Conservation Laws of K（m,n） and mK（m,n） Equations

Based on the rank analysis method, algorithmization idea, and symbolic computation, in this paper we have presented a method to construct the conservation laws for nonlinear evolution equations. The polynomial conservation laws for K (n 2,n) equations and mK (m,n) equations are found by using of this approach and some new results have been obtained.     

New Compacton Solutions of Nonlinearly Dispersive R(m, n) Equations

In this paper, we establish exact solutions for the R(m,n) equations by using an sn-cn method. As a result, abundant new compactons, i.e. solitons with the absence of infinite wings, new type of Jacobi elliptic function, solitary wave and periodic wave solutions, of this equation are obtained with minimal calculations. The properties of the R(m,n) equations are shown in figures.     

New Symmetry Reductions,Dromions—Like and Compacton Solutions for a 2D BS（m,n） Equations Hierarchy with Fully Nonlinear Dispersion

We have found two types of important exact solutions,compacton solutions,which are solitary waves with the property that after colliding with their own kind,they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction,in the (1 1)D,(1 2)D and even (1 3)D models,and dromion solutions (exponentially decaying solutions in all direction) in many (1 2)D and (1 3)D models.In this paper,symmetry reductions in (1 2)D are considered for the break soliton-type equation with fully nonlinear dispersion (called BS(m,n) equation)ut b(u^m)xxy 4b(u^n δx^-1uy)x=0,which is a generalized model of (1 2)D break soliton equation ut buxxy 4buuy 4buxδx^-1uy=0,by using the extended direct reduction method.As a result,six types of symmetry reductions are obtained.Starting from the reduction equations and some simple transformations,we obtain the solitary wavke solutions of BS(1,n) equations,compacton solutions of BS(m,m-1) equations and the compacton-like solution of the potential form (called PBS(3,2)) ωxt b(ux^m)xxy 4b(ωx^nωy)x=0.In addition,we show that the variable ∫^x uy dx admits dromion solutions rather than the field u itself in BS(1,n) equation.     

Hamiltonian Structures and Integrability of Frobenius Algebra-Valued (n,m)th KdV Hierarchy

We introduce Frobenius algebra ?-valued (n, m)^th KdV hierarchy and construct its bi-Hamiltonian structures by employing ?-valued pseudo-differential operators. As an illustrative example, the (1, 1)^th -valued case is analyzed in detail. Its Hamiltonian structures and recursion operator are derived. Infinitely many symmetries, conservation laws and explicit flow equations are also obtained.     

K(m,n)方程与B(m,n)方程的无穷序列新精确解

进一步研究了辅助方程法,给出了几种常用辅助方程的新解、B(a|¨)cklund变换和解的非线性叠加公式.在此基础上,根据m和n的不同情况,利用变换和直接积分相结合的方法,获得了K(m,n)方程与B(m,n)方程的无穷序列新精确解.这里包括无穷序列光滑孤立子解、无穷序列尖峰孤立子解和无穷序列紧孤立子解.     

Au_nAg_m~-(n+m=2～4)负离子团簇光脱附电子谱计算

利用密度泛函理论,通过几何优化和态密度计算了Au_nAg_m^-（n+m=2～4）团簇的光电子光谱,结果显示只有Au₂Ag₂^-团簇的第一个峰发生了0.5eV的红移,而其它团簇的峰位置符合的很好,因此理论计算给出的团簇结构是合理的.     

AunAgm- (n+m=2～4)负离子团簇光脱附电子谱计算

利用密度泛函理论，通过几何优化和态密度计算了AunAgm- (n+m=2～4)团簇的光电子光谱，结果显示只有Au2Ag2-团簇的第一个峰发生了0.5eV的红移，而其它团簇的峰位置符合的很好，因此理论计算给出的团簇结构是合理的。     

14MeV中子引起的Pb(n,x)203Hg, W(n,x)182Ta和W(n,x)183Ta的核反应截面测量

利用活化方法测量了14MeV中子引起的Pb(n,x)²⁰³Hg,W(n,x)¹⁸²Ta和W(n,x)¹⁸³Ta的反应截面.中子注量由监督反应⁹³Nb(n,2n)^92mNb给出,中子能量利用⁹⁰Zr(n,2n)^89m+gZr和⁹³Nb(n,2n)^92mNb反应的截面比来确定.     

