A transformation-based multivariate chart to monitor process dispersion

Multivariate monitoring techniques such as multivariate control charts are used to control the processes that contain more than one correlated characteristic. Although the majority of previous researches are focused on controlling only the mean vector of multivariate processes, little work has been performed to monitor the covariance matrix. In this research, a new method is presented to detect possible shifts in the covariance matrix of multivariate processes. The basis of the proposed method is to eliminate the correlation structure between the quality characteristics by transformation technique and then use an S chart for each variable. The performance of the proposed method is then compared to the ones from other existing methods and a real case is presented.

Maturation behavior of Maxi Gala grafetd on two rootstocks by no Destructive Method.

The evaluation of the maturation in apple orchards is checked using destructive methods, sampling fruits and analyzing them in the laboratory, making the process slow and expensive. The use of not destructive method to determine fruit maturation in the orchard could accelerate delivery of results and help in determining harvest time, because non-destructive data would allow to verify the maturation on different blocks in the orchard. The aim of this work was to chart fruit maturation in 'Maxi Gala' grafted on two different rootstocks, using destructive and not destructive methods. The non-destructive method used was the portable DA-Meter. The trial was realized at Vacaria, southern Brazillocated 28,44 S and 50,85 W. The samples were harvested on two orchards during the seasons 2014/15 and 2015/16, during six weeks before harvest from January until the second week of February. The sampling was realized in five different points of the orchard, on rootstocks M.9 or Marubakaido with M.9 interstem. Ten-apple samples were collected weekly in each point in the orchard and then evaluated by destructive method (flesh firmness, starch degradation, total soluble solids and acidity) and the not destructive method (DA-Meter). For both seasons, the evolution of the fruit maturation of Maxi Gala showed a similar progression for both rootstocks. The non-destructive method correlated well with the traditional destructive methods, making it a tool for more practical and easy determination of the harvest date.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.