广义求和与乘积算子中参数w的影响规律分析

广义求和算子与广义乘积算子是基于区间数的证据合成方法得以应用的两个重要参数,实际应用表明两者中参数w对证据合成结果影响较大,掌握参数w的影响规律对其应用将大有裨益。通过对关键函数fu和fi的数学分析,同时依据实例分析的结果,推导出广义求和算子与广义乘积算子中参数w对基于区间数的证据合成结果的三条主要影响规律：1）随着广义求和算子中的参数w增大,证据合成结果变得悲观;2）随着广义乘积算子中的参数w的增大,证据合成结果变得乐观;3）两者中参数w的同时增大或减小可以平衡各自对证据合成结果的悲观或乐观作用。总结出的影响规律可辅助选择适当的参数w,以更好地满足实际工程应用需要。     

Characterizing the measures on the unit circle with exact quadrature formulas in the space of polynomials

In the present paper we characterize the measures on the unit circle for which there exists a quadrature formula with a fixed number of nodes and weights and such that it exactly integrates all the polynomials with complex coefficients. As an application we obtain quadrature rules for polynomial modifications of the Bernstein measures on [−1,1], having a fixed number of nodes and quadrature coefficients and such that they exactly integrate all the polynomials with real coefficients.     

Efficient parallel implementation of Ewald summation in molecular dynamics simulations on multi-core platforms

We present a multi-step computation method to implement the Ewald summation for long-range electrostatic interactions in molecular dynamic simulations on a multi-core machine. Our methodology is based on the OpenMP programming model. It partitions computations of real-space summation among threads so that the global force of a single particle cannot be modified by more than one thread simultaneously. It requires neither a private copy of the force array for each thread nor an inspector at runtime. Compared with some other methods that can parallelise reduction operations on a force-array, our method achieves relatively higher speedups and lower L2 cache miss and bus utilisation ratios.     

Learning a subclass of k-quasi-Horn formulas with membership queries

Boolean formulas have been widely studied in the field of learning theory. We focus on the model of learning with queries, and study a restriction of the class of k-quasi-Horn formulas, that is, conjunctive normal form formulas where the number of unnegated literals per clause is at most k. This class is known to be as hard to learn as the general class CNF of conjunctive normal form formulas. By imposing some constraints, we define a fragment of this logic that can be learned using only membership queries. Also we prove that none of these constraints makes by itself the class learnable.     

A Complex View of Barycentric Mappings

Barycentric coordinates are very popular for interpolating data values on polyhedral domains. It has been recently shown that expressing them as complex functions has various advantages when interpolating two‐dimensional data in the plane, and in particular for holomorphic maps. We extend and generalize these results by investigating the complex representation of real‐valued barycentric coordinates, when applied to planar domains. We show how the construction for generating real‐valued barycentric coordinates from a given weight function can be applied to generating complex‐valued coordinates, thus deriving complex expressions for the classical barycentric coordinates: Wachspress, mean value, and discrete harmonic. Furthermore, we show that a complex barycentric map admits the intuitive interpretation as a complex‐weighted combination of edge‐to‐edge similarity transformations, allowing the design of “home‐made” barycentric maps with desirable properties. Thus, using the tools of complex analysis, we provide a methodology for analyzing existing barycentric mappings, as well as designing new ones.     

《C程序设计》教学方法探讨

C程序设计是计算机专业及相关专业的一门重要的基础课,是多门后续课程的基础。为提高学生的编程能力,本文讨论了C程序设计教学中存在的一些问题,并给出了解决问题的方法。另外,本文提出了利用通项公式或递推公式求和及在黑板上调试程序的思想。     

地震预测模型

文章旨在研究地震预测问题,讨论了全球16个强震活动区的强震活动次数与其后一年我国强震发生与否的关系。首先,由模糊聚类和变量规格化的思想,结合前15年的数据求出全球16个区发生强震次数与中国后一年发生强震的相关系数矩阵,通过对前15年16个区发生强震次数加权求和,得到各地的影响值,取其中的最小值作为影响值的下限值,建立预测预测中国后一年是否发生强震模型;其次,从数据中筛选出云南地区每月最高震级组成固定时间间隔的地震序列,利用气象学预测中的均生函数方法生成一列相应的时间序列,经周期性外延、残差值逐步拟合得到对当地地震最大震级的预测模型。     

递归程序设计的公式化方法

如果在设计递归程序时首先写出它的递归公式,那么编码过程会大大简化,而且得到的程序具有极好的可读性。这一思想有助于递归程序的标准化,并具有很大的普遍性。     

Evaluation of suspended load transport rate using transport formulas and artificial neural network models （Case study： Chelchay Catchment）＊

Accurate estimation of sediment load or transport rate is very important to a wide range of water resources projects. This study was undertaken to determine the most appropriate model to predict suspended load in the Chelchay Watershed, northeast of Iran. In total, 59 data series were collected from four gravel bed-rivers and a sand bed river and two depth integrating suspended load samplers to evaluate nine suspended load formulas and feed forward backpropagation Artificial Neural Network (ANN) structures. Although the Chang formula with higher correlation coefficient (r = 0.69) and lower Root Mean Square Error (RMSE = 0.013) is the best suspended load predictor among the nine studied formulas, the ANN models significantly outperform traditional suspended load formulas and show their superior performance for all statistical parameters. Among different ANN structures two models including 4 inputs, 4 hidden and one output neurons, and 4 inputs, 4 and one hidden and one output neurons provide the best simulation with the RMSE values of 0.0009 and 0.001, respectively.     

Some quadrature formulas for functions partially holomorphic with respect to each variable in a Jordan polydomain in C 2 and a complex double integral formula

In this paper, quadrature formulas with remaining term in integral form for functions partially holomorphic with respect to each variable in a Jordan polydomain in C ² and a complex double integral formula are given. For this, we used the Cauchy Integral formula for Jordan polydomain in C ².