Unavoidable Traces Of Set Systems

Sauer, Shelah, Vapnik and Chervonenkis proved that if a set system on n vertices contains many sets, then the set system has full trace on a large set. Although the restriction on the size of the groundset cannot be lifted, Frankl and Pach found a trace structure that is guaranteed to occur in uniform set systems even if we do not bound the size of the groundset. In this note we shall give three sequences of structures such that every set system consisting of sufficiently many sets contains at least one of these structures with many sets.     

On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance

The graph-theoretic operation of rooted subtree prune and regraft is increasingly being used as a tool for understanding and modelling reticulation events in evolutionary biology. In this paper, we show that computing the rooted subtree prune and regraft distance between two rooted binary phylogenetic trees on the same label set is NP-hard. This resolves a longstanding open problem. Furthermore, we show that this distance is fixed parameter tractable when parameterised by the distance between the two trees.Received March 16, 2004     

Admissible slopes for monotone and convex interpolation

Summary In many applications, interpolation of experimental data exhibiting some geometric property such as nonnegativity, monotonicity or convexity is unacceptable unless the interpolant reflects these characteristics. This paper identifies admissible slopes at data points of variousC ¹ interpolants which ensure a desirable shape. We discuss this question, in turn for the following function classes commonly used for shape preserving interpolations: monotone polynomials,C ¹ monotone piecewise polynomials, convex polynomials, parametric cubic curves and rational functions.     

On the electron energy spectrum in heavily doped non-parabolic semiconductors

An attempt is made to present a simple theoretical analysis of the energy-wave vector dispersion relation of the conduction electrons in heavily doped non-parabolic semiconductors forming band tails. We observe that the complex energy spectrum in doped small-gap materials whose unperturbed conduction band is described by the three band model of Kane is due to the interaction of the impurity atoms in the tail with the spin-orbit splitting constant of the valence band (Δ), For band-gap (E_g)<Δ the imaginary part predominates which tails in to the conduction band. For the opposite inequality the real part comes in to play which tails in to the split-off band. In the absence of the band tailing effect, the imaginary part of the complex energy spectrum vanishes and the same is also true for doped two-band Kane-type and parabolic energy bands respectively. The present formulation helps us in investigating the Boltzmann transport equation dependent transport properties of degenerate semiconductors and are expected to agree better with experiments. The well-known results of unperturbed three and two band models of Kane together with wide-gap parabolic energy bands have been obtained as special cases of our generalized analysis under certain limiting conditions.     

一种基于新型寄存器结构的逐次逼近A/D转换器

介绍了一种10位CMOS逐次逼近型A/D转换器。在25 kSPS采样频率以下,根据模拟输入端输入的0~10 V模拟信号,通过逐次逼近逻辑,将其转化为10位无极性数字码。转换器的SAR寄存器结构采用了一种新的结构来实现D触发器。该转换器采用3μm CMOS工艺制作,信噪比为49 dB,积分非线性为±0.5 LSB。     

宽带固定增益放大器THS4302特性及应用

THS4302是TI公司推出的新型固定增益放大器，具有2.4GHz的带宽和 5V／V的固定增益。其性能是现有同类产品的四倍，可为高速应用系统提供高速低噪声的模拟解决方案。文中介绍了THS4302的特点、工作原理及使用注意事项，并在此基础上给出了几种典型应用。     

双积分A/D转换器的量程自动转换

介绍了一种双积分式A/D转换器在宽范围量程测量中的自动量程转换技术.在测量仪表的输入通道中,用计数器对双积分型A/D转换器本身所固有的过量程/欠量程信号计数,计数器的输出作为量程编码去控制量程的选择,同时又是送到CPU的量程指示信号.该技术扩大了A/D转换量程,提高了精度,设计简单,工作可靠.     

Study of the dynamic structure factor of strong glasses

The dynamic structure factors (DSFs) of several strong glasses (SF6, SF10, BK7, SUPRASIL) measured by Brillouin light scattering spectroscopy are reported. Spectra have been collected, at and above room temperature, at two scattering angles, θ=90° and θ=180° corresponding to exchanged wavevector q values ranging from 0.0256 to 0.0448 nm⁻¹. In particular we find that the isotropic spectral lineshapes are in all cases well described by the simple hydrodynamic theory of an amorphous solid. The width of the Brillouin peaks are found to be consistent with the predicted q² dependence at both investigated temperatures. This damping is however found to account only partially for the strong asymmetry of the Brillouin line clearly visible on a logarithmic intensity scale. As a matter of fact there is an excess intensity in the very low frequency plateau underlying the central component. The height of this plateau and hence the entire lineshape is well reproduced if a relaxation process is taken into account in the hydrodynamic equations. Owing to the intense elastic scattering we are able to determine unambiguously only the ratio between amplitude and characteristic time of this process which quantifies the sound dispersion to be of the order of a few percent in all samples. The temperature dependence of the parameters indicates that this relaxation cannot be attributed to thermally activated relaxation phenomena. These general findings favorably compare with molecular dynamics simulation results on similar systems.     

Theoretical study of exchange coupling constants in an Fe19 complex

The application of theoretical methods based on density functional theory using generalized-gradient approximation functionals provides reasonable estimates of the exchange coupling constants for polynuclear transition metal complexes. Calculations for the complete, non-modeled Fe₁₉ complex have been performed and a comparison with the experimental magnetic susceptibility values using Monte Carlo simulations is presented.     

Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds

This paper studies several aspects of asymptotically hyperbolic (AH) Einstein metrics, mostly on 4-manifolds. We prove boundary regularity (at infinity) for such metrics and establish uniqueness under natural conditions on the boundary data. By examination of explicit black hole metrics, it is shown that neither uniqueness nor finiteness holds in general for AH Einstein metrics with a prescribed conformal infinity. We then describe natural conditions which are sufficient to ensure finiteness.