Binuclear cyclopentadienylcobalt sulfur and phosphinidene complexes Cp2Co2E2 (E = S, PX): Comparison with their Iron carbonyl analogues

Density functional theory studies on a series of Cp₂Co₂E₂ derivatives (E = S and PX; X = H, Cl, OH, OMe, NH₂, NMe₂) predict global minimum butterfly structures with one Co-Co bond for the “body” of the butterfly and four Co-E bonds at the edges of the “wings” of the butterfly. Tetrahedrane structures with both Co-Co and E-E bonds are higher in energy for Cp₂Co₂S₂ and Cp₂Co₂(PH)₂ and are not found in the other systems. This differs from the corresponding Fe₂(CO)₆S₂ and Fe₂(CO)₆(PX)₂ derivatives where tetrahedrane structures are predicted to be the lowest energy structures for all cases except X = NR₂ and OH and such a tetrahedrane structure is found experimentally for Fe₂(CO)₆S₂. The butterfly structures for the Cp₂Co₂E₂ derivatives are of two types. For Cp₂Co₂(PX)₂ (X = H, OH, OMe, NH₂, NMe₂) the lowest energy structures are unsymmetrical butterflies Cp₂Co₂(P)(PX₂) with two X groups on one phosphorus atom and a lone pair on the other (naked) phosphorus atom. Related low-energy unsymmetrical butterfly Fe₂(CO)₆(P)(PX₂) structures, not observed in previous theoretical studies, are now found for the corresponding Fe₂(CO)₆(PX)₂ derivatives. Symmetrical butterfly singlet diradical structures with one X group on each phosphorus atom in relative cis or trans positions are also found for the Cp₂Co₂(PX)₂ derivatives and are the global minima for Cp₂Co₂(PCl)₂ as well as Cp₂Co₂S₂. In all cases the cis structures are of lower energy than the corresponding trans structures. Rhombus structures having neither Co-Co nor E-E bonds are also found for all of the Cp₂Co₂(PX)₂ derivatives but always at higher energies than the butterfly structures, ranging from 17 to 29 kcal/mol above the global minima.     

Thermal desorption/gas chromatography/mass spectrometry approach for characterization of the volatile fraction from amber specimens: A possibility of tracking geological origins

Research on the chemical composition of fossil resins has evolved during the last decades as a multidisciplinary field and is strongly oriented toward the correlation with their geological and botanical origin. Various extraction procedures and chromatographic techniques have been used together for identifying the volatile compounds contained in the fossil resin matrix. Hyphenation between thermal desorption (TD), gas chromatography (GC) and mass spectrometry detection (MS) has been chosen to investigate the volatile compounds fraction from ambers with a focus on Romanite (Romanian amber) and Baltic amber species. A data analysis procedure was developed for the main purpose of fingerprinting ambers based on the MS identity of the peaks generated by the volatile fraction, together with their relative percentual area within the chromatogram. Chromatographic data analysis was based entirely on Automated Mass Spectral Deconvolution & Identification System (AMDIS) software to produce deconvoluted mass spectra which were used to build-up a mixed mass spectra and relative retention scale library. Multivariate data analysis was further applied on AMDIS results with successful discrimination between Romanite and Baltic ambers. A special trial was conducted to generate pyrolysis “like” macromolecular structure breakdown to volatile compounds by gamma irradiation with a high absorbed dose of 500 kGy. Contrary to our expectations the volatile fraction fingerprints were not modified after irradiation experiments. A complementary non-destructive new approach by ESR spectroscopy was also proposed for discriminating between Romanite and Baltic ambers.     

Stagnation-point flow past a shrinking sheet in a nanofluid

In this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al₂O₃ and TiO₂. It was found that nanoparticles of low thermal conductivity, TiO₂, have better enhancement on heat transfer compared to nanoparticles Al₂O₃ and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0.     

Bond percolation on isoradial graphs: criticality and universality

In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star–triangle transformation, by transporting the box-crossing property across the family of isoradial graphs. As a consequence, we obtain the universality of these models at the critical point, in the sense that the one-arm and $2j$ -alternating-arm critical exponents (and therefore also the connectivity and volume exponents) are constant across the family of such percolation processes. The isoradial graphs in question are those that satisfy certain weak conditions on their embedding and on their track system. This class of graphs includes, for example, isoradial embeddings of periodic graphs, and graphs derived from rhombic Penrose tilings.     

On the best constant in Hyers–Ulam stability of some positive linear operators

We obtain the infimum of the Hyers–Ulam stability constants for Stancu, Bernstein and Kantorovich operators and prove that in a class of certain positive linear operators this infimum for Bernstein operator has a minimality property.     

The Landau–Hall problem on canal surfaces

In this note we study the Landau–Hall problem on a generalized canal surface and classify all uniform magnetic trajectories of a charged particle moving on such a surface under the action of a uniform magnetic field.     

On the contact interfaces in sonic composites

The paper analyses the effect of normal contact with friction on the generation of full band-gaps in sonic composites. The behavior of contact interfaces are computed by using LISA (local interaction simulation approach). LISA is an efficient tool for numerical simulation of the acoustic wave propagation in heterogeneous material specimens, in particular those with contact interfaces between different materials, like in sonic composites. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Forward-Backward and Tseng’s Type Penalty Schemes for Monotone Inclusion Problems

We deal with monotone inclusion problems of the form 0 ∈ A x + D x + N _C (x) in real Hilbert spaces, where A is a maximally monotone operator, D a cocoercive operator and C the nonempty set of zeros of another cocoercive operator. We propose a forward-backward penalty algorithm for solving this problem which extends the one proposed by Attouch et al. (SIAM J. Optim. 21(4): 1251-1274, 2011). The condition which guarantees the weak ergodic convergence of the sequence of iterates generated by the proposed scheme is formulated by means of the Fitzpatrick function associated to the maximally monotone operator that describes the set C. In the second part we introduce a forward-backward-forward algorithm for monotone inclusion problems having the same structure, but this time by replacing the cocoercivity hypotheses with Lipschitz continuity conditions. The latter penalty type algorithm opens the gate to handle monotone inclusion problems with more complicated structures, for instance, involving compositions of maximally monotone operators with linear continuous ones.     

Employing different loss functions for the classification of images via supervised learning

Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach is applied to an image classification task. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove that, whenever strong duality holds, the function to be learned can be expressed via the dual optimal solutions. Corresponding dual problems are then derived for different loss functions. The theoretical results are applied by numerically solving a classification task using high dimensional real-world data in order to obtain optimal classifiers. The results demonstrate the excellent performance of support vector classification for this particular problem.     

Rigidity around Poisson submanifolds

We prove a rigidity theorem in Poisson geometry around compact Poisson submanifolds, using the Nash–Moser fast convergence method. In the case of one-point submanifolds (fixed points), this implies a stronger version of Conn’s linearization theorem [2], also proving that Conn’s theorem is a manifestation of a rigidity phenomenon; similarly, in the case of arbitrary symplectic leaves, it gives a stronger version of the local normal form theorem [7]. We can also use the rigidity theorem to compute the Poisson moduli space of the sphere in the dual of a compact semisimple Lie algebra [17].