关于一个Diophantus不等式的整数解个数

命t(m,q;r)=(m+r+g)~α-(m-r+q)~α—(m+r-q)~α+(m-r-q)~α,其中α(α-1)(α-2)(α-3)≠0。本文的目的是给出Diophantus不等式,满足条件的整数解数的较精确上界估计。其中。     

大整数的素性测试软件

本文讨论了利用分圆域中分圆整数的Jacobi和进行大整数素性测试的原理与算法,给出了基于Adleman和Pomerance所发现后由Cohen和Lenstra改进的一种确定性方法而开发研制的素性测试软件。该软件已在IBM 486计算机上调试通过。其运行结果表明,本软件可以根据待测试整数的大小,选取适当的参数,对大整数进行快速素性测试。     

关于三角函数有理式积分的探讨

三角函数有理式积分在积分的计算中占有很重要的地位 ,且计算较为复杂 ,属教学中难点。本文就一类三角函数有理式的积分的特殊性及一般性进行探讨 ,特殊性给出一题多解 ,一般性推出求解公式。     

向量空间的模结构分解

将数域F上n维向量空间视为数域F上多项式环F[s]上的模，给出了向量空间的模结构分解，指出任一数域上的向量空间都可表示为若干多项式环上循环模的直和形式，特别讨论了复数域和实数域上向量空间的分解情形，引入了变换(或矩阵)的特征值对应的生成根向量的定义，得到了循环模的生成元与变换的生成根向量之间的关系。     

Approximations to the Non-Central t,with Applications

A mildly conservative but very rapid calculation technique is proposed for problems requiring the use of the Non-central t distribution. Examples and a brief table are provided.     

Continuous penetration depth computation for rigid models using dynamic Minkowski sums

We present a novel, real-time algorithm for computing the continuous penetration depth (CPD) between two interpenetrating rigid models bounded by triangle meshes. Our algorithm guarantees gradient continuity for the penetration depth (PD) results, unlike conventional penetration depth (PD) algorithms that may have directional discontinuity due to the Euclidean projection operator involved with PD computation. Moreover, unlike prior CPD algorithms, our algorithm is able to handle an orientation change in the underlying model and deal with a topologically-complicated model with holes. Given two intersecting models, we interpolate tangent planes continuously on the boundary of the Minkowski sums between the models and find the closest point on the boundary using Phong projection. Given the high complexity of computing the Minkowski sums for polygonal models in 3D, our algorithm estimates a solution subspace for CPD and dynamically constructs and updates the Minkowski sums only locally in the subspace. We implemented our algorithm on a standard PC platform and tested its performance in terms of speed and continuity using various benchmarks of complicated rigid models, and demonstrated that our algorithm can compute CPD for general polygonal models consisting of tens of thousands of triangles with a hole in a few milli-seconds while guaranteeing the continuity of PD gradient. Moreover, our algorithm can compute more optimal PD values than a state-of-the-art PD algorithm due to the dynamic Minkowski sum computation.     

液态法白酒、固态法白酒和固液法白酒的总酯与色谱总酯量的差异分析

固态法白酒、液态法白酒、固液法白酒总酯与气相色谱分析数据单酯总和存在一定的差异,其原因主要由总酯的表示方法造成的。     

DECENTRALIZED SUPPLY CHAIN FORMATION USING MAX‐SUM LOOPY BELIEF PROPAGATION

Supply chain formation is the process by which a set of producers within a network determine the subset of these producers able to form a chain to supply goods to one or more consumers at the lowest cost. This problem has been tackled in a number of ways, including auctions, negotiations, and argumentation‐based approaches. In this paper we show how this problem can be cast as an optimization of a pairwise cost function. Optimizing this class of energy functions is NP‐hard but efficient approximations to the global minimum can be obtained using loopy belief propagation (LBP). Here we detail a max‐sum LBP‐based approach to the supply chain formation problem, involving decentralized message‐passing between supply chain participants. Our approach is evaluated against a well‐known decentralized double‐auction method and an optimal centralized technique, showing several improvements on the auction method: it obtains better solutions for most network instances which allow for competitive equilibrium (Competitive equilibrium in Walsh and Wellman is a set of producer costs which permits a Pareto optimal state in which agents in the allocation receive non‐negative surplus and agents not in the allocation would acquire non‐positive surplus by participating in the supply chain) while also optimally solving problems where no competitive equilibrium exists, for which the double‐auction method frequently produces inefficient solutions.     

Variable amplitude fatigue of high-strength cast iron alloys for automotive applications

In the automotive sector, the cumulative damage calculation method generally applied is the Palmgren–Miner-Hypothesis with its modification according to Haibach (steeper slope of the SN-line after the knee-point) as a means of also including the damage by stress amplitudes below the knee-point. This approach results in the total damage sum of the spectrum D_spec. However, the resulting question is the value of the allowable damage sum D_al for the evaluation of D_spec ⩽ D_al. The only design code that considers the assessment of cast iron components under spectrum loading is the FKM-Guideline of the Cooperative Research Association for Mechanical Engineering (FKM, Frankfurt/Germany) for designing machine components. Here, the theoretical Palmgren–Miner-damage sum D_th = 1.0 is still suggested as the allowable damage sum D_al despite the fact that this damage sum renders unsafe calculated fatigue lives in about 90% of all published results.The results obtained with component-like notched specimens of modern high-strength cast iron alloys (R_m = 650–800 MPa) such as EN-GJS-500-7, SiboDur 700-10 and MADI (Machinable Austempered Ductile Iron), which were investigated under a standard Gaussian spectrum for chassis applications and also for a fuller injection pump spectrum, suggest the allowable damage sum D_al = 0.3 for fatigue life estimations of components manufactured with these materials can be proposed; i.e. the allowable fatigue life is about one third compared to calculations with the theoretical damage sum D_th = 1.0 that is still used.