单调性条件在Fourier级数收敛性中的最终推广:历史、发展、应用和猜想

为了对Fourier级数进行近似计算和有效应用,必须研究其收敛性,这个课题有长久的历史,形成了数学分析中吸引包括许多著名数学家在内的学者研究的一条热烈但困难的主流.其中,在三角级数(Fourier级数)一致收敛性和平均收敛性问题中人们一直关心Fourier系数的单调递减条件最终的推广.这个开始于英国Chaundy-Jollife(1916年)和Young(1913年)的工作最近出现了突破性的进展,产生了许多完善的结果.本文将对这方面的历史、发展给出综述,并重点介绍最近的应用成果,并对以后的工作给出研究思路和线索.     

Characterization of heterogeneous solids via wave methods in computational microelasticity

Real solids are inherently heterogeneous bodies. While the resolution at which they are observed may be disparate from one material to the next, heterogeneities heavily affect the dynamic behavior of all microstructured solids. This work introduces a wave propagation simulation methodology, based on Mindlin's microelastic continuum theory, as a tool to dynamically characterize microstructured solids in a way that naturally accounts for their inherent heterogeneities. Wave motion represents a natural benchmark problem to appreciate the full benefits of the microelastic theory, as in high-frequency dynamic regimes do microstructural effects unequivocally elucidate themselves. Through a finite-element implementation of the microelastic continuum and the interpretation of the resulting computational multiscale wavefields, one can estimate the effect of microstructures upon the wave propagation modes, phase and group velocities. By accounting for microstructures without explicitly modeling them, the method allows reducing the computational time with respect to classical methods based on a direct numerical simulation of the heterogeneities. The numerical method put forth in this research implements the microelastic theory through a finite-element scheme with enriched super-elements featuring microstructural degrees of freedom, and implementing constitutive laws obtained by homogenizing the microstructure characteristics over material meso-domains. It is possible to envision the use of this modeling methodology in support of diverse applications, ranging from structural health monitoring in composite materials to the simulation of biological and geomaterials. From an intellectual point of view, this work offers a mathematical explanation of some of the discrepancies often observed between one-scale models and physical experiments by targeting the area of wave propagation, one area where these discrepancies are most pronounced.     

互补对偶结构的三值ECL锁存器设计

在分析发射极耦合逻辑(ECL)电路的互补对偶特性基础上,指出了差分对的两个开关变量的不独立性及互补对偶特性,并设计了互补对偶结构的ECL三值D型锁存器.这种新型的D型锁存器电路比传统电路具有更简单的电路结构.它的输出是互补的双轨三值输出系统.应用这种新型锁存器设计的D触发器及时序电路将具有更简单的电路结构.     

Spin observables in small-angle elastic → d scattering with an L-type deuteron target at 800 MeV

We have measured spin correlation parameters that describe the elastic scattering of 800 MeV polarized protons from an L-type polarized deuteron target at laboratory angles below 20°. The measured parameters include the correlated analyzing powers A_SL, A_LL and A_NLL and the proton spin-transfer coefficients C_0L,S, C_0L,L, C_SL,N, C_NL,S, C_NL,L and C_LL,N. The results are compared with single-scattering predictions based on different phase-shift solutions for the nucleon-nucleon scattering matrix.     

A unified theory of Stark broadening for hydrogenic ions—II: Line wings

The consequences of the attractive Coulomb force between positively charged hydrogenic radiators and electrons on line broadening in the quasistatic wings are examined. Due to the speeding up of the electrons by the Coulomb attraction, static results are not obtained until further out into the wings for (e.g.) He II lines, as compared to the analogous hydrogen lines. In fact, for low principal quantum numbers the region of validity is outside of, or close to, the limit ?Δω ? kT imposed by the weak coupling approximation. The effects of doubly-excited bound states are discussed in detail and we conclude that within the validity range of the Unified Theory all except possibly the most tightly bound doubly-excited states (which can give rise to “satellites” to the ionic lines) are relatively unimportant. In the near line wings the profile goes approximately as Δω^{-$\text{5}\text{2}$}. But in the far line wings (?Δω ? kT) the wings lie somewhat above the Δω^{-$\text{5}\text{2}$} wing of neutral species and a Δω^{-$\text{9}\text{4}$} dependence is more appropriate. No exponential divergence of the spectrum is obtained for large Δω when bound states (for which a classical distribution of states is inappropriate) are excluded. Unfortunately, no conclusive experimental comparisons are possible with presently available data.     

Synthesis of new allenic prostanoids

New allenic prostanoids 5c, d, 7,9c, and 15b have been prepared by total synthesis. In each case a cuprate-propargylic acetate reaction was used as the key step.