Due to advantages in solid modeling with complex geometry and its ideal suitability for 3D printing, the implicit representation has been widely used in recent years. The demand for free-form shapes makes the implicit tensor-product B-spline representation attract more and more attention. However, it is an important challenge to deal with the storage and transmission requirements of enormous coefficient tensor. In this paper, we propose a new compression framework for coefficient tensors of implicit 3D tensor-product B-spline solids. The proposed compression algorithm consists of four steps, i.e., preprocessing, block splitting, using a lifting-based 3D discrete wavelet transform, and coding with 3D set partitioning in hierarchical trees algorithm. Finally, we manage to lessen the criticism of the implicit tensor-product B-spline representation of surface for its redundancy store of 3D coefficient tensor. Experimental results show that the proposed compression framework not only achieves satisfactory reconstruction quality and considerable compression ratios, but also supports progressive transmissions and random access by employing patch-wise coding strategy.

In this paper, we present an analysis of the air quality in a traffic-congested area in Ranchi, the proposed smart city as identified by the government of India. The main purpose of this study is to analyze the concentration of pollutants over a long period and to find the best possible way for its prediction. We have selected four air pollutants, particularly RSPM, SPM, SO₂ and NO _X, analyzed their distribution and compared with the National Ambient Air Quality standards over the period 2005–2015. The obtained data have been processed with two different methods and probability model as well as multiple regression models has been established for the prediction purpose. Since pollutants data are in continuous form, we have employed Easyfit software to find out the distribution pattern. Johnson SB, Error, Burr (4P) and Cauchy distributions were found to be the appropriate representatives of the RSPM, SPM, SO₂ and NO _X concentration patterns, respectively. Inverse cumulative density function has been used to predict the future concentration of particulate matters. With the help of SPSS 17 software, the impacts of the meteorological conditions on the variation of major pollutants have been examined by identifying the correlation between each pollutant and meteorological parameters and among the pollutants themselves.

One type of covariance structure is known as blocked compound symmetry. Recently, Roy et al. (J Multivar Anal 144:81–90, 2016) showed that, assuming this covariance structure, unbiased estimators are optimal under normality and described hypothesis testing for independence as an open problem. In this paper, we derive the distributions of unbiased estimators and consider hypothesis testing for independence. Representative test statistics such as the likelihood ratio criterion, Wald statistic, Rao’s score statistic, and gradient statistic are derived, and we evaluate the accuracy of the test using these statistics through numerical simulations. The power of the Wald test is the largest when the dimension is high, and the power of the likelihood ratio test is the largest when the dimension is low.

In this article, we propose a new biased estimator, namely stochastic restricted modified almost unbiased Liu estimator by combining modified almost unbiased Liu estimator (MAULE) and mixed estimator (ME) when the stochastic restrictions are available and the multicollinearity presents. The conditions of superiority of the proposed estimator over the ordinary least square estimator, ME, ridge estimator, Liu estimator, almost unbiased Liu estimator, stochastic restricted Liu estimator and MAULE in the mean squared error matrix sense are obtained. Finally, a numerical example and a Monte Carlo simulation are given to illustrate the theoretical findings.

Assume G is a group of order $2^n, n\ge 5$. Let $s_k(G)$ denote the number of subgroups of order $2^k$ of G. We classify finite 2-groups G with $s_k(G)\le 2^4,$ where $1\le k\le n$.

Which Lévy processes satisfy Hunt’s hypothesis (H) is a long-standing open problem in probabilistic potential theory. The study of this problem for one-dimensional Lévy processes suggests us to consider (H) from the point of view of the sum of Lévy processes. In this paper, we present theorems and examples on the validity of (H) for the sum of two independent Lévy processes. We also give a novel condition on the Lévy measure which implies (H) for a large class of one-dimensional Lévy processes.