具多滞量的非线性中立型差分方程的振动性定理

研究了一类较为广泛的具有多个滞量的非线性中立型差分方程的振动性，得到了该类方程振动的一个判定定理     

Crystal structure and phase transition of 2-methoxyanilinium perchlorate-18-crown-6

A new phase transition compound,2-methoxyanilinium perchlorate-18-crown-6(1) {(oCH3OC6H4NH3)+(18-crown-6) ClO4 },has been synthesized and separated as crystals.Differential scanning calorimetry(DSC) measurements show a pair of sharp peaks at 225 K(heating) and 210 K(cooling),indicating the phase transition is first-order.Dielectric anomalies observed at 225 K(heating)and 210 K(cooling) further confirm the phase transition.The crystal structures determined at 298 K and123 K are both triclinic in P 1.The most distinct difference between room-temperature and lowtemperature structures is the order–disorder transition of the host 18-crown-6 molecule,which is the driving force of the phase transition.     

Doping effects on structural and magnetic evolutions of orthoferrite SmFe（1-x） Alx O3

The structural and magnetic properties of SmFeO3 with B site substitution of non-magnetic atom A1 are investigated. The x-ray diffraction patterns show that SmFe（1-x）AlxO3 remains an orthorhombic structure within the whole doping range, and the unit-cell volume decreases monotonically with the increase of doped A1 concentration. Besides, the octa- hedral tilting distortions of FeO6 are found to be alleviated while the tolerance factor increases. However, the relationship between the lattice parameters and Al concentration is observed to deviate from Vegard＇s rule, and this may be caused by magnetostriction effects. For the doping content values in a range 0 〈 x 〈 0.6, the ferromagnetism, antiferromagnetism, and paramagnetism are observed to occur continuously. Moreover, the magnetization and the spin reorientation temperature （Tk） decrease monotonically as Al content value increases. With the doping content values being x = 0.8 and 1.0, these compounds only show paramagnetic behavior.     

哈希编码优化的IRON逆渲染模型：重建几何与材质

将神经网络用于场景几何材质的高效表达，结合逆向渲染在二维光度图的监督下重建高质量的网格和材质贴图，为现有的图形学流水线提供服务——神经渲染已成为近年来计算机图形学新的研究热点。在IRON(inverse rendering by optimizing neural SDFs and materials from photometric images)神经渲染模型基础上，通过引入多分辨率哈希编码，采用冻结训练等方法提高原始模型的训练速度。在多个数据集上的对比实验表明，优化后的IRON逆渲染模型训练速度提升了约40%，且重建结果中包含更多细节。     

顶空气相色谱-质谱法测定食品接触用苯乙烯类聚合材料及制品中5种单体迁移量

建立了顶空-气相色谱质谱法测定食品接触用苯乙烯类聚合物材料及制品中1,3-丁二烯、2-甲基-1,3-丁二烯、苯乙烯、乙苯、丙烯腈等5种单体在10%（体积分数）乙醇溶液、4%（体积分数）乙酸溶液、20%（体积分数）乙醇溶液、50%（体积分数）乙醇溶液，以及橄榄油等5种食品模拟物中的迁移量。分别对色谱柱、载气流量、分流比、顶空平衡温度和时间等条件进行了优化，目标物采用TG-WAX MS色谱柱（60 m×0.25 mm,0.25μm）分离，质谱法检测。实现了对苯乙烯类聚合物及材料中5种单体的同时快速分析检测。5种单体的质量分数在0.01～1 mg/kg范围内与其色谱峰面积线性关系良好，各单体的线性相关系数均大于0.998，检出限为0.001～0.003 mg/kg。测定结果的相对标准偏差为0.6%～8.7%(n=6)，回收率为80.2%～119%。该方法是对国标方法的完善补充，适用于对食品接触用PS、AS、ABS等苯乙烯类聚合材料中的1,3-丁二烯、2-甲基-1,3-丁二烯、丙烯腈、苯乙烯、乙苯迁移量的检测分析。     

函数符号f(x)中“对应关系f”特征解读

人教A版《数学》(必修1)"函数及其表示"给出了函数的定义及其表示,但学生在学习过程中仍然感到:理解困惑多、解题疑虑多.究其原因不外乎对函数概念的理解有问题,下面从几个方面对覼(x)中"覼"的特征解读如下:     

双圈图的距离无符号拉普拉斯谱半径

连通图$G$的距离无符号拉普拉斯矩阵定义为$\mathcal{Q}(G)=Tr(G)+D(G)$, 其中$Tr(G)$和$D(G)$分别为连通图$G$的点传输矩阵和距离矩阵. 图$G$的距离无符号拉普拉斯矩阵的最大特征值称为$G$的距离无符号拉普拉斯谱半径. 本文确定了给定点数的双圈图中具有最大的距离无符号拉普拉斯谱半径的图.     

不存在秩为r(G)+2c(G)-1或r(G)-2c(G)+1的符号图

设Γ=(G,σ)是一个符号图,其中G是Γ的基图.设r(G,σ)是Γ的秩.[Linear Algebra Appl.,2018,538:166-186]和[Linear Multilinear Algebra,2019,67:2520-2539]分别证明了r(G)-2c(G)≤r(G,σ)≤r(G)+2c(G),其中,r(G)和c(G)分别是G的秩和圈空间维数.本文主要证明没有符号图的秩能够达到r(G)+2c(G)-1和r(G)-2c(G)+1,并且证明了存在无穷多个符号图的秩r(G,σ)=r(G)+2c(G)-s,其中s∈[0,4c(G)]且s≠1及4c(G)-1.