Enveloping algebras that are principal ideal rings

Let L be a restricted Lie algebra over a field of positive characteristic. We prove that the restricted enveloping algebra of L is a principal ideal ring if and only if L is an extension of a finite-dimensional torus by a cyclic restricted Lie algebra.     

Lipase-catalyzed kinetic resolution approach toward enantiomerically enriched 1-(β-hydroxypropyl)indoles

In a route towards enantiomerically enriched 1-(β-hydroxypropyl)indoles, which are potentially useful building blocks for high value-added chemicals synthesis, a kinetic resolution approach by means of lipase-catalyzed enantioselective acylation as well as hydrolysis/methanolysis has been elaborated for the first time. The enzymatic resolution of chiral N-substituted indole-based sec-alcohols was successfully accomplished, yielding both enantiomeric forms of the employed derivatives with up to >99% enantiomeric purity via an enantioselective transesterification under mild reaction conditions. The most selective resolutions were obtained using fungal (CAL-B and TLL) and bacterial (PFL and BCL) lipases and vinyl acetate as the acyl?group donor. The synthetic protocol described herein is very simple, user-friendly and efficient, thus paving the way for future access towards more complex compounds of this type. The absolute configurations of novel enantiomeric derivatives, and thus stereoselectivity of the described enzymatic reactions were confirmed by application of CDA-based NMR methodology and single-crystal X-ray diffraction analysis.     

An Analogy Principle in Inductive Logic

We propose an Analogy Principle in the context of Unary Inductive Logic and characterize the probability functions which satisfy it. In particular in the case of a language with just two predicates the probability functions satisfying this principle correspond to solutions of Skyrms? ‘Wheel of Fortune’.     

Development and validation of a UPLC‐MS/MS method for the determination of cucurbitacin B in rat plasma and application to a pharmacokinetic study

Cucurbitacin B (CuB), one of the most abundant forms of cucurbitacins, is a promising natural anticancer drug candidate. Although the anticancer activity of CuB has been well demonstrated, information regarding the pharmacokinetics is limited. A rapid, selective and sensitive UPLC‐MS/MS for CuB was developed and validated using hemslecin A (HeA) as internal standard (IS). Plasma samples were pre‐treated by liquid–liquid extraction with dichloromethane. Separation was achieved on a reversed‐phase C₁₈ column (50 × 4.6 mm, 5 µm) at 35°C using isocratic elution with water–methanol (25:75, v/v) at a flow rate of 0.3 mL/min. The analytes were monitored by a triple quadrupole tandem mass spectrometer with positive electrospray ionization mode. The calibration curve was linear (r > 0.995) in a concentration range of 0.3–100 ng/mL with a limit of quantification of 0.3 ng/mL. Intra‐ and inter‐day accuracy and precision were validated by percentage relative error and relative standard deviation, respectively, which were both lower than the limit of 15%. This assay was successfully applied to a pharmacokinetic study of CuB in Wistar rats. Copyright © 2015 John Wiley & Sons, Ltd.     

Kinetic and thermodynamic studies on the adsorption behavior of Rhodamine B dye on Duolite C-20 resin

The adsorption behavior of Rhodamine B dye from aqueous solutions was investigated onto the cation-exchange resin, Duolite C-20 (hydrogen form). The effects of various experimental factors; sorbent amount, contact time, dye concentration and temperature, were studied by using the batch technique. Lagergren pseudo-first-order equation shows good applicability with high correlation coefficients for all ranges of initial dye concentrations and at different temperatures. This equation was used to describe the kinetics of the dye adsorption process. The adsorption constants were evaluated by using both the Langmuir and Freundlich adsorption isotherm models. Thermodynamic parameters were obtained and it was found that the adsorption of Rhodamine B dye onto Duolite C-20 resin was an endothermic and spontaneous process at the temperatures under investigation.     

Melham's Conjecture on Odd Power Sums of Fibonacci Numbers

Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at a certain Fibonacci number of odd order. We prove that this polynomial and its derivative both vanish at 1, and will be an integer polynomial after multiplying it by a product of the first consecutive Lucas numbers of odd order. This presents an a?rmative answer to a conjecture of Melham.     

Eisenstein type series for Calabi–Yau varieties

In this article we introduce an ordinary differential equation associated to the one parameter family of Calabi–Yau varieties which is mirror dual to the universal family of smooth quintic three folds. It is satisfied by seven functions written in the q-expansion form and the Yukawa coupling turns out to be rational in these functions. We prove that these functions are algebraically independent over the field of complex numbers, and hence, the algebra generated by such functions can be interpreted as the theory of (quasi) modular forms attached to the one parameter family of Calabi–Yau varieties. Our result is a reformulation and realization of a problem of Griffiths around seventies on the existence of automorphic functions for the moduli of polarized Hodge structures. It is a generalization of the Ramanujan differential equation satisfied by three Eisenstein series.     

A non-metric perfectly normal hereditarily indecomposable continuum

We construct an example of a non-metric perfectly normal hereditarily indecomposable continuum. The example is constructed as an inverse limit of non-metric analogues of solenoids. Theorems needed to insure perfect normality are stated and proven. It is shown that the example cannot be embedded in a countable product of Hausdorff arcs.     

Partial Synthesis of Coenzyme B12 from Cobyric Acid

Here we report the direct chemical synthesis of coenzyme B₁₂ (AdoCbl) from Co_β ‐5′‐deoxyadenosylcobyric acid (AdoCby) and the preparation of the latter from crystalline CN ,H₂O‐cobyric acid (CN ,H₂OC by). AdoCby is a suggested common key intermediate in the biosynthesis of AdoCbl and of other cobamides in microorganisms. AdoCby was thoroughly characterized by spectroscopic means, including homo‐nuclear and hetero‐nuclear NMR , as such data are not available in published work. AdoCbl was prepared from AdoCby in one‐step in over 85% yield, by covalent attachment in aqueous solution of the integral B₁₂‐nucleotide moiety using 1‐ethyl‐3‐(3‐dimethylaminopropyl)‐carbodiimide (EDC ·HC l) and N‐hydroxybenzotriazole (HOB t) as coupling reagents. By the same procedure crystalline vitamin B₁₂ (CNC bl) was also prepared in 92% yield from CN ,H₂OC by. Coordination of the B₁₂‐nucleotide base at the Co_α ‐face of AdoCby or of CN ,H₂OC by was indicated to assist in the efficient covalent coupling at the activated f‐side chain function to furnish the complete corrinoids AdoCbl and CNC bl.