具有三次代数曲线解的五次系统的极限环

本文利用Maple软件强大的符号计算能力,得到了以 y=ax~3+bx~2+cx+d 为解的平面五次多项式系统的特征,由此证明了该系统在奇点的邻域内可以存在极限环。     

Pre‐procreative ages in population stability and cyclicity

Age‐specific models of population renewal (with and without feedback) which imply convergence to a stable state for some levels of fertility or feedback may imply the presence of long‐term cycling around a constant or exponentially changing equilibrium for other levels of fertility or feedback. The switch from one regime to the other is a “bifurcation.”; The conditions for bifurcation involve the roots of an analogue of Lotka's Equation.

Typically bifurcation is induced by raising the strength of feedback or the level of fertility. It has been known since the early 1980s, however, that this is sometimes impossible. It is sometimes impossible even with the linear renewal equation itself and with the most basic of non‐linear models, Lee's cohort feedback model.

Here it is proved that this typical route to bifurcation does not fail for these basic models in the presence of a condition which always holds for realistic applications with higher organisms: the existence of a span of ages before the onset of fertility.

Specifically, a strictly positive lower bound on ages of procreation is proved to be sufficient to guarantee the existence of a rescaling of Lotka's Equation for which the real part of some complex root vanishes. This result holds for absolutely Lebesgue‐integrable (signed) net maternity functions on the positive real line and for absolutely summable (signed) net maternities on the positive integers.

It follows that Coale's rescaling device for the analysis of approach to stability in stable population theory can be implemented for all realistic human net maternity schedules. It also follows that the many special cases of the cohort feedback model throughout population biology will all generate persistent cycling instead of stability if feedback is sufficiently strong.     

论经济周期波动的随机统计规律

从经济周期波动的特征出发，分析经济周期现象中考虑随机性的合理性和必要性，可看出经济周期运动的内在机制中蕴含着大量的不确定随机因素及对经济周期波动的影响，从随机周期现象入手，针对周期波动的研究历史和现状，就可得到新的启示和评价．     

Inference on Filtered and Smoothed Probabilities in Markov-Switching Autoregressive Models

ABSTRACT

We derive a statistical theory that provides useful asymptotic approximations to the distributions of the single inferences of filtered and smoothed probabilities, derived from time series characterized by Markov-switching dynamics. We show that the uncertainty in these probabilities diminishes when the states are separated, the variance of the shocks is low, and the time series or the regimes are persistent. As empirical illustrations of our approach, we analyze the U.S. GDP growth rates and the U.S. real interest rates. For both models, we illustrate the usefulness of the confidence intervals when identifying the business cycle phases and the interest rate regimes.     

Quantitative Risk Assessment of FMD Virus Transmission via Water

Foot-and-mouth disease (FMD) is a viral disease of domesticated and wild cloven-hoofed animals. FMD virus is known to spread by direct contact between infected and susceptible animals, by animal products such as meat and milk, by the airborne route, and mechanical transfer on people, wild animals, birds, and by vehicles. During the outbreak of 2001 in the Netherlands, milk from dairy cattle was illegally discharged into the sewerage as a consequence of transport prohibition. This may lead to contaminated discharges of biologically treated and raw sewage in surface water that is given to cattle to drink. The objective of the present study was to assess the probability of infecting dairy cows that were drinking FMD virus contaminated surface water due to illegal discharges of contaminated milk. So, the following data were collected from literature: FMD virus inactivation in aqueous environments, FMD virus concentrations in milk, dilution in sewage water, virus removal by sewage treatment, dilution in surface water, water consumption of cows, size of a herd in a meadow, and dose-response data for ingested FMD virus by cattle. In the case of 1.6 x 10(2) FMD virus per milliliter in milk and discharge of treated sewage in surface water, the probability of infecting a herd of cows was estimated to be 3.3 x 10(-7) to 8.5 x 10(-5), dependent on dilution in the receiving surface water. In the case of discharge of raw sewage, all probabilities of infection were 100 times higher. In the case of little dilution in small rivers, the high level of 8.5 x 10(-3) is reached. For 10(4) times higher FMD virus concentrations in milk, the probabilities of infecting a herd of cows are high in the case of discharge of treated sewage (3.3 x 10(-3) to 5.7 x 10(-1)) and very high in the case of discharge of raw sewage (0.28-1.0). It can be concluded that illegal and uncontrolled discharges of contaminated milk into the sewerage system may lead to high risks to other cattle farms at 6-50 km distance of the location of discharge within one day. This clearly underlines current measures that prohibit such discharges, and also asks for strict control. This risk assessment clearly demonstrated the potential significance of FMD virus transmission via water, and the results will be useful on an international scale, and could also serve as a basis for other FMD risk-assessment models.     

