Correction to: Distance between vertices of lattice polytopes

Optimization Letters - The erratum mostly concerns Table 4 and Figure 6 where two polytopes were misrepresented in the original version.     

Multilayered polycarbonate/poly(vinylidene fluoride‐co‐hexafluoropropylene) for high energy density capacitors with enhanced lifetime

The dielectric lifetime and corresponding damage morphology of polycarbonate/poly(vinylidene fluoride‐co‐hexafluoropropylene) (PC/P(VDF‐HFP)) layered systems are studied under constant direct current (DC) field. Melt blends of the two polymers are also considered for comparison. The dielectric lifetimes of the latter are systematically much shorter than the layered systems. The interfaces between the polymers act as flaws that induce up to two orders of magnitude difference between the layered and blend systems. The capacitance values versus time during breakdown progression exhibit an inversed S‐shape pattern. The three regimes in the S‐shape pattern are consecutively attributed to randomly isolated breakdowns, interconnecting breakdowns, and wearing‐out of the capacitor film. The film breakdown images during dielectric lifetime test confirmed the transition from randomly isolated breakdowns to interconnecting breakdowns. This transition was further evidenced by a bimodal distribution in the Weibull analysis. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Azaphosphatrane Organocatalysts in Confined Space: Cage Effect in CO2 Conversion

The endohedral functionalization of a molecular cage by an azaphosphatrane unit has allowed for the creation of highly engineered catalytic cavities for efficient conversion of CO ₂ into cyclic carbonates. Strong structure/activity/stability correlations have been demonstrated by careful adjustment of the size, shape, and electronic properties of the hemicryptophane host.     

Dielectric and charge transport properties of the spin crossover complex [Fe(Htrz)2(trz)](BF4)

Spin crossover compounds are considered to be a viable alternative for creating display, memory and switching devices due to the bistability of their magnetic, optical, mechanical and electrical properties. This Letter presents the study of the dielectric and transport properties of the [Fe(Htrz)₂(trz)](BF₄) (Htrz = 1H‐1,2,4‐triazole) complex in a wide temperature and frequency range. Our results reveal a singular behavior of the dielectric modulus upon the spin transition in conjunction with the switching of the conductivity between the high spin and low spin states.

     

Equilibrium existence and uniqueness in network games with additive preferences

A directed network game of imperfect strategic substitutes with heterogeneous players is analyzed. We consider concave additive separable utility functions that encompass the quasi-linear ones. It is found that pure strategy Nash equilibria verify a non-linear complementarity problem. By requiring appropriate concavity in the utility functions, the existence of an equilibrium point is shown and equilibrium uniqueness is established with a P-matrix. For this reason, it appears that previous findings on network structure and sparsity hold for many more games.     

The diameter of associahedra

It is proven here that the diameter of the d  -dimensional associahedron is 2d−4$2d-4$ when d is greater than 9. Two maximally distant vertices of this polytope are explicitly described as triangulations of a convex polygon, and their distance is obtained using combinatorial arguments. This settles two problems posed about twenty-five years ago by Daniel Sleator, Robert Tarjan, and William Thurston.     

Fullerene-based processable polymers as plausible acceptors in photovoltaic applications

To develop n-type processable polymeric materials for photovoltaic applications, a series of polymers was synthesized by grafting fullerene C₆₀ onto polystyrene (PS). Grafted polymers were studied and compared with PS:fullerene blends. Electronical and electrical properties were first measured to define the minimal amount of C₆₀ required for solar cells application. Then, thermal properties and rheological behavior of grafted polymers were analyzed to determine whether they could be processed from the melt. A throughout experimental study revealed that C₆₀-grafted polymers exhibit two thresholds. The first threshold at 3–4 vol % (detected by electrical conductivity, electron mobility, and melt viscosity measurements) is associated to the percolation of C₆₀ molecules. The second threshold (evidenced by glass transition and melt viscosity measurements and confirmed by optical and atomic force micrograph observations) at about 12–13 vol % is assumed to be related to the formation of C₆₀ aggregates. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013