Proof complexity of propositional default logic

Default logic is one of the most popular and successful formalisms for non-monotonic reasoning. In 2002, Bonatti and Olivetti introduced several sequent calculi for credulous and skeptical reasoning in propositional default logic. In this paper we examine these calculi from a proof-complexity perspective. In particular, we show that the calculus for credulous reasoning obeys almost the same bounds on the proof size as Gentzen??s system LK. Hence proving lower bounds for credulous reasoning will be as hard as proving lower bounds for LK. On the other hand, we show an exponential lower bound to the proof size in Bonatti and Olivetti??s enhanced calculus for skeptical default reasoning.     

Nonlinear elliptic problems with a singular weight on the boundary

We study existence of solutions to $$-\Delta u = \frac{u^p}{|x|^2}\quad u\, >\,0 \,{\rm in }\,\Omega$$ with u?=?0 on ???, where ?? is a smooth bounded domain in ${\mathbb {R}^N}$ , N??? 3 with ${0\,\in\,\partial \Omega}$ and ${1< p < \frac{N+2}{N-2}}$ . The existence of solutions depends on the geometry of the domain. On one hand, if the domain is starshaped with respect to the origin there are no energy solutions. On the other hand, in dumbbell domains via a perturbation argument, the equation has solutions.     

A compactness theorem for scalar-flat metrics on manifolds with boundary

Let (M ⁿ , g) be a compact Riemannian manifold with boundary ?M. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have ?M as a constant mean curvature hypersurface. We prove that this set is compact for dimensions n ?? 7 under the generic condition that the trace-free 2nd fundamental form of ?M is nonzero everywhere.     

Determination of Chlorophenoxy Acid Herbicides in Water Samples by Suspended Liquid-Phase Microextraction�CLiquid Chromatography

In this study, directly suspended liquid-phase microextraction was investigated for the extraction and determination of five chlorophenoxy acid herbicides in water samples. The optimized parameters for extraction of chlorophenoxy acid herbicides were 1 M HCl concentration in sample solution, solution temperature 20 °C, 45-min extraction time, 1,000 rpm stirring rate, 25 ??L extracting solvent volume and without NaCl addition. Under the optimum conditions, the enrichment factor ranged from 192 to 390. Calibration curves yielded good linearity (R ² > 0.999) and the linear range was 5.0?C500.0 ??g L^?1, limit of detection was 0.3?C0.4 ??g L^?1 and limit of quantification was 1?C2 ??g L^?1 for analytes and the relative standard deviations were in the range of 3?C10% (n = 3). Finally, the proposed method was successfully applied to the quantification of five chlorophenoxy acid herbicides in water samples and recovery was in the range of 74?C110%.     

High-Efficiency Liquid Chromatography Using Sub-2?��m Columns at Elevated Temperature for the Analysis of Sulfonamides in Wastewater

Efficiency in HPLC can be enhanced by increasing the column length and/or decreasing the particle size. The use of high temperature in HPLC has emerged as a valuable tool to overcome the increase in column backpressure when using small packing particles, as it allows for reduction in mobile phase viscosity. In this study, high plate count was obtained by coupling sub-2 ??m columns at elevated temperature to reduce the viscosity of the mobile phase, thus reducing the column backpressure. At 80 °C, up to three columns of 15 cm × 4.6 mm I.D. packed with 1.8 ??m particles could be coupled generating ~84,000 theoretical plates for the last eluting compound. The number of theoretical plates was increased on average by a factor of ~3.6 when three columns were coupled at 80 °C compared with one column at 30 °C. The relationships between separation efficiency and column length were examined using Van Deemter plots constructed at 30 °C and 80 °C for different column lengths. The advantages of using coupled columns in combination with elevated temperature for the environmental analysis were illustrated using test mixtures comprised of eight sulfonamides separated on one column at 30 °C and three coupled columns at 80 °C by isocratic elution. Sample clean up was carried out by employing solid-phase extraction (SPE) using Oasis HLB cartridges. The method developed was validated based on parameters such as linearity, precision, accuracy, detection and quantification limits. Recoveries generally ranged from 71.7 to 99% (with the exception of sulfanilamide), with standard deviations not higher than 4.7%. The detection limits of the method ranged from 0.6?C2 ??g L^?1, while limits of quantification were in the range 2?C6.7 ??g L^?1 with UV detection.     

