On the Spectra of Striped Sign Patterns

Sign patterns consisting of some positive and some negative columns, with at least one of each kind, are shown to allow any self-conjugate spectrum, and thus to allow any inertia. In the case of the n ×n sign pattern with all columns positive, given any self-conjugate multiset consisting of n -1 complex numbers supplemented by a sufficiently large positive number, it is shown how to construct a positive normal matrix whose spectrum is this multiset. Thus, the positive sign pattern allows any inertia with at least one positive eigenvalue.     

树的稳定子集和稳定指标

一个实矩阵的符号稳定性问题在经济学、生态学等诸多领域中都有应用背景．本文利用[1]中给出的不可约矩阵的符号稳定性的有关结论，将一个实矩阵的符号稳定性判定问题转化为一个等价的图论问题，即判定无向树中一个点子集的稳定性问题．本文引入了树的稳定子集的概念并给出了稳定子集的递归判别方法．本文还提出井研究了树的稳定指标，即树中所有稳定子集的最小基数，证明了关于稳定指标的一个min—max型定理，井给出了n阶树的稳定指标的最好上界及达到上界的极树的完全刻划。     

Fitting models to correlated data III: A comparison between residual analysis and other methods

Applications of the χ² test, the F test, the Durbin-Watson d test, and the f (or Sign) test, to examples of correlated data treatment, show important drawbacks with the d test and (apparently) with the f test. An analytical approach based on residual analysis suggests an improvement in their use that leads to better results at lowest order; it also points out a distinction between goodness-of-fit tests, as the f test, and goodness-of-modeling tests, as the χ² and F tests. The residual analysis method is applied to the same examples; it looks faster, simpler, and often more accurate than the classical ones.     

Thinking machines

We propose that a sufficiently advanced civilisation may employ Cepheid variable stars as beacons to transmit all-call information throughout the galaxy and beyond. They might employ a pulsed neutrino beam to trigger the expansion of a Cepheid at an earlier than normal time, generating a binary signature of normal period or artificially shortened period. One can construct many scenarios wherein it would be desirable for such a civilisation of star ticklers to transmit data to anyone else within viewing range. The beauty of employing Cepheids is that these stars can be seen from afar (we monitor them out through the Virgo cluster), and any developing technological society would seem to be likely to closely observe them as distance markers. Records exist of Cepheids for well over 100 years. We propose that these (and other regularly variable types of stars) be searched for signs of phase modulation (in the regime of short pulse duration) and patterns, which could be indicative of intentional signalling.     

An exactly soluble case of the triangular ising model in a magnetic field

An anisotropic triangular Ising model in which the first- and second-order parameters and the field parameters are functionally related is solved exactly by representing the distribution of the atom patterns in terms of a suitably constructed Markov process. The probabilities of patterns, defined as the probabilities generated by this process, are a mathematically tractable alternative to the classical representation of these probabilities in terms of the partition function. The interaction and field parameters of this Ising model, its magnetization, free energy, and its nearest neighbor correlation functions, are expressed in terms of the parameters of this Markov process. Special cases are worked out in detail and numerical examples are given.     

不同种植方式对陆生植物去除富营养化水体中磷的影响

以陆生植物美人蕉（Canna generalis）、紫背万年青（Rhoeo discolor）为对象,研究了其不同的种植方式对净化富营养化水体中磷的影响．结果表明,美人蕉、紫背万年青的双倍生物量组对水体中TP、DTP和DIP的去除率与它们的单倍生物量组呈显著性差异,植物对水体中P的去除效果随着植物生物量的适度增加而提高．两种陆生植物的复合种植体系对TP、DTP和DTP的去除率和单一种植体系差别不明显,说明美人蕉、紫背万年青的不同种植体系对水体中TP、DTP和DIP去除率的影响不大．从美人蕉、紫背万年青去除水体中TP、DTP和DIP的动态过程拟合模型可以看出各植物处理组对水体中不同形态P有良好的去除效应．     

Piezoelectric activities and domain patterns of orthorhombic Ba(Zr,Ti)O3 ceramics

Ba(Zr_xTi_1?x)O₃ (0.025 ≤ x ≤ 0.065) ceramics were prepared by conventional solid-state reaction method. Crystalline structures were analyzed by X-ray diffraction. It was shown that all the Ba(Zr_xTi_1?x)O₃ (0.025 ≤ x ≤ 0.065) ceramics were of orthorhombic phase at room temperature. Piezoelectric activities and domain patterns were investigated and compared with those of BaTiO₃ ceramic. All the Ba(Zr_xTi_1?x)O₃ ceramics showed nearly the same d₃₃ values of about 265 pC/N and the same domain width of about 220 nm. By comparing the grain sizes and domain width of the Ba(Zr_xTi_1?x)O₃ ceramics with those of BaTiO₃ ceramic, it is speculated that the variation of domain width with grain sizes in orthorhombic Ba(Zr_xTi_1?x)O₃ ceramics may be different with that in tetragonal BaTiO₃ ceramic. Besides domain width, the effective inertia mass of domain wall is also considered to be a very important factor that impacts the piezoelectric activities of the Ba(Zr_xTi_1?x)O₃ ceramics.     

Building and analyzing the US airport network based on en-route location information

From a complex network perspective, this study sets out two aims around the US airport network (USAN) which is built from en-route location information of domestic flights in the US. First, we analyze the structural properties of the USAN with respect to its binary and weighted graphs, and second we explore the airport patterns, which have wide-ranging implications. Results from the two graphs indicate the following. (1) The USAN exhibits scale-free, small-world and disassortative mixing properties, which are consistent with the mainstream perspectives. Besides, we find (2) a remarkable power relationship between the structural measurements in the binary graph and the traffic measurements in the weighted counterpart, namely degree versus capacity and attraction versus volume. On the other hand, investigation of the airport patterns suggests (3) that all the airports can be classified into four categories based on multiple network metrics, which shows a complete typology of the airports. And it further indicates (4) that there is a subtle relationship between the airport traffic and the geographical constraints as well as the regional socioeconomic indicators.     

Towards a geometrical classification of statistical conservation laws in turbulent advection

The paper revisits the compressible Kraichnan model of turbulent advection in order to derive explicit quantitative relations between scaling exponents and Lagrangian particle configuration geometry.     

空气/油水乳状液泡状流/弹状流流型及其转换的研究

本文采用空气／油水乳状液为介质,在不同含水率下,得到垂直上升管内W／O和O／W状态下泡状流及弹状流的流型特征、用压降脉动法判别流型的判据,同时研究了含水率对流型转换的影响,并建立了流型转换的预测模型,模型计算值与实验结果符合良好。