Asymptotic analysis and estimates of blow‐up time for the radial symmetric semilinear heat equation in the open‐spectrum case

We estimate the blow‐up time for the reaction diffusion equation u_t=Δu+ λf(u), for the radial symmetric case, where f is a positive, increasing and convex function growing fast enough at infinity. Here λ>λ^*, where λ^* is the ‘extremal’ (critical) value for λ, such that there exists an ‘extremal’ weak but not a classical steady‐state solution at λ=λ^* with ∥w(?, λ)∥_∞→∞ as 0<λ→λ^*?. Estimates of the blow‐up time are obtained by using comparison methods. Also an asymptotic analysis is applied when f(s)=e^s, for λ?λ^*?1, regarding the form of the solution during blow‐up and an asymptotic estimate of blow‐up time is obtained. Finally, some numerical results are also presented. Copyright © 2007 John Wiley & Sons, Ltd.     

质量缺陷整改中异常心态及监施关系分析

分析了质量缺陷整改中常见的几种异常心态及其危害，阐述了正确合理的监理与施工方的关系以及监理与承包商的关系。     

Influence of surface energy and relative humidity on AFM nanomechanical contact stiffness

The effects of surface functionality and relative humidity (RH) on nanomechanical contact stiffness were investigated using atomic force acoustic microscopy (AFAM), a contact scanned-probe microscopy (SPM) technique. Self-assembled monolayers (SAMs) with controlled surface energy were studied systematically in a controlled-humidity chamber. AFAM amplitude images of a micropatterned, graded-surface-energy SAM sample revealed that image contrast depended on both ambient humidity and surface energy. Quantitative AFAM point measurements indicated that the contact stiffness remained roughly constant for the hydrophobic SAM but increased monotonically for the hydrophilic SAM. To correct for this unphysical behavior, a viscoelastic damping term representing capillary forces between the tip and the SAM was added to the data analysis model. The contact stiffness calculated with this revised model remained constant with RH, while the damping term increased strongly with RH for the hydrophilic SAM. The observed behavior is consistent with previous studies of surface energy and RH behavior using AFM pull-off forces. Our results show that surface and environmental conditions can influence accurate measurements of nanomechanical properties with SPM methods such as AFAM.     

Working group report: Flavor physics and model building

This is the report of flavor physics and model building working group at WHEPP-9. While activites in flavor physics have been mainly focused on B-physics, those in model building have been primarily devoted to neutrino physics. We present summary of working group discussions carried out during the workshop in the above fields, and also briefly review the progress made in some projects subsequently.     

Dielectric relaxation and aging effect in interpenetrating network polymers of poly(urethane)-poly(methyl methacrylate)

The permittivity and loss of poly(methyl methacrylate) (PMMA) network crosslinked with trimethylol-1,1,1 propane and its interpenetrating network polymers with 10, 34, and 50% (by weight) poly(urethane) have been measured from 100 to 400 K over a frequency range of 12 to 1 × 10⁵ Hz. Two relaxation processes, γ and β, are observed in the PMMA network, and a third process, α_pu, in the 10% poly(urethane) IPN. At higher concentrations of poly(urethane), the γ process is removed from the temperature-frequency range of our study. Crosslinking in pure PMMA slows the segmental motions involved in the β process and raises its activation energy. Physical aging of the 10 wt% poly(urethane)-PMMA causes its γ process to become indiscernible and the α_pu process to become better resolved. A discussion of these results in terms of local regions of segmental motion is provided.     

1.2 Anorganische analyse

Ohne Zusammenfassung     

Isobar separation at FRS-ESR – a development towards pure isomeric stored beams

One important goal of the ILIMA project at FAIR is the study of masses and decay properties of relativistic isomeric beams stored and cooled in the planned storage-ring complex. A new scheme is described, where a storage-cooler ring is used for high-resolution mass separation. Experimental results on the separation of the isobaric pair ¹⁴⁰Pr-¹⁴⁰Ce are presented. P. Beller, deceased.     

Stable atomic structure and magnetism of Pt–Cr binary surface alloys on Pt(0 0 1): First-principle calculations

The possibility of Pt–Cr surface alloys formation on Pt(0 0 1) was investigated and their magnetism was calculated by the full-potential linearized augmented plane wave (FLAPW) method with eight different atomic configurations. The most stable structure was calculated to be the Pt-segregated L1₂ ferromagnetic surface alloy. A₃B types (L1₂ or D0₂₂) were more stable compared to AB types (L1₀). It implies that the A₃B type surface alloys may be formed when depositing a monolayer of Cr on Pt(0 0 1). It was found from the total energy calculations that there exists a strong tendency of the Pt segregation. The segregation further stabilizes the surface alloy significantly. The work function of the most stable surface alloy was calculated to be 6.02 eV and the magnetic moment of the surface Cr was much enhanced to 3.3 μ_B. It is a quite interesting finding that the coupling between Cr and Pt atoms on the surface plane is ferromagnetic in the Pt-segregated L1₂ ferromagnetic surface alloy, while the coupling is antiferromagnetic in the bulk.     

How to Exhibit Toroidal Maps in Space

Steinitz's theorem states that a graph is the 1-skeleton of a convex polyhedron if and only if it is 3-connected and planar. The polyhedron is called a geometric realization of the embedded graph. Its faces are bounded by convex polygons whose points are coplanar. A map on the torus does not necessarily have such a geometric realization. In this paper we relax the condition that faces are the convex hull of coplanar points. We require instead that the convex hull of the points on a face can be projected onto a plane so that the boundary of the convex hull of the projected points is the image of the boundary of the face. We also require that the interiors of the convex hulls of different faces do not intersect. Call this an exhibition of the map. A map is polyhedral if the intersection of any two closed faces is simply connected. Our main result is that every polyhedral toroidal map can be exhibited. As a corollary, every toroidal triangulation has a geometric realization.