古希腊三大几何问题的近似尺规作图

尺规作图是初等几何教育中的一个课题.它对培养学生的几何想象能力起到了重要作用.在古代,尺规作图的研究曾经促成过多个数学领域的发展.一些结果就是为解决古希腊的三大几何问题而得到的副产品.对尺规作图的探索推动了对圆锥曲线的研究,并发现了一批著名的曲线.     

Quantum Swap Gate with Molecular Ensembles via Cavity Quantum Electrodynamics

We present a simple method to realize a swap gate at one step with two molecular ensembles in a stripline cavity. In this scheme, we can benefit from the enhancement of the coherent coupling and acquire a long coherent time with encoding qubits in different spin states of the rotational ground state in the molecular ensembles. As a by-product, a scheme to create an entangled state with one excitation stored in two ensembles is proposed.     

《问题征解》栏目中几个优美不等式的简解与拓展

《数学通讯》上半月学生刊作为国内最优秀,最权威的期刊,其中《问题征解》栏目每期都有有趣、新颖、灵巧的问题,这些问题有很好的研究价值.其中不等式问题每期都有,笔者对最近几期的不等式问题进行了研究,例1,例2,例4的证法不同于原证法,比原证法简洁;例3,例5是对第11,12期问题提供的解法,并得到一些副产品.现整理成文,以飨读者.     

FDA修订食品添加剂条例

美国食品药品管理局(FDA)于11月30日发布一项最终规则,修订美国食品添加剂条例,它规定了非冷藏以及冷藏的未煮的肉类、肉类副产品和某些肉类食品可接受最大吸收剂量为4.5 kGy(Kilogray)的电离辐射处理,以减少食源性致病菌,并延长保存期限。     

正弦定理推证中的三个“副产品”

现行高中教材（人教版试验修订本必修第一册（下））中证明正弦定理时用的是向量方法，但未给出等于2R的证明．笔者在教学中对正弦定理“等于2R”推导的探究中，利用常用的三角形的外接圆方法来推导．在完成了任务的同时还得到了几个非常优美的“副产品”．     

并组训练——提高学生的思辨能力

文[1]在推证正弦定理时，得到了三个“副产品”，其中前两个是： 结论1 在ΔABC中，sinA＋sinB＋sinC/cosA＋cosB＋cosC〈2;     

大孔树脂吸附分离速溶茶副产品中茶多酚的研究

通过静态试验比较了不同树脂对速溶茶副产品中茶多酚的吸附和解析特性,筛选出对茶多酚有较好的吸附率和解析率的NKA-9型树脂。动态试验确定了最佳的吸附和解析参数:上样流速为0.8mL/min、上样液温度为60℃、pH为5,洗脱流速为0.9mL/min、乙醇浓度为80%、洗脱剂用量为3BV。经过NKA-9纯化后速溶茶副产品中茶多酚含量达到58.7%,得率为14%。     

Chromaticity of complete 6-partite graphs with certain star or matching deleted II

Let P(G,λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G～H, if P(G,λ)=P (H,λ). We write [G]={H|H～G}. If[G]={G}, then G is said to be chromatically unique. In this paper, we first characterize certain complete 6-partite graphs with 6n+1 vertices according to the number of 7-independent partitions of G. Using these results, we investigate the chromaticity of G with certain star or matching deleted. As a by-product, many new families of chromatically unique complete 6-partite graphs with certain star or matching deleted are obtained.     

Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics

We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）]｜0 in the coordinate representation. A new operator＇s disentangling formula is derived as a by-product.     

Categorification of integrable representations of quantum groups

We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac–Moody algebra. As a byproduct, we obtain a geometric realization of Lusztig's canonical bases of these representations as well as a new positivity result. The main ingredient in the underlying geometric construction is a class of micro-local perverse sheaves on quiver varieties.