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.     

The covalent functionalization of few-layered MoTe2 thin films with iodonium salts

Covalent functionalization of 2D materials provides a tailored approach towards tuning of their chemical, optical, and electronic properties making the search for new ways to graft small molecules important. Herein, the reaction with (3,5-bis(trifluoromethyl)phenyl)iodonium salt is revealed as an effective strategy for functionalization of MoTe₂ thin films. Upon decomposition of the salt, the generated radicals graft covalently as aryl-(CF₃)₂ groups at the surface of both metallic (1T’) and semiconducting (2H) polymorphs of MoTe₂. Remarkably, the reactivity of the salt is governed by the electronic structure of the given polymorph. While the functionalization of the metallic MoTe₂ occurs spontaneously, the semiconducting MoTe₂ requires activation by light. The reaction proceeds with the elimination of oxide from the original films yielding the functionalized products that remain protected in ambient conditions, presenting a viable solution to the ageing of MoTe₂ in air.     

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 $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=\infty$.     

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.     

焦炉上升管内壁结焦炭层的光谱学分析及结焦机理研究

以焦炉上升管内壁结焦炭层块为研究对象，采用X射线荧光光谱仪（XRF）、X射线衍射仪（XRD）、傅里叶红外光谱仪（FTIR）和激光共聚焦拉曼光谱仪（Raman）对结焦炭层的元素组成，以及各结焦炭层的矿物组成、组成结构和分子结构进行测试。分析从结焦炭层块外表面向内表面过渡的各结焦炭层的差异性，揭示焦炉上升管内壁结焦机理。结果表明焦炉上升管内粉尘中Fe，S和Cr极易催化荒煤气中蒽、萘等稠环芳烃化合物成炭，在焦炉上升管内壁形成炭颗粒沉积，为焦油凝结挂壁提供载体，在荒煤气温度降至结焦温度时易结焦积碳。结焦炭层均含有芳香层结构，随着结焦炭层从外表面向内表面过渡，各结焦炭层的面层间距(d₀₀₂)逐渐降低、层片直径(L_a)先降低后增加、层片堆砌高度(Lc)和芳香层数(N)先稳定后增加。结焦炭层石墨化过程是由结焦炭层内表面向外表面进行，主要包括其片层外缘的羧基和部分C-O结构的降解剥离，从而形成高度规整的共轭结构。结焦炭层块中C元素是以结晶碳与无定型碳的混合物形式存在。以上研究为解决焦炉上升管内壁结焦及腐蚀问题，提高换热器换热效率，有效回收焦炉荒煤气显热，降低焦化企业能耗提供实验基础和理论依据。     

Synthesis,spectroscopic studies,thermal analyses,biological activity of tridentate-coordinated transition-metal complexes [M(L)X2] and crystal structure of [ZnBr2(2,6-bis(tert-butylthiomethyl)pyridine)]

A new terdentate acyclic pincer ligand, 2,6-bis(tert-butylthiomethyl)pyridine (tbtmp), was synthesized and reacted with several complexes of iron, zinc, nickel, cobalt, and copper. The ligand and its coordination compounds were characterized using elemental analysis, infrared, ¹H- and ¹³C-NMR-spectroscopy, thermal analyses, plus—for the Zn complex—single-crystal X-ray diffractometry. The structure of [Zn(L)Br₂] was solved in the tetragonal crystal system, chiral space groups P4₁2₁2 and P4₃2₁2 (No. 92 and No. 96, a = 947.2(1) pm, c = 2265.2(5) pm), revealing five-fold coordination of the metal atoms. According to spectroscopy, all complexes share the same coordination environment around the metal atoms, consisting of two halide anions and a sulfur-methylene-pyridine-methylene-sulfur entity; tbtmp acts as a tridentate ligand with the pyridine N atom and both tert-butylthio S atoms coordinating to the metal ions (NS2). The analysis results indicate that the metal ions are coordinated as distorted pseudo-bipyramids, LMX₂, with the chelate ligand meridionally arranged. One of the complexes contains ethanol as an additional ligand, resulting in a pseudo-octahedral coordination sphere [Ni(L)Cl₂EtOH]. The latter was obtained in the form of green crystals, which turn into a red powder with loss of the ethanol molecule. Fe (III), Co(II), Ni(II) and Cu(II) metal complexes [M(L)Cl₂] were screened for their antibacterial activity against B. subtilis G(+) and Escherichia coli G(−) bacteria, and fungus (Candida albicans and Aspergillus flavus).     

n-In0.35Ga0.65N/p-Si异质结的制备及其电学性能研究

采用双光路双靶材脉冲激光沉积(PLD)系统在p-Si衬底上外延生长InGaN薄膜,研究了InGaN薄膜的显微组织结构和n-InGaN/p-Si异质结的电学性能。研究表明,InGaN薄膜为单晶结构,沿[0001]方向择优生长,薄膜表面光滑致密,In的原子含量为35%。霍尔(Hall)效应测试表明In_0.35Ga_0.65N薄膜呈n型半导体特性,具有高的载流子浓度和迁移率及低的电阻率。I-V曲线分析表明In_0.35Ga_0.65N/p-Si异质结具有良好的整流特性,在±4 V时的整流比为25,开路电压为1.32 V。In_0.35Ga_0.65N/p-Si异质结中存在热辅助载流子隧穿和复合隧穿两种电流传输机制。经拟合,得到异质结的反向饱和电流为1.05×10^-8 A,势垒高度为0.86 eV,理想因子为6.87。     

Non‐self‐adjoint singular second‐order dynamic operators on time scale

In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.