Second Order Nonlinear Evolution Inclusions Ⅰ： Existence and Relaxation Results

This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.     

Hele-Shaw type problems with dynamical boundary conditions

In this paper, we study the nonlinear evolution equation of Hele-Shaw type with dynamical boundary conditions. That is, the equation ut=Δw+f where u∈H(w) and H is the Heaviside function, with boundary condition μ(x,w)t_∂w+k∇w⋅ν=g, where ν denotes the outward normal vector of the fixed boundary of the domain. We prove existence, uniqueness and some qualitative properties of the solution.     

Evolutionary rate variation and RNA secondary structure prediction

Predicting RNA secondary structure using evolutionary history can be carried out by using an alignment of related RNA sequences with conserved structure. Accurately determining evolutionary substitution rates for base pairs and single stranded nucleotides is a concern for methods based on this type of approach. Determining these rates can be hard to do reliably without a large and accurate initial alignment, which ideally also has structural annotation. Hence, one must often apply rates extracted from other RNA families with trusted alignments and structures. Here, we investigate this problem by applying rates derived from tRNA and rRNA to the prediction of the much more rapidly evolving 5'-region of HIV-1. We find that the HIV-1 prediction is in agreement with experimental data, even though the relative evolutionary rate between A and G is significantly increased, both in stem and loop regions. In addition we obtained an alignment of the 5' HIV-1 region that is more consistent with the structure than that currently in the database. We added randomized noise to the original values of the rates to investigate the stability of predictions to rate matrix deviations. We find that changes within a fairly large range still produce reliable predictions and conclude that using rates from a limited set of RNA sequences is valid over a broader range of sequences.     

人3型腺病毒六邻体蛋白同源建模及其进化轨迹分析

用同源建模方法构建了人3型腺病毒六邻体完整的空间结构, 对此结构模型的合理性进行检验, 并通过基于多重序列比对的进化轨迹分析发现, 不同型别的人腺病毒六邻体型特异性序列主要存在于六邻体的塔区上, 结合二级结构分析, 预测位于六邻体塔区表面的几个环区是型特异性中和表位的所在区域.     

Heteronuclear 1D and 2D NMR Resonances Detected by Chemical Exchange Saturation Transfer to Water

A method to detect NMR spectra from heteronuclei through the modulation that they impose on a water resonance is exemplified. The approach exploits chemical exchange saturation transfers, which can magnify the signal of labile protons through their influence on a water peak. To impose a heteronuclear modulation on water, an HMQC‐type sequence was combined with the FLEX approach. 1D ¹⁵N NMR spectra of exchanging sites could thus be detected, with about tenfold amplifications over the ¹⁵N modulations afforded by conventionally detected HMQC NMR spectroscopy. Extensions of this approach enable 2D heteronuclear acquisitions on directly bonded ¹H–¹⁵N spin pairs, also with significant signal amplification. Despite the interesting limits of detection that these signal enhancements could open in NMR spectroscopy, these gains are constrained by the rates of solvent exchange of the targeted heteronuclear pairs, as well as by spectrometer instabilities affecting the intense water resonances detected in these experiments.     

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用KMR模型研究了等离子体中多光子非线性Compton散射下电子相轨道的演化,发现电子与光子进行能量交换后,只有未被俘获电子的相轨道才能从周期性向非周期性、随机型演化,其演化剧烈程度随电子吸收光子数的增大而加剧,随电子与光子碰撞非弹性成分和碰撞前初始速度的增大而迅速减弱,但低于强激光场中的剧烈程度。当电子被光场俘获时,这种演化过程结束并做稳定的运动,光子不再为电子提供能量。     

Adsorbents and columns in analytical high-performance liquid chromatography: a perspective with regard to development and understanding

A brief historical survey is presented on the evaluation of silica adsorbents in analytical HPLC. The theory of analytical HPLC is mostly still being based on the height equivalent to a theoretical plate concept and the van Deemter equation that was derived from gas phase adsorption involving a linear adsorption isotherm and fast mass transfer kinetics. One can obviously wonder whether the use of the van Deemter equation is relevant and valid for the evaluation of the performance of HPLC systems, where most often the liquid solutes involve charged molecules in electrolytes and in very many cases the adsorbates are macromolecules having diffusion coefficients of small magnitude. Instead of the van Deemter equation, a multi-scale modelling approach that involves microscopic and macroscopic dynamic non-linear mass-transfer-rate models should be employed. Furthermore, advanced experimental methods for the characterisation of porous media and the distribution of the density of immobilised active sites (e.g., ligands) on surfaces as well as microscopic pore-network modelling and molecular dynamics modelling and simulation methods could be used for the design of novel adsorbents whose porous structures and immobilised active sites would provide effective mass transport and adsorption rates for realising efficient separations as well as high dynamic capacities when larger throughputs are required.     

Revealing Capacity Degradation of Ge Anodes in Lithium-Ion Batteries Triggered by Interfacial LiH

The Germanium (Ge), as a fast-charging and high specific capacity (1568 mAh g⁻¹) alloy anode, is greatly hampered in practical application by poor cyclability. To date, the understanding of cycling performance degradation remains elusive. This study illustrates that, contrary to conventional beliefs, most of the Ge material in failed anodes still retains good integrity and does not undergo severe pulverization. It is revealed that capacity degradation is clearly correlated to the interfacial evolution of lithium hydride (LiH). Tetralithium germanium hydride (Li₄Ge₂H), as a new species derived from LiH, is identified as the culprit of Ge anode degradation, which is the dominant crystalized component in an ever-growing and ever-insulating interphase. The significantly increased thickness of the solid electrolyte interface (SEI) is accompanied by the accumulation of insulating Li₄Ge₂H upon cycling, which severely retards the charge transport process and ultimately triggers the anode failure. We believe that the comprehensive understanding of the failure mechanism presented in this study is of great significance to promoting the design and development of alloy anode for the next generation of lithium-ion batteries.     

Dual Photosensitizer Coupled Three-Dimensional Metal-Covalent Organic Frameworks for Efficient Photocatalytic Reactions

In this work, we innovatively assembled two types of traditional photosensitizers, that is pyridine ruthenium/ferrum (Ru(bpy)₃²⁺/Fe(bpy)₃²⁺) and porphyrin/metalloporphyrin complex (2HPor/ZnPor) by covalent linkage to get a series of dual photosensitizer-based three-dimensional metal-covalent organic frameworks (3D MCOFs), which behaved strong visible light-absorbing ability, efficient electron transfer and suitable band gap for highly efficient photocatalytic hydrogen (H₂) evolution. Rubpy-ZnPor COF achieved the highest H₂ yield (30 338 μmol g⁻¹ h⁻¹) with apparent quantum efficiency (AQE) of 9.68 %@420 nm, which showed one of the best performances among all reported COF based photocatalysts. Furthermore, the in situ produced H₂ was successfully tandem used in the alkyne hydrogenation with ≈99.9 % conversion efficiency. Theoretical calculations reveal that both the two photosensitizer units in MCOFs can be photoexcited and thus contribute optimal photocatalytic activity. This work develops a general strategy and shows the great potential of using multiple photosensitive materials in the field of photocatalysis.