Averaged Decay Estimates for Fourier Transforms of Measures over Curves with Nonvanishing Torsion

We study averaged decay estimates for Fourier transforms of measures when the averages are taken over space curves with non-vanishing torsion. We extend the previously known results to higher dimensions and discuss sharpness of the estimates.     

On the mean value parametrization of natural exponential families — a revisited review

It is well known that any natural exponential family (NEF) is characterized by its variance function on its mean domain, often much simpler than the corresponding generating probability measures. The mean value parametrization appeared to be crucial in some statistical theory, like in generalized linear models, exponential dispersion models and Bayesian framework. The main aim of the paper is to expose the mean value parametrization for possible statistical applications. The paper presents an overview of the mean value parametrization and of the characterization property of the variance function for NEF’s. In particular it introduces the relationships existing between the NEF’s generating measure, Laplace transform and variance function as well as some supplemental results concerning the mean value representation. Some classes of polynomial variance functions are revisited for illustration. The corresponding NEF’s of such classes are generated by counting probabilities on the nonnegative integers and provide Poisson-overdispersed competitors to the homogeneous Poisson distribution.     

Computer-Assisted Analysis of the Anderson–Hájek Ontological Controversy

A universal reasoning approach based on shallow semantical embeddings of higher-order modal logics into classical higher-order logic is exemplarily employed to analyze several modern variants of the ontological argument on the computer. Several novel findings are reported which contribute to the clarification of a long-standing dispute between Anderson and Hájek. The technology employed in this work, which to some degree realizes Leibniz’s dream of a characteristica universalis and a calculus ratiocinator for solving philosophical controversies, is ready to be fruitfully adopted in larger scale by philosophers.     

Antimicrobial Activity of Pyrazinamide Coordination Frameworks Synthesized by Mechanochemistry

The urge for the development of a more efficient antibiotic crystalline forms led us to the disclosure of new antibiotic coordination frameworks of pyrazinamide, a well-known drug used for the treatment of tuberculosis, with some of the novel compounds unravelling improved antimycobacterial activity. Mechanochemistry was the preferred synthetic technique to yield novel compounds, allowing the reproduction of a 1D zinc framework, the synthesis of a novel hydrogen bonding manganese framework, and three new compounds with silver. The structural characterization of the novel forms is presented along with stability studies. The increased antimicrobial activity of the new silver-based frameworks against Escherichia coli, Staphylococcus aureus, and Mycobacterium smegmatis is particularly relevant.     

Nanocomposite Polymer Electrolytes of Sodium Alginate and Montmorillonite Clay

Nanocomposite polymer electrolytes (NPEs) were synthesized using sodium alginate (Alg) and either sodium (SCa-3-Na⁺)- or lithium (SCa-3-Li⁺)-modified montmorillonite clays. The samples were characterized by structural, optical, and electrical properties. SCa-3-Na⁺ and SCa-3-Li⁺ clays’ X-ray structural analyses revealed peaks at 2θ = 7.2° and 6.7° that corresponded to the interlamellar distances of 12.3 and 12.8 Å, respectively. Alg-based NPEs X-ray diffractograms showed exfoliated structures for samples with low clay percentages. The increase of clay content promoted the formation of intercalated structures. Electrochemical Impedance Spectroscopy revealed that Alg-based NPEs with 5 wt% of SCa-3-Na⁺ clay presented the highest conductivity of 1.96 × 10⁻² S/cm², and Alg with 10 wt% of SCa-3-Li⁺ showed conductivity of 1.30 × 10⁻² S/cm², both measured at 70 °C. From UV-Vis spectroscopy, it was possible to infer that increasing concentration of clay promoted a decrease of the samples’ transmittance and, consequently, an increase of their reflectance.     

Enantioselective Total Synthesis of (+)-Nordasycarpidone, (+)-Dasycarpidone,and (+)-Uleine

The structure of uleine type alkaloids is characterized by the presence of a bridged tetracyclic hexahydro-1H-1,5-methanoazocino[4,3-b]indole ring system 1 . Various strategies have been developed to access this polycyclic structural motif. We report herein a one-step conversion of appropriately functionalized 1,3,4-trisubstituted cyclopent-1-ene to 1 by way of an integrated oxidation/reduction/cyclization (iORC) process. This domino sequence, initiated by oxidative cleavage of cyclopentene ring, generated subsequently a cyclohexenone, an indole and a 1,3-bridged piperidine ring through formation of one C−C and two C−N bonds. Compound 1 is subsequently converted to nordasycarpidone, dasycarpidone and uleine. The chirality of the molecule was introduced by enzymatic desymmetrization of commercially available meso cis-3,5-diacetoxy-1-cyclopentene.     

Secondary Metabolites of Clinacanthus nutans

Chemistry of Natural Compounds -     

Secondary Metabolites of Mahonia bealei

Chemistry of Natural Compounds -