C?X⋅⋅⋅O Halogen Bonding: Interactions of Trifluoromethyl Halides with Dimethyl Ether

The formation of weakly bound molecular complexes between dimethyl ether (DME) and the trifluoromethyl halides CF₃Cl, CF₃Br and CF₃I dissolved in liquid argon and in liquid krypton is investigated, using Raman and FTIR spectroscopy. For all halides evidence is found for the formation of C? X???O halogen‐bonded 1:1 complexes. At higher concentrations of CF₃Br, a weak absorption due to a 1:2 complex is also observed. Using spectra recorded at temperatures between 87 and 125 K, the complexation enthalpies for the complexes are determined to be ?6.8(3) kJ mol^?1 (DME?CF₃Cl), ?10.2(1) kJ mol^?1 (DME?CF₃Br), ?15.5(1) kJ mol^?1 (DME?CF₃I), and ?17.8(5) kJ mol^?1 [DME(?CF₃Br)₂]. Structural and spectral information on the complexes is obtained from ab initio calculations at the MP2/ 6‐311++G(d,p) and MP2/6‐311++G(d,p)+LanL2DZ* levels. By applying Monte Carlo free energy perturbation calculations to account for the solvent influences, and statistical thermodynamics to estimate the zero‐point vibrational and thermal influences, the ab initio complexation energies are converted into complexation enthalpies for the solutions in liquid argon. The resulting values are compared with the experimental data deduced from the cryosolutions.     

Stir bar sorptive extraction for the analysis of short‐chain chlorinated paraffins in water

An optimised method using stir bar sorptive extraction (SBSE) and a thermal desorption‐GC‐electron capture detector (GC‐ECD) for the determination of short‐chain chlorinated paraffins from water samples was developed. Recoveries near to 100% were obtained by using 20 mm×0.5 mm (length×film thickness) PDMS commercial stir bars from 200 mL spiked water samples and 20% methanol addition with an extraction period of 24 h. Method sensitivity, linearity and precision were evaluated for surface water and wastewater spiked samples. A LOD of 0.03 and 0.04 μg/L was calculated for surface and wastewater, respectively. The precision of the method given as an RSD was below 20% for both matrices. The developed method was applied for the analysis of two real samples from a contaminated river and a wastewater treatment plant. Results were in accordance with those obtained using a previously developed method based on solid phase microextraction (SPME).     

The study of cyclooctene oxidation with molecular oxygen catalyzed by VSi2

The catalytic effect of VSi₂ on initial stages of the liquid-phase oxidation of cyclooctene by molecular oxygen was studied. The vanadium disilicide influences on the oxidation process in the presence of hydroperoxide. VSi₂ takes part in a radical formation stage by catalysis of hydroperoxide decomposition reaction. The catalyst was investigated before and after reaction using FTIR spectroscopy. From the data obtained, the kinetic model of the catalytic oxidation process was proposed and the equation for the reaction rate was derived. The equation has described all observed dependences of reaction rate on the concentration of reactants and content of catalyst.      

Weak maximum principle and accessory problem for control problems on time scales

In this paper we derive the first and second variations for a nonlinear time scale optimal control problem with control and state-endpoints equality constraints. Using the first variation, a first order necessary condition for weak local optimality is obtained under the form of a weak maximum principle generalizing the Dubois–Reymond Lemma to the optimal control setting and time scales. A second order necessary condition in terms of the accessory problem is derived by using the nonnegativity of the second variation at all admissible directions. The control problem is studied under a controllability assumption, and with or without the shift in the state variable. These two forms of the problem are shown to be equivalent.     

Convergence of a finite element/ALE method for the Stokes equations in a domain depending on time

We consider the approximation of the unsteady Stokes equations in a time dependent domain when the motion of the domain is given. More precisely, we apply the finite element method to an Arbitrary Lagrangian Eulerian (ALE) formulation of the system. Our main results state the convergence of the solutions of the semi-discretized (with respect to the space variable) and of the fully-discrete problems towards the solutions of the Stokes system.     

Rough set approach to multiple criteria classification with imprecise evaluations and assignments

Dominance-based Rough Set Approach (DRSA) has been introduced to deal with multiple criteria classification (also called multiple criteria sorting, or ordinal classification with monotonicity constraints), where assignments of objects may be inconsistent with respect to dominance principle. In this paper, we consider an extension of DRSA to the context of imprecise evaluations of objects on condition criteria and imprecise assignments of objects to decision classes. The imprecisions are given in the form of intervals of possible values. In order to solve the problem, we reformulate the dominance principle and introduce second-order rough approximations. The presented methodology preserves well-known properties of rough approximations, such as rough inclusion, complementarity, identity of boundaries and precisiation. Moreover, the meaning of the precisiation property is extended to the considered case. The paper presents also a way to reduce decision tables and to induce decision rules from rough approximations.     

Semitoric integrable systems on symplectic 4-manifolds

Let (M,ω) be a symplectic 4-manifold. A semitoric integrable system on (M,ω) is a pair of smooth functions J,H∈C ^∞(M,ℝ) for which J generates a Hamiltonian S ¹-action and the Poisson brackets {J,H} vanish. We shall introduce new global symplectic invariants for these systems; some of these invariants encode topological or geometric aspects, while others encode analytical information about the singularities and how they stand with respect to the system. Our goal is to prove that a semitoric system is completely determined by the invariants we introduce. A. Pelayo was partially supported by an NSF Postdoctoral Fellowship.