Song and Chissom established fuzzy time series forecasting model in 1993. Stevenson and Porter improved the forecasting model of Jilani, Burney, and Ardil in 2009, and researched the forecasting problem of enrollments of the University of Alabama 1971-1992. Although they obtained the best prediction accuracy by 2009, the prediction accuracy was still not ideal. In this paper, we improved the forecasting model of Stevenson and Porter, and got the SFBODR (The Set of Fuzzy Time Series Forecasting Models Based on the Ordered Difference Rate). The forecasting model SFBODR(0.00004, 0.00003) can get the ideal state of AFER(Average Forecasting Error Rate) = 0% and MSE(Mean Square Error) = 0 in forecasting the enrollments of the University of Alabama. Keywords-fuzzy time series forecasting method; fuzzy number function of SFBODR; inverse fuzzy number function of SFBODR; forecasting function of SFBODR

This paper deals with the application of the adjoint variable approach to sensitivity analysis of objective functions used for defect detection from knowledge of supplementary boundary data, in connexion with the use of BIE/BEM formulations for the relevant forward problem. The main objective is to establish expressions for crack shape sensitivity, based on the adjoint variable approach, that are suitable for BEM implementation.In order to do so, it is useful to consider first the case of a cavity defect, for which such boundary-only sensitivity expressions are obtained for general initial geometry and shape perturbations. The analysis made in the cavity defect case is then seen to break down in the limiting case of a crack. However, a closer analysis reveals that sensitivity formulas suitable for BEM implementation can still be established. First, particular sensitivity formulas are obtained for special shape transformations (translation, rotation or expansion of the crack) for either two-or threedimensional geometries which, except for the case of crack expansion together with dynamical governing equations, are made only of surface integrals (three-dimensional geometries) or line integrals (two-dimensional geometries). Next, arbitrary shape transformations are accommodated by using an additive decomposition of the transformation velocity over a tubular neighbourhood of the crack front, which leads to sensitivity formulas . This leads to sensitivity formulas involving integrals on the crack, the tubular neighbourhood and its boundary. Finally, the limiting case of the latter results when the tubular neighbourhood shrinks around the crack front is shown to yield a sensitivity formula involving the stress intensity factors of both the forward and the adjoint solutions. Classical path-independent integrals are recovered as special cases.The main exposition is done in connexion with the scalar transient wave equation. The results are then extended to the linear time-domain elastodynamics framework. Linear static governing equations are contained as obvious special cases. Numerical results for crack shape sensitivity computation are presented for two-dimensional time-domain elastodynamics.

No abstract

The variation of elastic constants stiffness coefficients with respect to different percentage ratios of defects in monolayer molybdenum disulfide (MLMoS2) is reported for a particular set of atomistic nanostructural characteristics. The common method suggested is to use conventional defects such as single vacancy or di vacancy, and the recent studies use stone-walled multiple defects for highlighting the differences in the mechanical and electronic properties of 2D materials. Modeling the size influence of monolayer MoS2 by generating defects which are randomly distributed for a different percentage from 0% to 25% is considered in the paper. In this work, the geometry of the monolayer MoS2 defects modeled as randomized over the domain are taken into account. For simulation, the molecular static method is adopted and study the effect of elastic stiffness parameters of the 2D MoS2 material. Our findings reveals that the expansion of defects concentration leads to a decrease in the elastic properties, the sheer decrease in the elastic properties is found at 25%. We also study the diffusion of Molybdenum (Mo) in Sulphur (S) layers of atoms within MoS2 with Mo antisite defects. The elastic constants dwindle in the case of antisite defects too, but when compared to pure defects, the reduction was to a smaller extent in monolayer MoS2. Nevertheless, the Mo diffusion in sulfur gets to be more and more isotropic with the increase in the defect concentrations and elastic stiffness decreases with antisite defects concentration up to 25%. The distribution of antisite defects plays a vital role in modulating Mo diffusion in sulfur. These results will be helpful and give insights in the design of 2D materials.