Σ-原子能级的理论计算与分析

通过对Σ-原子的理论分析,数值求解了相应的Dirac方程,得到 了一组Σ-原子的能级值,与实验数据相当吻合;其结果连同K-原子的情况支持了Batty 光学模型势在奇异原子中应用的正确性,进而表明核子间的强相互作用力为吸引力.     

Primary abelian <Emphasis Type="Italic">n</Emphasis>-Σ-groups

We prove the following theorem: Any abelian p-group is an n-Σ-group which is a strong ω-elongation of a totally projective group by a p ^ω+n -projective group precisely when it is totally projective. In particular, each p-torsion p ^ω+n -projective n-Σ-group is a direct sum of countable p-groups of length not exceeding ω + n and vice versa. These two claims generalize our recent results in [6] and [7]. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 155–162, April–June, 2007.     

NO(3+1)共振增强的多光子离化谱

用皮秒脉冲高功率Nd∶YAG激光器抽运的光学参量发生/放大器作激发源,获得了NO分子在420～500 nm波长范围内的多光子离化谱,光谱图呈现分离谱的特征,表明在该波长区间NO分子以多光子共振方式离化。离化信号随激光强度的近四次方变化关系表明,在420～500 nm波长范围内NO分子吸收4个光子而离化。通过对谱线的标识,首次分离出NO分子以E 2Σ激发电子态为中间共振态的(3+1)多光子离化光谱序列,由谱线序列峰值波长得到NO分子E 2Σ电子态的振动常数,从而实现了采用多光子离化技术对该态能级结构的实验研究。     

On Fitting Ideals of Certain étale K-groups

Let F be an Abelian number field and S the set of primes of F that are either ramified or over p, with p an odd prime. In this paper we compute the (first) Fitting ideal of K _2i–2 ^ét (O _F ^S () for i 2, where O _F ^S is the ring of S-integers of F and is a character of Gal(F/) of order prime to p different from the ith power of the Teichmüller character. This Fitting ideal proves to be principal and generated by a Stickelberger element.     

K-Theory for the Integer Heisenberg Groups

We give a closed formula for topological K-theory of the homogeneous space N/, where is the standard integer lattice in the simply connected Heisenberg Lie group N of dimension 2n+1, n . The main tools in our calculations are obtained by computing diagonal forms for certain incidence matrices that arise naturally in combinatorics.     

On Cyclotomic Numbers and the Reduction Map for the K-Theory of the Integers

We apply the recently proven compatibility of Beilinson and Soulé elements in K-theory to investigate density of rational primes p, for which the reduction map K _2n+1() K_{2n+1}(F_p)is nontrivial. Here n is an even, positive integer and F_p denotes the field of p elements. In the proof we use arithmetic of cyclotomic numbers which come from Soulé elements. Divisibility properties of the numbers are related to the Vandiver conjecture on the class group of cyclotomic fields. Using the K-theory of the integers, we compute an upper bound on the divisibility of these cyclotomic numbers.     

Quasi-Permutation Representations of Metacyclic p-Groups With Non-Cyclic Center

By a quasi-permutation matrix we mean a square matrix over the complex field with non-negative integral trace. Thus every permutation matrix over is a quasi-permutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q (G) denote the minimal degree of a faithful representation of G by quasi-permutation matrices over the rational field , and let c(G) be the minimal degree of a faithful representation of G by complex quasi-permutation matrices. In this paper we will calculate c(G), q(G), and p(G), where G is a metacyclic p-group with non-cyclic center and p is either 2 or an odd prime number.AMS Subject Classification (2000) 20C15     

Unusual Pathways of Triplet State Dynamic Relaxation in Meso-Aryl-Substituted Porphyrins and Their Chemical Dimers at 295 K

It was found that mono- and di-meso-phenyl substitution in octaethylporphyrins (OEP)and their chemical dimers with the phenyl ring as a spacer manifests itself in the dramatical shortening of T₁ state lifetimes at 295 K (from 1.5 ms down to 2–5 s in degassed toluene solutions). On the other hand, this substitution does not influence spectral-kinetic parameters of S₀ and S₁ states. The enhancement of the T₁ state non-radiative deactivation is explained by torsional librations of the phenyl ring around a single C-C bond in sterically encumbered OEP molecules leading to non-planar dynamic distorted conformations in the excited T₁ states. For these compounds with electron-accepting NO₂-groups in the meso-phenyl ring the strong non-radiative deactivation of S₁ and T₁ states (by 2–3 orders of magnitude) is observed upon the displacement of NO₂-group from para-to ortho-position of the phenyl ring. The S₁ state quenching is caused by the direct intramolecular electron transfer to low-lying CT state of the radical ion pair (the normal region, non-adiabatic case presumably, V = 130–190 cm^–1 in dimethylformamide). The additional deactivation of the T₁ state is connected with thermally activated transitions to upper-lying CT states as well as the strengthening of intersystem crossing probabilities.     

A monotone version of the Sokolov property and monotone retractability in function spaces

We introduce the monotone Sokolov property and show that it is dual to monotone retractability in the sense that X   is monotonically retractable if and only if _Cp(X)$C_p(X)$ is monotonically Sokolov. Besides, a space X   is monotonically Sokolov if and only if _Cp(X)$C_p(X)$ is monotonically retractable. Monotone retractability and monotone Sokolov property are shown to be preserved by R$\mathbb{R}$-quotient images and _Fσ$F_{\sigma }$-subspaces. Furthermore, every monotonically retractable space is Sokolov so it is collectionwise normal and has countable extent. We also establish that if X   and _Cp(X)$C_p(X)$ are Lindelöf Σ-spaces then they are both monotonically retractable and have the monotone Sokolov property. An example is given of a space X   such that _Cp(X)$C_p(X)$ has the Lindelöf Σ-property but neither X   nor _Cp(X)$C_p(X)$ is monotonically retractable. We also establish that every Lindelöf Σ-space with a unique non-isolated point is monotonically retractable. On the other hand, each Lindelöf space with a unique non-isolated point is monotonically Sokolov.