A Dodecalogue of Basic Didactics from Applications of Abstract Differential Geometry to Quantum Gravity

We summarize the twelve most important in our view novel concepts that have arisen, based on results that have been obtained, from various applications of Abstract Differential Geometry (ADG) to Quantum Gravity (QG). The present document may be used as a concise, yet informal, discursive and peripatetic conceptual guide-cum-terminological glossary to the voluminous technical research literature on the subject. In a bonus section at the end, we dwell on the significance of introducing new conceptual terminology in future QG research by means of ‘poetic language’.     

A theoretical study of calcium monohydride, CaH: low-lying states and their permanent electric dipole moments

Potential energy curves, energy parameters, and spectroscopic values for the X (2)Sigma(+), A (2)Pi, B (2)Sigma(+), a (4)Pi, and b (4)Sigma(+), states of CaH have been calculated using the multireference configuration interaction and coupled cluster levels of theory, while employing quantitative basis sets (of augmented quintuple-zeta quality) and taking also into account core/valence correlation and one-electron relativistic effects. For the ground (X (2)Sigma(+)) and the first two following excited states (A (2)Pi, B (2)Sigma(+)) of CaH, the permanent electric dipole moments have been calculated. Our best finite field dipole moment of the A (2)Pi state of 2.425 D (upsilon = 0) is in very good agreement with the experimental literature value of 2.372(12) D. However, a discrepancy is observed in the dipole moment of the X (2)Sigma(+) state. Our most extensive calculation gives mu = 2.623 D (upsilon = 0), which is considerably smaller than the experimental value of mu = 2.94(16) D (upsilon = 0). Small van der Waals minima were found for both "repulsive" quartet states. Spectroscopic constants and energy parameters for all states are in remarkable agreement with available experimental values.     

Combined use of β-cyclodextrin and ionic liquid as electrolyte additives in EKC for separation and determination of carob's phenolics—A study of the synergistic effect

In this work, a simple, reliable, and fast capillary electrophoretic method was developed and validated for the simultaneous determination of 12 polyphenolic compounds, the most frequently found in carob's pulp and seeds. The present work deals with the development of a novel dual electrophoretic system based on the combined use of β-CD and ionic liquid (IL) as buffer additives. A baseline separation of the target analytes was achieved in less than 10 min by using a BGE consisting of 35 mM borate along with 15 mM β-CD and 3 mM l -alanine tert butyl ester lactate (l -AlaC₄Lac) IL as buffer additives at pH 9.5, a temperature of 25°C, and an applied voltage of 30 kV. The application of the developed electrophoretic method to real samples enabled the identification and quantification of the main phenolic constituents of both ripe and unripe carob pulp extracts. The results revealed the predominance of gallic acid in both ripe (183.92 μg/g carob pulp) and unripe (205.10 μg/g carob pulp) carob pulp and highlighted the great influence of the ripening stage on carobs polyphenolic composition, with unripe pods being more enriched in polyphenols (total phenolics detected: 912.58 and 283.13 μg/g unripe and ripe carob pulp).     

Molecular simulation of the hydration Gibbs energy of barbiturates

In the present work, molecular dynamics calculations of the Gibbs energy of hydration of 10 different substituted barbiturates in SPC/E water were performed using thermodynamic integration. Given that experimental determination of the Gibbs hydration energy for this class of compounds is currently unfeasible, computer simulations appear as the only alternative for the estimation of this important quantity. Several simulation parameters are discussed and optimized based on calculations for barbituric acid. It is concluded that accounting for electrostatic interactions with the Reaction-Field method can be up to two times faster than with Particle-Mesh-Ewald method, without loss of accuracy. Different number of solvent molecules and simulation lengths were also tested. Lennard-Jones and electrostatic contributions were scaled down to zero in an independent way. It is shown that the electrostatic contribution is dominant (representing approximately 90% of the total Gibbs energy of hydration) and that barbiturate intra-molecular interactions cannot be neglected. The importance of the electrostatic contribution is attributed to the formation of hydrogen bonds between the barbiturates and water, which play an important role in the solvation process. The influence of the different substituents and their contribution to the Gibbs energy of hydration was assessed. Finally, the Lennard-Jones contributions and the total hydration Gibbs energy can both be correlated against molecular weight or partition coefficient data for mono- and di-substituted barbiturates.     

