Conventional vs. Microwave- or Mechanically-Assisted Synthesis of Dihomooxacalix[4]arene Phthalimides: NMR,X-ray and Photophysical Analysis §

Direct O-alkylation of p-tert-butyldihomooxacalix[4]arene (1) with N-(bromopropyl)- or N-(bromoethyl)phthalimides and K₂CO₃ in acetonitrile was conducted under conventional heating (reflux) and using microwave irradiation and ball milling methodologies. The reactions afforded mono- and mainly distal di-substituted derivatives in the cone conformation, in a total of eight compounds. They were isolated by column chromatography, and their conformations and the substitution patterns were established by NMR spectroscopy (¹H, ¹³C, COSY and NOESY experiments). The X-ray structures of four dihomooxacalix[4]arene phthalimide derivatives (2a, 3a, 3b and 5a) are reported, as well as their photophysical properties. The microwave (MW)-assisted alkylations drastically reduced the reaction times (from days to less than 45 min) and produced higher yields of both 1,3-di-substituted phthalimides (3a and 6a) with higher selectivity. Ball milling did not reveal to be a good method for this kind of reaction.     

Repdigits as sums of three Pell numbers

In this paper, all base 10 repdigits expressible as sums of three Pell numbers are found.     

Merging the Isonitrile-Tetrazine (4+1) Cycloaddition and the Ugi Four-Component Reaction into a Single Multicomponent Process

Multicomponent reactions are of utmost importance at generating a unique, wide, and complex chemical space. Herein we describe a novel multicomponent approach based on the combination of the isonitrile-tetrazine (4+1) cycloaddition and the Ugi four-component reaction to generate pyrazole amide derivatives. The scope of the reaction as well as mechanistic insights governing the 4H-pyrazol-4-imine tautomerization are provided. This multicomponent process provides access to a new chemical space of pyrazole amide derivatives and offers a tool for peptide modification and stapling.     

Numerical semigroups with many gaps of the same parity

Let g _e (S) (respectively, g _o (S)) be the number of even (respectively, odd) gaps of a numerical semigroup S. In this work we study and characterize the numerical semigroups S that verify 2|g _e (S)−g _o (S)|+1∈S. As a consequence we will see that every numerical semigroup can be represented by means of a numerical semigroup with maximal embedding dimension with all its minimal generators odd. The first author is supported by the project MTM2007-62346 and FEDER funds. The authors want to thank P.A. García-Sánchez and the referee for their comments and suggestions.     

Order-free Recursion on the Real Numbers

We investigate operations, computable in the sense of Recursive Analysis, which can be generated recursively from the arithmetic operations and the limit operation without using any tests on the real numbers. These functions, called order-free recursive, can be shown to include a large class of computable functions. As main tools we provide an effective version of the Stone-Weierstraß Approximation Theorem, as well as recursive partitions of unity.     

Catalytic Asymmetric Oxidative γ‐Coupling of α,β‐Unsaturated Aldehydes with Air as the Terminal Oxidant

A novel concept for catalytic asymmetric coupling reactions is presented. Merging organocatalysis with single‐electron oxidation by using a catalytic amount of a copper(II) salt and air as the terminal oxidant, we have developed a highly stereoselective carbon–carbon oxidative coupling reaction of α,β‐unsaturated aldehydes. The concept relies on the generation of a dienamine intermediate, which is oxidized to an open‐shell activated species that undergoes highly selective γ‐homo‐ and γ‐heterocoupling reactions. In the majority of examples presented, only a single stereoisomer was formed.     

A new process for acrylic acid synthesis by fermentative process

With the synthesis of chemical products through biotechnological processes, it is possible to discover and to explore innumerable routes that can be used to obtain products of high added value. Each route may have particular advantages in obtaining a desired product, compared with others, especially in terms of yield, productivity, easiness to separate the product, economy, and environmental impact. The purpose of this work is the development of a deterministic model for the biochemical synthesis of acrylic acid in order to explore an alternative process. The model is built-up with the tubular reactor equations together with the kinetic representation based on the structured model. The proposed process makes possible to obtain acrylic acid continuously from the sugar cane fermentation.     

Feasibility of post-gadolinium three-dimensional gradient-echo sequence to evaluate the pulmonary arterial vasculature

Purpose

To determine the feasibility of post-gadolinium three-dimensional gradient-echo (3D-GE) sequence for the evaluation of the pulmonary arterial vasculature in patients with suspected pulmonary embolism (PE) and in patients with a variety of other disease processes.

Materials and Methods

Twenty-six consecutive patients (18 females, 8 males; mean age±S.D., 46.6±21.1 years) who underwent chest magnetic resonance imaging (MRI) including post-gadolinium 3D-GE sequence for the evaluation of PE (Group A, n=13) and a variety of other disease processes (Group B, n=13) were included in the study. Post-gadolinium 3D-GE MR sequences were retrospectively, independently and blindly evaluated by two reviewers for the image quality of pulmonary arterial vasculature, and findings of PE and other disease processes. Clinical and imaging follow-up data for all patients were obtained. Interobserver agreement was calculated by kappa statistics.

Results

All central and lobar pulmonary arteries, 71.4–89.6% of segmental arteries and 46.7–52.7% of subsegmental arterial units in both groups were visualized with sufficient diagnostic image quality on post-gadolinium 3D-GE sequences. PE involving lobar and segmental arteries was diagnosed in two patients in each group. Other disease processes including pneumonia, lung nodules, superior vena cava stenosis, lung metastases, chronic lymphocytic leukemia and aortic aneurysm were detected in 10 of 26 patients. There was good to excellent interobserver agreement (0.73 to 1.00) for all findings.

Conclusion

Post-gadolinium 3D-GE sequence may be an alternative technique for the visualization of central, lobar and segmental arteries, and may diagnose PE and other pathologies involving the chest in different patient populations.     

Comment on: “From classical to modern ether-drift experiments: the narrow window for a preferred frame” [Phys. Lett. A 333 (2004) 355]

In a recent article [M. Consoli, E. Costanzo, Phys. Lett. A 333 (2004) 355], M. Consoli and E. Costanzo have investigated classical and modern aether drift experiments and explored the narrow window for detection of a preferred reference frame. This Letter proposes an easy to perform variant of Fizeau's experiment, which may confirm or deny Consoli–Costanzo's claims.