Smooth Stable and Unstable Manifolds for Stochastic Evolutionary Equations

Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of stochastic partial differential equations. We first show the existence of Lipschitz continuous stable and unstable manifolds by the Lyapunov–Perrons method. Then, we prove the smoothness of these invariant manifolds.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.     

A Fully Synthetic Four‐Component Antitumor Vaccine Consisting of a Mucin Glycopeptide Antigen Combined with Three Different T‐Helper‐Cell Epitopes

In a new concept of fully synthetic vaccines, the role of T‐helper cells is emphasized. Here, a synthetic antitumor vaccine consisting of a diglycosylated tumor‐associated MUC1 glycopeptide as the B‐cell epitope was covalently cross‐linked with three different T‐helper‐cell epitopes via squaric acid ligation of two linear (glyco)peptides. In mice this four‐component vaccine administered without external immune‐stimulating promoters elicit titers of MUC1‐specific antibodies that were about eight times higher than those induced by a vaccine containing only one T‐helper‐cell epitope. The promising results indicate that multiple activation of different T‐helper cells is useful for applications in which increased immunogenicity is required. In personalized medicine, in particular, this flexible construction of a vaccine can serve as a role model, for example, when T‐helper‐cell epitopes are needed that match human leukocyte antigens (HLA) in different patients.     

A Reversible and Selective Inhibitor of Monoacylglycerol Lipase Ameliorates Multiple Sclerosis

Monoacylglycerol lipase (MAGL) is the enzyme responsible for the inactivation of the endocannabinoid 2‐arachidonoylglycerol (2‐AG). MAGL inhibitors show analgesic and tissue‐protecting effects in several disease models. However, the few efficient and selective MAGL inhibitors described to date block the enzyme irreversibly, and this can lead to pharmacological tolerance. Hence, additional classes of MAGL inhibitors are needed to validate this enzyme as a therapeutic target. Here we report a potent, selective, and reversible MAGL inhibitor (IC₅₀=0.18 μM ) which is active in vivo and ameliorates the clinical progression of a multiple sclerosis (MS) mouse model without inducing undesirable CB₁‐mediated side effects. These results support the interest in MAGL as a target for the treatment of MS.     

On the Mechanism of the Organocatalytic Asymmetric Epoxidation of α,β‐Unsaturated Aldehydes

Mechanistic studies on the organocatalytic epoxidation of α,β‐unsaturated aldehydes explore the autoinductive behavior of the reaction and establish that the hydrate/peroxyhydrate of the product is acting as a phase‐transfer catalyst. Based on these studies, an improved methodology that provides high selectivities and decreased catalyst loading, through the addition of chloral hydrate, is developed.     

The Local Atomic Structures of Liquid CO at 3.6 GPa and Polymerized CO at 0 to 30 GPa from High‐Pressure Pair Distribution Function Analysis

The local atomic structures of liquid and polymerized CO and its decomposition products were analyzed at pressures up to 30 GPa in diamond anvil cells by X‐ray diffraction, pair distribution function (PDF) analysis, single‐crystal diffraction, and Raman spectroscopy. The structural models were obtained by density functional calculations. Analysis of the PDF of a liquid CO‐rich phase revealed that the local structure has a pronounced short‐range order. The PDFs of polymerized amorphous CO at several pressures revealed the compression of the molecular structure; covalent bond lengths did not change significantly with pressure. Experimental PDFs could be reproduced with simulations from DFT‐optimized structural models. Likely structural features of polymerized CO are thus 4‐ to 6‐membered rings (lactones, cyclic ethers, and rings decorated with carbonyl groups) and long bent chains with carbonyl groups and bridging atoms. Laser heating polymerized CO at pressures of 7 to 9 GPa and 20 GPa resulted in the formation of CO₂.     

Penultimate effects in the copolymerization of maleic anhydride with electron‐rich styrene derivatives

The (controlled) free‐radical copolymerization of maleic anhydride and styrene or derivatives thereof is often thought to provide nearly perfect alternating copolymers. Here, the RAFT copolymerization of electron‐rich styrene derivatives with maleic anhydride is reported. This copolymerization shows distinct penultimate effects, resulting in polymers with increased incorporation of styrene monomers, that is, where a tendency toward periodic (S‐S‐MA) copolymers exists. This work could be a first step towards periodic copolymers based on maleic anhydride and styrene derivatives. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 2932–2939     

Alkyl chain order in a lamellar lyotropic liquid crystal with varying surface charge density

Abstract

The alkyl chain order in the lamellar liquid-crystalline phase formed in the octylamine/octylammonium chloride/water system has been investigated by ²H N.M.R. at constant mole ratio water/amphiphile and varying charge of the lamellae. The results are correlated to the dimensions of the aggregate obtained from X-ray low angle diffraction measurements.