关于减算子的正特征值问题

证明了在一定条件下,非线性算子方程 Ax=λx 有唯一确定的正解 x_λ,并且 x_λ关于λ是严格单减的、连续的,且当λ→ ∞时,‖x_λ‖→0;当λ→0~ 时,‖x_λ‖→ ∞。最后,利用该结论来研究一类非线性积分方程的正解。     

供应链生产柔性有效边界研究

本文研究了需求不确定条件下供应链生产柔性优化决策时,供应链期望总成本与柔性水平之间函数关系,提出了供应链生产柔性有效边界的概念,研究了有效边界的性质,得出供应链生产柔性有效边界具有单调递增和凸函数性,并且给予了严格的数学证明。     

Omniscience at the Edge of Chaos: complexity,defences and change in a Children and Families Social Work department

ABSTRACT

This paper will explore a period of organisational change in a Children and Families Social Work team, applying ideas from complexity theory and psychoanalysis to explore the changes that occurred. In doing so it will critique the Newtonian concept of cause-and-effect linear causality, instead positing a nonlinear model of an organisation as a complex adaptive system in flux as it interacts with its environment. The paper will go on to posit that Bion’s psychoanalytic concepts of Omniscience and K Activity are self-organising forces in social care organisations, and when anxiety is not managed effectively, reductionist technical-rationale approaches to Children and Families Social Work dominate practice. It will conclude by outlining how the organisation’s effective management of anxiety through the creation of containment, created a series of organisational changes. These changes better supported the management of the complexity and uncertainty inherent in the social work task, raising possibilities of improvements in social work practice beyond the organisation.     

A Matching Prior for the Shape Parameter of the Skew‐Normal Distribution

Abstract. This paper deals with the issue of performing a default Bayesian analysis on the shape parameter of the skew‐normal distribution. Our approach is based on a suitable pseudo‐likelihood function and a matching prior distribution for this parameter, when location (or regression) and scale parameters are unknown. This approach is important for both theoretical and practical reasons. From a theoretical perspective, it is shown that the proposed matching prior is proper thus inducing a proper posterior distribution for the shape parameter, also when the likelihood is monotone. From the practical perspective, the proposed approach has the advantages of avoiding the elicitation on the nuisance parameters and the computation of multidimensional integrals.     

Aggregating the Single Crossing Property

The single crossing property plays a crucial role in economic theory, yet there are important instances where the property cannot be directly assumed or easily derived. Difficulties often arise because the property cannot be aggregated: the sum or convex combination of two functions with the single crossing property need not have that property. We introduce a new condition characterizing when the single crossing property is stable under aggregation, and also identify sufficient conditions for the preservation of the single crossing property under multidimensional aggregation. We use our results to establish properties of objective functions (convexity, logsupermodularity), the monotonicity of optimal decisions under uncertainty, and the existence of monotone equilibria in Bayesian games.     

Likelihood Ratio Tests Under Local and Fixed Alternatives in Monotone Function Problems

Abstract.  We focus on a class of non-standard problems involving non-parametric estimation of a monotone function that is characterized by n ^1/3 rate of convergence of the maximum likelihood estimator, non-Gaussian limit distributions and the non-existence of     -regular estimators. We have shown elsewhere that under a null hypothesis of the type ψ ( z ₀) =  θ ₀ ( ψ being the monotone function of interest) in non-standard problems of the above kind, the likelihood ratio statistic has a 'universal' limit distribution that is free of the underlying parameters in the model. In this paper, we illustrate its limiting behaviour under local alternatives of the form ψ _n ( z ), where ψ _n (·) and ψ (·) vary in O ( n ^−1/3) neighbourhoods around z ₀ and ψ _n converges to ψ at rate n ^1/3 in an appropriate metric. Apart from local alternatives, we also consider the behaviour of the likelihood ratio statistic under fixed alternatives and establish the convergence in probability of an appropriately scaled version of the same to a constant involving a Kullback–Leibler distance.     

PARTIAL CORRELATION AND CONDITIONAL CORRELATION AS MEASURES OF CONDITIONAL INDEPENDENCE

This paper investigates the roles of partial correlation and conditional correlation as measures of the conditional independence of two random variables. It first establishes a sufficient condition for the coincidence of the partial correlation with the conditional correlation. The condition is satisfied not only for multivariate normal but also for elliptical, multivariate hypergeometric, multivariate negative hypergeometric, multinomial and Dirichlet distributions. Such families of distributions are characterized by a semigroup property as a parametric family of distributions. A necessary and sufficient condition for the coincidence of the partial covariance with the conditional covariance is also derived. However, a known family of multivariate distributions which satisfies this condition cannot be found, except for the multivariate normal. The paper also shows that conditional independence has no close ties with zero partial correlation except in the case of the multivariate normal distribution; it has rather close ties to the zero conditional correlation. It shows that the equivalence between zero conditional covariance and conditional independence for normal variables is retained by any monotone transformation of each variable. The results suggest that care must be taken when using such correlations as measures of conditional independence unless the joint distribution is known to be normal. Otherwise a new concept of conditional independence may need to be introduced in place of conditional independence through zero conditional correlation or other statistics.     

一类具有弱单调Fourier系数的Fourier和逼近的一个问题

对于具有非负Fourier系数的连续周期函数，利用弱单调条件给出了其Fourier和的逼近达到最佳逼近的一个充分条件．     

An alternative approach to minimize model inadequacy

In this article Bock's (1975) approach is used to fit a class of lower order polynomials to a higher order response function. For a wide class of conditions our fitted models offer greater protection, in some sense, against model inadequacies than the one fitted by Karson, Manson and Hader (1969). However, our approach is applicable to the situations where the assumption of normality about the distribution of the response variable is appropriate.