n维广义函数的集值导数

本文将文献［9］中给出的一维广义函数的集值导数的某些结果，推广到n维情形，并给出一些与优化有关的其他结果．     

Experience Gained Using Second-Moment Closure Modeling for Transitional Flows Due to Boundary Layer Separation

This paper presents detailed information on the experience gained during the attempts to model a set of transitional flows due to boundary layer separation. These flows are developed on a flat plate with a semi-circular leading edge and they have been coded by the ERCOFTAC Special Interest Group on Transition, as T3L flows. Different freestream velocities and turbulence intensities configure these transitional flows and, by consequence, govern the transition mechanism, resulting in larger or smaller transitional regions. The modeling of the T3L flows has been performed by adopting a low-Reynolds number second-moment closure turbulence model. The results showed satisfactory agreement with the experimental measurements, although some difficulties regarding successful convergence have been faced. The final conclusion is that turbulence modeling can present quite accurate results for transitional flows without any additional use of ad-hoc modifications or additional equations based on various transition models and intermittency transport modeling.     

Critical points in the Bragg glass phase of a weakly pinned crystal of Ca3Rh4Sn13

New experimental data are presented on the scan rate dependence of the magnetization hysteresis width ΔM(H) (∞ critical current densityJ _c(H)) in isothermalMH scans in a weakly pinned single crystal of Ca₃Rh₄Sn₁₃, which displays second magnetization peak (SMP) anomaly as distinct from the peak effect (PE). We observe an interesting modulation in the field dependence of a parameter which purports to measure the dynamical annealing of the disordered bundles of vortices injected through the sample edges towards the destined equilibrium vortex state at a givenH. These data, in conjunction with the earlier observations made while studying the thermomagnetic history dependence inJ _c(H) in the tracing of the minor hysteresis loops, imply that the partially disordered state heals towards the more ordered state between the peak field of the SMP anomaly and the onset field of the PE. The vortex phase diagram in the given crystal of Ca₃Rh₄Sn₁₃ has been updated in the context of the notion of the phase coexistence of the ordered and disordered regions between the onset field of the SMP anomaly and the spinodal line located just prior to the irreversibility line. A multi-critical point and a critical point in the (H,T) region of the Bragg glass phase have been marked in this phase diagram and the observed behavior is discussed in the light of recent data on multi-critical point in the vortex phase diagram in a single crystal of Nb.     

三维Minkowski空间中的曲面及其可积性

利用可积系统的思想,借助三维Minkowski空间L3的矩阵模型,研究了L3中具有调和逆平均曲率的类空曲面和洛伦兹调和逆平均曲率类时曲面的可积性及其形变.     

Universal Overconvergence of Polynomial Expansions of Harmonic Functions

For each compact subset K of ^N let (K) denote the space of functions that are harmonic on some neighbourhood of K. The space (K) is equipped with the topology of uniform convergence on K. Let Ω be an open subset of ^N such that 0Ω and ^N\Ω is connected. It is shown that there exists a series ∑H_n, where H_n is a homogeneous harmonic polynomial of degree n on ^N, such that (i) ∑H_n converges on some ball of centre 0 to a function that is continuous on Ω and harmonic on Ω, (ii) the partial sums of ∑H_n are dense in (K) for every compact subset K of ^N\Ω with connected complement. Some refinements are given and our results are compared with an analogous theorem concerning overconvergence of power series.     

SECOND BEST TAXES AND QUOTAS IN NITROGEN REGULATION

This paper investigates second best policies to regulate nitrogen leaching. When the policy maker controls the total nitrogen use, an overall tax is superior to an action equivalent overall quota. When the goal is to regulate the expected level of nitrogen leaching, expected profit of a risk neutral farmer is greater under an overall tax than under an overall quota under a reasonable condition. The welfare ranking of action equivalent taxes and quotas for a risk averse farmer is generally ambiguous. In the numerical analyses, overall taxes turned out to be superior to overall quotas with both targets, despite a very high value of absolute risk aversion, 0.01. These results suggest that an overall tax is probably a superior policy to an overall quota to regulate expected total nitrogen use or expected nitrogen leaching for risk neutral and most of risk averse farmers.     

Second row transition metal mixed hydride-halide triatomic molecules

Summary The ground state structures and bond energies have been obtained for the triatomic MHX systems where M is the entire sequence of second row transition metal atoms and X is a halide. The most interesting results of this study appear when these systems are compared to the triatomic MH₂ and MX₂ systems. It turns out that the structure of the MHX systems are quite similar to the corresponding MH₂ systems in general. Most of the MHX systems to the right thus have bent low-spin ground states, indicating large covalent contributions to the bonding. RuHX is a special case and has a high-spin linear ground state. For the systems to the left ionicity dominates the bonding. An important result, with implications for halide ligand effects on carbonyl and olefin insertion into M-H and M-R bonds, is that the M-H bonds for the systems to the right have a different character and are significantly weaker for the MHX than for the MH₂ systems. A similar effect is noted when the M-Cl bond strengths of MCl₂ are compared to the ones in MHCl. Both these effects can be explained by a more cationic metal with mores ⁰-state character when halide ligands are present.     

关于S概周期调和函数

本文将给出S概周期调和函数的两个定理     

RECURSIVE BAIRE CLASSIFICATION AND SPEEDABLE FUNCTIONS

Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine-independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].     

The Spaces b~p with 0 < p < 1

Let 0 < p < 1. In this paper we prove that the Bergman norm on the p-th Bergman space bp(H) is equivalent to certain "normal direction norm" as well as certain "tangential direction norm", where H = Rn-1 × R is the upper half space. As an application, we get the boundedness of harmonic conjugation operators on bp(H).