关于一个Pl型缺项插值问题

对基于节点组(1,4)的修改的(0;1;2)插值多项式Qn（f，x）的收敛性，本文改进了Akhlaghi的结果，也即对于［－1，1]上的r（≥2）次连续可微函数f（x），当n≥4/3（r+2）时，成立|f(x)-Qn(f,x)|=O(1)n~(2-r)ω(f~(r),1/n),x∈[-1,1]     

多项式的一种无重因式的分解方法

本文利用多项或重因式的判定法，论证一种更接近ｆ（ｘ）典型分解式的一种既无相同重数，又无重因式的分解方法。     

基于二次插值的GM(1,1)模型预测方法的改进

从理论上分析了GM(1,1)模型中背景值的计算,指出文[11]利用Newton-Cotes公式构造模型背景值的方法是不可靠的,提出用二次插值构造模型中的背景值,同时用最小二乘法对预测公式中的初值进行改进,并用改进的方法进行了短期预测.其理论分析及仿真结果均表明本文所提出的方法有效可靠,为提高预测精度提供了新的途径.     

A New Fully Polynomial Time Approximation Scheme for the Knapsack Problem

A fully polynomial time approximation scheme (FPTAS) is presented for the classical 0-1 knapsack problem. The new approach considerably improves the necessary space requirements. The two best previously known approaches need O(n + 1/³) and O(n · 1/) space, respectively. Our new approximation scheme requires only O(n + 1/²) space while also reducing the running time.     

Inverse Polymatroidal Flow Problem

Let D = (V, A) be a directed graph, for each vertex v V, let ⁺(v) and ^– (v) denote the sets of arcs leaving and entering v, and be intersecting families on ⁺(v) and ^–(v), respectively, and and be submodular functions on intersecting pairs. A flow f : A R is feasible if

基于整数规划强对偶求解一类局域性资源受限项目调度问题

资源受限项目调度问题(简称RCPSP)是最具代表性的项目调度问题之一,调度过程可理解为,将受资源约束的平行工序调整为顺序工序。本文针对实际中广泛存在的资源局域、而非全局受限的情况,研究局域性RCPSP,并重点考虑一类问题：项目某环节的一系列平行工序,可用资源量只有一半,各资源可重复利用且具有相应多功能,但最多能承担2个工序,需将这些工序两两排列成对,实现项目工期最短。本文首先探索问题“局域性”特征,量化局域调度对项目工期的影响;基于此,构建只涵盖“局域调度工序”的0-1规划模型;再者,发展整数规划强对偶理论,结合Dangzig-Wolfe分解等方法,提出多项式时间的精确算法;最后通过算例测试,验证算法优势,例如,计算大规模算例的最优解,运用该算法比常规精确方法可快数万倍以上。     

Statistical inference for Cox proportional hazards models with a diverging number of covariates

For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often violated under Cox proportion hazards models, leading to biased estimates with under-coverage confidence intervals. We propose a modified debiased lasso method, which solves a series of quadratic programming problems to approximate the inverse information matrix without posing sparse matrix assumptions. We establish asymptotic results for the estimated regression coefficients when the dimension of covariates diverges with the sample size. As demonstrated by extensive simulations, our proposed method provides consistent estimates and confidence intervals with nominal coverage probabilities. The utility of the method is further demonstrated by assessing the effects of genetic markers on patients' overall survival with the Boston Lung Cancer Survival Cohort, a large-scale epidemiology study investigating mechanisms underlying the lung cancer.