Direct and inverse estimates for a new family of linear positive operators

In the present paper we introduce a new family of linear positive operators and study some direct and inverse results in simultaneous approximation.     

Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters

In this paper, the problem of stochastic stability for a class of time-delay Hopfield neural networks with Markovian jump parameters is investigated. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. Without assuming the boundedness, monotonicity and differentiability of the activation functions, some results for delay-dependent stochastic stability criteria for the Markovian jumping Hopfield neural networks (MJDHNNs) with time-delay are developed. We establish that the sufficient conditions can be essentially solved in terms of linear matrix inequalities.     

New Branch-and-Cut Algorithm for Bilevel Linear Programming

Linear mixed 0–1 integer programming problems may be reformulated as equivalent continuous bilevel linear programming (BLP) problems. We exploit these equivalences to transpose the concept of mixed 0–1 Gomory cuts to BLP. The first phase of our new algorithm generates Gomory-like cuts. The second phase consists of a branch-and-bound procedure to ensure finite termination with a global optimal solution. Different features of the algorithm, in particular, the cut selection and branching criteria are studied in details. We propose also a set of algorithmic tests and procedures to improve the method. Finally, we illustrate the performance through numerical experiments. Our algorithm outperforms pure branch-and-bound when tested on a series of randomly generated problems. Work of the authors was partially supported by FCAR, MITACS and NSERC grants.     

Analysis of heterojunction resonant cavity-enhanced Schottky photodiodes by using two-valley transport model

The article concerns heterojunction resonant cavity-enhanced (RCE) Schottky photodiodes with GaAs in the absorption layer. The quantum efficiency and linear pulse response have thoroughly been analysed. For the first time, the response of a heterojunction photodiode has been modelled by the phenomenological model for a two-valley semiconductor. The results obtained have shown that the satellite valleys, as well as the parasitic time constant, significantly influence the response and, accordingly, have to be taken into account when analysing and optimizing RCE photodetectors.     

An optimal design of collateralized mortgage obligation with PAC-companion structure using dynamic cash reserve

This paper presents a model for optimally designing a collateralized mortgage obligation (CMO) with a planned amortization class (PAC)-companion structure using dynamic cash reserve. In this structure, the mortgage pool’s cash flow is allocated by rule to the two bond classes such that PAC bondholders receive substantial prepayment protection, that protection being provided by the companion bondholders. The structure we propose provides greater protection to the PAC bondholders than current structures during periods of rising interest rates when this class of bondholders faces greater extension risk. We do so by allowing a portion of the cash flow from the collateral to be reserved to meet the PAC’s scheduled cash flow in subsequent periods. The greater protection is provided by the companion bondholders exposure to interest loss. To tackle this problem, we transform the problem of designing the optimal PAC-companion structure into a standard stochastic linear programming problem which can be solved efficiently. Moreover, we present an extended model by considering the quality of the companion bond and by relaxing the PAC bondholder shortfall constraint. Based on numerical experiments through Monte Carlo simulation, we show the utility of the proposed model.     

Pattern Search Method for Discrete <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>–Approximation

We propose a pattern search method to solve a classical nonsmooth optimization problem. In a deep analogy with pattern search methods for linear constrained optimization, the set of search directions at each iteration is defined in such a way that it conforms to the local geometry of the set of points of nondifferentiability near the current iterate. This is crucial to ensure convergence. The approach presented here can be extended to wider classes of nonsmooth optimization problems. Numerical experiments seem to be encouraging. This work was supported by M.U.R.S.T., Rome, Italy.     

Local polynomial fitting under association

We consider the estimation of multivariate regression functions r(x₁,…,x_d) and their partial derivatives up to a total order p1 using high-order local polynomial fitting. The processes {Y_i,X_i} are assumed to be (jointly) associated. Joint asymptotic normality is established for the estimates of the regression function r and all its partial derivatives up to the total order p. Expressions for the bias and variance/covariance matrix (of the asymptotic distribution) are given.     

服装主观热感觉的统计分析

本文用多因子方差分析模型和多重比较分析了服装穿着时的主观热感觉与服装品种、环境条件、穿着者的活动状态与籍贯之间的关系。通过主成分回归建立了用生理指标预测主观热感觉的模型，从而得出一种定量地评价服装属性的方法。     

BAHADUR ASYMPTOTIC EFFICIENCY IN A SEMIPARAMETRIC REGRESSION MODEL

ＢＡＨＡＤＵＲＡＳＹＭＰＴＯＴＩＣＥＦＦＩＣＩＥＮＣＹＩＮＡＳＥＭＩＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＭＯＤＥＬ￥ＬＩＡＮＧＨＵＡ；ＣＨＥＮＧＰＩＮＧＡｂｓｔｒａｃｔ：ＴｈｅａｕｔｈｏｒＳｇｉｖｅＭＬＥθ１ＭＬｏｆθ１ｉｎｔｈｅｍｏｄｅｌＹ＝θ...     

带框形约束的线性规划问题的鞍点法

根据作者最近提出的求解线性规划问题的鞍点法[3],本文对带框形约束的问题 min c~Tx, s,t A_x=b, l≤x≤h,给出简单的迭代公式.该法的主要优点是它的强收敛性和它的迭代公式非常容易实现.