In this paper, we study the non-global existence of solutions to the following time fractional nonlinear diffusion equations $$\begin{cases} ^cD^{\alpha}_{0|t}u-\Delta u+(1+t)^ru_t=I^{\beta}_{0|t}(|u|^{p-1}u), \ x\in \mathbb{R}^n, \ t>0 \\ u(0,x)=u_0(x), \ u_t(0,x)=u_1(x), \ x\in\mathbb{R}^n, \end{cases}$$ where $1<\alpha<2$, $\beta\in(0,1)$, $1<\alpha+\beta<2$, $r\in (-1,1)$, $p>1$, $u_0, u_1\in L^q(\mathbb{R}^n)(q>1)$ and $^cD^{\alpha}_{0|t}u$ denotes left Caputo fractional derivative of order $\alpha$. By using the test function method, we prove that the problem admits no global weak solution with suitable initial data when $p$ falls in different intervals. Our results generalize that in [4].

Based on the monthly sea surface temperature (SST) data provided by Hadley Centre, the characteristics of Southern Subtropical Atlantic SST variation and its relationship with ENSO are discussed. The results of this paper show that: 1) In the summer of the southern hemisphere, the SST anomaly (SSTA) of the Southern Subtropical Atlantic presents a southwest-northeast antiphase dipole modes, that is, the South Atlantic Subtropical Dipole (SASD), which develops from September to November. It reaches its peak in austral summer(December January February, the next year), weakens from March to May (the next year), and declines until austarl winter(June July August, the next year). 2) SASD is significantly correlated with ENSO, and positive SASD and negative SASD are correlated with El Niño and La Niña events respectively.

Benefitting from Fully Convolutional Networks (FCNs), salient object detection methods have achieved prominent performance. However, there are still some challenges in this task: 1) lack of effective feature representation and integration make the result salient maps lose some regions of object, or bring some non-saliency regions. 2) suffering from the continuous pooling or stride operations, the predicted maps will lose some important spatial detail information, especially the boundary of object. To address these two problems, we propose the Content-aware and Edge-aware network (CENet) which contains three sub-modules: 1) we design a content-aware feature extraction module which uses a transformer block and channel-wise attention mechanism to capture the distinct content features and suppresses the non-saliency regions. 2) an edge-aware feature extraction module is introduced to learn the boundary features and predict the intact edge of the salient object. 3) a feature fusion module is proposed to integrate features from the first two module in a learning way. We also design a hybrid loss function which has better performance than the widely-used binary cross entropy loss. Results show that, our method can detect the intact salient object without losing regions of object or bring some non-saliency regions, and can also obtain the precise boundary. Experimented on several datasets, our method can achieve the state-of-art performance.

In order to simulate the hot metal flow and erosion behavior within blast furnace hearth, a 3D system simulation platform is established, which would be a great help to analyze all kinds of working condition due to arbitrary setting parameters about hearth structure and material properties. With the flexible parameterized control mechanism, the distribution about velocity field, pressure field, and temperature field can be simulated in this platform. The simulation results, which are mainly revolving round seven work conditions, show that the erosion degree about blast furnace hearth could be flexible and conveniently analyzed.

In this paper we present analytic solutions of a class of matrix minimization model with unitary constraints as follows:$$\mathop{\rm min}_{U_k\in {\rm U}_n, W_k\in {\rm U}_t, V_k\in {\rm U}_m} \ | {\rm det}(cI_m\pm \prod\limits_{k=1}^s A_k U_k B_k W_k C_k V)|$$ $$\mathop{\rm min}_{U_k\in {\rm U}_n, W_k\in {\rm U}_t, V_k\in {\rm U}_m} |{\rm tr}(cI_m \pm \prod^s_{k=1}A_k U_K B_k W_k C_k V)| $$ where $A_k\in C^{m\times n}$, $B_k\in C^{n\times t}$, $C_k\in C^{t\times m}$, $C^{m\times n}$ denotes $m\times n$ complex matrix set, and $c$ is a complex number, $I_m$ denotes the $m$-order identity matrix, det$(\cdot)$ and tr$(\cdot)$ denote matrix determinant and trace function, respectively. The proposed results improve some existing ones in Xu (2019) [1]. Numerical examples are given to verify the validity of the theoretical results.

Based on the monthly temperature data of 34 stations in Jianghuai region of China from 1961 to 2005, we proposed a functional downscaling model of summer temperature, which taking into consideration the related optimal regional climate factors. The sample independence test is used to verify the robustness of the model. The ability in simulating summer temperatures in Jianghuai region is evaluated. The main results show: (1) The best selected predictors and their regions are 850hPa air temperature (27.5-37.5°N, 107.5-125°E) and sea level pressure (25-35°N, 102.5-125°E). (2) The first four principal components of the two factors can account for more than 85% of the original information after downscaling. (3) The independent sample test proves that the functional downscaling model has a good ability to simulate the spatial and temporal structure and the changes of summer temperature in Jianghuai region during the period of 1991-2005, especially for the northeast coastal part.

In many computer vision tasks, the extraction of features invariant to affine transform plays an important role. To achieve better accuracy, region-based approaches usually need expensive computation. Whereas, contour-based methods need less computation, but their performance is strongly dependant on the boundary extraction. A method, generic polar radius integral transform (GPRIT), is proposed to combine region-based and contour-based method together for the extraction of affine invariant features. Polar radius integral transform and central projection transform are all special cases of the proposed GPRIT. With GPRIT, any object is converted into a closed curve for data reduction. Consequently, stationary wavelet transform is conducted to construct affine invariants. Several experiments have been presented to evaluate performance of the proposed GPRIT.

Electrocardiogram (ECG) signals are the impulses generated by the heart which are used to analyze the proper functioning of heart. This paper applies a functional data analysis method to classify ECG signals. The classification of functional data can be divided into regression model-based classification methods and density-based classification methods. In this paper, Generalized Functional Linear Models (GFLM) and Functional Linear Discriminant Analysis (FLDA) are introduced. Finally, we apply GFLM, FLDA and SVM, neural network, KNN in the actual data, and find that the functional data classification method performs better in the classification of ECG signals.