Beijing Lectures on the Grade Restriction Rule

The authors describe the relationships between categories of B-branes in different phases of the non-Abelian gauged linear sigma model.The relationship is described explicitly for the model proposed by Hori and Tong with non-Abelian gauge group that connects two non-birational Calabi-Yau varieties studied by Rφdland.A grade restriction rule for this model is derived using the hemisphere partition function and it is used to map B-type D-branes between the two Calabi-Yau varieties.     

Cleft extensions of a family of braided Hopf algebras

We introduce a family of braided Hopf algebras that (in characteristic zero) generalizes the rank 1 Hopf algebras introduced by Krop and Radford and we study its cleft extensions.     

Solubility of methane in pure non-ionic surfactants and pure and mixtures of linear alcohols at 298 K and 101.3 kPa

The emissions of methane (CH₄), a powerful greenhouse gas (GES), contribute to the increase in GES concentration level in the atmosphere. For this reason, the importance of controlling CH₄ emissions of anthropogenic origin has increased over the last decades. Physicochemical and biological processes are available for treating CH₄. For this reason, such properties as the solubility of CH₄ in aqueous solutions and organic solvents are of great relevance in different applications in environmental engineering and biotechnology. In this study, the solubility of CH₄ was determined at 298 K and 101.3 kPa in organic solvents, such as polyoxyethylenesorbates (Tween 20, Tween 40, and Tween 60), and linear alcohols (methanol, ethanol, and butan-1-ol) alone and in their admixtures. Admixtures of methanol with butan-1-ol exhibited the highest solubility of CH₄, of around 0.49 g m⁻³ of solvent, whereas the solubility of CH₄ in linear alcohols varied from 0.167 g m⁻³ to 0.41 g m⁻³ of solvent. In the case of Tweens, CH₄ solubility decreased with the hydrophilic-lipophilic balance (HLB) number.     

Combined chemical and phase equilibrium for the hydration of ethylene to ethanol calculated by means of the Peng-Robinson-Stryjek-Vera equation of state and the Wong-Sandler mixing rules

Due to the economics of the ethylene market and the subsidized production of fermentation-based ethanol in some countries, use of the ethylene hydration process to make ethanol has been steadily declining. The economics of this process might improve by combining the reaction and separation in a reactive distillation column, whose conceptual design requires a study of the combined chemical and phase equilibrium (CPE) of the reacting system. In this work, the Peng-Robinson-Stryjek-Vera equation of state was combined with the UNIQUAC activity coefficient model through the Wong-Sandler (WS) mixing rules in order to correlate the available experimental data for the vapor-liquid equilibria (VLE) of the ethylene-water, ethylene-ethanol, and ethanol-water binary systems at 200 °C. The interaction energies of the UNIQUAC model and the binary interaction coefficient of the WS mixing rules were used as the fitting parameters. From the optimum values of these parameters, both the VLE and the combined CPE of the ethylene-water-ethanol ternary system were predicted at 200 °C and various pressures. At this temperature, the catalytic activity of a H-pentasil zeolite has already been reported to exhibit a maximum for ethylene hydration, and also the experimentally measured two-phase region of the ternary system is sufficiently wide. By means of the reactive flash method, the chemical equilibrium compositions of the liquid and vapor phases were determined for several pressures, and the equilibrium conversion and the vapor fraction were calculated as functions of the ethylene to water feed mole ratio. It turns out that the vapor-liquid mixed-phase hydration of ethylene achieves equilibrium conversions much higher than those computed for a vapor-phase reaction that would hypothetically occur at the same conditions of pressure and feed mole ratio. It was found that the reactive phase diagram of the ternary system exhibits a critical point at 200 °C and 155 atm.     

Hydrogen bonding interactions between α-, β-glucose,and methacrylic acid

Intermolecular interactions between α-, β-glucose, and methacrylic acid (MAA) have been investigated. Twenty-two possible conformations have been optimized at the DFT(B3LYP) level of theory with the 6-31G(d) basis set. The geometrical parameters for the most stable configurations of hydrogen bonding sites in the optimized systems have been determined. The binding energies ΔE _bind have been calculated at the MP2/6-311++G(d,p) level of approximation taking into account the basis set superposition error (BSSE) and the zero-point vibrational energies corrections. Results indicate that the most stabilized complexes form hydrogen bonds either through carboxylic and hemiacetal oxygen atoms acting as proton acceptors. Both, α- and β-anomers are studied in the pyranose six-membered ring. In all complexes, the nuclear quadrupole coupling constants (χ) for ¹⁷O nuclei were obtained about 10.0 MHz, while for the ²H atoms they vary from ≈200.0 to ≈350.0 kHz.     

Stereospecific ring expansion of chiral vinyl aziridines

In this report, it is demonstrated that chiral vinyl aziridines can be stereospecifically ring expanded. This synthetic approach allows controlled access to chiral 2,5-cis- or 2,5-trans-3-pyrroline products from starting materials with the appropriate aziridine geometry. Twenty three ring expansion examples, most of which feature a stereospecific cyclization, are presented.     

Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimention 2n

The subject of this paper concerns with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension 2n perturbed inside a class of continuous and discontinuous piecewise linear differential systems. Our main results show that at most one limit cycle and at most one invariant cylinder can bifurcate using the expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving these results we use the averaging theory in a form where the differentiability of the system is not needed.     

Solving the vendor–buyer integrated inventory system with arithmetic–geometric inequality

In the past, economic order quantity (EOQ) and economic production quantity (EPQ) were treated independently from the viewpoints of the buyer or the vendor. In most cases, the optimal solution for one player was non-optimal to the other player. In today’s competitive markets, close cooperation between the vendor and the buyer is necessary to reduce the joint inventory cost and the response time of the vendor–buyer system. The successful experiences of National Semiconductor, Wal-Mart, and Procter and Gamble have demonstrated that integrating the supply chain has significantly influenced the company’s performance and market share (Simchi-Levi et al. (2000) [1]). Recently, Yang et al. (2007) [2] presented an inventory model to determine the economic lot size for both the vendor and buyer, and the number of deliveries in an integrated two stage supply chain. In this paper, we present an alternative approach to determine the global optimal inventory policy for the vendor–buyer integrated system using arithmetic–geometric inequality.     

A new tool to assess ceramide bioactivity: 6-bromo-7-hydroxycoumarinyl-caged ceramide

The bioactivity of natural, long-chain ceramides has until now been studied after its delivery to cells in organic solvent mixtures containing dodecane. We have synthesized ceramides conjugated to a (6-bromo-7-hydroxycoumarin-4-yl)methyl group. The photocaged ceramide is efficiently released with 350 nm light in aqueous solution at neutral pH, thus providing a promising new tool to study ceramide's properties.     

Determination of heats of tautomerization nitrile-ketenimine by mass spectrometry

Tautomerism of some nitriles has been studied by mass spectrometry. The analysis of the corresponding mass spectra has allowed to assign some fragmentations to specific tautomers and to determine heats of tautomerization through temperature effects and electron energy studies. Experimental determinations are supported by theoretical calculations. The joint analysis of mass spectrometry and DFT-B3LYP data indicate that this tautomeric equilibrium can be studied by the experimental spectrometric strategy employed.