Analysis of a new variational model for image multiplicative denoising

In this paper, we study the mathematical properties of a new variational model for image multiplicative noise removal. Some important properties of the model, including the lower semicontinuity, the differential property, the convergence and regularization property, are established for the first time. The existence and uniqueness of a solution for the problem as well as a comparison principle have also been established

DAGKT: Difficulty and Attempts Boosted Graph-based Knowledge Tracing

In the field of intelligent education, knowledge tracing (KT) has attracted increasing attention, which estimates and traces students' mastery of knowledge concepts to provide high-quality education. In KT, there are natural graph structures among questions and knowledge concepts so some studies explored the application of graph neural networks (GNNs) to improve the performance of the KT models which have not used graph structure. However, most of them ignored both the questions' difficulties and students' attempts at questions. Actually, questions with the same knowledge concepts have different difficulties, and students' different attempts also represent different knowledge mastery. In this paper, we propose a difficulty and attempts boosted graph-based KT (DAGKT), using rich information from students' records. Moreover, a novel method is designed to establish the question similarity relationship inspired by the F1 score. Extensive experiments on three real-world datasets demonstrate the effectiveness of the proposed DAGKT.Comment: 12 pages, 3figures, conference:ICONI

Numerical assessment of the reduction of specific absorption rate by adding high dielectric materials for fetus MRI at 3 T

The specific absorption rate (SAR) is an important issue to be considered in fetus MRI at 3 T due to the high radiofrequency energy deposited inside the body of pregnant woman. The high dielectric material (HDM) has shown its potential for enhancing B field and reducing SAR in MRI. The aim of this study is to assess the feasibility of SAR reduction by adding an HDM to the fetus MRI. The feasibility of SAR reduction is numerically assessed in this study, using a birdcage coil in transmission loaded with an electromagnetic pregnant woman model in the SEMCAD-EM solver. The HDMs with different geometric arrangements and dielectric constants are manually optimized. The B1+ ${B-1}^ +$ homogeneity is also considered while calculating the optimized fetus 10 g local SAR among different strategies in the application of HDM. The optimum maximum fetus 10 g local SAR was obtained as 2.25 W/kg, by using two conformal pads placed left and right with the dielectric constant to be 400, reduced by 24.75% compared to that without the HDM. It indicated that the SAR can be significantly reduced with strategic placement of the HDM and the use of HDM may provide a simple, effective and low-cost method for reducing the SAR for the fetus MRI at 3 T

Bis{μ-4,4′,6,6′-tetra­bromo-2,2′-[o-phenyl­enebis(nitrilo­methyl­idyne)]­diphenol­ato}­bis­[(dimethyl­formamide)cadmium(II)]

The Schiff base ligand derived from the condensation of 3,5-dibromo­salicylaldehyde and 1,2-phenyl­enediamine, in the presence of dimethyl­formamide, forms the centrosymmetric title neutral binuclear distorted complex, [Cd2(C20H10Br4N2O2)2(C3H7NO)2], with the two octa­hedral Cd atoms linked by two O atoms. All bond lengths and angles show normal values

A note on the boundedness in a chemotaxis-growth system with nonlinear sensitivity

This paper deals with a parabolic-elliptic chemotaxis-growth system with nonlinear sensitivity \begin{equation*}\label{1a} \begin{cases} u_t=\Delta u-\chi\nabla\cdot(\psi(u)\nabla v)+f(u), &(x,t)\in \Omega\times (0,\infty), \\ 0=\Delta v-v+g(u), &(x,t)\in \Omega\times (0,\infty), \end{cases} \end{equation*} under homogeneous Neumann boundary conditions in a smooth bounded domain $\Omega\subset \mathbb{R}^{n}$ $(n\geq1)$, where $\chi>0$, the chemotactic sensitivity $\psi(u)\leq(u+1)^{q}$ with $q>0$, $g(u)\leq(u+1)^{l}$ with $l\in \mathbb{R}$ and $f(u)$ is a logistic source. The main goal of this paper is to extend a previous result on global boundedness by Zheng et al. [J. Math. Anal. Appl. 424(2015), 509–522] under the condition that $1\leq q+l<\frac{2}{n}+1$ to the case $q+l<1$