On the Lattice Structure of Probability Spaces in Quantum Mechanics

Let $\mathcal{C}$ be the set of all possible quantum states. We study the convex subsets of $\mathcal{C}$ with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes’ Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models’ approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.     

Soil δ15N patterns in old-growth forests of southern Chile as integrator for N-cycling

Old-growth forests of southern Chile represent an important reserve of temperate (rain) forests in the world. Wetter and colder forest ecosystems appear to be more efficient in conserving and recycling N such that mostly non-plant available N species are lost, which could be indicated by more depleted δ¹⁵N values of the soil and plants. Hydrological N loss from the old-growth forests in southern Chile occurs mainly via dissolved organic nitrogen and not via dissolved inorganic N. Forest disturbances (e.g. fire, clear-cutting or enhanced N deposition) cause (abrupt) changes in ecosystem N-cycling processes. In this study, we hypothesized that δ¹⁵N signatures of soil profiles under old-growth forests could be used as an integrator for ecosystem N-cycling, and changes of these δ¹⁵N profiles could be valuable to assess ecosystem resilience towards disturbances. Six old-growth forests were selected in the phytogeographical region of the Valdivian rain forest in southern Chile. One of the sites has been partly burned in February 2002. First, we observed that ecosystems with higher mean annual precipitation and lower mean annual temperature were relatively more depleted in ¹⁵N. Secondly, we found that a forest fire caused a 100-fold increase of the nitrate export and induced an enrichment of the soil δ¹⁵N signal in the upper 20 cm.     

Basic Module Theory for General Rings

We show how to construct a theory of modules over general rings (i.e., rings which do not necessarily have an identity element) in such a form that most of the known results of the usual theory of modules over unital rings are obtained by particularizing the results of the general theory.     

On the Iterated Biclique Operator

A biclique of a graph G is a maximal induced complete bipartite subgraph of G. The biclique graph of G, denoted by , is the intersection graph of the bicliques of G. We say that a graph G diverges (or converges or is periodic) under an operator F whenever ( for some m, or for some k and , respectively). Given a graph G, the iterated biclique graph of G, denoted by , is the graph obtained by applying the biclique operator k successive times to G. In this article, we study the iterated biclique graph of G. In particular, we classify the different behaviors of when the number of iterations k grows to infinity. That is, we prove that a graph either diverges or converges under the biclique operator. We give a forbidden structure characterization of convergent graphs, which yield a polynomial time algorithm to decide if a given graph diverges or converges. This is in sharp contrast with the situsation for the better known clique operator, where it is not even known if the corresponding problem is decidable. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 181–190, 2013     

Radiative quantum efficiency of CdSe/ZnS core-shell colloidal solutions: Size-dependence

Thermo-optical parameters of CdSe/ZnS core-shell nanoparticles suspended in toluene were measured using a thermal lens (TL) technique. TL transient measurements were performed using the mode-mismatched dual-beam (excitation and probe) configuration. A He-Ne laser at λ_p = 632.8 nm was used as the probe beam and an Ar⁺ laser (at λ_e = 514.5 nm) was used as the excitation beam for studies as a function of both core size and concentration of CdSe/ZnS nanocrystals. The fraction thermal load (φ) and radiative quantum efficiencies (η) of the CdSe/ZnS were determined. Dependence on core size (∼2-5 nm) and concentration (∼0.01-0.62 mg/ml) was observed for both φ and η parameters.     

Strong optical nonlinearities of self-assembled polymorphic microstructures of phenylethynyl functionalized fluorenones

The polymorphs of a phenylethynyl functionalized fluorenone derivative, and their controlled self-assembly for microstructures with different morphologies have been studied. These polymorphic microcrystals exhibit very distinctive NLO properties, which are highly correlated to their electronic and supramolecular structures.     

Morphology and performance of CoOOH films synthesized via electrochemical oxidation: substrate effects

In the present work, CoOOH films are synthesized from the electrochemical oxidation of α-Co(OH)₂ as precursor. The substrate influences on the material electrochemical properties are studied. The samples are structural and morphologically characterized using techniques of X-ray diffraction (XRD) and scanning electronic microscopy (SEM). The cyclic voltammetry, galvanostatic charge-discharge, and electrochemical impedance spectroscopy techniques are used for the electrochemical characterization. The films deposited on steel substrate grew in the vertical hexagonal platelet form. Meanwhile, films on Ti plate presented morphology in agglomerated sphere form. After electrochemical oxidation, the film initial morphology is maintained. The films deposited on steel plate have a structure which favors charge storage showing a high specific capacity value (110.92 mA h g^?1) and cyclic stability of 92% after 1000 cycles. Finally, the relaxation time constant value calculated was 5.6 s. This fact is making this material as a possible good candidate for application as electrode material or additive for other materials, in energy storage devices.