Pyramidal Distribution: An Alternative Distribution for Bivariate Uniformity Test Power Comparison

The purpose of the multi-dimensional uniformity test is to check whether the underlying probability distribution, from which a random sample is drawn, differs from the multi-dimensional uniform distribution. The multi-dimensional uniformity test has applications in various fields such as biology, astronomy and computer science. Various statistical tests have been proposed for the multivariate uniformity. As a special case, the bivariate statistic test is discussed in this paper. To evaluate the performance of the uniformity tests, power comparison is the technique for selecting appropriate statistical test. The Monte Carlo simulations usually used to compare the power of the tests. Berrendero, Cuevas and Vazquez-Grande proposed a distance-to-boundary test, which was one of the latest published statistical tests for multi-dimensional uniformity [J. R. Berrendero, A. Cuevas and F. Vazquez-Grande, Testing multivariate uniformity: The distance-to-boundary method, Canad. J. Stat. 34 (2006) 693–707]. Chen and Hu proposed another test for multivariate uniformity [Z. Chen and T. Hu, Statistical test for bivariate uniformity, Adv. Stat. 2014 (2014) 740831]. Power comparison was conducted to compare these tests. In order to get more convincing power comparison results, more alternative distributions should be used when power study is conducted. This paper proposes a new bivariate distribution, named the pyramidal distribution, with support set [Formula: see text]. This distribution is quite flexible so that it can be used to produce different shapes of bivariate distributions. Because of that, the proposed distribution can be used as an alternative distribution in power comparison for bivariate uniformity test.

Design and experimental study on the freeform fabrication with polymer melt droplet deposition

Purpose 3D printing based on additive manufacturing has advantages in manufacturing products with high geometrical complexity. However, there are many limitations to print plastic products with the existing commercial 3D printers. The polymer materials processing industry needs new devices which can satisfy the trend of processing individual units and small batch sizes of plastic parts. Design/methodology/approach In this study, a freeform fabrication system with the method of polymer melt droplet deposition is proposed. The performance of this system under different conditions was studied by changing the operating parameters. Furthermore, the dimensional uniformity of droplets and their deposition process are analyzed, and a plastic sample was fabricated with this system as an example. Findings The results show a clear correlation between the processing parameters and the droplet diameter. In the experiment for examining the dimensional uniformity of the droplet, the droplets become spindles, and there appears a melt filament between the droplets. The variation of the droplet’s diameters is within 5 per cent. Furthermore, a successfully processed rectangular plastic sample verified the feasibility of this technology for the printing of plastic products. Originality/value A freeform fabrication system with polymer melt droplet deposition is proposed, which can process a wide variety of materials in the form of standard granulates like injection molding or extrusion. Based on the principle of droplet deposition, multi-component or colorful materials can be printed.

Fractional derivatives in electrical circuit theory – critical remarks

A number of critical remarks related to the application of fractional derivatives in electrical circuit theory have been presented in this paper. Few cases have been pointed out that refer to observed in selected publications violations of dimensional uniformity of physical equation rules as well as to a potential impact on the Maxwell equations.

An Advanced Support Method of Aircraft Skin Mirror Milling - Fluid Lubricating Support

A new support method used in aircraft skin mirror milling, liquid lubricating support, is proposed in order to solve the problems of scratching aircraft skin surface caused by rolling support or sliding support. The thickness and stiffness of liquid film between skin and support head are obtained with different feed pressure. The effects of thickness and stiffness of liquid film on surface quality and dimensional uniformity of workpiece are analyzed. The surface roughness is better under the condition of liquid film. With better film stiffness, dimensional uniformity is better, and actual axial cutting depth is closer to nominal axial cutting depth.

Density Weibull Analysis of Pineapple Leaf Fibers (PALF) with Different Diameters

Societal, economical, technical and environmental advantages are today justifying the replacement of synthetic fibers by natural fibers. However, natural fibers obtained from plants do not present the same dimensional uniformity. In fact, they show large dispersion of values, as compared to synthetic fibers. In the case of the lignocellulosic fiber extracted from the pineapple leaf, limited information exists regarding the correlation between its properties and dimensional characteristics. In particular, so far, no investigation has been carried out on the influence of the diameter and the density of pineapple fibers. Therefore, the objective of this work was to measure the density of pineapple fibers and to define, by means of the Weibull statistic method, its dependence on the corresponding fiber diameter.