Helly-Type Theorems for Line Transversals to Disjoint Unit Balls

We prove Helly-type theorems for line transversals to disjoint unit balls in ℝ ^d . In particular, we show that a family of n≥2d disjoint unit balls in ℝ ^d has a line transversal if, for some ordering ≺ of the balls, any subfamily of 2d balls admits a line transversal consistent with ≺. We also prove that a family of n≥4d−1 disjoint unit balls in ℝ ^d admits a line transversal if any subfamily of size 4d−1 admits a transversal. Andreas Holmsen was supported by the Research Council of Norway, prosjektnummer 166618/V30. Otfried Cheong and Xavier Goaoc acknowledge support from the French-Korean Science and Technology Amicable Relationships program (STAR).     

Linear and non-linear conduction regimes in broken down gate oxides

We have investigated conduction properties of gate oxides in metal-oxide–semiconductor structures in which dielectric breakdown has occurred. The measurements were performed on p- and n-type substrate samples with oxide thickness ranging from 2.0 to 13.5 nm. It is shown that the post-breakdown differential conductance has two typical modes, which, in terms of the physics of mesoscopic conducting systems, are referred to as linear and non-linear conduction regimes. In this work, we propose an analytic model for the conductance based on the electron transmission properties of quantum point contacts, which captures the essential features and consistently explains both breakdown modes.     

Two phase algorithms for the bi-objective assignment problem

In this paper, we present several algorithms for the bi-objective assignment problem. The algorithms are based on the two phase method, which is a general technique to solve multi-objective combinatorial optimisation (MOCO) problems.     

Route to chaos in the rising dynamics of a bubble chain in a polymeric fluid

We investigate the chaotic dynamics of a bubble chain rising in a polymeric fluid by the experimental temporary measurements, cognitive modelling and analytical analysis. The competition between the stress creation and the relaxation displays complex dynamical features and leads to chaos through a sequence of period doubling bifurcations.     

Quasilinear elliptic system with coupling on nonhomogeneous critical term

We study the existence of multiple solutions for a quasilinear elliptic system of gradient type with the possibility of coupling on the critical and subcritical terms which are not necessarily homogeneous. The solutions are obtained from a version of the Symmetric Mountain Pass Theorem. A version of the Concentration-Compactness Principle for this class of systems allows us to verify that the Palais–Smale condition is satisfied below a certain level.     

Highly enantioselective fluoromalonate addition to α,β-unsaturated aldehydes

A highly enantioselective organocatalytic fluoromalonate addition to α,β-unsaturated aldehydes is reported. The reaction is catalyzed by simple and commercially available secondary amines, affording the corresponding 1,4-adducts with high yields and enantioselectivities.