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The study of certain union $$X(\mu , b)$$ of affine Deligne–Lusztig varieties in the affine flag varieties arose from the study of Shimura varieties with Iwahori level structure. In this paper, we give an explicit dimension formula for $$X(\mu , b)$$ associated to sufficiently large dominant coweight $$\mu $$ .

Flat panel detector (FPD) has been widely used as the imaging unit in the current X-ray digital radiography (DR) systems and Computed Tomography (CT) systems. Point spread function (PSF) is an important indicator of the FPD imaging system, but also the basis for image restoration. For the problem of poor accuracy of the FPD’s PSF measurement with the original pinhole imaging for DR systems, a new PSF measuring method with the pinhole imaging based on the image restoration is proposed in this paper. Firstly, some images collected with the pinhole imaging are averaged to one image to reducing the noise. Then, the original pinhole image is calculated according to the energy conservation principle of point spread. Finally, the PSF of the FPD is obtained using the operation of image restoration. On this basis, through the fitting of the characteristic parameters of the PSF on different scan conditions, the computational model of the PSF is established for any scan conditions. Experimental results show that the method can obtain a more accurate PSF of the FPD, and the PSF of the same system under any scan conditions can be directly calculated with the PSF model.

Industrial fault identification is significant for finding fault reason and remedying the potential safety problems. As kernel principal components analysis (KPCA) has excellent performance in nonlinear data processing, a kind of fault identification method is proposed based on KPCA and simple support vector machine (SSVM). KPCA was applied to choose the nonlinear principal component of the model input data space, and SSVM was applied to establish fault identification modeling, which could not only enhance the efficiency of calculation, but also could improve the fault identification ability. The proposed KPCA-SSVM was applied to the Tennessee Eastman Process (TEP). Simulation indicates that this method features high learning speed and good identification ability compared with SVM, PCA-SSVM and KPCA-SVM, and is proved to be an efficient fault identification modeling method.

Reconstruction speed and image quality are the keys of 3D image reconstruction in cone beam CT (CBCT), this article have researched on the 3D image reconstruction in CBCT, and a self-adapting fast reconstruction method for high resolution images is presented. The method is based on the FDK algorithm and Z-line data first algorithm, which introduces the reconstruction task division algorithm based on Z-line truncation, and load algorithm of filtered projection images based on the VOI reconstruction region. It divide the reconstruction task in a self-adapting method according to the task amount and memory size, thus reduce the data load amount and frequency of filtered projection images. The experimental results show that the method achieves fast reconstruction speed for high resolution images in CBCT, and the image quality almost has no difference with FDK algorithm.