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In the manufacturing and production of hypoid gears, it is a necessary key problem to improve the tooth surface heat treatment precision and production efficiency of the hypoid gears. How to use advanced statistical theory and methods to evaluate the whole batch machining quality of the tooth surface after heat treatment is particularly urgent. In this connection, for the same batch of hypoid gears with the same gear material, numerical control gear milling method, and heat treatment specifications, a bootstrap-based statistics scheme of tooth surface errors after heat treatment is proposed in this paper. The bootstrap statistics model of the tooth surface errors for the batch hypoid gears is established. The bootstrap probability eigenvalues and confidence intervals of the measurement sequence points on the tooth surface errors are solved, and the optimizing selection of the single sampling numbers and the repeated sampling times is completed. On this basis, by applying the cubic NURBS surface fitting method, the mean value difference surface of the batch tooth surface errors data is constructed, the statistics laws of the whole batch tooth surface errors after heat treatment is determined, and the effective evaluation of the whole batch tooth surface accuracy is realized. Finally, the feasibility and correctness of the bootstrap-based statistics scheme are verified by the tooth surface errors bootstrap statistics application experiment of one kind of hypoid gear. The results show that with the help of the bootstrap statistics method proposed in this paper, it is not necessary to accurately measure the tooth surface errors of the whole batch of hypoid gears one by one. Only by randomly selecting 10 tooth surface samples and repeatedly sampling 2000 times, the original sample characteristic values of the whole batch tooth surface errors can be accurately estimated, and the heat treatment deformation statistics laws of the whole patch tooth surfaces can be also counted.

Airborne missile servo system (AMSS) is a complex time-varying nonlinear system and the design of which is a multi-objective optimization problem. Fuzzy PID controller (FPC) is demonstrated appropriate for complex time-varying nonlinear systems but the design of which needs a tedious trial and error process. Non-dominated Sorting Genetic Algorithm III (NSGA-III) is a multi-objective evolutionary algorithm with good generality and robustness which can do a big favor for parameter tuning of complex system. This paper develops NSGA-III for parameter tuning in design process of FPC. Resulting FPCs are tested with model of AMSS on simulink. For further comparison, performance of conventional PID controller and sectional PID controller which is widely used in the engineering are also shown. Comparison shows that NSGA-III tuned FPCs have the better performance in AMSS.

Gradient vector flow (GVF) is an effective external force for active contours, but its isotropic nature handicaps its performance. The recently proposed NGVF model is an isotropic since it only keeps the diffusion along the normal direction of the isophotes, however, it is sensitive to noise and could erase weak boundaries. In this paper, we propose a novel external force called adaptively normal biased gradient vector flow (ANBGVF) for active contours, which adaptively generates the diffusion along the tangential direction of the isophotes and biases that along the normal direction. Consequently, the ANBGVF snake can preserve weak edges and smooth out noise while maintaining other desirable properties of GVF and NBGVF, such as enlarged capture range, initialization insensitivity and good convergence at concavities. We demonstrate the advantages on synthetic and real images.

This paper uses the principle of Gini Coefficient which measures the equity of income distribution, based on the sample of the financial expenditure of typical public goods and the data of population size which belong to each province and municipality in 2007 to construct the mathematical model. It investigates the regional distribution structure of national public goods’ financial expenditure and calculates the corresponding “Gini coefficient” values through the quantitative research method, regression analysis. The calculated results show that it is reasonable on the distribution of the population that China’s finance invests in major public products and services vital to the people’s livelihood, and the investment does not exceed the bottom line of inequity. At last, the paper analyzes the reasons for the conclusions.

According to the strain nonlinear softening constitutive model of practical rock, pressure tunnel with liner is analyzed. The model is considered the influence of intermediate principal stress s2. Stress distribution laws of surrounding rock plastic zone of tunnel, the mechanism of load bearing and acting relation between surrounding rock and support are studied. Some important conceptions of working status of practical tunnel surrounding rock are obtained: such superior certain limit [Smax] of self-support geo-stress and inferior certain limit [Smin] of supportless tunnel surrounding rock. The relations between [Smax] and geo-stress, between [Smin] and geo-stress are given. Calculation shows that the assumed model agrees well with practical condition of rocks. Analysis shows that the ideal plastic model and the brittle model are special cases of the proposed solution.