On the Relative Twist Formula of l-adic Sheaves

We propose a conjecture on the relative twist formula of l-adic sheaves, which can be viewed as a generalization of Kato—Saito's conjecture. We verify this conjecture under some transversal assumptions. We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward. A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.     

On the Brauer p-dimension of Henselian discrete valued fields of residual characteristic p > 0

Let $(K,v)$ be a Henselian discrete valued field with residue field $\stackrel{?}{K}$ of characteristic $p>0$, and ${\text{Brd}}_p(K)$ be the Brauer p-dimension of K. This paper shows that ${\text{Brd}}_p(K)\ge n$ if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=p^n$, for some $n\in \mathbb{N}$. It proves that ${\text{Brd}}_p(K)=\infty$ if and only if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=\infty$.     

输电铁塔四地脚螺栓塔脚板抗拉承载力试验与计算方法研究

针对架空输电线路铁塔中常用的四地脚螺栓塔脚板进行了抗拉承载力试验和理论计算方法研究。首先,选取8个试件进行塔脚板抗拉承载力试验研究,分析塔脚底板板厚及有无加劲板对塔脚板抗拉承载力的影响;其次,通过有限元模拟塔脚板的应力分布情况,并结合“塑性分析,弹性设计”的思想,提出了一种基于屈服线理论的四地脚螺栓塔脚板抗拉承载力计算公式;最后,与试验结果、有限元仿真结果、已有技术规定中的计算结果进行了对比。结果表明:建议公式与试验结果和仿真结果较为吻合,相关技术规定中的计算结果偏于保守,验证了本文建议公式的精确性;底板厚度和加劲板的作用对塔脚板承载力影响较大。研究结果可为输电铁塔四地脚螺栓塔脚板结构设计提供参考。     

基于临界状态的砂土本构模型研究

砂土孔隙比及所受压力是其力学特性的重要影响因素. 本文基于砂土临界状态线特性分析,采用以e-(p/p_a)ξ平面内的线性关系描述其等向压缩线. 通过对比分析两种不同压缩线函数 与临界状态线函数之间的关系提出更适合描述砂土在等向压缩下的参考压缩线,并给出了基于参考压缩线的等向硬化规律. 建议了适用于 描述砂土剪切特性的屈服面函数,并给出利用等向压缩和等p路径确定屈服面形状参数μ的方法. 将不同应力比对应的压缩线作为砂土状态参量参考线,以获取潜在强度M_f与特征状态应力比M_c,进而描述砂土压缩与剪切特性;基于等向压缩与等p路径建立了当前应力比与状态参量参考线之间的相关关系,从而实现了砂土状 态参量参考线由参考压缩线向临界状态线平稳过渡. 建立的砂土本构模型共11个参数,均能够通过常规土工试验或经验获取. 基于模型预测与Toyoura砂的等向压缩、三轴不排水剪切试验及排水剪切试验的对比结果,本文建立的砂土本构模型很好地描述了Toyoura 砂在不同孔隙比和不同压力下的压缩与剪切特性.      

求解低秩矩阵填充的改进的交替最速下降法

矩阵填充是指利用矩阵的低秩特性而由部分观测元素恢复出原矩阵,在推荐系统、信号处理、医学成像、机器学习等领域有着广泛的应用。采用精确线搜索的交替最速下降法由于每次迭代计算量小因而对大规模问题的求解非常有效。本文在其基础上采用分离地精确线搜索,可使得每次迭代下降更多但计算量相同,从而可望进一步提高计算效率。本文分析了新算法的收敛性。数值结果也表明所提出的算法更加有效。     

有耗介质层上多导体传输线的电磁耦合时域分析方法

目前,针对空间电磁场作用有耗介质层上传输线的电磁耦合,仍缺乏有效的数值分析方法.因此,本文提出一种高效的时域混合算法,很好地解决了有耗介质层上传输线电磁耦合建模难的问题.首先,对经典传输线方程进行改进,推导了适用于有耗介质层上多导体传输线电磁耦合分析的修正传输线方程.然后,结合时域有限差分方法和相应插值技术,求解修正传输线方程,获得多导线及其端接负载上的电压和电流响应,并实现空间电磁场辐射与多导线瞬态响应的同步计算.最后,通过相应计算实例的数值模拟,与CST软件的仿真结果进行对比,验证了时域混合算法的正确性和高效性.     

Nano-sized Cu(II) and Zn(II) complexes and their use as a precursor for synthesis of CuO and ZnO nanoparticles: A study on their sonochemical synthesis,characterization, and DNA-binding/cleavage,anticancer, and antimicrobial activities

Two new divalent copper (C1) and zinc (C2) chelates having the formulae [M(PIMC)₂] (where M = Cu(II), Zn(II) and PIMC = Ligand [(E)-3-(((3-hydroxypyridin-2-yl)imino)methyl)-4H-chromen-4-one] were obtained and characterized by several techniques. Structures and geometries of the synthesized complexes were judged based on the results of alternative analytical and spectral tools supporting the proposed formulae. IR spectral data confirmed the coordination of the ligands to the copper and zinc centers as monobasic tridentate in the enol form. Thermal analysis, UV-Vis spectra and magnetic moment confirmed the geometry around the copper center to be tetrahedral, square pyramidal and octahedral. Study of the binding ability of the synthesized compounds with Circulating tumor DNA (CT-DNA) bas been evaluated applying UV-Vis spectral titration and viscosity measurements. The copper and zinc oxides were achieved from the copper and zinc nano-particles structures Schiff base complexes as the raw material after calcination for 5 hr at 600°C. On the other hand, synthesized of C1 and C2 NPs were used as suitable precursors to the preparation of CuO and ZnO NPs. Finally, the synthesized of the two complexes exhibited enhanced activity against the tested bacterial (Staphylococcus aureus and Escherichia Coli) and fungal strains (Candida albicans and Aspergillus fumigatus) as compared to HPIMC. Among all these synthesized compounds, C1 exhibits good cleaving ability compared to other newly synthesized C2.     

传输线方程的高精度龙格−库塔数值求解方法

提出了一种求解传输线方程的高精度龙格-库塔(RK)方法。此方法在空间上采取高阶泰勒展开,提高了对空间微分的近似精度,减少了数值色散所带来的误差。与传统的时域有限差分法(FDTD)方法相比,在每波长采样数相同时,RK方法的计算精度更高。同时,根据Taylor模型,对外界平面波激励源进行离散,成功利用RK方法对外部场激励传输线进行求解,扩大了龙格-库塔方法在求解传输线方程时的应用范围。通过编程对平面波辐照下无限大地平面上的单导体与双导体的算例分别应用FDTD方法与RK方法进行了计算,验证了RK方法的正确性。结果表明同等计算条件下RK方法的计算精度更高。     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.