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Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including identification of parameter regimes under which the density is bounded, asymptotic approximations of tail probabilities, and fractional moments; in particular, we see that the mean is undefined. In the case that $X$ and $Y$ are independent symmetric variance-gamma random variables, an exact formula is also given for the cumulative distribution function of the ratio $X/Y$.

This paper presents an efficient hybrid asynchronous three-dimensional (3D) perfectly matched layer (PML) for modeling unbounded domains. The proposed unsplit explicit or implicit 3D PML formulation is implemented in the framework of a heterogeneous asynchronous time integrator. It is fully versatile in terms of time integrators and time step sizes according to partitions while conserving classical finite element formulations in the elastic domain without complex-valued stretched coordinates. Examples of a semi-infinite bar, Lamb’s test, and a soil–structure interaction problem with PML-truncated semi-infinite heterogeneous media are investigated to illustrate the efficiency of the proposed PML in terms of accuracy and CPU time.

In order to further improve the operation level of the provincial grid direct thermal power units, optimize the data quality of the provincial thermal power unit system, diagnose and analyze the operation data of the thermal power unit system, and comprehensively analyze and evaluate the unit regulation ability from the aspects of heating capacity, the minimum startup mode of the whole plant, and the load capacity of the heating state, so as to provide support for the accurate scheduling of the unit.

In order to further improve the operation level of the thermal power units of the provincial grid thermal power plant, optimize the data quality of the online monitoring system of the provincial thermal power units, through the diagnosis and analysis of the operation data of the thermal power online monitoring system, and from an all-round perspective, analyze and evaluate the peak shaving and frequency modulation capabilities of the heat supply units of the thermal power plant from the aspects of the load carrying capacity of the heat supply units, the optimization of the startup mode of the whole plant, and the heating capacity, to provide support for the accurate scheduling of the heat supply units. This paper analyzes the heat supply, peak regulation and frequency regulation capacity of the whole thermal power plant through the operation data, draws the peak regulation interval and heat supply capacity interval, and provides support for the optimal operation of the whole plant.

The smart grid is the latest trend and complex scientific issue in the development of power systems in the world today. With the new round of power system reform and the deregulation of the power market, comprehensive and scientific evaluation of the development level of the smart grid plays an important role in achieving the overall goal of smart grid construction. This paper constructed a comprehensive evaluation index system from the aspects of safety and reliability, economy, intelligence level and sustainability of smart distribution network. Then the comprehensive evaluation model of AHPTOPSIS intelligent distribution network was established. Finally, an empirical study on the development level of smart distribution networks of four power companies in a province was carried out, and corresponding conclusions were drawn.