Some Properties of A Lack-of-Fit Test for a Linear Errors in Variables Model

The relationship between the linear errors-in-variables model and the corresponding ordinary linear model in statistical inference is studied. It is shown that normality of the distribution of covariate is a necessary and sufficient condition for the equivalence. Therefore, testing for lack-of-fit in linear errors-in-variables model can be converted into testing for it in the corresponding ordinary linear model under normality assumption. A test of score type is constructed and the limiting chi-squared distribution is derived under the null hypothesis.Furthermore, we discuss the power of the test and the choice of the weight function involved in the test statistic.     

MODELING IMPACTS OF BIOENERGY MARKETS ON NONINDUSTRIAL PRIVATE FOREST MANAGEMENT IN THE SOUTHEASTERN UNITED STATES

Abstract The potential impacts of bioenergy markets on slash pine plantation management on nonindustrial private forestlands in the southeastern United States were analyzed. We developed an integrated Black–Scholes and modified Hartman model to achieve this task. The risk of damage from catastrophic natural disturbances such as wildfires and pest outbreaks associated with the exclusion/incorporation of thinnings and variation in timber salvage rates was also included. Three scenario sets were considered: status quo or no thinning scenario, thinning scenario for pulpwood, and thinning scenario for bioenergy at differing levels of risk and salvage. The results indicated that the incorporation of thinnings either for pulpwood or bioenergy increases the forestland value regardless of the risk when the salvage value of the stand is 0.8. When the two thinning scenarios were compared, the land expectation value for the thinning scenario for bioenergy was greater at any level of risk compared with the thinning scenario for pulpwood, averaging a difference of 11.5% and 11.7% for salvageable portions of 0.8 and 0, respectively.     

Solvability results for sublinear functions and operators

In this paper there are stated asymptotic solvability results which yield a Farkas' lemma for sublinear functions and operators. Applications to duality for homogeneous programming and to necessary optimality conditions for nonlinear programming are given. Some closedness conditions used in the paper are also discussed.

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Zusammenfassung In dieser Arbeit werden asymptotische Lösbarkeitsresultate angegeben, die ein Farkas-Lemma für sublineare Funktionen und Operatoren liefern. Es werden Anwendungen auf die Dualitätstheorie homogener Programme und auf notwendige Optimalitätsbedingungen der nichtlinearen Programmierung angegeben. Einige Abgeschlossenheitsvoraussetzungen, die in der Arbeit benutzt werden, werden diskutiert.

     

Expectation Values in Spin-Averaged Douglas–Kroll and Infinite-Order Relativistic Methods

The change of picture for the r ^–1 operator which occurs on passing from the four component relativistic schemes to two component theories is investigated for the spin-averaged Douglas–Kroll approximation and the recently proposed infinite-order approach. For nuclei already with moderately large values of the nuclear charge the change of picture contribution is found to be relatively important. Its neglect significantly affects the calculated values of the total relativistic contribution to the expectation value of r ^–1. A numerical method for the calculation of the total relativistic contribution to the expectation values of r ^–1, which avoids the explicit use of the appropriately transformed r ^–1 operator, is devised and tested. Also the differences between the Douglas–Kroll approximation and the infinite-order scheme are investigated.     

A General Procedure to Obtain Quantum Mechanical Charge and Bond Order Molecular Parameters

In an approach alternative to that of Mayer, a Hermitian operator is defined within the LCAO MO framework, which allows to obtain molecular charges and bond orders as expectation values of the first and second-order densities respectively. Such expectation values result to be nothing else than Mullikens atom and bond populations. Thus, Mulliken populations appear to be non arbitrary condensed electron density partitions, obtained according to quantum mechanical usual procedures for molecular one and two electron observables. The theoretical simplicity of the outlined procedure can be easily extended in order to obtain the expectation values for higher-order electronic chemical bonds.     

Approximating average parameters of graphs

Inspired by Feige (36th STOC, 2004), we initiate a study of sublinear randomized algorithms for approximating average parameters of a graph. Specifically, we consider the average degree of a graph and the average distance between pairs of vertices in a graph. Since our focus is on sublinear algorithms, these algorithms access the input graph via queries to an adequate oracle. We consider two types of queries. The first type is standard neighborhood queries (i.e., what is the ith neighbor of vertex v?), whereas the second type are queries regarding the quantities that we need to find the average of (i.e., what is the degree of vertex v? and what is the distance between u and v?, respectively). Loosely speaking, our results indicate a difference between the two problems: For approximating the average degree, the standard neighbor queries suffice and in fact are preferable to degree queries. In contrast, for approximating average distances, the standard neighbor queries are of little help whereas distance queries are crucial. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

具有(F,α,ρ,d)—凸的分式规划问题的最优性条件和对偶性

给出了一类非线性分式规划问题的参数形式和非参数形式的最优性条件,在此基础上,构造出了一个参数对偶模型和一个非参数对偶模型,并分别证明了其相应的对偶定理,这些结果是建立在次线性函数和广义凸函数的基础上的.     

一类次线性算子在齐型广义Orlicz-Campanato空间上的加权有界性

设X是齐型空间,Φ为Young函数,并设次线性算子T是从L^Φ（X,ω）到L^Φ（X^＋,β）有界的.建立了算子T从广义Orlicz-Campanato空间L^Φ,φ（X,ω）到L^Φ,φ（X^＋,β）的加权有界性,并特别建立了广义极大算子M的有界性.     

雅各布·伯努利的《猜度术》研究

《猜度术》是概率论的第一部奠基性著作,其出版是概率论成为独立数学分支的标志．本文详细分析了雅各布·伯努利的概率新思想,尤其对伯努利数及伯努利大数定律进行了较为深刻地探讨．另外,还澄清了长期以来对《猜度术》整理出版者的—个误传．