Loss of hyperbolicity changes the number of wave groups in Riemann problems

Themain goal of ourwork is to showthat there exists a class of 2×2 Riemann problems for which the solution comprises a singlewave group for an open set of initial conditions. This wave group comprises a 1-rarefaction joined to a 2-rarefaction, not by an intermediate state, but by a doubly characteristic shock, 1-left and 2-right characteristic. In order to ensure that perturbations of initial conditions do not destroy the adjacency of the waves, local transversality between a composite curve foliation and a rarefaction curve foliation is necessary.     

Synthesis of poly(n‐butyl acrylate) homopolymer and poly(styrene‐b‐n‐butyl acrylate‐b‐styrene) triblock copolymer via AGET emulsion ATRP using a cationic surfactant

Cationic emulsions of triblock copolymer particles comprising a poly(n‐butyl acrylate) (PⁿBA) central block and polystyrene (PS) outer blocks were synthesized by activator generated by electron transfer (AGET) atom transfer radical polymerization (ATRP). Difunctional ATRP initiator, ethylene bis(2‐bromoisobutyrate) (EBBiB), was used as initiator to synthesize the ABA type poly(styrene‐b‐n‐butyl acrylate‐b‐styrene) (PS‐PⁿBA‐PS) triblock copolymer. The effects of ligand and cationic surfactant on polymerizations were also discussed. Gel permeation chromatography (GPC) was used to characterize the molecular weight (M_n) and molecular weight distribution (MWD) of the resultant triblock copolymers. Particle size and particle size distribution of resulted latexes were characterized by dynamic light scattering (DLS). The resultant latexes showed good colloidal stability with average particle size around 100–300 nm in diameter. Glass transition temperature (T_g) of copolymers was studied by differential scanning calorimetry (DSC). © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 611–620     

Merging and splitting in cooperative games: some (im)possibility results

Allocation rules for cooperative games can be manipulated by coalitions merging into single players, or, conversely, players splitting into a number of smaller units. This paper collects some (im)possibility results on merging- and splitting-proofness of (core) allocation rules for cooperative games with side-payments.     

Intermolecular exchange-induction energies without overlap expansion

An approach to evaluate the second-order exchange-induction energies of symmetry-adapted intermolecular perturbation theory (SAPT) for single-determinant ground-state monomer wavefunctions has been derived. This approach is correct to all orders of the intermonomer overlap, that is, it takes multiple electron exchange between the monomers into account. The resulting formulae can be written in a compact way and implemented efficiently. Here, the method is employed to investigate the performance of the S ²- or single-exchange approximation at the Hartree-Fock-SAPT level. The list of test systems comprises the prototypical van der Waals- and hydrogen-bridge complexes Ne₂, Ar–HF, and (H₂O)₂, but also the systems HeCl^?, NeNa⁺ and Li⁺F^? involving closed-shell ions. It was found that the errors introduced by the S ²-approximation are more pronounced for the second-order exchange-induction energy than for the first-order exchange energy. While these errors tend to be negligible throughout the well region of complexes such as the neon dimer, they start to be significant in the repulsive part of the well regions of systems such as the water dimer, and in particular for the ionic lithium fluoride molecule. The consequences of these findings for the Hartree-Fock level estimate of higher-order induction plus exchange-induction energies, which is frequently employed in SAPT are also discussed.     

Applying the canonical dual theory in optimal control problems

This paper presents some applications of the canonical dual theory in optimal control problems. The analytic solutions of several nonlinear and nonconvex problems are investigated by global optimizations. It turns out that the backward differential flow defined by the KKT equation may reach the globally optimal solution. The analytic solution to an optimal control problem is obtained via the expression of the co-state. Some examples are illustrated.     

The eigenpairs of a Sylvester–Kac type matrix associated with a simple model for one-dimensional deposition and evaporation

A straightforward model for deposition and evaporation on discrete cells of a finite array of any dimension leads to a matrix equation involving a Sylvester–Kac type matrix. The eigenvalues and eigenvectors of the general matrix are determined for an arbitrary number of cells. A variety of models to which this solution may be applied are discussed.