ALMOST SURE CONVERGENCE OF THE STABLE TAIL EMPIRICAL DEPENDENCE FUNCTION IN MULTIVARIATE EXTREME STATISTICS

ThisresearchissupportedbytheNationalNaturalScienceFoundationofChina.1.IntroductionandTheoremsSupposethatF(x,y)isabivariatedistributionfunctionwithtwocontinuousmarginaldistributionfunctions,say,FIandF2.DefineFissaidtohaveastabletaildependencefunction(STDF)l(x,y)ifforx20andy20,whereF(x,y)~1--F(QI(x),QZ(y)).TheconceptofSTDFwasintroducedin[6].Supposethat{(Xi,K),i21}isasequenceofi.i.d.randomvectorswithdistributionF(x,y).Ifthereedestsomesequencesofconstantsan>0,on>0,b.ERandd.ER,n>1.suc…     

一类浮游生物植化相克时滞抛物方程的稳态解

本文研究了水生生态系统中种群间能产生抑制毒素的Volterra竞争模型,用上下解的方法讨论了稳态解的渐近行为,得到了系统存在唯一全局稳定正稳态解的充分条件.     

n维可投影LOtka-Volterra竞争系统的渐近性

对于二维和三维的Lotka-Volterra竞争系统,已有文献证明:当每一个坐标轴上的平衡点均为渐近稳定时,该系统几乎所有解趋于坐标轴上平衡点所组成的点集,即,不趋于坐标轴上平衡点的解集,其测度为零.由此, van den Driessche和Zeeman于1998年提出猜测:对n(n>3)维Lotka-Volterra竞争系统,当每一个坐标轴上的平衡点均为渐近稳定时,该系统几乎所有解趋于坐标轴上平衡点所组成的点集,即,不趋于坐标轴上平衡点的解集,其在n维空间的测度为零.本文证明当n维Lotka-Volterra竞争系统可被逐维投影到一维系统时,该猜测成立,并给出了可投影条件的代数判据.本文所得结论包含了已有文献的结果.     

Hyperbolic structure and stickiness effect: A case of a 2D area-preserving twist mapping

The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper. Previous works have shown that the hyperbolic structures in the phase space play an essential role in causing the stickiness effect. We present in this paper the relationship between the stickiness effect and the geometric property of hyperbolic structures. Using a two-dimensional area-preserving twist mapping as the model, we develop the numerical algorithms for computing the positions of the hyperbolic periodic orbits and for calculating the angle between the stable and unstable manifolds of the hyperbolic periodic orbit. We show how the stickiness effect and the orbital diffusion speed are related to the angle.     

A delayed modified Ricker map and its cicada-type oscillations

Without trying to develop a model for a biological system, we introduce a delay map that shows a large spike followed by 16 iterations of much smaller values. Upon variation of one of the parameters, we can get a 13 cycles stable oscillation. The analyses of the bifurcation diagrams for the delayed extended Ricker's map yield a straightforward approach to find parameter values for any periodicity. In particular, we determine the values for the 13 and 17 periodic oscillations. We also notice that the bifurcation diagrams show no chaotic regions, and their structures show self-similarity properties. In general, the bifurcation diagrams have self-similarity structures, where n-periodic oscillations change into (n-1)-periodic oscillations.     

The Value of Information Searching against Fake News

Inspired by the Daley-Kendall and Goffman-Newill models, we propose an Ignorant-Believer-Unbeliever rumor (or fake news) spreading model with the following characteristics: (i) a network contact between individuals that determines the spread of rumors; (ii) the value (cost versus benefit) for individuals who search for truthful information (learning); (iii) an impact measure that assesses the risk of believing the rumor; (iv) an individual search strategy based on the probability that an individual searches for truthful information; (v) the population search strategy based on the proportion of individuals of the population who decide to search for truthful information; (vi) a payoff for the individuals that depends on the parameters of the model and the strategies of the individuals. Furthermore, we introduce evolutionary information search dynamics and study the dynamics of population search strategies. For each value of searching for information, we compute evolutionarily stable information (ESI) search strategies (occurring in non-cooperative environments), which are the attractors of the information search dynamics, and the optimal information (OI) search strategy (occurring in (eventually forced) cooperative environments) that maximizes the expected information payoff for the population. For rumors that are advantageous or harmful to the population (positive or negative impact), we show the existence of distinct scenarios that depend on the value of searching for truthful information. We fully discuss which evolutionarily stable information (ESI) search strategies and which optimal information (OI) search strategies eradicate (or not) the rumor and the corresponding expected payoffs. As a corollary of our results, a recommendation for legislators and policymakers who aim to eradicate harmful rumors is to make the search for truthful information free or rewarding.     

Soil matrix tracer contamination and canopy recycling did not impair 13CO2 plant–soil pulse labelling experiments

When conducting ¹³CO₂ plant–soil pulse labelling experiments, tracer material might cause unwanted side effects which potentially affect δ¹³C measurements of soil respiration (δ¹³C_SR) and the subsequent data interpretation. First, when the soil matrix is not isolated from the atmosphere, contamination of the soil matrix with tracer material occurs leading to a physical back-diffusion from soil pores. Second, when using canopy chambers continuously, ¹³CO₂ is permanently re-introduced into the atmosphere due to leaf respiration which then aids re-assimilation of tracer material by the canopy. Accordingly, two climate chamber experiments on European beech saplings (Fagus sylvatica L.) were conducted to evaluate the influence of soil matrix ¹³CO₂ contamination and canopy recycling on soil ¹³CO₂ efflux during ¹³CO₂ plant–soil pulse labelling experiments. For this purpose, a combined soil/canopy chamber system was developed which separates soil and canopy compartments in order to (a) prevent diffusion of ¹³C tracer into the soil chamber during a ¹³CO₂ canopy pulse labelling and (b) study stable isotope processes in soil and canopy individually and independently. In combination with laser spectrometry measuring CO₂ isotopologue mixing ratios at a rate of 1 Hz, we were able to measure δ¹³C in canopy and soil at very high temporal resolution. For the soil matrix contamination experiment, ¹³CO₂ was applied to bare soil, canopy only or, simultaneously, to soil and canopy of the beech trees. The obtained δ¹³C_SR fluxes from the different treatments were then compared with respect to label re-appearance, first peak time and magnitude. By determining the δ¹³C_SR decay of physical ¹³CO₂ back-diffusion from bare soils (contamination), it was possible to separate biological and physical components in δ¹³C_SR of a combined flux of both. A second pulse labelling experiment, with chambers permanently enclosing the canopy, revealed that ¹³CO₂ recycling at canopy level had no effect on δ¹³C_SR dynamics.     

Platinized Magnesium as Reducing Agent for Hydrogen Isotope Analysis

Abstract

Platinized magnesium has recently been proposed as a new reducing agent for the conversion of small quantities of water to hydrogen in a flame-sealed borosilicate glass tube at 400°C for isotopic analysis. The reagent, Mg-Pt, in contrast to zinc can be prepared in every laboratory by coating a magnesium granulate with a thin layer of platinum by reaction with H₂PtCl₆·6H₂O dissolved in acetone-ether mixture. Excellent reproducibility of the isotope ratios in hydrogen gas prepared from water samples has been obtained using 4 μl of water and 120 mg of the reagent.