The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stoc...The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes Wp?（Id） and H∞k（Id） is intractable in worst case setting, but is tractable with respect to stochastic and average case setting.展开更多
Background and Purpose: To investigate target functional independence measure (FIM) items to achieve the prediction goal in terms of the causal relationships between prognostic prediction error and FIM among stroke pa...Background and Purpose: To investigate target functional independence measure (FIM) items to achieve the prediction goal in terms of the causal relationships between prognostic prediction error and FIM among stroke patients in the convalescent phase using the structural equation modeling (SEM) analysis. Methods: A total of 2992 stroke patients registered in the Japanese Rehabilitation Database were analyzed retrospectively. The prediction error was calculated based on a prognostic prediction formula proposed in a previous study. An exploratory factor analysis (EFA) then the factor was determined using confirmatory factorial analysis (CFA). Finally, multivariate analyses were performed using SEM analysis. Results: The fitted indices of the hypothesized model estimated based on EFA were confirmed by CFA. The factors estimated by EFA were applied, and interpreted as follows: “Transferring (T-factor),” “Dressing (D-factor),” and “Cognitive function (C-factor).” The fit of the structural model based on the three factors and prediction errors was supported by the SEM analysis. The effects of the D- and C-factors yielded similar causal relationships on prediction error. Meanwhile, the effects between the prediction error and the T-factor were low. Observed FIM items were related to their domains in the structural model, except for the dressing of the upper body and memory (p < 0.01). Conclusions: Transfer, which was not heavily considered in the previous prediction formula, was found in causal relationships with prediction error. It is suggested to intervene to transfer together with positive factors to recovery for achieving the prediction goal.展开更多
We derived an equation for saturation in carbonate reservoirs based on the electrical efficiency model in the case of lacking core data. Owing to the complex pore structure and strong heterogeneity in carbonate reserv...We derived an equation for saturation in carbonate reservoirs based on the electrical efficiency model in the case of lacking core data. Owing to the complex pore structure and strong heterogeneity in carbonate reservoirs, the relation between electrical efficiency and water porosity is either complex or linear. We proposed an electrical efficiency equation that accounts for the relation between electrical efficiency and water porosity. We also proposed a power-law relation between electrical efficiency and deep-formation resistivity and analyzed the factors controlling the error in the water saturation computations. We concluded that the calculation accuracy of the electrical efficiency is critical to the application of the saturation equation. The saturation equation was applied to the carbonate reservoirs of three wells in Iraq and Indonesia. For relative rock electrical efficiency error below 0.1, the water saturation absolute error is also below 0.1. Therefore, we infer that the proposed saturation equation generally satisfies the evaluation criteria for carbonate reservoirs.展开更多
In 1956, Tong established an asymptotic formula for the mean square of the error term of the summatory function of the Piltz divisor function d3（n）. The aim of this paper is to generalize Tong＇s method to a class o...In 1956, Tong established an asymptotic formula for the mean square of the error term of the summatory function of the Piltz divisor function d3（n）. The aim of this paper is to generalize Tong＇s method to a class of Dirichlet series L（s） which satisfies a functional equation. Let a（n） be an arithmetical function related f t to a Dirichlet series L（s）, and let E（x） be the error term of ∑＇n≤x a（n）. In this paper, after introducing a class of Diriclet series with a general functional equation （which contains the well-known Selberg class）, we establish a Tong-type identity and a Tong-type truncated formula for the error term of the Riesz mean of the coefficients of this Dirichlet series L（s）. This kind of Tong-type truncated formula could be used to study the mean square of E（x） under a certain assumption. In other words, we reduce the mean square of E（x） to the problem of finding a suitable constant σ＊ which is related to the mean square estimate of L（s）. We shall represent some results of functions in the Selberg class of degrees 2 -4.展开更多
Numerical atomic orbitals have been successfully used in molecular simulations as a basis set,which provides a nature,physical description of the electronic states and is suitable for ■(N)calculations based on the st...Numerical atomic orbitals have been successfully used in molecular simulations as a basis set,which provides a nature,physical description of the electronic states and is suitable for ■(N)calculations based on the strictly localized property.This paper presents a numerical analysis for some simplified atomic orbitals,with polynomial-type and confined Hydrogen-like radial basis functions respectively.We give some a priori error estimates to understand why numerical atomic orbitals are computationally efficient in electronic structure calculations.展开更多
基金Project supported by the Natural Science Foundation of China(10371009) and Research Fund for the Doctoral Program Higher Education.
