Black hole state counting in loop quantum gravity: a number-theoretical approach

We give an efficient method, combining number-theoretic and combinatorial ideas, to exactly compute black hole entropy in the framework of loop quantum gravity. Along the way we provide a complete characterization of the relevant sector of the spectrum of the area operator, including degeneracies, and explicitly determine the number of solutions to the projection constraint. We use a computer implementation of the proposed algorithm to confirm and extend previous results on the detailed structure of the black hole degeneracy spectrum.     

On suspension polymerization of vinyl chloride. Polymerization of vinyl chloride in the presence of epoxidized oil

A study has been made on the suspension polymerization of vinyl chloride in the presence of epoxidized cottonseed oil. Inclusion of the additive into the polymer chain was proved by i.r. spectrophotometry. The effects of epoxidized cottonseed oil on polymerization rate and K-value were slight, but plasticizer absorption by the polymer was reduced. Thermogravimetric curves of the product have been obtained, and show that epoxidized cottonseed oil improves the thermostability of the polymer.     

Testing of microorganisms for ω-transaminase activity

Various bacterial cells were tested to identify ω-transaminase activity. For this purpose, the kinetic resolution of a rac-amine was chosen as an assay reaction transforming, in the ideal case, one enantiomer into the corresponding ketone and leaving the other enantiomer untouched. Sodium pyruvate was employed as an amino acceptor. To test also for the amination of the prochiral ketone various amino donors were investigated. Alanine proved to be the most suitable amino donor especially when coupled with a pyruvate decarboxylase to shift the reaction equilibrium; however, much lower conversions were achieved compared to the kinetic resolution. Janibacter terrae DSM 13953 was identified as the most suitable microorganism to possess ω-transaminase activity.     

Geometric aspects influencing N-NTB transition - implication of intramolecular torsion

Herein we report a comprehensive study on novel carbonyl- and ethenyl-linked symmetric dimers that combine synthesis, mesomorphic properties and molecular modelling. The study has been focused on the impact of geometry imposed by the linkage group on the incidence of the twist-bend nematic (N_TB) phase. Comparison of the mesomorphic properties of these two series complemented with computational studies of conformational space around the linkage group points molecular curvature and intramolecular torsion plays important role in the appearance of the N_TB phase and can be regarded as the basic structural requirements for design of new twist-bend nematogen materials.     

Synthesis and molecular-mass characteristics of some cardo poly(benzimidazoles)

The GPC procedure for analyzing molecular mass characteristics of cardo poly(benzimidazoles) has been developed. In most cases, the reaction between 4,4′-oxydibenzene-1,2-diamine and 4,4′-(3-oxo-1,3-dihydroisobenzofuran-1,1-diyl)dibenzoic acid in Eaton’s reagent is accompanied by formation of a microgel. Depending on the synthesis conditions (temperature, duration of heating, and content of phosphorus pentoxide in the reaction mixture), polymers with both unimodal and bimodal molecular mass distributions can be prepared. Formation of the microgel fraction is observed for many representatives of poly(benzimidazoles) of various chemical structures. Based on the experimental evidence, the most probable pathway is suggested for the branching side reaction of poly(benzimidazoles) during their synthesis in Eaton’s reagent.     

Electrolyte diodes with weak acids and bases. II. Numerical model calculations and experiments

This is the second part of our work dealing with electrolyte diodes with weak acids and bases. In the first part an approximative analytical solution was derived for the steady-state current-voltage characteristic (CVC) of a reverse-biased diode (a quasi-one-dimensional gel connecting an acidic and an alkaline reservoir), applying either strong or weak electrolytes. An approximative analytical solution is compared here with a numerical solution free of any approximations and with CVCs measured experimentally with both strong and weak electrolytes. It is shown that the deviations between the numerical and analytical solutions are mostly due to assumptions made for the fixed charge concentration profiles. The concept of optimal analytical solution is introduced which does not use such assumptions and applies only the quasielectroneutrality and quasiequilibrium approximations. It is proven that the slope of the CVC based on the optimum analytical solution can be calculated without the complicated derivation of that solution itself. The calculation of that slope is based on the fact that in the optimum analytical solution all currents are inversely proportional to the length if the boundary conditions are held constant and realizing that in the middle part of the gel the only mobile counterions of the fixed ionized groups are hydrogen ions. In the experimental part the apparatus and the preparation of the gel are described together with the CVCs measured with strong and weak electrolytes. From these CVCs the fixed ion concentration in the middle part of the gel can be determined. That fixed ion concentration is 1.96 x 10(-4)M measured with weak electrolytes and 3.48 x 10(-4)M measured with strong electrolytes. The deviation indicates that the strong base causes some hydrolysis of the gel. Finally, possible applications of weak acid-weak base diodes are discussed.     

