This paper concerns the linearization problem on rational maps of degree d≥2 and polynomials of degree d>2 from the perspective of non-linearizability.The authors introduce a set l_(∞) of irrational numbers and s...This paper concerns the linearization problem on rational maps of degree d≥2 and polynomials of degree d>2 from the perspective of non-linearizability.The authors introduce a set l_(∞) of irrational numbers and show that if α∈l_(∞),then any rational map is not linearizable and has infinitely many cycles in every neighborhood of the fixed point with multiplier λ=e^(2πiα),Adding more constraints to cubic polynomials,they discuss the above problems by polynomial-like maps.For the family of polynomials,with the help of Yoccoz's method,they obtain its maximum dimension of the set in which the polynomials are non-linearizable.展开更多
A finite group G is said to be a B(n,k)group if for any n-element subset[a_(1),…,a_(n)]of G,|{a_(i)a_(j)|1≤i,j≤n}|≤k.It is of interest to characterize the structure of B(n,k)groups for n(n+1)/2≤k≤n^(2)-1.The B(5...A finite group G is said to be a B(n,k)group if for any n-element subset[a_(1),…,a_(n)]of G,|{a_(i)a_(j)|1≤i,j≤n}|≤k.It is of interest to characterize the structure of B(n,k)groups for n(n+1)/2≤k≤n^(2)-1.The B(5,k)groups for 15≤k≤19 have been investigated by several authors.In this paper,we give a complete characterization of B(5,20)2-groups by showing there are five classes of such groups which are nontrivial and nonabelian.展开更多
Small specimens are increasingly being used in getting mechanical properties directly when there are limited materials to facilitate standard specimens,which play a great role in the rapid measurement of mechanical pr...Small specimens are increasingly being used in getting mechanical properties directly when there are limited materials to facilitate standard specimens,which play a great role in the rapid measurement of mechanical properties and residual life assessment of in-service reactor components.Although tensile and fatigue properties of the small specimens are investigated extensively,theoretical models for describing the mechanical properties of small specimens need to be established.Here,we conduct a systematic investigation of tensile and fatigue properties of pure Cu specimens with thicknesses ranging from 3 to 0.2 mm.The results show that the decrease in uniform elongation of the 0.2 mm-thick specimens is mainly due to the efects of grain boundary and free surface on the strain hardening rate.A modifed theoretical model correlated with the ratio of the surface grain layer thickness to the grain size is proposed to predict variation in yield strength of the small specimens more accurately.Furthermore,the mechanism for the diference in fatigue life between the 0.2 mm-thick specimen and other thicker specimens is elucidated.The Basquin equation-based model is presented as a potential way to evaluate the fatigue life of metals using small specimens.展开更多
以3,4,9,10-苝四酸二酐为原料,通过在分子两端芳香环(bay位)分别连接2-甲氧基乙氧基和硝基,合成了两个不对称苝酰亚胺小分子N,N'-二(2-乙基己基)-1-(2-甲氧基乙氧基)-7-硝基-3,4,9,10-苝四羧酸二酰亚胺(Ⅲ)和N,N'-二(2-乙基己基...以3,4,9,10-苝四酸二酐为原料,通过在分子两端芳香环(bay位)分别连接2-甲氧基乙氧基和硝基,合成了两个不对称苝酰亚胺小分子N,N'-二(2-乙基己基)-1-(2-甲氧基乙氧基)-7-硝基-3,4,9,10-苝四羧酸二酰亚胺(Ⅲ)和N,N'-二(2-乙基己基)-1-(2-甲氧基乙氧基)-6,7-二硝基-3,4,9,10-苝四羧酸二酰亚胺(Ⅳ)。利用1HNMR,13CNMR和MS对其结构进行了表征。通过密度泛函理论计算优化了分子空间立体构象、扭曲结构和电子云分布;紫外-可见吸收光谱结果表明,Ⅲ和Ⅳ的最大吸收峰红移至559和572 nm,半峰宽变宽,为104和112 nm;经循环伏安(CV)测试估算,分子Ⅲ和Ⅳ的HOMO、LUMO能级分别为-5.85、-3.55 e V和-5.87、-3.62 e V;在相对湿度为50%的大气环境中,Ⅲ和Ⅳ分别与窄带隙聚合物(PTB7-Th)共混构建了有机太阳能电池器件,Ⅲ与PTB7-Th共混时对应的短路电流密度Jsc=3.6 m A/cm2,开路电压Voc=0.30 V,填充因子FF=0.40,光电转换效率η=0.42%;Ⅳ与PTB7-Th共混时对应的Jsc=4.00 m A/cm2,Voc=0.25 V,FF=0.41,η=0.40%。展开更多
文摘This paper concerns the linearization problem on rational maps of degree d≥2 and polynomials of degree d>2 from the perspective of non-linearizability.The authors introduce a set l_(∞) of irrational numbers and show that if α∈l_(∞),then any rational map is not linearizable and has infinitely many cycles in every neighborhood of the fixed point with multiplier λ=e^(2πiα),Adding more constraints to cubic polynomials,they discuss the above problems by polynomial-like maps.For the family of polynomials,with the help of Yoccoz's method,they obtain its maximum dimension of the set in which the polynomials are non-linearizable.
