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51.
Bilender P. Allahverdiev 《Mathematical Methods in the Applied Sciences》2019,42(1):229-236
In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators. 相似文献
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We consider systems that are subject to an external mixed Poisson shock process. Each shock can result in a failure of a system with a given probability and is survived with the complementary probability. Each shock additionally decreases the quality function that describes the performance of a system, thus forming the corresponding stochastic process. Expectations (unconditional and conditional on survival) and relevant variability characteristics for the stochastic quality function are derived. Some monotonicity properties of the conditional quality function are investigated and the future values of this function are derived. 相似文献
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《Physics letters. A》2019,383(19):2272-2276
Magnetic field design is important in cylindrical Hall thrusters and using permanent magnets to generate magnetic field is very promising in the future. In two typical permanent magnet configurations (i.e., ring and cylindrical configurations) of cylindrical Hall thrusters, discharge characteristics are compared in this paper through the experiments and simulations. The study shows that the cylindrical configuration can bring about higher thruster performance in the same working condition. The reason is that the potential drop of the cylindrical configuration is mainly concentrated in the channel, which is beneficial for the electrons to obtain energy to promote the ionization of the propellant. However, the voltage regulation range of the cylindrical configuration is lower because the anode is more easily overheated. 相似文献
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J. Chevallier A. Duarte E. Löcherbach G. Ost 《Stochastic Processes and their Applications》2019,129(1):1-27
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
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《Stochastic Processes and their Applications》2020,130(12):7547-7574
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