Air‐Stable Solid Aryl and Heteroaryl Organozinc Pivalates: Syntheses and Applications in Organic Synthesis

A wide range of air‐stable, solid, polyfunctional aryl and heteroarylzinc pivalates were efficiently prepared by either magnesium insertion or Hal/Mg exchange followed by transmetalation with Zn(OPiv)₂ (OPiv=pivalate). By reducing the amount of LiCl the air stability could be significantly enhanced compared with previously prepared reagents. An alternative route is directed magnesiation using TMPMgCl ? LiCl (TMP=2,2,6,6‐tetramethylpiperidyl) followed by transmetalation with Zn(OPiv)₂ or, for very sensitive substrates, direct zincation by using TMPZnOPiv. These zinc reagents not only show excellent stability towards air, but they also undergo a broad range of C?C bond‐formation reactions, such as allylation and carbocupration reactions, as well as addition to aldehydes and 1,4‐addition reactions. Acylation reactions can be performed by using an excess of TMSCl to overcome side reactions of the omnipresent pivalate anion.     

Switchable dielectric permittivity with temperature and Dc-bias in a semifluorinated azobenzene derivative

The thermodynamic, optical, structural, and dynamic properties of the semifluorinated (E)-1-(4-octylphenyl)-2-(4-(perfluorooctyl)phenyl)diazene (4) and the corresponding (E)-1,2-bis(4-octylphenyl)diazene (5) have been studied with differential scanning calorimetry, polarizing optical microscopy, X-ray diffraction, and dielectric spectroscopy. 4 combines the azobenzene properties with the fluorophobic effect and gives rise to a responsive material with a temperature and dc-bias-driven switchable dielectric permittivity within the narrower nematic phase. This is caused by the nematic potential that inevitably brings some fluorocarbon chains in proximity to the hydrocarbon chains from adjacent molecules. Frustration is alleviated by reducing the nematic-to-isotropic transition temperature and by increasing the crystalline-to-nematic transition temperature, thus limiting the stability of the nematic phase. Unlike the normal isotropic phase of compound 5, the isotropic phase of compound 4 contains dipoles with short-range orientation correlations. Optimizing the type of interactions may result in materials with applications as molecular switches and electrooptic devices.     

Distributions with Heavy Tails in Orlicz Spaces

This paper relies on the application of Kantorovich functionals on quasi-interior points of the positive cone for certain classes of Orlicz spaces. Particularly we provide the asymptotic calculation of the ruin probability in the renewal risk model under heavy-tailed claims in the Orlicz spaces. This application assures the extension of classical asymptotic theory of regular variation.     

Resource contention games in multiclass stochastic flow models

We consider resource contention games in a stochastic hybrid system setting using Stochastic Flow Models (SFM) with multiple classes and class-dependent objectives. We present a general modeling framework for such games, where Infinitesimal Perturbation Analysis (IPA) estimators are derived for the derivatives of various class-dependent objectives. This allows us to study these games from the point of view of system-centric optimization of a performance metric and compare it to the user-centric approach where each user optimizes its own performance metric. We derive explicit solutions for a specific model in which the competing user classes employ threshold control policies and service is provided on a First Come First Serve (FCFS) basis. The unbiasedness of the IPA estimators is established in this case and it is shown that under certain conditions the system-centric and user-centric optimization solutions coincide.     

Global solution of nonlinear mixed-integer bilevel programs

An algorithm for the global optimization of nonlinear bilevel mixed-integer programs is presented, based on a recent proposal for continuous bilevel programs by Mitsos et al. (J Glob Optim 42(4):475–513, 2008). The algorithm relies on a convergent lower bound and an optional upper bound. No branching is required or performed. The lower bound is obtained by solving a mixed-integer nonlinear program, containing the constraints of the lower-level and upper-level programs; its convergence is achieved by also including a parametric upper bound to the optimal solution function of the lower-level program. This lower-level parametric upper bound is based on Slater-points of the lower-level program and subsets of the upper-level host sets for which this point remains lower-level feasible. Under suitable assumptions the KKT necessary conditions of the lower-level program can be used to tighten the lower bounding problem. The optional upper bound to the optimal solution of the bilevel program is obtained by solving an augmented upper-level problem for fixed upper-level variables. A convergence proof is given along with illustrative examples. An implementation is described and applied to a test set comprising original and literature problems. The main complication relative to the continuous case is the construction of the parametric upper bound to the lower-level optimal objective value, in particular due to the presence of upper-level integer variables. This challenge is resolved by performing interval analysis over the convex hull of the upper-level integer variables.     

Spectra of Some Interesting Combinatorial Matrices Related to Oriented Spanning Trees on a Directed Graph

The Laplacian of a directed graph G is the matrix L(G) = O(G) –, A(G) where A(G) is the adjaceney matrix of G and O(G) the diagonal matrix of vertex outdegrees. The eigenvalues of G are the eigenvalues of A(G). Given a directed graph G we construct a derived directed graph D(G) whose vertices are the oriented spanning trees of G. Using a counting argument, we describe the eigenvalues of D(G) and their multiplicities in terms of the eigenvalues of the induced subgraphs and the Laplacian matrix of G. Finally we compute the eigenvalues of D(G) for some specific directed graphs G. A recent conjecture of Propp for D(H _n ) follows, where H _n stands for the complete directed graph on n vertices without loops.     

Formation of sulfines in the peroxyacid oxidation of neopentyl neopentanethiolsulfinate

Low temperature ¹H NMR and ¹³C NMR, and IR suggest that the $\text{m}$-chloroperbenzoic acid (MCPBA) oxidation of neopentyl neopentanethiolsulfinate leads to the formation of (E)- and (Z)-2,2-dimethylpropanethial S-oxide, neopentyl neopentanethiolsulfonate, and other products.     

Modelling of discontinuities through dipole distribution

An indirect boundary element method using dipole distribution is employed in order to model discontinuities inside the flow region. The problem of flow under a dam is treated with a sheet-pile in its foundation. The discontinuity across the sheet-pile is demonstrated, a general boundary element procedure for a mixed problem is outlined and the coefficients of the linear system are given in analytical form. Very good agreement with existing analytical results is obtained.     

Mesostructured selenides with cubic MCM-48 type symmetry: large framework elasticity and uncommon resiliency to strong acids

The metal mesostructured Pt/Sn/Se chalcogenides with cubic MCM-48 type pore symmetry are found to be surprisingly stable in concentrated oxidizing acids. Their metal chalcogenide framework exhibits high flexibility during reversible proton exchange as it expands and contracts in an apparent breathing-like action.