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Mohammed Harunor Rashid 《计算数学(英文版)》2022,40(1):44-69
In the present paper,we study the restricted inexact Newton-type method for solving the generalized equation 0∈f(x)+F(x),where X and Y are Banach spaces,f:X→Y is a Frechet differentiable function and F:X■Y is a set-valued mapping with closed graph.We establish the convergence criteria of the restricted inexact Newton-type method,which guarantees the existence of any sequence generated by this method and show this generated sequence is convergent linearly and quadratically according to the particular assumptions on the Frechet derivative of f.Indeed,we obtain semilocal and local convergence results of restricted inexact Newton-type method for solving the above generalized equation when the Frechet derivative of f is continuous and Lipschitz continuous as well as f+F is metrically regular.An application of this method to variational inequality is given.In addition,a numerical experiment is given which illustrates the theoretical result. 相似文献
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Dehydrogenation of an organic compound is the first and the most fundamental elementary reaction in many organic reactions. In ethanol oxidation reaction (EOR) to form CO2, there are a total of 46 pathways in C2HxO (x=1–6) species leading to the removal of all six hydrogen atoms in five C−H bonds and one O−H bond. To investigate the degree of dehydrogenation in EOR under operando conditions, we performed density function theory (DFT) calculations to study 28 dehydrogenation steps of C2HxO on Ir(100). An activation energy surface was then constructed and compared with that of the C−C bond cleavages to understand the importance of the degree of dehydrogenation in EOR. The results show that there are likely 28 dehydrogenations in EOR under fuel cell temperatures and the last two hydrogens in C2H2O are less likely cleaved. On the other hand, deep dehydrogenation including 45 dehydrogenations can occur under ethanol steam reforming conditions. 相似文献
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The observation and study of nonlinear dynamical systems has been gaining popularity over years in different fields. The intrinsic complexity of their dynamics defies many existing tools based on individual orbits, while the Koopman operator governs evolution of functions defined in phase space and is thus focused on ensembles of orbits, which provides an alternative approach to investigate global features of system dynamics prescribed by spectral properties of the operator. However, it is difficult to identify and represent the most relevant eigenfunctions in practice. Here, combined with the Koopman analysis, a neural network is designed to achieve the reconstruction and evolution of complex dynamical systems. By invoking the error minimization, a fundamental set of Koopman eigenfunctions are derived, which may reproduce the input dynamics through a nonlinear transformation provided by the neural network. The corresponding eigenvalues are also directly extracted by the specific evolutionary structure built in. 相似文献
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Triple Positive Solutions of Boundary Value Problems for High-order Fractional Differential Equation at Resonance with Singularities 下载免费PDF全文
In this paper, we investigate the existence of triple positive solutions of boundary value problems for high-order fractional differential equation at resonance with singularities by using the fixed point index theory and the Leggett-Williams theorem. The spectral theory and some new height functions are also employed to establish the existence of triple positive solutions. The nonlinearity involved is arbitrary fractional derivative, and permits singularity. 相似文献
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Having shown promising performance with high flexibility and efficiency in vehicular edge computing (VEC) network, the parked vehicles (PVs) received an increasing number of attentions in recent years. However, PVs’ residual battery power restricts their running time. In addition, there is still no alternate resource pool for the PVs to cope with the emergencies in the previous VEC framework. To alleviate these problems, we model a cloud-assisted parked vehicular edge computing (PVEC) framework, in which the PVs are classified based on their residual battery power. PVs corporate with the cloud servers (CSs) for the computational resources provision. In addition, we formulate the utilities of the service provider (SP) and PVs and design a contract-based resource allocation problem for the maximization of the SP’s utility. Considering that it is intractable to solve the optimization problem directly, the primal problem is simplified and decoupled into two sub-problems. To design the optimal contracts, we solve the sub-problems by Lagrangian multiplier method and dual function. Simulation results prove that the utilities of PVs can reach to the maximum when they choose the contract corresponding to their types. In addition, the simulation results illustrate the superiority of proposed scheme over previous schemes in improving the utilities of the SP and social welfare. 相似文献
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利用微环谐振腔阵列进行光码分多址编解码过程中,微环谐振腔反射谱的自由频谱宽度(FSR)范围制约该系统用户容量的提升.本文提出了一种新型的基于游标效应的串联哑铃型微环谐振腔光编解码器.利用Matlab建立了半径分别为40μm-30μm-40μm的哑铃型微环谐振腔光编解码器模型.详细分析了光反射谱伪模抑制与耦合系数的关系,研究了耦合系数、码片速率对串联哑铃型微环谐振腔光编解码器性能的影响.结果表明,与半径分别为40μm-40μm-40μm的传统串联微环谐振腔编解码器相比,哑铃型微腔编解码器FSR值扩大了4倍.理想情况下,用户容量可呈指数增长.同时,互相关峰值比(P/W)与自相关峰值旁瓣比(P/C)分别提高了约33%和8%. 相似文献
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The ultrasound-assisted extraction (UAE) was conducted using the stainless steel (SS) and polyether ether ketone (PEEK) columns and analyzed with high-performance liquid chromatography (HPLC) to understand the mechanism of ultrasound-assisted chromatography (UAC). Empty SS and PEEK columns were used to extract dyes from a fabric under identical conditions with several parameters including the initial ultrasonic bath temperatures (30 °C and 40 °C), ultrasound power intensities (0, 20, 40, 60, 80, and 100 %), ultrasound operation modes (normal and sweep), and ultrasound frequencies (25 kHz, 40 kHz, and 132 kHz) to compare their extraction capabilities. After 30 min of extraction, the amount of extract was determined by HPLC. The PEEK material was significantly affected by ultrasonic radiation compared to the SS material, especially at a higher temperature (40 °C), power intensity (100 %), and frequency (132 kHz) with sweep mode. At a maximum power density of 45 W/L, the extraction effectiveness ratio of PEEK to SS was in the range of 1.8 - 3.9 depending on the specific frequency, initial temperature, and with or without temperature control. The most optimal ultrasound frequencies, in terms of enhancing extraction effectiveness, are in the order of 132 kHz, 40 kHz, and 25 kHz. Unlike the SS material, the PEEK material was more affected by temperature and acoustic effects under identical conditions, especially at 132 kHz ultrasound frequency. In contrast, at lower frequencies of 40 kHz and 25 kHz, no significant differences in the acoustic effects were observed between the PEEK and SS materials. The findings of this study contribute to elucidating the roles of column materials in UAE and UAC. 相似文献