Dual stimuli‐responsive polyamines derived from modified N‐vinylpyrrolidones through CuAAC click chemistry

The synthesis via copper(I)‐catalyzed azide alkyne cycloaddition (CuAAC) of three new monomer derivatives of N‐vinyl‐2‐pyrrolidone (VP) carrying cyclic pyrrolidine, piperidine, and piperazine groups and the corresponding copolymers with unmodified VP is shown. The systems bearing pyrrolidine and piperidine displayed both thermo‐ and pH‐response, which has not been reported previously for a polymer with polyvinylpyrrolidone (PVP) backbone. A broad modulation of the LCST with the copolymer composition and pH was observed in a temperature range 0–100 °C. The polymers carrying piperazine exhibited broad buffering regions and no thermosensitivity. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1098–1108     

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.     

Brazilian <Emphasis Type="Italic">Dioscoreaceas</Emphasis> starches

Determination of the characteristics of native starches is crucial in order to select their best application in various industrial fields. Thus, two different types of non-traditional native starches from the Dioscoreaceas species (Dioscorea sp. and Dioscorea piperifolia Humb. var. Wild) were studied regarding their thermal, structural and rheological properties. The results were contrasted with traditional commercial starch sources (potato, cassava and corn). From the thermogravimetric results (TG/DTG), D. piperifolia starch obtained the highest thermal stability of the samples, except for potato starch. Furthermore, using differential scanning calorimetry and viscoamylograph profiles (RVA), it was found that the Dioscoreaceas starches presented a higher onset (T _o) temperature and susceptibility to retrogradation. They also showed lower values in relation to relative crystallinity, which was calculated from their X-ray patterns and tendency to white (L*) colour. The shapes of the Discoreaceas starch granules were determined using electron microscopy; it was found that as the potato starch the Dioscoreaceas starches showed a wide range of particle size.     

Natural abundance 13C - 13C coupling constants observed via double quantum coherence. Structural elucidation by the one- and the two-dimensional NMR experiements of velloziolone,a new seco-diterpene.

With the help of Natural Abundance ¹³C - ¹³C Coupling Constants, observed via double quantum coherence, the structural determination of VELLOZIOLONE (1), a new diterpene, has been carried out.     

Separation dichotomy and wavefronts for a nonlinear convolution equation

This paper is concerned with a scalar nonlinear convolution equation, which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that, at each end of the real line, every bounded positive solution of the convolution equation should either be separated from zero or be exponentially converging to zero. This dichotomy principle is then used to establish a general theorem guaranteeing the uniform persistence and existence of semi-wavefront solutions to the convolution equation. Finally, we apply our theoretical results to several well-studied classes of evolution equations with asymmetric non-local and non-monotone response. We show that, contrary to the symmetric case, these equations can possess simultaneously stationary, expansion and extinction waves.     

Spatial Vector Solitons in Nonlinear Photonic Crystal Fibers

We study spatial vector solitons in a photonic crystal fiber (PCF) made of a material with the focusing Kerr nonlinearity. We show that such two-component localized nonlinear waves consist of two mutually trapped components confined by the PCF linear and the self-induced nonlinear refractive indices, and they bifurcate from the corresponding scalar solitons. We demonstrate that, in a sharp contrast with an entirely homogeneous nonlinear Kerr medium where both scalar and vector spatial solitons are unstable and may collapse, the periodic structure of PCF can stabilize the otherwise unstable two-dimensional spatial optical solitons. We apply the matrix criterion for stability of these two-parameter solitons, and verify it by direct numerical simulations.     

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.     

An indefinite concave-convex equation under a Neumann boundary condition I

We investigate the problem (P _λ) ?Δu = λb(x)|u| ^q?2 u + a(x)|u| ^p?2 u in Ω, ?u/?n = 0 on ?Ω, where Ω is a bounded smooth domain in R ^N (N ≥ 2), 1 < q < 2 < p, λ ∈ R, and a, b ∈ \({C^\alpha }\left( {\overline \Omega } \right)\) with 0 < α < 1. Under certain indefinite type conditions on a and b, we prove the existence of two nontrivial nonnegative solutions for small |λ|. We then characterize the asymptotic profiles of these solutions as λ → 0, which in some cases implies the positivity and ordering of these solutions. In addition, this asymptotic analysis suggests the existence of a loop type component in the non-negative solutions set. We prove the existence of such a component in certain cases, via a bifurcation and a topological analysis of a regularized version of (P _λ).     

A geometric construction of local representations of local Lie groups

Local transformation groups acting on a manifold X define a natural action of on a space D(X), of functions on X. The natural action induces a local representation of on a Hilbert subspace of the space of distributions on D(X).