一类非线性常微分方程振荡解的渐近表示

在本文中,我们讨论了非线性常微分方程y"=a0|x|αy3 a1|x|βy2 α2|x|γy α3|x|δ振荡解的渐近表示．在这个方程中将α0,α,α1,β,α2,γ,α3,δ分别换成0,0,6,0,0,0,sgn(x),1就是著名的第一类Painleve方程,而将α0,α,α1,β,α2,γ,α3,δ分别换成2,0,0,0,sgn(x),1,α0,就是著名的第二类Painleve方程．当α0,α,α1,β,α2,γ,α3,δ分别换成-β/3γ,0,0,0,1/γ,1,α,0时,可用于组合KdV方程孤立子解的化简．     

Bayesian networks applied to credit scoring

Email: kchang{at}gmu.eduEmail: RobertFung{at}Fairlsaac.comEmail: alan.lucas{at}hotmail.com^¶Email: BobOliver{at}Fairlsaac.com^||Email: NShikaloff{at}Fairlsaac.com The objectives of this paper are to apply the theory and numericalalgorithms of Bayesian networks to risk scoring, and comparethe results with traditional methods for computing scores andposterior predictions of performance variables. Model identification,inference, and prediction of random variables using Bayesiannetworks have been successfully applied in a number of areas,including medical diagnosis, equipment failure, informationretrieval, rare-event prediction, and pattern recognition. Theability to graphically represent conditional dependencies andindependencies among random variables may also be useful incredit scoring. Although several papers have already appearedin the literature which use graphical models for model identification,as far as we know there have been no explicit experimental resultsthat compare a traditionally computed risk score with predictionsbased on Bayesian learning algorithms. In this paper, we examine a database of credit-card applicantsand attempt to ‘learn’ the graphical structure ofthe characteristics or variables that make up the database.We identify representative Bayesian networks in a developmentsample as well as the associated Markov blankets and cliquestructures within the Markov blanket. Once we obtain the structureof the underlying conditional independencies, we are able toestimate the probabilities of each node conditional on its directpredecessor node(s). We then calculate the posterior probabilitiesand scores of a performance variable for the development sample.Finally, we calculate the receiver operating characteristic(ROC) curves and relative profitability of scorecards basedon these identifications. The results of the different modelsand methods are compared with both development and validationsamples. Finally, we report on a statistical entropy calculationthat measures the degree to which cliques identified in theBayesian network are independent of one another.     

IS THERE UNIT ROOT IN THE NITROGEN OXIDES EMISSIONS: A MONTE CARLO INVESTIGATION?

Abstract Use of the time‐series econometric techniques to investigate issues about environmental regulation requires knowing whether air pollution emissions are trend stationary or difference stationary. It has been shown that results regarding trend stationarity of the pollution data are sensitive to the methods used. I conduct a Monte Carlo experiment to study the size and power of two unit root tests that allow for a structural change in the trend at a known time using the data‐generating process calibrated to the actual pollution series. I find that finite sample properties of the Perron test are better than the Park and Sung Phillips‐Perron (PP) type test. Severe size distortions in the Park and Sung PP type test can explain the rejection of a unit root in air pollution emissions reported in some environmental regulation analyses.     

二阶非线性带有阻尼项微分方程的一个振荡定理

在这篇文章中,利用Riccati变换和积分不等式,对非线性带有阻尼项微分方程,我们给出了—个新的振荡解的判别准则.特别是我们给出的判别准则是比较宽的.     

Valence bond analysis of the bonding in transition metal compounds: the RuNO group in nitrosyl complexes

The ab initio and semi-empirical configuration interaction wave functions of ruthenium complexes [RuL₅(XY) ^q (L &; = NH₃, Cl^?, CN^?, XY &;= N₂, CO) are presented in the form of linear combinations of the valence bond (VB) structures, each structure being referred to some covalent or ionic model of the bonding in the M-XY group. The results of this VB analysis showed that [RuL₅(NO)] ^q complexes can be described as compounds of Ru(III) and neutral NO⁰ with a covalent π-bond in addition to the usual coordination bond.     

EVALUATING THE IMPACT OF ENVIRONMENTAL POLICY ON THE TREND BEHAVIOR OF US EMISSIONS OF NITROGEN OXIDES AND VOLATILE ORGANIC COMPOUNDS

The nature of this paper is a practical application of a proper time‐series methodology to evaluate policy impacts when there is uncertainty about the data being difference‐stationary (DS) or trend‐stationary (TS). We use this methodology to examine the trend behavior of two air pollutants, nitrogen oxides (NO_X) and volatile organic compounds (VOC). In particular, we concentrate on answering two questions. First, were there breaks in the trends of NO_X and VOC emissions around the same time environmental policies such as the Clean Air Act Amendments (CAAA) of 1970 were passed? And second, accounting for possible breaks are the US emissions of NO_X and VOC TS or DS? Our empirical results show a clear evidence of a trend shift in NO_X and VOC emissions at the time the CAAA of 1970 were passed, implying that this policy has been effective in reducing air pollution emissions, as well as additional breaks that correspond to other events and environmental policies before and after 1970. The unit root tests indicate that NO_X are DS irrespective of the number of breaks in the trend whereas results for VOC emissions depend on the number of breaks assumed.