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We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable which can take values . Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc. 相似文献
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Jennifer Perez-Oregon Fernando Angulo-Brown Nicholas Vassiliou Sarlis 《Entropy (Basel, Switzerland)》2020,22(11)
Nowcasting earthquakes, suggested recently as a method to estimate the state of a fault and hence the seismic risk, is based on the concept of natural time. Here, we generalize nowcasting to a prediction method the merits of which are evaluated by means of the receiver operating characteristics. This new prediction method is applied to a simple (toy) model for the waiting (natural) time of the stronger earthquakes, real seismicity, and the Olami-Feder-Christensen earthquake model with interesting results revealing acceptable to excellent or even outstanding performance. 相似文献
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Azobenzene‐Functionalized Cage Silsesquioxanes as Inorganic–Organic Hybrid,Photoresponsive, Nanoscale,Building Blocks 下载免费PDF全文
Prof. Hongzhi Liu 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(12):4731-4738
Mono‐ and octa‐azobenzene‐functionalized cage silsesquioxanes were easily synthesized by the reaction of 4‐bromoazobenzene with monovinyl‐substituted octasilsesquioxane and cubic octavinylsilsesquioxane through the Heck coupling reaction. Excited‐state energies obtained from time‐dependent density functional theory (TDDFT) and the CAM‐B3LYP functional correlate very well with experimental trans–cis photoisomerization results from UV/Vis spectroscopy. These azobenzene‐functionalized cages exhibit good thermal stability and are fluorescent with maximum emission at approximately 400 nm, making them potential materials for blue‐light emission. 相似文献
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Samuel Clark Ligon Konstanze Seidler Christian Gorsche Markus Griesser Norbert Moszner Robert Liska 《Journal of polymer science. Part A, Polymer chemistry》2016,54(3):394-406
The rapid and uncontrolled nature of network formation from di(meth)acrylate monomers produces high shrinkage stress and results in polymers with oftentimes brittle mechanical properties. Methods for regulating polymerization and network formation are sought. One option is the use of addition–fragmentation chain transfer (AFCT) agents, which are well known to control molecular weight and molecular weight distribution of monofunctional (meth)acrylates. A series of novel and previously described AFCT reagents were synthesized and screened with laser flash photolysis to determine reactivity. Well‐performing AFCT reagents were then tested in polymerizations with monofunctional and difunctional methacrylates. With monofunctional monomers, the molecular weight and polydispersity of the resultant linear polymers tend to decrease with the addition of AFCT agent. In copolymerization with dimethacrylate monomers, the AFCT agents were found to substantially lower and sharpen the glass transition. Sharpness of the glass transition is here indicative of a more regular and homogenous network. After coupling of the instruments, photorheology was performed simultaneously with real‐time IR to show an increase in monomer conversion at the time of gelation, which appears to have a positive effect on reducing shrinkage stress. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 394–406 相似文献
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ShiJun Liao 《中国科学:物理学 力学 天文学(英文版)》2020,(3):70-81
A new non-perturbative approach is proposed to solve time-independent Schr?dinger equations in quantum mechanics.It is based on the homotopy analysis method(HAM)that was developed by the author in 1992 for highly nonlinear equations and has been widely applied in many fields.Unlike perturbative methods,this HAM-based approach has nothing to do with small/large physical parameters.Besides,convergent series solution can be obtained even if the disturbance is far from the known status.A nonlinear harmonic oscillator is used as an example to illustrate the validity of this approach for disturbances that might be one thousand times larger than the possible superior limit of the perturbative approach.This HAM-based approach could provide us rigorous theoretical results in quantum mechanics,which can be directly compared with experimental data.Obviously,this is of great benefit not only for improving the accuracy of experimental measurements but also for validating physical theories. 相似文献
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对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大. 相似文献