文摘The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes Wp?（Id） and H∞k（Id） is intractable in worst case setting, but is tractable with respect to stochastic and average case setting.
文摘Background and Purpose: To investigate target functional independence measure (FIM) items to achieve the prediction goal in terms of the causal relationships between prognostic prediction error and FIM among stroke patients in the convalescent phase using the structural equation modeling (SEM) analysis. Methods: A total of 2992 stroke patients registered in the Japanese Rehabilitation Database were analyzed retrospectively. The prediction error was calculated based on a prognostic prediction formula proposed in a previous study. An exploratory factor analysis (EFA) then the factor was determined using confirmatory factorial analysis (CFA). Finally, multivariate analyses were performed using SEM analysis. Results: The fitted indices of the hypothesized model estimated based on EFA were confirmed by CFA. The factors estimated by EFA were applied, and interpreted as follows: “Transferring (T-factor),” “Dressing (D-factor),” and “Cognitive function (C-factor).” The fit of the structural model based on the three factors and prediction errors was supported by the SEM analysis. The effects of the D- and C-factors yielded similar causal relationships on prediction error. Meanwhile, the effects between the prediction error and the T-factor were low. Observed FIM items were related to their domains in the structural model, except for the dressing of the upper body and memory (p < 0.01). Conclusions: Transfer, which was not heavily considered in the previous prediction formula, was found in causal relationships with prediction error. It is suggested to intervene to transfer together with positive factors to recovery for achieving the prediction goal.
基金supported by the National Science and Technology Major Project(2011ZX05030)
文摘We derived an equation for saturation in carbonate reservoirs based on the electrical efficiency model in the case of lacking core data. Owing to the complex pore structure and strong heterogeneity in carbonate reservoirs, the relation between electrical efficiency and water porosity is either complex or linear. We proposed an electrical efficiency equation that accounts for the relation between electrical efficiency and water porosity. We also proposed a power-law relation between electrical efficiency and deep-formation resistivity and analyzed the factors controlling the error in the water saturation computations. We concluded that the calculation accuracy of the electrical efficiency is critical to the application of the saturation equation. The saturation equation was applied to the carbonate reservoirs of three wells in Iraq and Indonesia. For relative rock electrical efficiency error below 0.1, the water saturation absolute error is also below 0.1. Therefore, we infer that the proposed saturation equation generally satisfies the evaluation criteria for carbonate reservoirs.
基金supported by National Key Basic Research Program of China (Grant No. 2013CB834201)National Natural Science Foundation of China (Grant No. 11171344)+1 种基金Natural Science Foundation of Beijing (Grant No. 1112010)the Fundamental Research Funds for the Central Universities in China (Grant No. 2012YS01)
文摘In 1956, Tong established an asymptotic formula for the mean square of the error term of the summatory function of the Piltz divisor function d3（n）. The aim of this paper is to generalize Tong＇s method to a class of Dirichlet series L（s） which satisfies a functional equation. Let a（n） be an arithmetical function related f t to a Dirichlet series L（s）, and let E（x） be the error term of ∑＇n≤x a（n）. In this paper, after introducing a class of Diriclet series with a general functional equation （which contains the well-known Selberg class）, we establish a Tong-type identity and a Tong-type truncated formula for the error term of the Riesz mean of the coefficients of this Dirichlet series L（s）. This kind of Tong-type truncated formula could be used to study the mean square of E（x） under a certain assumption. In other words, we reduce the mean square of E（x） to the problem of finding a suitable constant σ＊ which is related to the mean square estimate of L（s）. We shall represent some results of functions in the Selberg class of degrees 2 -4.
基金The research for this paper has been enabled by the Alexander von Humboldt Foundation,whose support for the long term visit of Huajie Chen at Technische Universit¨at Berlin is gratefully acknowledged.
文摘Numerical atomic orbitals have been successfully used in molecular simulations as a basis set,which provides a nature,physical description of the electronic states and is suitable for ■(N)calculations based on the strictly localized property.This paper presents a numerical analysis for some simplified atomic orbitals,with polynomial-type and confined Hydrogen-like radial basis functions respectively.We give some a priori error estimates to understand why numerical atomic orbitals are computationally efficient in electronic structure calculations.
