We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in 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. 相似文献
This review gives an overview of the evolution of the technology of condensed mode cooling, primarily for the case of ethylene polymerization on supported catalysts in fluidized bed reactors. It is well known that this mode of heat removal is quite effective in allowing polyolefin manufacturers to increase significantly production rates. What is perhaps less well understood are all of the issues that, in addition to the effect of the latent heat of vaporization of injected liquid components, also have an impact on the rate of production and behavior of the reactor. However, the liquid components injected into the reactor can vaporize rapidly under full‐scale conditions, leaving behind several heavy components (with respect to ethylene) that have numerous effects on how the particles behave, on the reaction rate, and on fluidization, fouling, and other parameters related to reactor and process performance. 相似文献
A novel 6-endo-dig cyclization followed by oxidation/elimination of o-alkynylarylaldimines with 4-hydroxybenzylamine was developed for preparation of isoquinolines. The intermediates of this tandem reaction were monitored by mass spectroscopy (MS) to confirm the reaction pathway. This methodology was further applied to the design and synthesis of a novel ratiometric chemosensor for determination of fluoride. 相似文献
Ring‐opening metathesis polymerization (ROMP) has become one of the most important living polymerizations. Cyclopropenes (CPEs) remain underexplored for ROMP. Described here is that the simple swap of 1‐methyl to 1‐phenyl on 1‐(benzoyloxymethyl)CPEs elicited strikingly different modes of reactivity, switching from living polymerization to either selective single‐addition or living alternating ROMP. The distinct reactivity stems from differences in steric repulsions at the Ru alkylidene after CPE ring opening. Possible olefin or oxygen chelation from ring‐opened CPE substituents was also observed to significantly affect the rate of propagation. These results demonstrate the versatility of CPEs as a new class of monomers for ROMP, provide mechanistic insights for designing new monomers with rare single‐addition reactivity, and generate a new functionalizable alternating copolymer scaffold with controlled molecular weight and low dispersity. 相似文献
A single function approximation (SFA) approach for event-triggered output-feedback tracker design is presented for uncertain nonlinear time-delay systems in lower-triangular form. Contrary to the existing event-triggered output-feedback control methods dependent on multiple function approximators in the presence of lower-triangular nonlinearities, the proposed SFA approach provides the following advantages: (i) the simple observer structure independent of function approximators; (ii) one event-triggering condition based on only a tracking error; and (iii) the simple control scheme using one function approximator. Thus, the structural simplicity is allowed for implementing the observer and the event-triggering law in the sensor part and the adaptive tracker in the control part. Under the proposed SFA-based event-triggered control scheme, it is shown that the boundedness of closed-loop signals and the existence of a minimum inter-event time are guaranteed regardless of unknown time-delay nonlinearities and unmeasurable state variables.
Luminescent seven-coordinated zirconium and hafnium complexes bearing three mono-anionic 2,2′-pyridylpyrrolide ligands and one chloride were synthesized. Solid-state structures and the dynamic behaviors in solution were probed by X-ray crystallography and variable temperature 1H NMR experiments, respectively. Absorption spectroscopy and time-dependent density functional theory (TD-DFT) calculations supported a hybrid of ligand-to-metal charge transfer (LMCT)/ligand-to-ligand charge transfer (LLCT) for the visible light absorption band. The complexes (MePMPMe)3MCl (M=Zr, Hf, MePMPMe=3,5-dimethyl-2-(2-pyridyl)pyrrolide) are emissive in solution at room temperature upon irradiation with visible light due to a combination of phosphorescence and fluorescence characterized by excited state lifetimes in the μs and low to sub-ns timescale, respectively. Electrochemical experiments revealed that the zirconium complex possesses a reversible redox event under highly reducing condition (−2.29 V vs. Fc+/0). 相似文献
A range of oxobis(phenyl-1,3-butanedione) vanadium(IV) complexes have been successfully synthesized from cheap starting materials and a simple and solvent-free one-pot dry-melt reaction. This direct, straightforward, fast and alternative approach to inorganic synthesis has the potential for a wide range of applications. Analytical studies confirm their successful synthesis, purity and solid-state coordination, and we report the use of such complexes as potential drug candidates for the treatment of cancer. After a 24 hour incubation of A549 lung carcinoma cells with the compounds, they reveal cytotoxicity values elevenfold greater than cisplatin and remain non-toxic towards normal cell types. Additionally, the complexes are stable over a range of physiological pH values and show the potential for interactions with bovine serum albumin. 相似文献
Influence theory is a foundational theory of physics that is not based on traditional empirically defined concepts, such as positions in space and time, mass, energy, or momentum. Instead, the aim is to derive these concepts, and their empirically determined relationships, from a more primitive model. It is postulated that there exist things, which are call particles, that influence one another in a discrete and directed fashion resulting in a partially ordered set of influence events. The problem of consistent quantification of the influence events is considered. Observers are modeled as particle chains (observer chains) as if an observer were able to track a particle and quantify the influence events that the particle experiences. From these quantified influence events, consistent quantification of the universe of events based on the observer chains is studied. Herein, the kinematics and dynamics of particles from the perspective of influence theory are both reviewed and further developed. 相似文献