On distance-regular Cayley graphs of generalized dicyclic groups

Let G be a generalized dicyclic group with identity 1. An inverse closed subset S of $G?\{1\}$ is called minimal if $〈S〉=G$ and there exists some $s\in S$ such that $〈S?\{s,s^{?1}\}〉\ne G$. In this paper, we characterize distance-regular Cayley graphs $\mathrm{Cay}(G,S)$ of G under the condition that S is minimal.     

零维到三维结构中三核铜自旋阻挫簇单元的磁构关系和反对称交换

量子自旋液体是最近几年刚被人们证实除铁磁体、反铁磁体之外的第三种磁性类型,因其有望解释高温超导的运行机制、改变计算机硬盘信息存储方式而在物理、材料等领域备受关注。自旋阻挫作为量子自旋液体的最小单元可能是解开量子自旋液体诸多问题的钥匙,所以在磁学、电学研究领域再一次成为人们研究的热点。基于文献报道的三核铜配合物[Cu3(μ3-OH)(μ-OPz)3(NO3)2(H2O)2]·CH3OH(1),我们合成了三维金属有机框架配合物{[Ag(HOPz)Cu3(μ3-OH)(NO3)3(OPz)2Ag(NO3)]·6H2O}n(2)(HOPz=甲基(2-吡嗪基)酮肟),并从自旋阻挫的角度对二者磁性质进行对比和详细分析。磁化率数据表明自旋间有很强的反铁磁相互作用和反对称交换。通过包含各向同性和反对称交换的哈密顿算符对两者磁学数据进行拟合并研究其磁构关系,所获最佳拟合参数为:配合物1:Jav=-426 cm^-1,g⊥=1.83,g∥=2.00;配合物2:Jav=-401 cm^-1,g⊥=1.85,g∥=2.00。     

On Generalized Douglas–Weyl(α, β)-Metrics

In this paper, we study generalized Douglas–Weyl(α, β)-metrics. Suppose that a regular(α, β)-metric F is not of Randers type. We prove that F is a generalized Douglas–Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover, by ignoring the regularity, if F is not a Berwald metric, then we find a family of almost regular Finsler metrics which is not Douglas nor Weyl. As its application, we show that generalized Douglas–Weyl square metric or Matsumoto metric with isotropic mean Berwald curvature are Berwald metrics.     

Could chroman-4-one derivative be a better inhibitor of PTR1? – Reason for the identified disparity in its inhibitory potency in Trypanosoma brucei and Leishmania major

Most notable Kinetoplastids are of the genus Trypanosoma and Leishmania, affecting several millions of humans in Africa and Latin America. Current therapeutic options are limited by several drawbacks, hence the need to develop more efficacious inhibitors. An investigation to decipher the mechanism behind greater inhibitory potency of a chroman-4-one derivative (compound 1) in Trypanosoma brucei pteridine reductase 1 (TbPTR1) and Leishmania major pteridine reductase 1 (LmPTR1) was performed. Estimation of ΔG_bind revealed that compound 1 had a greater binding affinity in TbPTR1 with a ΔG_bind value of −49.0507 Kcal/mol than −29.2292 Kcal/mol in LmPTR1. The ΔGbind in TbPTR1 were predominantly contributed by “strong” electrostatic energy compared to the “weak” van der Waals in LmPTR1. In addition to this, the NADPH cofactor contributed significantly to the total energy of TbPTR1. A characteristic weak aromatic π interaction common in PTR1 was more prominent in TbPTR1 than LmPTR1. The consistent occurrence of high-affinity conventional hydrogen bond interactions as well as a steady interaction of crucial active site residues like Arg14/Arg17, Ser95/Ser111, Phe97/Phe113 in TbPTR1/LmPTR1 with chroman-4-one moiety equally revealed the important role the moiety played in the activity of compound 1. Overall, the structural and conformational analysis of the active site residues in TbPTR1 revealed them to be more rigid than LmPTR1. This could be the mechanism of interaction TbPTR1 employs in exerting a greater potency than LmPTR1. These findings will further give insight that will be assistive in modifying compound 1 for better potency and the design of novel inhibitors of PTR1.     

Inner derivations and norm equality

We characterize when the norm of the sum of two bounded operators on a Hilbert space is equal to the sum of their norms.

     

An M/G/1 Retrial Queueing System with Two-Phase Service and Preemptive Resume

An M/G/1 retrial queueing system with additional phase of service and possible preemptive resume service discipline is considered. For an arbitrarily distributed retrial time distribution, the necessary and sufficient condition for the system stability is obtained, assuming that only the customer at the head of the orbit has priority access to the server. The steady-state distributions of the server state and the number of customers in the orbit are obtained along with other performance measures. The effects of various parameters on the system performance are analysed numerically. A general decomposition law for this retrial queueing system is established.     

矩阵方程A^TXB=C的正定和半正定解

给出了矩阵方程Ａ＾ＴＸＢ＝Ｃ在正定和半正定矩阵类中有解的充要条件及解的一般表达式。     

Recursive partition and amalgamation with the exponential family: Theory and applications

The theory of tree-growing (RECPAM approach) is developed for outcome variables which are distributed as the canonical exponential family. The general RECPAM approach (consisting of three steps: recursive partition, pruning and amalgamation), is reviewed. This is seen as constructing a partition with maximal information content about a parameter to be predicted, followed by simplification by the elimination of ‘negligible’ information. The measure of information is defined for an exponential family outcome as a deviance difference, and appropriate modifications of pruning and amalgamation rules are discussed. It is further shown how the proposed approach makes it possible to develop tree-growing for situations usually treated by generalized linear models (GLIM). In particular, Poisson and logistic regression can be tree-structured. Moreover, censored survival data can be treated, as in GLIM, by observing a formal equivalence of the likelihood under random censoring and an appropriate Poisson model. Three examples are given of application to Poisson, binary and censored survival data.     

Bilateral generating functions and operational methods

Bilateral generating functions are those involving products of different types of polynomials. We show that operational methods offer a powerful tool to derive these families of generating functions. We study cases relevant to products of Hermite polynomials with Laguerre, Legendre and other polynomials. We also propose further extensions of the method which we develop here.