基于复杂网络的能源互联网信息物理融合系统跨空间风险传递研究

能源互联网呈现物理信息深度融合的趋势,为电力系统管理研究定义了新的研究框架。作为一个先进的复杂系统,能源互联网信息物理系统(Energy Internet Cyber-Physical System,ECPS)在其发展过程中面临着一些新的挑战,其中一个就是耦合结构下的风险管理。本文结合复杂网络理论和风险传递理论,着重在拓扑层面分析了ECPS跨空间交互机理,并在此基础上定义了交互路径和交互系数;接着建立了ECPS跨空间风险传递模型,量化描述了风险的传递和演化过程,并进行了风险影响评估;最后,通过仿真实验分析了三种不同交互系数节点故障的风险传递过程和不同攻击模式下系统的崩溃过程。对仿真结果的讨论阐述了能源互联网风险跨空间传递的特点,为更深入地研究ECPS的风险管理提供了参考。     

Fractional powers of the noncommutative Fourier's law by the S‐spectrum approach

Let e_?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory.     

1,2-Diketones as photoinitiators of both cationic and free-radical photopolymerization under UV (392 nm) or Blue (455 nm) LEDs

The photoinitiation abilities of three 1,2-diketones [i.e., acenaphthenequinone ( ANPQ ), aceanthrenequinone ( AATQ ), and 9,10-phenanthrenequinone ( PANQ )]-based photoinitiating systems [PISs, with additives such as iodonium salt, N-vinylcarbazole (NVK), tertiary amine, and phenacyl bromide (R-Br)] for cationic photopolymerization and free-radical photopolymerization under the irradiation of ultraviolet (UV; 392 nm) or blue (455 nm) light-emitting diode (LED) bulb are investigated. All 1,2-diketones studied exhibit ground state absorption that match with the emission spectra of UV (392 nm) or blue LED (455 nm) better than that of the well-known blue-light-sensitive photoinitiator camphorquinone (CQ). In particular, AATQ /iodonium salt/NVK can show high photoinitiating ability (with epoxide conversion yield >70%) under the UV light irradiation due to the effect of NVK. In addition, 1,2-diketone/iodonium salt (and optional NVK) systems are capable of initiating free-radical photopolymerization of methacrylates, with conversions of 50–58%. Furthermore, some 1,2-diketone/tertiary amine (and optional R-Br) combinations are found to demonstrate high efficiency to initiate free-radical photopolymerization, and 71% of methacrylate conversion can be achieved with PANQ /tertiary amine/R-Br PIS. Some 1,2-ketone-based PISs can even exhibit higher efficiency than the CQ-based systems. The photochemical mechanism of the radical generation from the 1,2-diketone-based PISs is investigated and found to be consistent with the related photopolymerization efficiency. © 2020 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 792–802     

Synthesis of heterobiaryls via Suzuki‐Miyaura coupling reaction of potassium aryltrifluoroborates with heteroaryl halides in aqueous systems

A variety of heterobiaryl compounds have been synthesized by the Suzuki‐Miyaura coupling reactions of heteroaryl halides with potassium aryltrifluoroborates. Pd (OAc)₂ was found to be highly efficient for the Suzuki‐Miyaura coupling reactions of various heteroaryl halides with potassium aryltrifluoroborates in aqueous systems, delivering the corresponding heterobiaryl compounds in good to excellent yields.     

‐Theory for Schrödinger systems

In this article, we study for the ‐realization of the vector‐valued Schrödinger operator . Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Prüss, we prove that the ‐realization of , defined on the intersection of the natural domains of the differential and multiplication operators which form , generates a strongly continuous contraction semigroup on . We also study additional properties of the semigroup such as extension to L¹, positivity, ultracontractivity and prove that the generator has compact resolvent.     

Multiple positive solutions for Schrödinger‐Poisson system involving singularity and critical exponent

In this paper, the existence and multiplicity of positive solutions is established for Schrödinger‐Poisson system of the form where 0 ∈ Ω is a smooth bounded domain in , , and λ > 0 is a real parameter. Combining with the variational method and Nehari manifold method, two positive solutions of the system are obtained.     

Relaxation oscillations in a slow–fast modified Leslie–Gower model

In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result.