This paper presents an attempt to finally solve the problem of constructing the squares of the same surface of the given circle, in a simple way: by determining the exact value of the number π. The value of this constant thus far implies the following: in the Universe there is no square of the same surface as the given circle!? It's pointless. The number π is not irrational, so it is not transcendental number either.
In this paper, two sampling plans have been discussed, when the lifetime of the items follows the generalized Pareto distribution, Chain Sampling Plan (ChSP-1) and an improved group acceptance sampling plan (IGASP) using weighted binomial.The minimum number of sample size (n) and minimum number of groups (g) are obtained for two plans respectively. The plans are explain with the help of examples whereas the proposed plan compared with Aslam et al. (2010). The results and comparison are discussed with the help of tables and figure. It observed that sometime proposed plan Improved group acceptance sampling plan (IGASP) using weighted binomial, when the lifetime of the test items followsgeneralized Pareto distribution showed better results than existing plan, under the same parameter settings.
Urban air pollution is one of the most urgent problems to be solved in the process of China's economic development and urbanization.Aiming at the spatial-temporal evolution problem of air quality in Henan province, this paper, based on the daily average data of urban air quality index of Henan province from 2014 to 2017, utilizes geostatistical analysis and spatial analysis methods to study the spatial and temporal distribution characteristics, as well as its evolution mechanism.The results show that: The urban air quality of Henan province is mainly Grade II and Grade III, there are obvious variations among cities, the air qualities of southern cities are significantly better than that of northern cities; From 2014 to 2017, the urban air quality has been gradually improved, the serious pollution process has been gradually reduced, the process duration has been gradually shortened, the air quality improvement in the southern cities is significantly better than that in the central and northern cities, but Luoyang in the western part of the province has gradually increased; the urban air quality shows seasonal distribution characteristics, autumn is the best season, from winter to autumn, air quality gradually improves.The urban air quality also presents the monthly distribution characteristics of low in the middle and high at two ends with a local extreme point in June, and August is the best month for air quality.The urban air quality index shows agglomeration characteristics, and the high value regions gradually shrink to the north, forming two heavily polluted regions centered on Zhengzhou and Anyang respectively.
We find existence and uniqueness results about solutions of Robin's problem for the general anisotropic hyperbolic heat equation in the case of infinitely differentiable coefficients but irregular distributions data for the internal heatsources and boundary and initial conditions.
In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-Infective-Removed), household epidemic model, with false negative and false positive misclassification probabilities. Maximum likelihood based algorithm is then employed for its inference. We then analyzed and compared the estimates of the two dimensional model with those of the three and four dimensional models associated with misclassified final size data over arrange of theoretical parameters, local and global infection rates and corresponding proportion infected in the permissible region, away from its boundaries and misclassification probabilities. The adequacies of the three models to the final size data are examined. The four and three-dimensional models are found to outperform the two dimensional model on misclassified final size data.