Sentiments

This paper develops a new theory of fluctuations—one that helps accommodate the notions of “animal spirits” and “market sentiment” in unique‐equilibrium, rational‐expectations, macroeconomic models. To this goal, we limit the communication that is embedded in a neoclassical economy by allowing trading to be random and decentralized. We then show that the business cycle may be driven by a certain type of extrinsic shocks which we call sentiments. These shocks formalize shifts in expectations of economic activity without shifts in the underlying preferences and technologies; they are akin to sunspots, but operate in unique‐equilibrium models. We further show how communication may help propagate these shocks in a way that resembles the spread of fads and rumors and that gives rise to boom‐and‐bust phenomena. We finally illustrate the quantitative potential of our insights within a variant of the RBC model.     

Do Political Institutions Shape Economic Policy?

Do political institutions shape economic policy? I argue that this question should naturally appeal to economists. Moreover, the answer is in the affirmative, both in theory and in practice. In particular, recent theoretical work predicts systematic effects of electoral rules and political regimes on the size and composition of government spending. Results from ongoing empirical work indicate that such effects are indeed present in the data. Some empirical results are consistent with theoretical predictions: presidential regimes have smaller governments and countries with majoritarian elections have smaller welfare‐state programs and less corruption. Other results present puzzles for future research: the adjustment to economic events appears highly institution‐dependent, as does the timing and nature of the electoral cycle.     

Sticky Price Models of the Business Cycle: Can the Contract Multiplier Solve the Persistence Problem?

We construct a quantitative equilibrium model with firms setting prices in a staggered fashion and use it to ask whether monetary shocks can generate business cycle fluctuations. These fluctuations include persistent movements in output along with the other defining features of business cycles, like volatile investment and smooth consumption. We assume that prices are exogenously sticky for a short time. Persistent output fluctuations require endogenous price stickiness in the sense that firms choose not to change prices much when they can do so. We find that for a wide range of parameter values, the amount of endogenous stickiness is small. Thus, we find that in a standard quantitative model, staggered price‐setting, alone, does not generate business cycle fluctuations.     

川西南藏族的神灵崇拜和驱鬼驱邪仪式研究

分布在藏彝走廊东南缘的川西南藏族,信仰万物有灵的多神崇拜。他们敬先祖,祭山神,驱邪除秽,驱鬼杀鬼。在他们的民间信仰活动里有一系列的敬祖祭神仪轨。包括纳木依藏族的牛王会、尔苏藏族的射箭节和还山鸡节以及为亡灵指路仪轨等,无不体现出敬神灵远鬼邪的民间信仰文化。     

A Dynamic Model of Investment in the U.S. Beef-Cattle Industry

Reproduction constraints lead to some a priori information that may prove valuable in econo- metrically modeling inventory dynamics within the U.S. cattle herd. The distributed-lag models estimated for animal inventories suggest an implicit incorporation of the age distribution of the herd that is crucial to understanding the retention/culling (investment) decisions. The estimated equations are validated using post-sample observations that were withheld prior to estimation. The final-form dynamic equations have complex roots and protracted price and investment effects. The parameter estimates are used to calculate intermediate and long-run elasticities at the means of relevant variables.