A Finite Hilbert-Style Axiomatization of the Implication-Less Fragment of the Intuitionistic Propositional Calculus

In this paper we obtain a finite Hilbert-style axiomatization of the implicationless fragment of the intuitionistic propositional calculus. As a consequence we obtain finite axiomatizations of all structural closure operators on the algebra of {–}-formulas containing this fragment. Mathematics Subject Classification: 03B20, 03B22, 06D15.     

Charge order superstructure with integer iron valence in Fe(2)OBO(3)

Solution-grown single crystals of Fe(2)OBO(3) were characterized by specific heat, M?ssbauer spectroscopy, and x-ray diffraction. A peak in the specific heat at 340 K indicates the onset of charge order. Evidence for a doubling of the unit cell at low temperature is presented. Combining structural refinement of diffraction data and M?ssbauer spectra, domains with diagonal charge order are established. Bond-valence-sum analysis indicates integer valence states of the Fe ions in the charge ordered phase, suggesting Fe(2)OBO(3) is the clearest example of ionic charge order so far.     

The Trifluoromethyl Anion

First evidence for the existence of free trifluoromethyl anion CF₃^? has been obtained. The 3D‐caged potassium cation in [K(crypt‐222)]⁺ is inaccessible to CF₃^?, thus rendering it uncoordinated (“naked”). Ionic [K(crypt‐222)]⁺ CF₃^? has been characterized by single‐crystal X‐ray diffraction, solution NMR spectroscopy, DFT calculations, and reactivity toward electrophiles.     

Surviving Mass Extinctions through Biomineralized DNA

Even in the worst of conditions, such as those which occurred during mass extinction events, life on Earth never totally stopped. Aggressive chemical and physical attacks able to sterilize or poison living organisms occurred repeatedly. Surprisingly, DNA was not degraded, denatured or modified to the point of losing the capability of transferring the genetic information to the next generations. After the events of mass extinction life was able to survive and thrive. DNA was passed on despite being an extremely fragile biomolecule. The potential implications of hydroxyapatite protection of DNA are discussed in this Concept article including how DNA acts as a template for hydroxyapatite (HAp) formation, how cell death can trigger biomineralization, and how DNA can be successfully released from HAp when the conditions are favorable for life.     

A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method

We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting-plane method. The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other state-of-the-art methods, which exhausted the (144 GB of) available memory in the largest instances.     

Exchange of Chemical Species between the Atmospheric Boundary Layer and the Reservoir Layer: An Analytical Interpretation

The exchange of chemical species between the atmospheric boundary layer and the reservoir layer is investigated by means of an analytical solution of the conservation equation of a decaying chemical species. The exchange mechanism is governed by two parameters: the Damköhler number (the ratio of the turbulence time scale to the chemical time scale) and the ratio of a concentration scale in the atmospheric boundary layer to the concentration in the reservoir layer. Depending on the value of these two parameters, the exchange flux between the two layers can vary in sign and by several orders of magnitude. The study demonstrates to what extent chemical transformation determines the transfer of chemical species between the atmospheric boundary layer and the reservoir layer.