Ill-posedness of the Camassa–Holm and related equations in the critical space

We prove norm inflation and hence ill-posedness for a class of shallow water wave equations, such as the Camassa–Holm equation, Degasperis–Procesi equation and Novikov equation etc., in the critical Sobolev space $H^{3/2}$ and even in the Besov space $B_{p,r}^{1+1/p}$ for $p\in [1,\infty ],r\in (1,\infty ]$. Our results cover both real-line and torus cases (only real-line case for Novikov), solving an open problem left in the previous works ([5], [14], [16]).     

Automated chemical resonance generation and structure filtration for kinetic modeling

This work discusses efficient and automated methods for constructing a set of representative resonance structures for arbitrary chemical species, including radicals and biradicals, consisting of the elements H, C, O, N, and S. Determining the representative reactive structures of chemical species is crucial for identification of reactive sites and consequently applying the correct reaction templates to generate the set of important reactions during automated chemical kinetic model generation. We describe a fundamental set of resonance pathway types, accounting for simple resonating structures, as well as global approaches for polycyclic aromatic species. Automatically discovering potential localized structures along with filtration to identify the representative structures was shown to be robust and relatively fast. The algorithms discussed here were recently implemented in the Reaction Mechanism Generator (RMG) software. The final structures proposed by this method were found to be in reasonable agreement with quantum chemical computation results of localized structure contributions to the resonance hybrid.     

The Special “Morse Code” between Solvent Polarity and Morphology Flexibility in a POSS–Dendrimer Supramolecular System

An amazing phenomenon of the relative magnitude of modulus of two liquid-crystal (LC) gels is found inverted under/above their phase transition temperature T_LC-iso, which is further proved to be caused by their diverse morphology flexibility. By testing the polarity of two LCs, gelator POSS-G1-Boc (POSS=polyhedral oligomeric silsesquioxane) was discovered to self-assemble into more flexible structures in a relatively low polar LC, whereas more rigid ones are formed in higher polar LC. Hence, a fitting function to connect morphology flexibility with solvent polarity was established, which can even be generalized to a number of common solvents. Experimental observations and coarse-grained molecular dynamics simulations revealed that solvent polarity mirrors a “Morse code”, with each “code” corresponding to a specific morphology flexibility.     

Influence of the pH Value on the Hydrothermal Degradation of Fructose

The hydrothermal treatment of sugars features a promising technology for the production of fine and platform chemicals from renewable resources. In this work the hydrothermal decomposition of fructose was studied in a buffered medium at a pH range between 2.2 and 8.0. It is demonstrated that at lower pH values mainly 5-hydroxymethylfurfural (HMF), levulinic acid and humin are generated, while lactic acid and acetic acid are produced at higher pH values. The work shows that the use of moderate acidic conditions may have advantages for the hydrothermal HMF production over the use of strongly acidic conditions, as especially the degradation into levulinic acid is suppressed. Besides, this study deals with a rather complex reaction network, hence limitations and need for adaption of the kinetic model are discussed.     

The Plasticity of the Carbohydrate Recognition Domain Dictates the Exquisite Mechanism of Binding of Human Macrophage Galactose-Type Lectin

The human macrophage galactose-type lectin (MGL), expressed on macrophages and dendritic cells (DCs), modulates distinct immune cell responses by recognizing N-acetylgalactosamine (GalNAc) containing structures present on pathogens, self-glycoproteins, and tumor cells. Herein, NMR spectroscopy and molecular dynamics (MD) simulations were used to investigate the structural preferences of MGL against different GalNAc-containing structures derived from the blood group A antigen, the Forssman antigen, and the GM2 glycolipid. NMR spectroscopic analysis of the MGL carbohydrate recognition domain (MGL-CRD, C181-H316) in the absence and presence of methyl α-GalNAc (α-MeGalNAc), a simple monosaccharide, shows that the MGL-CRD is highly dynamic and its structure is strongly altered upon ligand binding. This plasticity of the MGL-CRD structure explains the ability of MGL to accommodate different GalNAc-containing molecules. However, key differences are observed in the recognition process depending on whether the GalNAc is part of the blood group A antigen, the Forssman antigen, or GM2-derived structures. These results are in accordance with molecular dynamics simulations that suggest the existence of a distinct MGL binding mechanism depending on the context of GalNAc moiety presentation. These results afford new perspectives for the rational design of GalNAc modifications that fine tune MGL immune responses in distinct biological contexts, especially in malignancy.     

Incremental dynamic mode decomposition: A reduced-model learner operating at the low-data limit

The present work aims at proposing a new methodology for learning reduced models from a small amount of data. It is based on the fact that discrete models, or their transfer function counterparts, have a low rank and then they can be expressed very efficiently using few terms of a tensor decomposition. An efficient procedure is proposed as well as a way for extending it to nonlinear settings while keeping limited the impact of data noise. The proposed methodology is then validated by considering a nonlinear elastic problem and constructing the model relating tractions and displacements at the observation points.     

A Methodology for Estimating Kinetic Parameters and Reactivity Ratios of Multi‐site Type Catalysts Using Polymerization,Fractionation, and Spectroscopic Techniques

This work describes a polymer reaction engineering framework for understanding how catalyst kinetic parameters affect the microstructure of polyolefins made with single‐ or multi‐site catalysts. Moreover, a methodology for deconvolution and kinetic parameters estimation is presented to estimate the reactivity ratios of multi‐site catalysts based on the combination of polymerization, fractionation, and spectroscopic techniques, namely, gel permeation chromatography‐IR and carbon‐13 nuclear magnetic resonance spectroscopy. The methodology capabilities are then demonstrated and validated using a case study simulated via a Monte Carlo model including random noise in order to better represent experimental result uncertainties. The methodology can reverse engineer experimental results and estimate all relevant reaction performance parameters.     

The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

Media pressures on Welsh language preservation

Despite compulsory school instruction in the Welsh language and strong cultural incentives to acquire the language, the most recent UK Census showed a downward trend in the number of speakers. The asymmetry in explicit language acquisition incentives is here considered to be offset by the media dominance of the English language. This dominance is modeled by the introduction of time-dependent connectivity and infectivity among English speakers into an adapted epidemiological model. Extrapolations up to 2050 are made, this being the announced date of a Welsh Assembly language-planning target of one million Welsh speakers.