by 3 MCE (mixed cellulose ester) filters for smoke collection. The smoke condensate collected at the first two collection stages (chimney and impactor) was prepared as Triton X-100 slurry samples and the 3 MCE filters (third collection stage) used to collect smoke were microwave digested. Samples were analyzed by Thermospray Flame Furnace Atomic Absorption Spectrometry (TS-FF-AAS) for Cd and the results obtained were compared with Graphite Furnace Atomic Absorption Spectrometry (GFAAS). No significant differences were found between the values obtained with TS-FF-AAS and GFAAS at a 95% confidence level. The total concentration of Cd in the smoke of Brazilian and Paraguayan cigarettes tested ranged from 187 to 281 ng/cigarette and from 176 to 271 ng/cigarette, respectively. The LODs for Cd using TS-FF-AAS and GFAAS, were 5.8 and 1.5 ng/cigarette, respectively, for the analysis of smoke condensate from 1 cigarette. The main advantages of using the simple TS-FF-AAS system are its low running costs and the analysis time when compared to GFAAS.     

1H and 13C NMR spectral assignments of four dammarane triterpenoids from carnauba wax

The phytochemical investigation of carnauba wax led to the isolation of three new dammarane triterpenoids 1, 2 and 4, together with the known triterpene 3. The structures of the new compounds were determined by 1D and 2D NMR spectroscopy and by comparison with published data for closely related compounds.     

Phase portraits for quadratic homogeneous polynomial vector fields on $$ \mathbb{S}^2 $$

Let X be a homogeneous polynomial vector field of degree 2 on $ \mathbb{S}^2 $ \mathbb{S}^2 . We show that if X has at least a non-hyperbolic singularity, then it has no limit cycles. We give necessary and sufficient conditions for determining if a singularity of X on $ \mathbb{S}^2 $ \mathbb{S}^2 is a center and we characterize the global phase portrait of X modulo limit cycles. We also study the Hopf bifurcation of X and we reduce the 16 ^th Hilbert’s problem restricted to this class of polynomial vector fields to the study of two particular families. Moreover, we present two criteria for studying the nonexistence of periodic orbits for homogeneous polynomial vector fields on $ \mathbb{S}^2 $ \mathbb{S}^2 of degree n.