Differential Equations with Infinitely Many Derivatives and the Borel Transform

Differential equations with infinitely many derivatives, sometimes also referred to as “nonlocal” differential equations, appear frequently in branches of modern physics such as string theory, gravitation and cosmology. We properly interpret and solve linear equations in this class with a special focus on a solution method based on the Borel transform. This method is a far-reaching generalization of previous studies of nonlocal equations via Laplace and Fourier transforms, see for instance (Barnaby and Kamran, J High Energy Phys 02:40, 2008; Górka et al., Class Quantum Gravity 29:065017, 2012; Górka et al., Ann Henri Poincaré 14:947–966, 2013). We reconsider “generalized” initial value problems within the present approach and we disprove various conjectures found in modern physics literature. We illustrate various analytic phenomena that can occur with concrete examples, and we also treat efficient implementations of the theory.     

Asymmetric synthesis of 3,4-anti- and 3,4-syn-substituted aminopyrrolidines via lithium amide conjugate addition

The diastereoselective conjugate addition of homochiral lithium amides to methyl 4-(N-allyl-N-benzylamino)but-2-enoate has been used as the key step in a simple and efficient protocol for the preparation of 3,4-substituted aminopyrrolidines. This protocol provides a complementary and stereoselective route to both anti- and syn-3-amino-4-alkylpyrrolidines as well as anti- and syn-3-hydroxy-4-aminopyrrolidines, in high de and ee viabeta-amino enolate functionalisation. This methodology has been applied to the synthesis of anti-(3S,4S)- and syn-(3R,4S)-3-methoxy-4-(N-methylamino)pyrrolidine.     

Biocompatibility Study of Electrospun Nanocomposite Membranes Based on Chitosan/Polyvinyl Alcohol/Oxidized Carbon Nano-Onions

In recent decades, the number of patients requiring biocompatible and resistant implants that differ from conventional alternatives dramatically increased. Among the most promising are the nanocomposites of biopolymers and nanomaterials, which pretend to combine the biocompatibility of biopolymers with the resistance of nanomaterials. However, few studies have focused on the in vivo study of the biocompatibility of these materials. The electrospinning process is a technique that produces continuous fibers through the action of an electric field imposed on a polymer solution. However, to date, there are no reports of chitosan (CS) and polyvinyl alcohol (PVA) electrospinning with carbon nano-onions (CNO) for in vivo implantations, which could generate a resistant and biocompatible material. In this work, we describe the synthesis by the electrospinning method of four different nanofibrous membranes of chitosan (CS)/(PVA)/oxidized carbon nano-onions (ox-CNO) and the subdermal implantations after 90 days in Wistar rats. The results of the morphology studies demonstrated that the electrospun nanofibers were continuous with narrow diameters (between 102.1 nm ± 12.9 nm and 147.8 nm ± 29.4 nm). The CS amount added was critical for the diameters used and the successful electrospinning procedure, while the ox-CNO amount did not affect the process. The crystallinity index was increased with the ox-CNO introduction (from 0.85% to 12.5%), demonstrating the reinforcing effect of the nanomaterial. Thermal degradation analysis also exhibited reinforcement effects according to the DSC and TGA analysis, with the higher ox-CNO content. The biocompatibility of the nanofibers was comparable with the porcine collagen, as evidenced by the subdermal implantations in biological models. In summary, all the nanofibers were reabsorbed without a severe immune response, indicating the usefulness of the electrospun nanocomposites in biomedical applications.     

Conformational dependence of the second hyperpolarizability of quadrupolar molecules

Hatree–Fock calculations at ab initio and semiempirical levels were carried out for the averaged polarizability α and second hyperpolarizability γ of two pairs of quadrupolar isomers with different donor and acceptor groups. These properties were correlated with the antibonding/bonding π occupation number (π*/π ratio). It was found that isomers with extended π systems had low π*/π ratios and high α and γ values, while low α and γ values were obtained for isomers with large π*/π ratios and no extended π system. The PM3 and PM6 α values were found to be in excellent agreement with the HF/6-31+G(d,p) ones. The PM3 values for γ were significantly larger than those calculated by HF/6-31+G(d,p), with an average PM3/HF ratio of 1.43. The PM6 results were noticeably better with a ratio of 0.85. The calculation of α and γ at MP2/6-31+G(d,p) level for representative isomers showed that the contribution of the electron correlation to their values was small and that the HF/6-31+G(d,p) method provides reliable values at much lower computational cost.     

An efficient synthesis of (E)-α,β-unsaturated ketones and esters with total stereoselectivity by using chromium dichloride

(E)-α,β-Unsaturated ketones 1 or esters 2 can be obtained with complete stereoselectivity by reaction of different 2-chloro-3-hydroxy ketones 3 or esters 4 and CrCl₂. A comparative study of the results of synthesis of ketones 1 with CrCl₂ or samarium is performed. A mechanism to explain both β-elimination reactions has been proposed.