In this paper, we present a sufficient condition for uniform convergence of means to their expectations over the classes of real functions. Our proof is very simple via connecting this convergence to uniform convergen...In this paper, we present a sufficient condition for uniform convergence of means to their expectations over the classes of real functions. Our proof is very simple via connecting this convergence to uniform convergence over the class of indicator functions. Furthermore, we obtain a convergent result concerning a non=VC class with an application to variable transformation for fitting regression model.展开更多
A novel three-dimensional beam propagation method (BPM) based on the variable transformed Galerkin's method is introduced for simulating optical field propagation in three-dimensional dielectric structures. The in...A novel three-dimensional beam propagation method (BPM) based on the variable transformed Galerkin's method is introduced for simulating optical field propagation in three-dimensional dielectric structures. The infinite Cartesian x-y plane is mapped into a unit square by a tangent-type function transformation. Consequently, the infinite region problem is converted into the finite region problem. Thus, the boundary truncation is eliminated and the calculation accuracy is promoted. The three-dimensional BPM basic equation is reduced to a set of first-order ordinary differential equations through sinusoidal basis function, which fits arbitrary cladding optical waveguide, then direct solution of the resulting equations by means of the Runge-Kutta method. In addition, the calculation is efficient due to the small matrix derived from the present technique. Both z-invariant and z-variant examples are considered to test both the accuracy and utility of this approach.展开更多
In the analyses of the uncertainty propagation of buildings’energy-demand,the Monte Carlo method is commonly used.In this study we present two alternative approaches:the stochastic perturbation method and the transfo...In the analyses of the uncertainty propagation of buildings’energy-demand,the Monte Carlo method is commonly used.In this study we present two alternative approaches:the stochastic perturbation method and the transformed random variable method.The energy-demand analysis is performed for the representative single-family house in Poland.The investigation is focused on two independent variables,considered as uncertain,the expanded polystyrene thermal conductivity and external temperature;however the generalization on any countable number of parameters is possible.Afterwards,the propagation of the uncertainty in the calculations of the energy consumption has been investigated using two aforementioned approaches.The stochastic perturbation method is used to determine the expected value and central moments of the energy consumption,while the transformed random variable method allows to obtain the explicit form of energy consumption probability density function and further characteristic parameters like quantiles of energy consumption.The calculated data evinces a high accordance with the results obtained by means of the Monte Carlo method.The most important conclusions are related to the computational cost reduction,simplicity of the application and the appropriateness of the proposed approaches for the buildings’energy-demand calculations.展开更多
文摘In this paper, we present a sufficient condition for uniform convergence of means to their expectations over the classes of real functions. Our proof is very simple via connecting this convergence to uniform convergence over the class of indicator functions. Furthermore, we obtain a convergent result concerning a non=VC class with an application to variable transformation for fitting regression model.
文摘A novel three-dimensional beam propagation method (BPM) based on the variable transformed Galerkin's method is introduced for simulating optical field propagation in three-dimensional dielectric structures. The infinite Cartesian x-y plane is mapped into a unit square by a tangent-type function transformation. Consequently, the infinite region problem is converted into the finite region problem. Thus, the boundary truncation is eliminated and the calculation accuracy is promoted. The three-dimensional BPM basic equation is reduced to a set of first-order ordinary differential equations through sinusoidal basis function, which fits arbitrary cladding optical waveguide, then direct solution of the resulting equations by means of the Runge-Kutta method. In addition, the calculation is efficient due to the small matrix derived from the present technique. Both z-invariant and z-variant examples are considered to test both the accuracy and utility of this approach.
文摘In the analyses of the uncertainty propagation of buildings’energy-demand,the Monte Carlo method is commonly used.In this study we present two alternative approaches:the stochastic perturbation method and the transformed random variable method.The energy-demand analysis is performed for the representative single-family house in Poland.The investigation is focused on two independent variables,considered as uncertain,the expanded polystyrene thermal conductivity and external temperature;however the generalization on any countable number of parameters is possible.Afterwards,the propagation of the uncertainty in the calculations of the energy consumption has been investigated using two aforementioned approaches.The stochastic perturbation method is used to determine the expected value and central moments of the energy consumption,while the transformed random variable method allows to obtain the explicit form of energy consumption probability density function and further characteristic parameters like quantiles of energy consumption.The calculated data evinces a high accordance with the results obtained by means of the Monte Carlo method.The most important conclusions are related to the computational cost reduction,simplicity of the application and the appropriateness of the proposed approaches for the buildings’energy-demand calculations.