Water models based on a single potential energy surface and different molecular degrees of freedom

Up to now it has not been possible to neatly assess whether a deficient performance of a model is due to poor parametrization of the force field or the lack of inclusion of enough molecular properties. This work compares several molecular models in the framework of the same force field, which was designed to include many-body nonadditive effects: (a) a polarizable and flexible molecule with constraints that account for the quantal nature of the vibration [B. Hess, H. Saint-Martin, and H. J. C. Berendsen, J. Chem. Phys. 116, 9602 (2002), H. Saint-Martin, B. Hess, and H. J. C. Berendsen, J. Chem. Phys. 120, 11133 (2004)], (b) a polarizable and classically flexible molecule [H. Saint-Martin, J. Hernandez-Cobos, M. I. Bernal-Uruchurtu, I. Ortega-Blake, and H. J. C. Berendsen, J. Chem. Phys. 113, 10899 (2000)], (c) a polarizable and rigid molecule, and finally (d) a nonpolarizable and rigid molecule. The goal is to determine how significant the different molecular properties are. The results indicate that all factors--nonadditivity, polarizability, and intramolecular flexibility--are important. Still, approximations can be made in order to diminish the computational cost of the simulations with a small decrease in the accuracy of the predictions, provided that those approximations are counterbalanced by the proper inclusion of an effective molecular property, that is, an average molecular geometry or an average dipole. Hence instead of building an effective force field by parametrizing it in order to reproduce the properties of a specific phase, a building approach is proposed that is based on adequately restricting the molecular flexibility and/or polarizability of a model potential fitted to unimolecular properties, pair interactions, and many-body nonadditive contributions. In this manner, the same parental model can be used to simulate the same substance under a wide range of thermodynamic conditions. An additional advantage of this approach is that, as the force field improves by the quality of the molecular calculations, all levels of modeling can be improved.     

Modelling Inference in Argumentation through Labelled Deduction: Formalization and Logical Properties

Artificial Intelligence (AI) has long dealt with the issue of finding a suitable formalization for commonsense reasoning. Defeasible argumentation has proven to be a successful approach in many respects, proving to be a confluence point for many alternative logical frameworks. Different formalisms have been developed, most of them sharing the common notions of argument and warrant. In defeasible argumentation, an argument is a tentative (defeasible) proof for reaching a conclusion. An argument is warranted when it ultimately prevails over other conflicting arguments. In this context, defeasible consequence relationships for modelling argument and warrant as well as their logical properties have gained particular attention. This article analyzes two non-monotonic inference operators C_arg and C_war intended for modelling argument construction and dialectical analysis (warrant), respectively. As a basis for such analysis we will use the LDS_ar framework, a unifying approach to computational models of argument using Labelled Deductive Systems (LDS). In the context of this logical framework, we show how labels can be used to represent arguments as well as argument trees, facilitating the definition and study of non-monotonic inference operators, whose associated logical properties are studied and contrasted. We contend that this analysis provides useful comparison criteria that can be extended and applied to other argumentation frameworks. Mathematics Subject Classification (2000): Primary 03B22; Secondary 03B42.     

De-Equivariantization of Hopf Algebras

We study the de-equivariantization of a Hopf algebra by an affine group scheme and we apply Tannakian techniques in order to realize it as the tensor category of comodules over a coquasi-bialgebra. As an application we construct a family of coquasi-Hopf algebras A(H, G, Φ) attached to a coradically-graded pointed Hopf algebra H and some extra data.