Simulating events of unknown probabilities via reverse time martingales

Let s∈(0,1) be uniquely determined but only its approximations can be obtained with a finite computational effort. Assume one aims to simulate an event of probability s. Such settings are often encountered in statistical simulations. We consider two specific examples. First, the exact simulation of non‐linear diffusions ([ 3 ]). Second, the celebrated Bernoulli factory problem ([ 10 , 13 ]) of generating an f(p)‐coin given a sequence X₁,X₂,… of independent tosses of a p‐coin (with known f and unknown p). We describe a general framework and provide algorithms where this kind of problems can be fitted and solved. The algorithms are straightforward to implement and thus allow for effective simulation of desired events of probability s. Our methodology links the simulation problem to existence and construction of unbiased estimators. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 38, 441–452, 2011     

A comparative study of the adsorption of uranium on commercial and natural (Cypriot) sea sand samples

The adsorption of hexavalent uranium on two different types of sea sand [e.g. a local, Cypriot (N_SS) and a commercially available marine sediment (C_SS)] has been investigated as a function of pH, initial metal concentration, ionic strength and contact time under normal atmospheric conditions. Before carrying out the adsorption experiments, the sea sand samples have been characterized by XRD, XRF, N₂-adsorption, acid/base titrations and FTIR spectroscopy. Sample characterization showed clearly that the two sea sand types differ significantly in their composition, particularly in their calcite and FeOOH content. According to experimental data obtained from acid/base titrations and adsorption batch experiments sea sand composition affects the acid/base and the adsorption properties of the adsorbents. The extraordinary high affinity of N_SS for hexavalent uranium in the alkaline pH region can be attributed to the formation of mixed U(VI)–carbonato surface species on the FeOOH crystall phases present in N_SS, which effectively compete the formation of U(VI)–carbonato complexes in solution. On the other hand, data obtained by adsorption experiments carried out in solution of different ionic strengths don’t differ significantly from one another indicating the formation of inner-sphere complexes. Finally, the adsorption on sea sands is a relatively fast two-step process.     

Randomized on-line algorithms and lower bounds for computing large independent sets in disk graphs

We study the on-line version of the maximum independent set problem, for the case of disk graphs which are graphs resulting from intersections of disks on the plane. In particular, we investigate whether randomization can be used to break known lower bounds for deterministic on-line independent set algorithms and present new upper and lower bounds.     

Determination of Trace Tl(I) by Anodic Stripping Voltammetry on Novel Disposable Microfabricated Bismuth‐Film Sensors

This work reports the trace determination of Tl(I) by square‐wave anodic stripping voltammetry (SWASV) on novel microsensors equipped with a bismuth‐film electrode (BiFE). The sensors were fabricated by a multistep microfabrication approach combining sputtering (to deposit the electrode materialm, bismuth‐ and the insulator SiO₂, on the surface of a silicon wafer) and photolithography (to define the geometry of the sensor). The effect of the preconcentration time, the preconcentration potential and the SW stripping parameters were investigated. Using the selected conditions, the 3σ limit of detection was 0.6 µg L^?1 of Tl(I) at a preconcentration time of 240 s and the percent relative standard deviation was 4.3 % at the 10 µg L^?1 level (n=8). In order to eliminate the interference caused by Pb(II) and Cd(II), EDTA was added in the sample solution The method was successfully applied to the determination of Tl(I) in a certified lake water sample. These new sensors exhibit excellent mechanical stability and offer wide scope as mercury‐free disposable sensors for trace metal analysis.