On a spectral sequence for equivariant K-theory

We apply the “homotopy coniveau” machinery developed by the first-named author to the K-theory of coherent G-sheaves on a finite type G-scheme X over a field, where G is a finite group. This leads to a definition of G-equivariant higher Chow groups (different from the Chow groups of classifying spaces constructed by Totaro and generalized to arbitrary X by Edidin–Graham) and an Atiyah–Hirzebruch spectral sequence from the G-equivariant higher Chow groups to the higher K-theory of coherent G-sheaves on X. This spectral sequence generalizes the spectral sequence from motivic cohomology to K-theory constructed by Bloch–Lichtenbaum and Friedlander–Suslin. The first-named author gratefully acknowledges the support of the Humboldt Foundation through the Wolfgang Paul Program, and support of the NSF via grants DMS-0140445 and DMS-0457195.     

New potentialities of electrophilic addition in the assembly of polyfunctional compounds from simple precursors

A novel methodology of the multicomponent coupling based on the controlled sequence of the kinetically independent electrophilic additions is suggested and its promise as an efficient protocol for the short synthesis of the structurally diverse polyfunctional compounds from simple precursors is demonstrated.     

Boundary Dilatation and Degenerating Hamilton Sequences

In this paper, we study the boundary dilatation of quasiconformal mappings in the unit disc. By using Strebel mapping by heights theory we show that a degenerating Hamilton sequence is determined by a quasisymmetric function.     

p元序列的三项式特性

利用有限域上的迹函数理论研究了迹函数生成的p（p为素数）元周期序列的三项式特性的问题，给出了周期为p^n-1的迹函数生成的p元序列具有三项式特性的充分必要条件，给出了具有三项式特性的迹函数生成的p元周期序列的三项式对相同的条件及三项式对的分类（即正则三项式对和非正则三项式）；利用户元序列的迹表示分别用不同的方法证明了p元GMW序列和级联P元GMW序列都具有正则三项式特性，并给出了相应的正则三项式对．     

Fengenbaum映射的搓揉序列与特征集

设f为Feigenbaum映射,亦即函数方程fp(λx)=λf(x)满足一定条件的单峰解．f的搓揉序列为0-1无限序列,f的特征集是临界点轨迹的闭包．本文研究f的性质进而证明．f的搓揉序列是某代换在符号空间中的不动点,f在特征集上的限制是某代换子移位的一个因子．     

双轴晶体光轴角的计算

通过坐标变换把折射率椭球方程x~2/n_1~2 y~2/n_2~2 z~2/n_3~2=1从主介电坐标系Oxyz转换到另一个新的坐标系Ox′y′z′中,这个新的坐标系Ox′y′z′可以通过将坐标系Oxyz绕原点旋转得到.只要使新的折射率椭球方程与x′y′平面的交线是一个圆,就可以确定z′轴就是晶体的光轴.由此得出了双轴晶体光轴角的计算公式.     

Perfect Matrix Algebras ∑(λ)(Ⅱ)-AK-Property

In this paper, we introduce the concept of AK-property for the perfect ma-trix algebras ∑(λ) and give some characterizations of∑(λ)possessing AK-property.     

DNA detection by dye labeled oligonucleotides using surface enhanced Raman spectroscopy

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滞后序列分析视域下的高中化学高端备课师生互动行为研究*

为揭示“高端备课”项目下教师与学生行为互动的关键特征,研究采用视频分析法及滞后序列分析法(LSA)对2019年高端备课项目中“离子反应”课堂中的师生交互行为、比率、教师语言、师生操作技术以及教师与学生之间的交互行为等进行量化与质性分析。研究发现,高端备课更加关注学生对于本源性认识问题的科学认识逻辑,以传授核心观念建构以及基于学生认识发展为本为理念,由知识解析为本向促进学生认识发展转变,通过师生思维不断碰撞的过程促进学生知识迁移与应用,为常态化课堂优化提供了参考路径。     

Remarks on the distribution of colors in Gallai colorings

A Gallai coloring of a complete graph $K_n$ is an edge coloring without triangles colored with three different colors. A sequence $e_1\ge \cdots \ge e_k$ of positive integers is an $(n,k)$-sequence if ${\sum }_{i=1}^k{e}_i=\left(\genfrac{}{}{0ex}{}{n}{2}\right)$. An $(n,k)$-sequence is a G-sequence if there is a Gallai coloring of $K_n$ with $k$ colors such that there are $e_i$ edges of color $i$ for all $i,1\le i\le k$. Gyárfás, Pálvölgyi, Patkós and Wales proved that for any integer $k\ge 3$ there exists an integer $g\left(k\right)$ such that every $(n,k)$-sequence is a G-sequence if and only if $n\ge g\left(k\right)$. They showed that $g\left(3\right)=5,g\left(4\right)=8$ and $2k-2\le g\left(k\right)\le 8k^2+1$.We show that $g\left(5\right)=10$ and give almost matching lower and upper bounds for $g\left(k\right)$ by showing that with suitable constants $\alpha ,\beta >0$, $\frac{\alpha k^{1.5}}{lnk}\le g\left(k\right)\le \beta k^{1.5}$ for all sufficiently large $k$.