(p,n)和(p,2n)反应激发函数的系统学研究

从普朗克(Planck)黑体辐射公式和实验测量数据出发,采用唯象的方法提出了包含两个可调参量,入射质子能量从阈能到150MeV,靶核质量数在44相似文献   

替代反应法测量锕系核(n,f)和(n,xn)截面

对于某些中子反应截面,在直接测量上存在困难。为了获得那些对核能发展极其重要的核数据,人们提出替代反应法,即利用带电粒子代替中子进行反应,从而实现中子反应截面间接测量的方法。现有替代反应一般采用非弹激发、转移等周边反应,涉及的角动量远比中子反应的大,需要理论修正,这造成了一定的困难。有鉴于此,提出利用轻带电离子的俘获反应作为替代反应,其复合核自旋与中子反应的相当,有效避免了自旋修正的困难。根据这个思路,采用236U的（α,f）和（α,2n）反应作为替代反应,成功提取了239Pu的（n,f）和（n,2n）反应截面,与ENDFB7评价库数据在误差范围内符合较好,表明了替代反应法的优越性,可以在核数据测量中推广应用。There are always difficulties in the direct measurement of reactions induced by neutron, in order to obtain the neutron induced nuclear reaction data which are extremely important for nuclear power development, the surrogate reaction method, which uses charged particles instead of neutron, was proposed. The existing surrogate reaction method generally chooses peripheral reaction as the surrogate reaction, such as inelastic scattering excitation or transfer reaction. As a result, the angular momentum involved is always far larger than the neutron induced reaction, which causes difficulties in the theoretical calculation. Because of this, we proposed to use light-ion capture reaction as the surrogate reaction, the compound nuclei spin is similar with that of the neutron induced reaction, so that the difficulties in spin correction can be effectively avoided. Based on this idea, the 239Pu(n, f) and (n, 2n) reaction cross sections were successfully extracted using 236U(α,f) and (α,2n) reactions as the surrogate reaction. The results coincide well with the data of ENDFB7 within the error range, which shows that the surrogate reaction method has its own superiority, and it can be applied in the measurement of nuclear data.     

(LiH)_n(n=1～5)团簇与NH_3反应的密度泛函理论研究

采用密度泛函理论中杂化密度泛函B3LYP/6-311G(d,p)方法,对(LiH)_n(n=1～5)团簇结构进行计算,得到最稳定构型,并计算分析其与NH_3的反应机理.对各反应的中间体和过渡态进行频率分析和内禀反应坐标(IRC)计算,以验证反应的正确性.用QCISD/6-311G(d,p)方法计算各驻点的单点能,得到能量信息.结果表明:各反应所释放H_2中的两个氢原子分别来源于NH_3和(LiH)_n(n=1～5)团簇.弱化N-H键的作用有利于反应能垒的降低,是反应脱氢的关键.LiH团簇尺寸变化对反应能垒没有太大影响.     

(n,2n)反应同质异能态截面比

在统计理论及考虑角动量守恒的激子模型的基础上,运用Monte Carlo方法计算(n,20)反应同质异能态截面比. 以⁵⁹Co(n,2n)⁵⁸Co、⁹³Nb(n,2n)⁹²Nb和¹⁸¹Ta(n,2n)¹⁸⁰Ta的3个反应道为例,计算从其阈能到20MeV能区的同质异能态截面比,并和已有实验数据做了比较,结果符合较好. 这表明本文提供的方法是计算(n,2n)反应同质异能态截面比的一种有效方法.     

A (2+1)-dimensional KdV equation and mKdV equation: Symmetries,group invariant solutions and conservation laws

In this paper, we analyse the (2+1)-dimensional KdV and mKdV equations. Firtly, on the basis of the extended Lax pair, we derive these equations. Thereafter, the symmetry generators are determined followed by the application of the mCK method. Finally, conservation laws (including higher order) are studied.     

(CuIn)_n(n=1,2)小团簇的结构与稳定性的从头算理论研究

本文采用从头算理论MP2方法研究了合金团簇(Cu In)n(n=1,2)的结构和稳定性.计算得到的双原子分子Cu In几何参数、频率和解离能跟实验数据十分吻合.(Cu In)2团簇有五个稳定结构,基态结构是具有1A1/C2v对称性的蝴蝶结构,结合能为6.57 e V.将计算结果与同族元素体系(Cu Al)2和(Cu Tl)2对比,无论是在构型上,还是在电子特性上都有相似性.文中给出了(Cu In)2稳定构型的电子结合能能谱,希望在实验上得以验证.     

