N-phosphonio formamidine derivatives: Synthesis,characterization, X-ray crystal structures,and deprotonation reactions

A simple and efficient method for the preparation of N-phosphonio formamidine derivatives of the general formula [R”₂N?C(H)=N?P(R’)R₂]⁺X^? is described. The data recorded in solution and the single crystal X-ray studies revealed that these compounds are best described by the combination of the two mesomeric N-phosphonio formamidine [R”₂N?C(H)=N?P(R’)R₂]⁺ and iminium phosphazene [R”₂N=C(H)?N=P(R’)R₂]⁺ forms. Formamidine phosphorus ylides ⁱPr₂N?C(H)=N?P(CH₂)R₂ were prepared after addition of ^tBuLi at –78 °C from the corresponding N-phosphonio compounds. [(PhCN)₂Pd(Cl)₂] was reacted with ⁱPr₂N?C(H)=N?P(CH₂)ⁱPr₂ to form the dimeric complex [(ⁱPr₂N?C(H)=N?P(CH₂)ⁱPr₂)Pd(Cl)(μ-Cl)]₂ which was structurally characterized by X-ray analysis. The deprotonation reactions conducted on [ⁱPr₂N?C(H)=N?PPh₃]⁺X^? occurred via an intramolecular rearrangement to give the cyanamide compound ⁱPr₂N?C≡N and PPh₃; transient formation of the amino-phosphazene-carbene ⁱPr₂N?C?N=PPh₃ was not observed.     

Disparate effects of Cu and V on structures of exohedral transition metal-doped silicon clusters: a combined far-infrared spectroscopic and computational study

The growth mechanisms of small cationic silicon clusters containing up to 11 Si atoms, exohedrally doped by V and Cu atoms, are described. We find that as dopants, V and Cu follow two different paths: while V prefers substitution of a silicon atom in a highly coordinated position of the cationic bare silicon clusters, Cu favors adsorption to the neutral or cationic bare clusters in a lower coordination site. The different behavior of the two transition metals becomes evident in the structures of Si(n)M(+) (n = 4-11 for M = V, and n = 6-11 for M = Cu), which are investigated by density functional theory and, for several sizes, confirmed by comparison with their experimental vibrational spectra. The spectra are measured on the corresponding Si(n)M(+)·Ar complexes, which can be formed for the exohedrally doped silicon clusters. The comparison between experimental and calculated spectra indicates that the BP86 functional is suitable to predict far-infrared spectra of these clusters. In most cases, the calculated infrared spectrum of the lowest-lying isomer fits well with the experiment, even when various isomers and different electronic states are close in energy. However, in a few cases, namely Si(9)Cu(+), Si(11)Cu(+), and Si(10)V(+), the experimentally verified isomers are not the lowest in energy according to the density functional theory calculations, but their structures still follow the described growth mechanism. The different growth patterns of the two series of doped Si clusters reflect the role of the transition metal's 3d orbitals in the binding of the dopant atoms.     

DC programming and DCA for globally solving the value-at-risk

The value-at-risk is an important risk measure that has been used extensively in recent years in portfolio selection and in risk analysis. This problem, with its known bilevel linear program, is reformulated as a polyhedral DC program with the help of exact penalty techniques in DC programming and solved by DCA. To check globality of computed solutions, a global method combining the local algorithm DCA with a well adapted branch-and-bound algorithm is investigated. An illustrative example and numerical simulations are reported, which show the robustness, the globality and the efficiency of DCA.     

Portfolio selection under downside risk measures and cardinality constraints based on DC programming and DCA

In this paper, we consider the case of downside risk measures with cardinality and bounding constraints in portfolio selection. These constraints limit the amount of capital to be invested in each asset as well as the number of assets composing the portfolio. While the standard Markowitz’s model is a convex quadratic program, this new model is a NP-hard mixed integer quadratic program. Realizing the computational intractability for this class of problems, especially large-scale problems, we first reformulate it as a DC program with the help of exact penalty techniques in Difference of Convex functions (DC) programming and then solve it by DC Algorithms (DCA). To check globality of computed solutions, a global method combining the local algorithm DCA with a Branch-and-Bound algorithm is investigated. Numerical simulations show that DCA is an efficient and promising approach for the considered problem.      

Quantitative testing of robustness on superomniphobic surfaces by drop impact

The quality of a liquid-repellent surface is quantified by both the apparent contact angle θ(0) that a sessile drop adopts on it and the value of the liquid pressure threshold the surface can withstand without being impaled by the liquid, hence maintaining a low-friction condition. We designed surfaces covered with nanowires obtained by the vapor-liquid-solid (VLS) growth technique that are able to repel most of the existing nonpolar liquids including those with very low surface tension as well as many polar liquids with moderate to high surface tension. These superomniphobic surfaces exhibit apparent contact angles ranging from 125 to 160° depending on the liquid. We tested the robustness of the surfaces against impalement by carrying out drop impact experiments. Our results show how this robustness depends on Young's contact angle θ(0) related to the surface tension of the liquid and that the orientational growth of nanowires is a favorable factor for robustness.     

Microstructure and mechanical properties of bacterial cellulose/chitosan porous scaffold

A family of polysaccharide based scaffold materials, bacterial cellulose/chitosan (BC/CTS) porous scaffolds with various weight ratios (from 20/80 to 60/40 w/w%) were prepared by freezing (−30 and −80 °C) and lyophilization of a mixture of microfibrillated BC suspension and chitosan solution. The microfibrillated BC (MFC) was subjected to 2,2,6,6-tetramethylpyperidine-1-oxyl radical (TEMPO)-mediated oxidation to introduce surface carboxyl groups before mixing. The integration of MFC within chitosan matrix was performed by 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide hydrochloride (EDC)-mediated cross-linking. The covalent amide bond formation was determined by ATR-FTIR. Because of this covalent coupling, the scaffolds retain their original shapes during autoclave sterilization. The composite scaffolds are three-dimensional open pore microstructure with pore size ranging from 120 to 280 μm. The freezing temperature and mean pore size take less effect on scaffold mechanical properties. The compressive modulus and strength increased with increase in MFC content. The results show that the scaffolds of higher MFC content contribute to overall better mechanical properties.     

Lattices generated by Chip Firing Game models: Criteria and recognition algorithms

It is well-known that the class of lattices generated by Chip Firing Games (CFGs) is strictly included in the class of upper locally distributive lattices (ULD). However a necessary and sufficient criterion for this class is still an open question. In this paper we settle this problem by giving such a criterion. This criterion provides a polynomial-time algorithm for constructing a CFG which generates a given lattice if such a CFG exists. Going further we solve the same problem on two other classes of lattices which are generated by CFGs on the classes of undirected graphs and directed acyclic graphs.     

On a nonlinear wave equation with boundary conditions of two-point type

The paper is devoted to the study a nonlinear wave equation with boundary conditions of two-point type. Existence of a weak solution is proved by using Faedo-Galerkin method. Uniqueness, regularity and decay properties of solutions are also discussed.