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).     

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.     

Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).     

Diabatic investigation for the NaRb molecule

An extensive diabatic investigation of the NaRb species has been carried out for all excited states up to the ionic limit Na^‐Rb⁺. An ab initio calculation founded on the pseudopotential, core polarization potential operators and full configuration interaction has been used with an efficient diabatization method involving a combination of variational effective hamiltonian theory and an effective overlap matrix. Diabatic potential energy curves and electric dipole moments (permanent and transition) for all the symmetries Σ⁺, Π, and Δ have been studied for the first time. Thanks to a unitary rotation matrix, the examination of the diabatic permanent dipole moment (PDM) has shown the ionic feature clearly seen in the diabatic ¹Σ⁺ potential curves and confirming the high imprint of the Na^‐Rb⁺ ionic state in the adiabatic representation. Diabatic transition dipole moments have also been computed. Real crossings have been shown for the diabatic PDM, locating the avoided crossings between the corresponding adiabatic energy curves.     

Thorium(IV) and neptunium(V) uptake from carbonate containing aqueous solutions by HDTMA-modified natural zeolites

The ²³²Th-uptake ([Th(IV)]° = 9.7 × 10^?5 M) from carbonate solutions ([CO ₃ ² ]_tot = 0.25 M, 9.0 < pH_c < 10.8) by raw and HDTMA-modified HEU-type zeolitic-, chabazitic- and phillipsitic-tuffs was investigated. The strong uptake by the HDTMA-tuffs at pH_c≈9 was assigned to the Th(CO₃) ₅ ^6? and ThOH(CO₃) ₄ ^5? predominance. The sorption coefficients (R _d) decreased with increasing pH_c indicating carbonate competition. Enhanced R _d values for pH_c > 10.5 are likely due to ThO₂(am)-precipitation. The ²³⁷Np-uptake ([Np(V)]° = 2.6 × 10^?5 M) from carbonate solutions ([CO ₃ ² ]_tot = 0.25 and 3.0 × 10^?4 M) by raw and HDTMA-modified HEU-type zeolitic tuff and pulverized pure heulandite crystals was studied under Ar-atmosphere at 6 < pH_c < 11. The R _d values for both elements indicated the modified tuffs potential to remove tetravalent- and pentavalent actinides from environmental matrices.