利用国家认可的实验室风量检测台,对螺旋风管基本系列17种规格样品的沿程阻力进行了测试,得到了不同风速下不同规格螺旋风管的沿程阻力实测值。参照ANSI/ASHRAE Standard 120-2008,采用最小二乘法对实测值进行拟合,得到了17个螺旋风管...利用国家认可的实验室风量检测台,对螺旋风管基本系列17种规格样品的沿程阻力进行了测试,得到了不同风速下不同规格螺旋风管的沿程阻力实测值。参照ANSI/ASHRAE Standard 120-2008,采用最小二乘法对实测值进行拟合,得到了17个螺旋风管沿程阻力算式。使用数理统计方法分析得出了这些算式的相关关系,对各算式数值优化整理后采用最小二乘法再次拟合,最终将17个算式拟合为1个可适用于全系列规格螺旋风管沿程阻力计算的通用算式。计算结果表明,采用拟合通用算式计算得到的螺旋风管沿程阻力值与实测值相比平均误差小于3%,精度满足设计计算要求。展开更多
The purpose of this paper is to solve the problem of determining the limits of multivariate rational functions.It is essential to decide whether or not limxˉ→0f g=0 for two non-zero polynomials f,g∈R[x1,...,xn]with...The purpose of this paper is to solve the problem of determining the limits of multivariate rational functions.It is essential to decide whether or not limxˉ→0f g=0 for two non-zero polynomials f,g∈R[x1,...,xn]with f(0,...,0)=g(0,...,0)=0.For two such polynomials f and g,we establish two necessary and sufcient conditions for the rational functionf g to have its limit 0 at the origin.Based on these theoretic results,we present an algorithm for deciding whether or not lim(x1,...,xn)→(0,...,0)f g=0,where f,g∈R[x1,...,xn]are two non-zero polynomials.The design of our algorithm involves two existing algorithms:one for computing the rational univariate representations of a complete chain of polynomials,another for catching strictly critical points in a real algebraic variety.The two algorithms are based on the well-known Wu’s method.With the aid of the computer algebraic system Maple,our algorithm has been made into a general program.In the final section of this paper,several examples are given to illustrate the efectiveness of our algorithm.展开更多
文摘利用国家认可的实验室风量检测台,对螺旋风管基本系列17种规格样品的沿程阻力进行了测试,得到了不同风速下不同规格螺旋风管的沿程阻力实测值。参照ANSI/ASHRAE Standard 120-2008,采用最小二乘法对实测值进行拟合,得到了17个螺旋风管沿程阻力算式。使用数理统计方法分析得出了这些算式的相关关系,对各算式数值优化整理后采用最小二乘法再次拟合,最终将17个算式拟合为1个可适用于全系列规格螺旋风管沿程阻力计算的通用算式。计算结果表明,采用拟合通用算式计算得到的螺旋风管沿程阻力值与实测值相比平均误差小于3%,精度满足设计计算要求。
基金supported by National Natural Science Foundation of China(Grant No.11161034)the Science Foundation of the Eduction Department of Jiangxi Province(Grant No.Gjj12012)
文摘The purpose of this paper is to solve the problem of determining the limits of multivariate rational functions.It is essential to decide whether or not limxˉ→0f g=0 for two non-zero polynomials f,g∈R[x1,...,xn]with f(0,...,0)=g(0,...,0)=0.For two such polynomials f and g,we establish two necessary and sufcient conditions for the rational functionf g to have its limit 0 at the origin.Based on these theoretic results,we present an algorithm for deciding whether or not lim(x1,...,xn)→(0,...,0)f g=0,where f,g∈R[x1,...,xn]are two non-zero polynomials.The design of our algorithm involves two existing algorithms:one for computing the rational univariate representations of a complete chain of polynomials,another for catching strictly critical points in a real algebraic variety.The two algorithms are based on the well-known Wu’s method.With the aid of the computer algebraic system Maple,our algorithm has been made into a general program.In the final section of this paper,several examples are given to illustrate the efectiveness of our algorithm.
