Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels

We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in ${\mathbb{R}}^d$ and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the evolution of a typical neuron, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis.     

Isomorphisms of spaces with large distortion

Let K and S be locally compact Hausdorff spaces and let X be a strictly convex Banach space of finite dimension at least 2. In this paper, we prove that if there exists an isomorphism T from onto satisfying then K and S are homeomorphic. Here denotes the Schäffer constant of X. Even for the classical cases , and , this result is the X‐valued Banach–Stone theorem via isomorphism with the largest distortion that is known so far, namely . On the other hand, it is well known that this result is not true for , even though K and S are compact Hausdorff spaces.     

A note on the eigenvalues of p‐fractional Hardy–Sobolev operator with indefinite weight

In this article, we study the eigenvalues of p‐fractional Hardy operator where , , , and Ω is an unbounded domain in with Lipschitz boundary containing 0. The weight function V may change sign and may have singular points. We also show that the least positive eigenvalue is simple and it is uniquely associated to a nonnegative eigenfunction. Moreover, we proved that there exists a sequence of eigenvalues as .     

In Situ Metal-Assisted Ligand Modification Induces Mn4 Cluster-to-Cluster Transformation: A Crystallography,Mass Spectrometry,and DFT Study

Dehydration of (S,S)-1,2-bis(1H-benzo[d]imidazol-2-yl)ethane-1,2-diol (H₄L) to (Z)-1,2-bis(1H-benzo[d]imidazol-2-yl)ethenol) (H₃L′) was found to be metal-assisted, occurs under solvothermal conditions (H₂O/CH₃OH), and leads to [Mn^II₄(H₃L)₄Cl₂]Cl₂ ⋅ 5 H₂O ⋅ 5 CH₃OH ( Mn₄L₄ ) and [Mn^II₄(H₂L′)₆(μ₃-OH)]Cl ⋅ 4 CH₃OH ⋅ H₂O ( Mn₄L′₆ ), respectively. Their structures were determined by single-crystal XRD. Extensive ESI-MS studies on solutions and solids of the reaction led to the proposal consisting of an initial stepwise assembly of Mn₄L₄ from the reactants via [MnL] and [Mn₂L₂] below 80 °C, and then disassembly to [MnL] and [MnL₂] followed by ligand modification before reassembly to Mn₄L′₆ via [MnL′], [MnL′₂], and [Mn₂L′₃] with increasing solvothermal temperature up to 140 °C. Identification of intermediates [Mn₄L_xL′_6−x] (x=5, 4, 3, 2, 1) in the process further suggested an assembly/disassembly/in situ reaction/reassembly transformation mechanism. These results not only reveal that multiple phase transformations are possible even though they were not realized in the crystalline state, but also help to better understand the complex transformation process between coordination clusters during “black-box” reactions.     

In situ green synthesis of Cu‐Ni bimetallic nanoparticles supported on reduced graphene oxide as an effective and recyclable catalyst for the synthesis of N‐benzyl‐N‐aryl‐5‐amino‐1H‐tetrazoles

In the present work, for the first time we have designed a novel approach for the synthesis of N‐benzyl‐N‐aryl‐5‐amino‐1H‐tetrazoles using reduced graphene oxide (rGO) decorated with Cu‐Ni bimetallic nanoparticles (NPs). In situ synthesis of Cu/Ni/rGO nanocomposite was performed by a cost efficient, surfactant‐free and environmentally benign method using Crataegus azarolus var. aronia L. leaf extract as a stabilizing and reducing agent. Phytochemicals present in the extract can be used to reduce Cu²⁺ and Ni²⁺ ions and GO to Cu NPs, Ni NPs and rGO, respectively. Analyses by means of FT‐IR, UV–Vis, EDS, TEM, FESEM, XRD and elemental mapping confirmed the Cu/Ni/rGO formation and also FT‐IR, NMR, and mass spectroscopy as well as elemental analysis were used to characterize the tetrazoles. The Cu/Ni/rGO nanocomposite showed the superior catalytic activity for the synthesis of N‐benzyl‐N‐aryl‐5‐amino‐1H‐tetrazoles within a short reaction time and high yields. Furthermore, this protocol eliminates the need to handle HN₃.     

Flexible,dicationic imidazolium salts for in situ application in palladium‐catalysed Mizoroki–Heck coupling of acrylates under aerobic conditions

The synthesis, characterization and in situ catalytic performance of new unsymmetric N,N′‐disubstituted imidazolium‐based dicationic salts in Mizoroki–Heck coupling of acrylates with aryl bromides under aerobic conditions are described. A series of flexible dicationic salts with varying steric and electronic properties were synthesized in good to excellent yields. All the salts were well characterized using spectroscopic techniques. X‐ray diffraction analysis of two salts with the same dicationic backbone and different counter anions shows that the ligand adopts two different conformations which are influenced by the nature of the anion. Thus, the ligand is capable of changing its conformation according to the change in environment due to its flexible nature. All the synthesized imidazolium salts were found to be active in in situ palladium‐catalysed Mizoroki–Heck coupling under aerobic conditions. Amongst the salts, the hydroxyl‐functionalized imidazolium salt, incorporating the features of both bidentate chelating O,O ligand and carbene, shows the maximum catalytic activity. A variety of aryl and heteroaryl methyl and ethyl cinnamates were synthesized using these imidazolium salts as preligands. In addition, NMR studies confirm in situ generation of normal N‐heterocyclic carbenes from the C‐2 position of imidazol‐2‐ylidene ring. The mercury poisoning test was also performed to ascertain the nature of catalytically active palladium species. Aerobic conditions, low catalytic loading (0.5 mol%), shorter reaction times, broad functional group tolerance and good to excellent isolated yields are some of the significant features of the novel catalytic systems described here. Copyright © 2016 John Wiley & Sons, Ltd.     

A Thermo‐ and Photo‐Switchable Ruthenium Initiator For Olefin Metathesis

A ruthenium carbene complex bearing azobenzene functionality is reported. The complex exists in the form of two isomers differing by the size of the chelate ring. Both isomers were isolated by applying kinetic or thermodynamic control during the synthesis and characterized by X‐ray diffraction analysis. The isomerization of the complex was studied by UV/Vis spectroscopy. The stable isomer was tested as a catalyst in olefin metathesis. The complex was activated at about 100 °C to promote ring‐closing and ring‐opening polymerization metathesis reactions. The activation took place also at room temperature under middle ultraviolet radiation.     

甲型H1N1流感的死亡率高吗——Bayes计量分析框架下的建模与估算

在全球甲型H1N1流感大流行背景下,本文在充分考虑各国甲流感死亡率可能存在个体混合效应、独立效应、相关效应及空间相关效应基础上,运用Bayes计量分析框架下的模型选择标准确定描述各国甲流感死亡率的最优模型,并基于该模型对不同国家甲流感死亡率进行估算。结果显示:个体独立、空间相关效应模型能很好拟合各国甲流感疫情统计数据,利用该模型估算的全球甲流感平均死亡率为0.577%。     

Palladium‐Catalyzed Insertion of an Allene into an Aminal: Aminomethylamination of Allenes by C?N Bond Activation

A new and atom‐economic palladium‐catalyzed aminomethylamination of allenes with aminals by C N bond activation is described. This direct and operationally simple method provides a fundamentally novel approach for the synthesis of 1,3‐diamines. Mechanistic studies suggest that a unique cationic π‐allylpalladium complex containing an aminomethyl moiety is generated as a key intermediate through the carbopalladation of the allene with a cyclometalated palladium–alkyl species.