The degree of maps of free G-manifolds

Suppose that M and N are orientable, closed, connected manifolds with free actions of compact Lie groups G and H of the same dimension, and suppose that u : G → H is a homomorphism. We study the degree of maps f : M → N that are “equivariant up to u”. For abelian actions and for a power map such maps satisfy the condition f(λx) = λ ^r x. To Albrecht Dold and Edward Fadell     

Zirconium‐chelate and mono‐η‐ cyclopentadienyl zirconium‐chelate/ methylalumoxane systems as soluble Ziegler–Natta olefin polymerization catalysts

Zirconium‐chelate and mono‐η‐cyclopentadienyl zirconium‐chelate complexes were tested as ethene and propene polymerization catalysts in combination with methylalumoxane (MAO) as a co‐catalyst: in particular (acac) _nZrCl_4−n (1a–c) (acac = acetylacetonato), (dbm) _nZrCl_4−n (2a–2c) (dbm = dibenzoylmethanato = 1,3‐diphenylpropanedionato) (n = 2–4) and (dbm)₂ZrCl₂(thf) (3) (thf = tetrahydrofuran), (η‐C₅H₅)[H₂B (C₃H₃N₂)₂]ZrCl₂ (4), (η‐C₅H₅)[HB (C₃H₃N₂)₃] ZrCl₂ (5) and (η‐C₅H₅)[(Me₃SiN)₂ CPh]ZrCl₂ (6). Polymerization productivities comparable with the (η‐C₅H₅)₂ZrCl₂ reference system were observed towards ethene for all of the above complexes. In addition, compound 6 showed some minor polymerization activity towards propene. Ethylalumoxane or isobutylalumoxane did not exhibit a co‐catalytic activity for these chelate complexes; in combination with MAO these higher alumoxanes were even found to be deactivating ⁹¹Zr NMR data are reported for 1b, 1c, 4 and 5. Copyright © 2000 John Wiley & Sons, Ltd.     

Design,synthesis and biological evaluation of 5-(2-(4-(substituted benzo[d]isoxazol-3-yl)piperazin-1-yl)acetyl)indolin-2-one and 5-(2-(4-substitutedpiperazin-1-yl)acetyl)indolin-2-one analogues as novel anti-tubercular agents

A series of thirty-six novel 5-(2-(4-(benzo[d]isoxazol-3-yl)piperazin-1-yl)acetyl)indolin-2-one and 5-(2-(4-substitutedpiperazin-1-yl)acetyl)indolin-2-one analogues were synthesized, characterized and screened for their in vitro anti-tubercular activity against Mycobacterium tuberculosis H37Rv strain. These compounds exhibited minimum inhibitory concentration between 1.56 and 50 μg/mL. Among these derivatives, compounds 10c, 10d, 10j, 10o and 10v (MIC 6.25 μg/mL) displayed moderate activity, while compounds 10e, 10l, 10q, 10w,10x, 12d, 12e and 12i (MIC 3.12 μg/mL) showed good anti-tubercular activity and compounds 10f, 10k, 10p, 10r, 12f, 12j and 12k (MIC 1.56 μg/mL) exhibited excellent anti-tubercular activity. In addition, MTT assay was accomplished on the active analogues of the series against mouse macrophage (RAW 264.7) cells to evaluate the cytotoxic effect of the newly synthesized compounds and selectivity index of the compounds was determined.     

时效温度对890MPa级含铜钢组织与性能的影响

根据纳米析出强化机制,设计了一种屈服强度为890MPa的超高强海洋工程用钢——NEU890钢.在相同固溶条件下,研究了时效温度对NEU890钢显微组织、室温拉伸性能、-40℃ Charpy冲击功的影响.用透射电子显微镜分析纳米级析出相分布,并计算出其强度贡献值.结果表明,固溶态试样屈服强度为852MPa,500℃时效屈服强度达到峰值1026MPa,呈现典型时效析出强化特征.NEU890钢的脆性时效温度区间为300~500℃.当时效温度为550~600℃时,NEU890钢的屈服强度为994~910MPa,-40℃冲击功为108~166J,可满足EQ91钢拉伸和冲击性能指标要求.     

Electronic structure of dysprosium silicide films grown on a Si(1 1 1) surface

The thickness-dependent electronic structures of Dy silicide films grown on a Si(1 1 1) surface have been investigated by angle-resolved photoelectron spectroscopy. Two (1×1) periodic bands, both of them cross the Fermi level, have been observed in the silicide films formed by Dy coverages of 1.0 monolayer and below, and more than five () periodic bands have been observed in thicker films. Taking the () periodic structure of Dy atoms in the submonolayer silicide film into account, the periodicity of the two metallic bands indicate that they mainly originate from the orbitals of Si atoms, which form a (1×1) structure. Of the () periodic bands observed in thick films, four of them are well explained by the folding of the (1×1) bands into a () periodicity. Regarding the other band, the three () periodic bands would originate from the electronic states related to the inner Si layers that form a () structure, and the one observed in the 3.0 ML film only might originate from the electron located at the interface between bulk Si and the Dy silicide film.     

A PDE approach to regularity of solutions to finite horizon optimal switching problems

We study optimal 2-switching and n-switching problems and the corresponding system of variational inequalities. We obtain results on the existence of viscosity solutions for the 2-switching problem for various setups when the cost of switching is non-deterministic. For the n-switching problem we obtain regularity results for the solutions of the variational inequalities. The solutions are C^1,1-regular away for the free boundaries of the action sets.     

Measuring the coupled risks: A copula-based CVaR model

Integrated risk management for financial institutions requires an approach for aggregating risk types (such as market and credit) whose distributional shapes vary considerably. The financial institutions often ignore risks’ coupling influence so as to underestimate the financial risks. We constructed a copula-based Conditional Value-at-Risk (CVaR) model for market and credit risks. This technique allows us to incorporate realistic marginal distributions that capture essential empirical features of these risks, such as skewness and fat-tails while allowing for a rich dependence structure. Finally, the numerical simulation method is used to implement the model. Our results indicate that the coupled risks for the listed company’s stock maybe are undervalued if credit risk is ignored, especially for the listed company with bad credit quality.