Equation of State Grid with the Quark-Meson-Coupling Model

In this work, we present the preliminary results of an equation of state (EoS) grid for possible use in core-collapse supernova simulations. We treat uniform matter made of nucleons using the quark-meson coupling (QMC) model. We show a table with a variety of thermodynamic quantities, which covers the proton fraction range Y _p = 0?0.65 with the linear grid spacing ΔY _p = 0.01 (66 points) and the density range ρ _B = 10¹⁴ ? 10¹⁶g cm^?3 with the logarithmic grid spacing Δlog₁₀(ρ _B /[g cm^?3]) = 0.1 (21 points). This preliminary study is performed at zero temperature, and our results are compared with the widely used EoS already available in the literature.     

Ultrafast Click Chemistry with Fluorosydnones

We report the synthesis and reactivity of 4‐fluorosydnones, a unique class of mesoionic dipoles displaying exquisite reactivity towards both copper‐catalyzed and strain‐promoted cycloaddition reactions with alkynes. Synthetic access to these new mesoionic compounds was granted by electrophilic fluorination of σ‐sydnone Pd^II precursors in the presence of Selectfluor. Their reactions with terminal and cyclic alkynes were found to proceed very rapidly and selectively, affording 5‐fluoro‐1,4‐pyrazoles with bimolecular rate constants up to 10⁴ m ^?1 s^?1, surpassing those documented in the literature with cycloalkynes. Kinetic studies were carried out to unravel the mechanism of the reaction, and the value of 4‐fluorosydnones was further highlighted by successful radiolabeling with [¹⁸F]Selectfluor.     

Chemical composition and evaluation of the antimicrobial activity of the essential oil from leaves of Eugenia platysema

This study describes the qualitative and quantitative chemical composition and evaluates the antibacterial activity of essential oil from Eugenia platysema leaves. Analysis by GC–FID and GC–MS allowed the identification of 22 compounds. Different from the other species of the Eugenia genus, the major compound found in the essential oil was the diterpene phytol (66.05%), being this the first report of the presence of this compound in the essential oils from Eugenia genus. The sesquiterpene elixene was the second most concentrated compound in the studied essential oil (9.16%). The essential oil from E. platysema was tested for its antibacterial activity against cell-walled bacteria and mollicute strains of clinical interest using the microdilution broth assay. The results showed that the essential oil of E. platysema was inactive until 1000 μg mL^?1 against tested bacteria.     

A Non-Standard Analysis of a Cultural Icon: The Case of Paul Halmos

We examine Paul Halmos’ comments on category theory, Dedekind cuts, devil worship, logic, and Robinson’s infinitesimals. Halmos’ scepticism about category theory derives from his philosophical position of naive set-theoretic realism. In the words of an MAA biography, Halmos thought that mathematics is “certainty” and “architecture” yet 20th century logic teaches us is that mathematics is full of uncertainty or more precisely incompleteness. If the term architecture meant to imply that mathematics is one great solid castle, then modern logic tends to teach us the opposite lesson, namely that the castle is floating in midair. Halmos’ realism tends to color his judgment of purely scientific aspects of logic and the way it is practiced and applied. He often expressed distaste for nonstandard models, and made a sustained effort to eliminate first-order logic, the logicians’ concept of interpretation, and the syntactic vs semantic distinction. He felt that these were vague, and sought to replace them all by his polyadic algebra. Halmos claimed that Robinson’s framework is “unnecessary” but Henson and Keisler argue that Robinson’s framework allows one to dig deeper into set-theoretic resources than is common in Archimedean mathematics. This can potentially prove theorems not accessible by standard methods, undermining Halmos’ criticisms.     

Carborane inclusion chemistry for the uncommon calix[7,9]arenes

The inclusion of o-carborane by p-Bu(t)-calix[7,9]arenes has been investigated by solid state and solution studies, with both resulting complexes in the solid state being rich in carborane with the ratio of calixarene to carborane at 1 : 7 and 2 : 7 respectively. The carboranes reside in clefts within the calixarenes which arise from specific local conformations of adjacent phenolic groups, or are included in the extended structure through other interplay of the calixarenes and carboranes in such clefts.     

A version of Fabry's theorem for power series with regularly varying coefficients

For real power series whose non-zero coefficients satisfy , we prove a stronger version of Fabry's theorem relating the frequency of sign changes in the coefficients and analytic continuation of the sum of the power series.

     

Banach Spaces with Property (M) and their Szlenk Indices

We show that a separable Banach space with property (M*) has a Szlenk index equal to ω₀, and a norm with an optimal modulus of asymptotic uniform smoothness. From this we derive a condition on the Szlenk functions of the space and its dual which characterizes embeddability into c ₀ or an ℓ _p -sum of finite dimensional spaces. We also prove that two Lipschitz-isomorphic Orlicz sequence spaces contain the same ℓ _p -spaces.