文摘A finite group G is said to be a B(n,k)group if for any n-element subset[a_(1),…,a_(n)]of G,|{a_(i)a_(j)|1≤i,j≤n}|≤k.It is of interest to characterize the structure of B(n,k)groups for n(n+1)/2≤k≤n^(2)-1.The B(5,k)groups for 15≤k≤19 have been investigated by several authors.In this paper,we give a complete characterization of B(5,20)2-groups by showing there are five classes of such groups which are nontrivial and nonabelian.
基金supported by the National Natural Science Foundation of China(NSFC,No.52171128)the Fundamental Research Project of Shenyang National Laboratory for Materials Science(No.L2019R18).
文摘Small specimens are increasingly being used in getting mechanical properties directly when there are limited materials to facilitate standard specimens,which play a great role in the rapid measurement of mechanical properties and residual life assessment of in-service reactor components.Although tensile and fatigue properties of the small specimens are investigated extensively,theoretical models for describing the mechanical properties of small specimens need to be established.Here,we conduct a systematic investigation of tensile and fatigue properties of pure Cu specimens with thicknesses ranging from 3 to 0.2 mm.The results show that the decrease in uniform elongation of the 0.2 mm-thick specimens is mainly due to the efects of grain boundary and free surface on the strain hardening rate.A modifed theoretical model correlated with the ratio of the surface grain layer thickness to the grain size is proposed to predict variation in yield strength of the small specimens more accurately.Furthermore,the mechanism for the diference in fatigue life between the 0.2 mm-thick specimen and other thicker specimens is elucidated.The Basquin equation-based model is presented as a potential way to evaluate the fatigue life of metals using small specimens.
文摘以3,4,9,10-苝四酸二酐为原料,通过在分子两端芳香环(bay位)分别连接2-甲氧基乙氧基和硝基,合成了两个不对称苝酰亚胺小分子N,N'-二(2-乙基己基)-1-(2-甲氧基乙氧基)-7-硝基-3,4,9,10-苝四羧酸二酰亚胺(Ⅲ)和N,N'-二(2-乙基己基)-1-(2-甲氧基乙氧基)-6,7-二硝基-3,4,9,10-苝四羧酸二酰亚胺(Ⅳ)。利用1HNMR,13CNMR和MS对其结构进行了表征。通过密度泛函理论计算优化了分子空间立体构象、扭曲结构和电子云分布;紫外-可见吸收光谱结果表明,Ⅲ和Ⅳ的最大吸收峰红移至559和572 nm,半峰宽变宽,为104和112 nm;经循环伏安(CV)测试估算,分子Ⅲ和Ⅳ的HOMO、LUMO能级分别为-5.85、-3.55 e V和-5.87、-3.62 e V;在相对湿度为50%的大气环境中,Ⅲ和Ⅳ分别与窄带隙聚合物(PTB7-Th)共混构建了有机太阳能电池器件,Ⅲ与PTB7-Th共混时对应的短路电流密度Jsc=3.6 m A/cm2,开路电压Voc=0.30 V,填充因子FF=0.40,光电转换效率η=0.42%;Ⅳ与PTB7-Th共混时对应的Jsc=4.00 m A/cm2,Voc=0.25 V,FF=0.41,η=0.40%。
