Lehmer序列中的平方数

设V_n(R,Q)表示参数为R和Q的Lehmer伴随序列,如果R和Q为互素奇数且D=R-4Q>0,我们找出了满足Q_n(R,Q)或nQ_n(R,Q)是平方数的所有奇数n,这里Q_n(R,Q)R~(1/2)=V_n(R,Q)。     

Ab initio study of sodium intercalation into metal oxides

Using the full-potential linearized augmented plane wave (FP-LAPW) method, we have studied the effect of chemistry on the average intercalation voltage (AIV) caused by the Na ions intercalating into transition metal oxides. The effect of transition metal was systematically studied by varying M=Co, Ni and Mn in NaMO₂ and fixing the α-NaFeO₂ layered structure. The effect of the guest atoms into the host material is discussed in terms of the structural and electronic properties. Comparatively to Li intercalation, a significant electron transfer towards transition metal was found. This observation suggests that the transition metal contribute to the AIV determination and confirms the common assumption that intercalated electron reduces M⁴⁺ to M³⁺.     

卤代对苝醌类光敏剂光敏活性影响的量子化学研究

以一种新型的醌类光敏剂—菌生素 (HMB)为模型化合物 ,利用量子化学从头算HF/ 6 31G和含时密度泛函TD B3LYP/ 6 31G方法计算研究了卤代作用对醌类光敏剂分子性质和光敏活性的影响 .结果发现 ,卤代作用降低了HMB母体的HOMO和LUMO能级 (EHOMO和ELUMO)及其差值△E ,随卤族元素从上到下 ,EHOMO和ELUMO呈增大趋势 ,而△E呈减小趋势 ,使得分子激发光谱有不同程度的红移 ,在增加PQP三重态量子产率的同时降低了分子最低三重激发态的能量 ,两种作用相互抵消 ,使得卤代物的 1O2 量子产率与母体相似 ;增加了分子的绝热电子亲合势 ,使分子产生O2 -的能力下降 ;卤原子的引入 ,降低了HMB母体分子内氢键的强度 ,同时使顺式构型的分子内质子传递势垒增大 ,而使反式构型势垒减小 .     

平台框架部件刚度的简化计算

利用卡氏定理,对惯性平台框架部件的刚度进行简化计算。通过微机编程获得数据,为结构设计初期合理选取结构参数提供参考。     

Software Cold Test Simulation of Coupled Cavity Slow-Wave Structure in Millimeter Wave TWT

In this paper, the software cold-test simulation method to obtain RF dispersion, interaction impedance by MAFIA software is discussed considering effect of the conducting barrel in the millimeter-wave TWT. The dispersion simulation result is obtained more consistent with experiment data than the method that ignoring effect of the conducting barrel. By changing the structure parameter, high frequency characteristic will be affected. The change relationship of high frequency characteristic with structure parameter is obtained. The different calculation methods of the interaction impedance are discussed. These results are received and are consistent with experiment data.     

Elliptic fibers over non-perfect residue fields

Kodaira and Néron classified and described the geometry of the special fibers of the Néron model of an elliptic curve defined over a discrete valuation ring with a perfect residue field. Tate described an algorithm to determine the special fiber type by manipulating the Weierstrass equation. In the case of non-perfect residue fields, we discover new fiber types which are not on the Kodaira-Néron list. We describe these new types and extend Tate's algorithm to deal with all discrete valuation rings. Specifically, we show how to translate a Weierstrass equation into a form where the reduction type may be easily determined. Having determined the special fiber type, we construct the regular model of the curve with explicit blow-up calculations. We also provide tables that serve as a simple reference for the algorithm and which succinctly summarize the results.     

Five-step phase-shifting algorithms with unknown values of phase shift

The presented work offers new algorithms for phase evaluation in interferometric measurements. Several phase-shifting algorithms with an arbitrary but constant phase-shift between captured intensity frames are proposed. These phase calculation algorithms need to measure five frames of the intensity of the interference field. The algorithms are similarly derived as so called Carré algorithm. The phase evaluation process then does not depend on the linear phase shift errors. Furthermore, the detailed analysis of the algorithms with respect to most important factors, which affect interferometric measurements, is carried out. It is also studied the dependency of the evaluation algorithms on the phase shift values, and the proposed phase calculation algorithms are compared with respect to the resulting phase errors. The influence of most important factors in the measurement and evaluation process was simulated as systematic and random errors using a proposed mathematical model.     

Functional analysis proofs of Abel's theorems

We give alternative proofs to the classical theorems of Abel, using the concept of Berezin symbol.