The geometry structures and electronic properties of Li_mB_n(m+n=12) clusters

The geometric structures, electronic properties, total and binding energies, harmonic frequencies, the highest occupied molecular orbital to the lowest unoccupied molecular orbital energy gaps, and the vertical ionization potential energies of small LimBn （m＋ n = 12） clusters were investigated by the density functional theory B3LYP with a 6-31 I＋G （2d, 2p） basis set. All the calculations were performed using the Gaussian09 program. For the study of the LimBn clusters, the global minimum of the B 12 cluster was chosen as the starting point and the boron atoms were gradually replaced by Li atoms. The results showed that as the number of Li atoms increased, the stability of the LimBn cluster decreased and the physical and chemical properties became more active. In addition, on average there was a large charge transfer from the Li atoms to the B atoms.     

Cross-section measurement for Ni(n,x)58(m+g)Co,Ni(n,x)60mCo,Ni(n,x)61Co and Ni(n,x)62mCo reactions induced by neutrons around 14MeV

The cross sections of Ni(n,x)58(m+g)CO,Ni(n,x)80mCo,Ni(n,x)61Co and Ni(n,x)62mCo reactions induced by neutrons around [14]MeV were measured in this work and calculated by a previously developed formula in this work.The neutron flux was determined using the monitor reaction 27Al(n,α)24Na and the neutron energies were measured with the method of cross-section ratios for 89Zr(n,2n)89Zr to 93Nb(n,2n)92mNbreactions.     

(KN3)n(n=1~5)团簇结构与性质的密度泛函理论研究

利用密度泛函理论B3LYP方法, 在6-311G*基组水平上对(KN3)n(n=1~5)团簇各种可能的结构进行了几何结构优化, 预测了各团簇的最稳定结构. 并对最稳定结构的振动特性、成键特性、电荷分布和稳定性性质进行了分析研究. 结果表明, 叠氮化合物中叠氮基以直线型存在, KN3团簇最稳定结构为直线型, (KN3)n(n=2~3)团簇最稳定结构为环形结构, (KN3)n(n=4~5)团簇最稳定结构是由(KN3)2团簇最稳定结构形成的平面和空间结构. N-N 键键长在0.1156~0.1196 nm之间, N-K键键长在0.2357~0.2927 nm之间; 叠氮基中间的N原子显示正电性, 两端的N原子显示负电性, 且与K原子直接作用的N原子负电性更强, 金属K原子与N原子之间形成离子键. (KN3)n(n=1~5)团簇最稳定结构的IR光谱最强振动峰均位于2180~2230 cm-1, 振动模式为叠氮基中N-N键的反对称伸缩振动. 稳定性分析显示, (KN3)3团簇具有相对较高的动力学稳定性.     

(KN3)n(n=1~5)团簇结构与性质的密度泛函理论研究

利用密度泛函理论B3LYP方法, 在6-311G*基组水平上对(KN3)n(n=1~5)团簇各种可能的结构进行了几何结构优化, 预测了各团簇的最稳定结构. 并对最稳定结构的振动特性、成键特性、电荷分布和稳定性性质进行了分析研究. 结果表明, 叠氮化合物中叠氮基以直线型存在, KN3团簇最稳定结构为直线型, (KN3)n(n=2~3)团簇最稳定结构为环形结构, (KN3)n(n=4~5)团簇最稳定结构是由(KN3)2团簇最稳定结构形成的平面和空间结构. N-N 键键长在0.1156~0.1196 nm之间, N-K键键长在0.2357~0.2927 nm之间; 叠氮基中间的N原子显示正电性, 两端的N原子显示负电性, 且与K原子直接作用的N原子负电性更强, 金属K原子与N原子之间形成离子键. (KN3)n(n=1~5)团簇最稳定结构的IR光谱最强振动峰均位于2180~2230 cm-1, 振动模式为叠氮基中N-N键的反对称伸缩振动. 稳定性分析显示, (KN3)3团簇具有相对较高的动力学稳定性.     

反应前驱物中n(S)∶n(Cd)对CdS薄膜结构及发光特性的影响

采用化学水浴以CdCl2·H2O、CS( NH2)2、NH4Cl、NH3·H2O和去离子水作为反应前驱物制备CdS纳米晶薄膜.采用扫描电镜( SEM)、X射线衍射(XRD)、透射光谱和稳态荧光光谱,研究了反应前驱物中不同的n(S)∶n(Cd)对所制备的CdS薄膜的形貌、结构和光学性能的影响.结果表明:反应前驱物中n(S...