Predictive control of uncertain nonlinear parabolic PDE systems using a Galerkin/neural-network-based model

In this paper, a model predictive control (MPC) scheme for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities, arising in the context of transport-reaction processes, is proposed. A spatial operator of a parabolic PDE system is characterized by a spectrum that can be partitioned into a finite slow and an infinite fast complement. In this view, first, Galerkin method is used to derive a set of finite dimensional slow ordinary differential equation (ODE) system that captures the dominant dynamics of the initial PDE system. Then, a Multilayer Neural Network (MNN) is employed to parameterize the unknown nonlinearities in the resulting finite dimensional ODE model. Finally, a Galerkin/neural-network-based ODE model is used to predict future states in the MPC algorithm. The proposed controller is applied to stabilize an unstable steady-state of the temperature profile of a catalytic rod subject to input and state constraints.     

Model selection based on Lorenz and concentration curves,Gini indices and convex order

In order to determine an appropriate amount of premium, statistical goodness-of-fit criteria must be supplemented with actuarial ones when assessing performance of a given candidate pure premium. In this paper, concentration curves and Lorenz curves are shown to provide actuaries with effective tools to evaluate whether a premium is appropriate or to compare two competing alternatives. The idea is to compare the premium income for sub-portfolios gathering low risks (identified as low by means of the premiums under consideration) to the true one, or equivalently, to the actual losses. Numerical illustrations performed on hypothetical data and real ones demonstrate the usefulness of the proposed approach.     

半导体纳米复合材料的制备及其光电催化CO2还原

本实验通过模拟植物光合作用,设计制备了新颖的光电联合催化池3D-ZnO/Ni BiVO4/FTO,用电化学沉积法制备了泡沫镍负载的ZnO纳米棒光电阴极和BiVO4光电阳极,以0.1 mol·L^−1 KHCO3水溶液作为电解质,1 mmol·L^−1曙红Y为光敏剂,在−0.6 V硅太阳电池的电压下光电催化还原CO2得到了乙醇、乙酸和甲醇,总产率22.5μmol·L^−1·h^−1·cm^−2。实现了将太阳能贮存为化学能并减少了空气中的CO2,加深了学生对绿色化学和植物Calvin循环机理的理解。     

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.     

The lifetime of CFC substitutes studied by a network trained with chaotic mapping modified genetic algorithm and DFT calculations

The hydrohaloalkanes have attracted much attention as potential substitutes of chlorofluorocarbons (CFCs) that deplete the ozone layer and lead to great high global warming. Having a short atmospheric lifetime is very important for the potential substitutes that may also induce ozone depletion and yield high global warming gases to be put in use. Quantitative structure–activity relationship (QSAR) studies were presented for their lifetimes aided by the quantum chemistry parameters including net charges, Mulliken overlaps, E _HOMO and E _LUMO based on the density functional theory (DFT) at B3PW91 level, and the C-H bond dissociation energy based on AM1 calculations. Outstanding features of the logistic mapping, a simple chaotic system, especially the inherent ability to search the space of interest exhaustively have been utilized. The chaotic mapping aided genetic algorithm artificial neural network training scheme (CGANN) showed better performance than the conventional genetic algorithm ANN training when the structure of the data set was not favorable. The lifetimes of HFCs and HCs appeared to be greatly dependent on their energies of the highest occupied molecular orbitals. The perference of the RMSRE comparing to RMSE as objective function of ANN training was better for the samples of interest with relatively short lifetimes. C₂H₆ and C₃H₈ as potential green substitutes of CFCs present relatively short lifetimes.     

Optimization of neural network for ionic conductivity of nanocomposite solid polymer electrolyte system (PEO-LiPF6-EC-CNT)

In this study, the ionic conductivity of a nanocomposite polymer electrolyte system (PEO-LiPF₆-EC-CNT), which has been produced using solution cast technique, is obtained using artificial neural networks approach. Several results have been recorded from experiments in preparation for the training and testing of the network. In the experiments, polyethylene oxide (PEO), lithium hexafluorophosphate (LiPF₆), ethylene carbonate (EC) and carbon nanotubes (CNT) are mixed at various ratios to obtain the highest ionic conductivity. The effects of chemical composition and temperature on the ionic conductivity of the polymer electrolyte system are investigated. Electrical tests reveal that the ionic conductivity of the polymer electrolyte system varies with different chemical compositions and temperatures. In neural networks training, different chemical compositions and temperatures are used as inputs and the ionic conductivities of the resultant polymer electrolytes are used as outputs. The experimental data is used to check the system’s accuracy following the training process. The neural network is found to be successful for the prediction of ionic conductivity of nanocomposite polymer electrolyte system.     

Coordination Polymers. 9. Chelate Polymers Derived from Bisphenolic Complexes and Propylenediamine

Chelate polymers derived from bis(2,4-dihydroxybenzaldehyde)propyl-enediimine M and bis(2,4-dihydroxyacetophenone)propylenediimine M (M = Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺) with aromatic acid chlorides were prepared by interfacial polycondensation. Also, chelate polysiloxanes were obtained from the same monomers and α,ω-dichloropolydimethyl-siloxane. The spectral, thermal, magnetic, and electrical properties of the polychelates were studied.     

Prediction of extraction efficiency in supported liquid membrane with a stagnant acceptor phase by means of artificial neural network

An artificial neural network model of supported liquid membrane extraction process with a stagnant acceptor phase is proposed. Triazine herbicides and phenolic compounds were used as model compounds. The model is able to predict the compound extraction efficiency within the same family based on the octanol–water partition coefficient, water solubility, molecular mass and ionisation constant of the compound. The network uses the back‐propagation algorithm for evaluating the connection strengths representing the correlations between inputs (octanol–water partition coefficients logP, acid dissociation constant pK_a, water solubility and molecular weight) and outputs (extraction efficiency in dihexyl ether and undecane as organic solvents). The model predicted results in good agreement with the experimental data and the average deviations for all the cases are found to be smaller than ±3%. Moreover, standard statistical methods were applied for exploration of relationships between studied parameters.