两类Mycielski图及一些平面图的均匀全色数

对于图G(V,E)的正常k-全染色φ称为G(V,E)的k-均匀全染色,当且仅当任意两个色类中的元素总数至多相差1.xvee(G)=m in{k存在图G的一个k-均匀全染色}称为G的均匀全色数.本文得到了两类M ycielsk i图及圈,轮图和扇形的均匀全色数.     

Application of Coordinate-Momentum Intermediate Representation in Solving Eigenstate Problem of a Coupled Oscillator System

We study the eigenstate problem of a kind of coupled oscillators in the new quantum mechanical representation ｜q,μ,υ〉, which is defined as the eigenvector of the operator （μQ ＋ υP）, whereμ and υ are two real parameters. We also use the U operator transformation method to deal with the same problem. We obtain the normally ordered product expressions of U operator and eigenvector. It is shown that the ground state of system Hamiltonian is a squeezed state.     

Possible Experimental Evidence of a Moderate Proton Halo in ^29S

The total reaction cross sections (TRCSs) of^29S ^28Si have been measured at intermediate energies. An obvious enhancement in TRCS of ^29S is observed as compared with its neighbouring nuclei. The TRCSs of ^29S ^28Si arecal culated with the modified Glauber theory in the optical limit and few-body approaches. The different factor d as a possible measure of halo appearance is deduced from the experimental and theoretical data. It is well accepted that ^27p is a proton halo nucleus. Although not as anomalous as ^27p, the different factor d of ^29S is obviously larger than that of its neighbouring isotones of N = 13. This result indicates that a moderate proton halo may exist in ~9S nucleus. We calculate the total reaction cross sections for ~9S with the modified Glaubertheory as a function of incident energy and compare the results with those for 2rSi which is a core nucleus 0f29S.The measured TRCSs of 27Si4-2SSi can be described to be satisfactory by the modified Glauber theory of theoptical limit approach. Although a diffused nuclear density distribution is used, the theories still inadequatelypredict the experimental TRCSs of 29S4-2SSi, which further indicates the possibility of proton halo in 29S.     

对数比电路原理与低频工作点反馈系统

 在合肥光源注入系统升级改造后，尝试了几种方法来改进机器注入束流稳定性。研制了用于抑制注入过程残余β振荡的水平和垂直方向的工作点振荡抑制模块，尝试了包括逐圈测量和锁相环原理来激励和稳定束流等方法来跟踪工作点变化。详细分析了基于对数比原理的逐圈测量系统，包括单束团和多束团模式，证明在多束团模式下逐圈测量的可行性和意义，更新了数据采集和可远程控制的软件集成环境。     

改进的交流跳圈演示实验的定量分析

交流跳圈演示实验是电磁学教学中常做的演示实验，传统的交流跳圈演示实验对楞次定律和法拉第电磁感应定律能给出很好的演示说明．我们对交流跳圈演示实验做了如图1所示的改进，原线圈(1600匝)套在L形的铁轭上；漆包线绕制成的动圈与外电路连接，并用细棉线悬挂起来．通过动圈的受力情况，能进一步演示说明交流电的三种电路特性．文献[1]对此仅作定性分析，在此我们再给予定量分析．     

图论中矩阵的可实现性

对图的关联矩阵,邻接矩阵,基本割集矩阵,基本圈矩阵的可实现性分别进行了论证,并将邻接矩阵的可实现性推广到一般形式.得到了同一个基本割集矩阵的奥凯达图形是不唯一的;以及这些奥凯达图形所对应的图是互相同构的结果;并且指出了基本圈矩阵的可实现性可以依靠基本割集矩阵的可实现性来解决.     

不含三角形图的$A_\alpha$-谱半径的界

设$G$是简单无向图. 对于实数$\alpha \in [0,1]$, Nikiforov于2017年定义图的$A_\alpha$-矩阵为$A_\alpha(G)=\alpha D(G)+(1-\alpha)A(G)$, 其中$A(G)$和$D(G)$分别为图$G$的邻接矩阵和度对角矩阵. 图的$A_\alpha$-矩阵可以看着是图的邻接矩阵和无符号拉普拉斯矩阵的共同推广, 其最大特征值称为图的$A_\alpha$- 谱半径. 对于$\alpha\in[0,1)$, 本文确定了不含三角形图的$A_\alpha$-谱半径的一个下界;对于$\alpha \in[1/2, 1)$, 本文确定了不含三角形$k$圈图的$A_\alpha$-谱半径的一个上界.     

刚性链嵌段共聚物的研究（Ⅳ）──聚醚醚酮／苯酞圈型聚芳醚砜有规嵌段共聚物的合成与部分性能

以聚醚醚酮（ＰＥＥＫ）和苯酞圈型聚芳醚砜（ＰＤＣ）齐聚物为原料，通过溶液缩聚法制备了ＰＥＥＫ／ＰＤＣ有规嵌段共聚物系列样品。经ＤＳＣ、ＷＡＸＤ、ＴＧＡ、ＤＭＡ等方法研究表明：共聚物没有微相分离现象；其结晶属于简单正交晶系，ＰＤＣ含量对共聚物结晶行为产生很大影响；热稳定性随ＰＤＣ含量增加而明显降低；共聚物具有优异的力学性能，拉伸强度和储能模量高于ＰＥＥＫ。     

恰有t行含s圈正元的布尔方阵的幂敛指数

设Ｄｎ，ｓ（ｔ）是恰有ｔ行含ｓ圈正元的ｎ阶布尔方阵的集合，ｓｔｎ．本文给出了当ｓ＝１或ｓ为素数时Ｄｎ，ｓ（ｔ）中矩阵的幂敛指数的一个上界，证明了除ｔ＞ｎ－ｓ（ｎ－１）＋１／４－３／２，且ｓ与ｎ不互素外，这个上界可以达到，对Ｄｎ，ｓ（ｔ）中幂敛指数达到这个上界的矩阵作了部分刻划．     

关于Whitney和Tutte猜想

ｗｈｉｔｎｅｙ和Ｔｕｔｔｅ把平面四色问题化为只与圈上的４染色集有关的问题来研究，从而探讨四色问题的理论证明；提出了一个蕴含着四色定理的猜想。本文研究开集的组合不变性，从而证明Ｗｈｉｔｎｅｙ和Ｔｕｔｔｅ的猜想不成立。