Quantum Dynamics of Systems Connected by a Canonical Transformation

Quantum Hamiltonian systems corresponding to classical systems related by a general canonical transformation are considered. The differential equation to find the unitary operator, which corresponds to the canonical transformation and connects quantum states of the original and transformed systems, is obtained. The propagator associated with their wave functions is found by the unitary operator. Quantum systems related by a linear canonical point transformation are analyzed. The results are tested by finding the wave functions of the under-, critical-, and over-damped harmonic oscillator from the wave functions of the harmonic oscillator, free-particle system, and negative harmonic potential system, using the unitary operator to connect them, respectively.     

Sets of Type (a, b) From Subgroups of ΓL(1, pR)

In this paper k-sets of type (a, b) with respect to hyperplanes are constructed in finite projective spaces using powers of Singer cycles. These are then used to construct further examples of sets of type (a, b) using various disjoint sets. The parameters of the associated strongly regular graphs are also calculated. The construction technique is then related to work of Foulser and Kallaher classifying rank three subgroups of AL(1, p ^R). It is shown that the sets of type (a, b) arising from the Foulser and Kallaher construction in the case of projective spaces are isomorphic to some of those constructed in the present paper.     

阻尼落体运动的分析力学研究

应用分析力学理论和方法,研究了两种情况下的阻尼落体运动:1)阻力大小与速度成正比;2)阻力大小与速度平方成正比.对两种运动分别给出了等效的Lagrange函数和Hamilton函数,并应用第一积分法、点变换法、正则变换法和Ham-ilton-Jacobi方程法等不同的求解方法进行了求解.     

Cycloparaphenylene (CPP) series are molecular models for graphene armchair edges: trends in their aromaticity and cyclic conjugation are evaluated

Cycloparaphenylene ([r]CPP) and cyclacene ([r]CA) series are models for short carbon nanotubes. It is shown that armchair edges in model cycloparaphenylenes possess greater aromaticity and cyclic conjugation than do zigzag edges in model cyclacenes. According to Aihara’s bond resonance energy (BRE) and Bosanac and Gutman energy effect (ef) measurements, cycloparaphenylenes are twice as aromatic as cyclacenes. The general solution of all eigenvalues of all members of the cycloparaphenylene series is given. The origin of the recurrence of some eigenvalues are determined.     

Off‐diagonal and asymptotic results on the Ramsey number r(K2,m,K2,n)

An upper bound on the Ramsey number r(K_2,n‐s,K_2,n) where s ≥ 2 is presented. Considering certain r(K_2,n‐s,K_2,n)‐colorings obtained from strongly regular graphs, we additionally prove that this bound matches the exact value of r(K_2,n‐s,K_2,n) in infinitely many cases if holds. Moreover, the asymptotic behavior of r(K_2,m,K_2,n) is studied for n being sufficiently large depending on m. We conclude with a table of all known Ramsey numbers r(K_2,m,K_2,n) where m,n ≤ 10. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 252–268, 2003     

Generalized Linear Mixing Rule for Classical Coulomb Mixtures

It is shown that the Coulomb energy U of fully ionized ionic mixture can be written as a sum over partial contributions of ion species j: U = T Σ_j N_ju (Γ_j, y_j) (generalized linear mixing rule). In contrast to the traditional linear mixing rule U_LM = T Σ_j N_ju_OCP(Γ_j), applicable for strong coupling, the partial contribution function u depends not only on Γ_j, but on an additional parameter y_j = (r_D/r_D^OCP)² also. Here r_D and r_DOCP are Debye radiuses in the mixture and in the one component plasma at coupling parameter Γ_j, correspondingly. The parameter y_j does not depend on a specific composition of the mixture, but on the Debye radius r_D only, making function u (Γ_j, y_j) universal. The generalized linear mixing rule can be applied at any coupling parameter, if ionic mixture is not crystallized. It reproduces results of the Debye‐Hückel theory at weak coupling and traditional linear mixing rule at strong coupling. It can be easily applied to the complicated mixtures, composed of a large number of ion species. Since y_j is temperature independent, the Coulomb contribution to Helmholtz free energy of the mixture can also be presented in a form of generalized linear mixing rule (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

约束优化的一个改进的强次可行SQP算法及数值试验

本文对约束优化一个强次可行SQP算法进行改进,使之产生的迭代点在有限次迭代后全落入可行域;并对算法数值效果进行了大量的比较试验.     

变形核强阻尼碰撞中巨复合体系的形成和衰变

利用改进的量子分子动力学（ImQMD）模型研究了质心系入射能量为980 MeV时变形核238U＋238U体系的3种不同碰撞模式（腹对腹、尖对腹和尖对尖）下强阻尼反应过程中初级超重碎块的产生几率和复合体系的寿命、形状和拉长取向等性质,发现尖对腹碰撞模式有利于初级超重碎块的产生,还发现这种碰撞模式产生的复合体系有最长的寿命。     

离子交换-双氧水氧化法制备纳米CeO2晶体

以99.995% Ce(NO₃)₃和强碱性阴离子交换树脂为原料，采用离子交换-双氧水氧化法合成制备出纳米CeO₂晶体。并就离子交换反应中的Ce³⁺浓度、树脂加入速度和离子交换温度及H₂O₂加入速度等条件对CeO₂粒径的影响进行了探讨，得出了离子交换-双氧水氧化法制备纳米CeO₂晶体的最佳工艺条件。FTIR、TEM分析表明，离子交换法无需对合成的Ce(OH)₃溶胶进行洗涤即可去除NO₃^-、CO₃^2-等阴离子杂质，并用H₂O₂将该溶胶氧化，经真空干燥可制得粒径分布均匀，平均晶粒尺寸约3 nm，高纯度的CeO₂粉体。