Qualitative and Quantitative Analysis of 17 Different Types of Tetra- and Pentacyclic Triterpenic Acids in Boswellia papyrifera by a Semi-Automatic Homomodal 2D HPLC method

A semi-automatic two dimensional high-performance liquid chromatography (HPLC) gradient method with photo diode array detection was developed, capable of separating and quantifying up to 17 different triterpenic acids in the gum resin of the frankincense species Boswellia papyrifera. The here reported quantitation of 14 of the possible 17 compounds contains boswellic, tirucallic and lupeolic acids. All compounds were isolated from B. papyrifera and used as external standards. Quantitation of these compounds was performed after minimizing the matrix by liquid?Cliquid separation, using alkaline, acidic and organic media to separate the acids from interfering matrix compounds. Therefore, two different extraction procedures were tested, giving two different extraction profiles. Within the first run (1st dimension) 13 compounds could be quantified. Quantitation of ??-boswellic acid, which was proved to elute as inhomogeneous peak, was achieved by introduction of a second dimension, leading to a fully validated semi-automatic homomodal 2D chromatography. The method is applicable for determination of compounds occurring in different types of frankincense and their pharmaceutical products. It also can be applied to distinguish between different kinds of frankincense. Moreover, it is the first published method feasible of separating and quantifying five different types of tirucallic acids.     

Influence of thermal degradation in the physicochemical properties of fish oil

Physicochemical and thermal analyses were undertaken to evaluate the influence of the temperature on the oxidation of sea fish oil once its polyunsaturated fatty acids deteriorate rapidly. Fish oil displayed four decomposition steps in synthetic air atmosphere and only one step in nitrogen atmosphere. The first step started at 189 and 222 °C for oxidizing and inert atmospheres, respectively. An OIT value of 53 min was measured at 100 °C. After the degradation process the peroxide index and the iodine index reduced from 35.38 to 9.85 meq × 1000 g^?1 and from 139.79 to 120.19 gI₂ × 100 g^?1, respectively. An increase of the free fatty acids amount from 0.07 to 0.17% was observed while viscosity increased from 57.2 to 58.0 cP. Absorption at 272 nm also increased. The thermogravimetric and spectroscopic techniques are reproducible and versatile being an option for characterization of edible oil oxidation.     

Kinetics and dynamics study of the H + CCl4?��?HCl(v��, j��)?+?CCl3 reaction

Based on a previous potential energy surface describing the H?+?CCl₄ reaction, a new analytical surface named PES-2010 was developed modifying both the functional form to give it more flexibility, and the calibration process in which exclusively theoretical information was used. Thus, the surface is completely symmetric with respect to the permutation of the four methane chlorine atoms, and no experimental information is used in the process. For the kinetics, the thermal rate constants were calculated using variational transition-state theory with semiclassical transmission coefficients over a wide temperature range, 300?C2,500?K. The theoretical results reproduce the experimental variation with temperature. The influence of the tunneling factor is small, since the abstraction reaction involves the motion of a heavy particle (a chlorine atom) that cannot easily tunnel through the reaction barrier. The coupling between the reaction coordinate and the vibrational modes shows qualitatively that the HCl stretching mode in the products appears vibrationally excited. The dynamics study was performed using quasi-classical trajectory calculations, including corrections to avoid the zero-point energy problem. First, we found that the HCl(????, j??) product mostly appears with small rotational energy and vibrational population inversion. Second, the state-specific scattering distributions show backward scattering, which becomes more noticeable as the HCl(????) vibrational state increases. Unfortunately, no experimental dynamics data are available for the title reaction, but the comparison with the kinematically similar and well-studied H?+?Cl₂ reaction shows good agreement, indicative of similar mechanisms. These kinetics and dynamics results seem to indicate that the potential energy surface is adequate to describe this reaction, and the reasonable agreement with experiment lends further confidence to this new surface.     

Composition depth profile analysis of electrodeposited alloys and metal multilayers: the reverse approach

The reverse depth profile analysis is a recently developed method for the study of a deposit composition profile in the near-substrate zone. The sample preparation technique enables one to separate the deposit and a thin cover layer from its substrate, and the initial roughness of the sample is much smaller than in the conventional sputtering direction. This technique is particularly suitable to study the zones being formed in the early phase of the electrodeposition of alloys. It has been demonstrated with the reverse depth profile analysis that in many cases when one component of an alloy is preferentially deposited, an initial zone is formed that is rich in the preferentially deposited component. This phenomenon is demonstrated for Ni–Cd, Ni–Sn, Fe–Co–Ni, Co–Ni, and Co–Ni–Cu alloys. The composition change is confined to the initial 150-nm-thick deposit, and it is the result of the interplay of the deposition preference and the depletion of the electrolyte near the cathode with respect to the ion reduced preferentially. The reverse depth profile analysis made it possible to compare the measured and the calculated composition depth profile of electrodeposited multilayers. It has been shown that the decay in the composition oscillation intensity in Co/Cu multilayers with the increase of the sputtering depth can be derived from the roughness measured as a function of the deposit thickness.     

An ab initio study of the proton transfer and tautomerization processes in hydroxycarbene

We have investigated the hydrogen-bonded complexes formed by hydroxycarbene in trans configuration at MP2 and CCSD computational levels. In addition, these complexes have been used as starting point in the potential tautomerization of hydroxycarbene to produce formaldehyde. The presence of molecules that can be involved in the tautomerization significantly reduces its barrier. The electron density of the different structures obtained has been analyzed with the Atoms in Molecules methodology.