Benchmark calculations of the complete configuration-interaction limit of Born-Oppenheimer diagonal corrections to the saddle points of isotopomers of the H + H2 reaction

We present a detailed ab initio study of the effect that the Born-Oppenheimer diagonal correction (BODC) has on the saddle-point properties of the H3 system and its isotopomers. Benchmark values are presented that are estimated to be within 0.1 cm(-1) of the complete configuration-interaction limit. We consider the basis set and correlation treatment requirements for accurate BODC calculations, and both are observed to be more favorable than for the Born-Oppenheimer energies. The BODC raises the H + H2 barrier height by 0.1532 kcal/mol and slightly narrows the barrier--with the imaginary frequency increasing by approximately 2%.     

The Hausmann-Weinberger 4-manifold invariant of abelian groups

The Hausmann-Weinberger invariant of a group is the minimal Euler characteristic of a closed orientable 4-manifold with fundamental group . We compute this invariant for finitely generated free abelian groups and estimate the invariant for all finitely generated abelian groups.

     

Convergent Rates for Solutions of Dirichlet Problems of Quasilinear Equations

The convergent rates for bounded solutions of Dirichlet problemsof quasilinear elliptic (possibly degenerate) equations in slab-likedomains are derived in terms of the convergent rates of theboundary data and the coefficients of the operator. The equationsconsidered include the prescribed mean curvature equation. Theresults are proved by constructing a family of local barrierfunctions based on the structure of the operator and the convergentrate of the boundary data. The construction of local barriersis inspired by early work due to Finn and Serrin that is relatedto the minimal surface equation.     

在不同温度下球墨鑄铁的冲击性能

本文描述高温冲击实验的技术,以及由-85℃至1070℃的铸态和锻造后的球墨铸铁的冲击性能。研究结果找到了基体主要为铁素体的球墨铸铁的两个变脆温度范围(-20℃以下和550℃至700℃之间)和一个比较具有韧性的温度范围(850℃与1050℃之间)。在这些温度范围内,曾考查试样的断口情况和断裂时的弯曲角度,并与其基体组织的变化相联系,进行讨论。最后,本文指出研究结果在球墨铸铁的应用上所起的作用,以及在球墨铸铁热加工时对于选择热加工温度的意义。     

Study of the centrally produced ωρ0 and ωω systems inpp interactions at 300 GeV/c

We have performed a search for vector-vector final states centrally produced in proton proton interactions at 300 GeV/c using the CERN Ω spectrometer. Evidence is found for ωρ⁰ production in the reactionpp→p _f (2π⁺2π^?2π⁰)p _s and for ωω production in the reactionpp→p _f (2π⁺2π^?2π⁰)p _s . However no evidence is found for ωø production in the reactionpp→p _f (K ⁺ K ^?π⁺π^?π⁰)p _s .     

Understanding anomalous delays in a model of intracellular calcium dynamics

In many cell types, oscillations in the concentration of free intracellular calcium ions are used to control a variety of cellular functions. It has been suggested [J. Sneyd et al., "A method for determining the dependence of calcium oscillations on inositol trisphosphate oscillations," Proc. Natl. Acad. Sci. U.S.A. 103, 1675-1680 (2006)] that the mechanisms underlying the generation and control of such oscillations can be determined by means of a simple experiment, whereby a single exogenous pulse of inositol trisphosphate (IP(3)) is applied to the cell. However, more detailed mathematical investigations [M. Domijan et al., "Dynamical probing of the mechanisms underlying calcium oscillations," J. Nonlinear Sci. 16, 483-506 (2006)] have shown that this is not necessarily always true, and that the experimental data are more difficult to interpret than first thought. Here, we use geometric singular perturbation techniques to study the dynamics of models that make different assumptions about the mechanisms underlying the calcium oscillations. In particular, we show how recently developed canard theory for singularly perturbed systems with three or more slow variables [M. Wechselberger, "A propos de canards (Apropos canards)," Preprint, 2010] applies to these calcium models and how the presence of a curve of folded singularities and corresponding canards can result in anomalous delays in the response of these models to a pulse of IP(3).