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g函数
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  g-function
     The Lipschitz Functions and Littlewood-Paley g-Function on Spaces of Homogeneous Type
     齐型空间上的Lipschitz函数与Littlewood-Paley g-函数
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     Abstract We apply the concept of G-function introduced by Nowosad and Hoffiman to obtain the lower bounds for the smallest singular value of matrices,and the reults generalize and improve those in[1,2,3].
     本文将Nowosad和Hoffman提出的G-函数概念应用于估计矩阵最小奇异值的下界和线代方程组的条件数,所得结果优于前人的结论。
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  相似匹配句对
     MULTIPLE WINDOW FUNCTION
     多窗口函数
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     The Lcm-sum Function
     最小公倍数的和函数
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     LOGISTIC PRODUCTION FUNCTION
     Logistic生产函数
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     G-FUNCTION AND SPECTRAL PROPERITIES
     G-函数和谱性质
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     Extended e-bent Functions
     广义ebent函数
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  g-function
this article, the distribution of the determinant of the sample correlation matrix from a mixture of two multivariate normal distributions has been obtained in terms of Meijer's G-function.
      
We give the Lp-boundedness for a class of Marcinkiewicz integral operators and μΩ,s related to the Littlewood-Paley g-function, -function and the area integral S, respectively.
      
Littlewood-Paley g-function on the Heisenberg Group
      
We consider the g-function related to a class of radial functions which gives a characterization
      
Riesz transform and g-function associated with Bessel operators and their appropriate Banach spaces
      
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Making the model experiment as similar to the actual operation of a blast furnace as possible, this paper presents a quantitative investigation on the behavior of the flow of primary slag in blast furnaces. It is found that a strongly horizontal gas flow occurs in blast furnaces due to the softening melting-zones and the coke layers.Primary slag is therefore forced to fall down out of the vertical and then outflow together to the lower ends of the softening melting-zones. The semiemperical relationship of the...

Making the model experiment as similar to the actual operation of a blast furnace as possible, this paper presents a quantitative investigation on the behavior of the flow of primary slag in blast furnaces. It is found that a strongly horizontal gas flow occurs in blast furnaces due to the softening melting-zones and the coke layers.Primary slag is therefore forced to fall down out of the vertical and then outflow together to the lower ends of the softening melting-zones. The semiemperical relationship of the angle 9 out of the vertical may be expressed aswhere (dP/dL)G/γl is the dimensionless pressure gradient, μl and γl the viscousityand the specific gravity of melts respectively, L and G the gravitational flow of melts in liquid and gaseous states, fs the surface area of piled melts and ε the porousity. These formulas imply that the angle θ relates to the air blast or its velocity, the specific gravity and viscousity of melts and other properties of burden. A metallurgic analysis has been made for the relation between the angle θ of the flow of primary slag and the operation of blast furnaces.

本文通过模型试验,在尽可能考虑与高炉相似条件下,研究了高炉内初渣流动规律。结果表明:由于高炉内存在软熔带和焦炭夹层,因而在在较强的水平煤气流。初渣带在水平煤气流的作用下产生偏离垂直方向的流动,使初渣有某种程度集中流下现象。初渣流动的偏角 θ 是无因次压力梯度(dP/dL)_g/γl、准数(Fr_l)/(Re_l)及无因次流量 L/G的函数。即偏角θ是风量,熔体比重、粘度及流量和炉料性质的函数。利用此式,分析了初渣流动的偏角θ与高炉冶炼的关系。

This paper drived the probability density functions of quotient of independent Beta, Gamma Variables. They can represents by Meijer's G-functions. The density functions of quotient of Beta, Gamma Variables are Meijer's G-funcfions which are expressible in closed analytical forms. When parameters F, S of Beta-distribution β(F,S ) and parameter Z of Gamma-distribution T ( Z,T ) are positive integral numbers, these results can applied to the problems of statistical estimation for the environmental factors of the...

This paper drived the probability density functions of quotient of independent Beta, Gamma Variables. They can represents by Meijer's G-functions. The density functions of quotient of Beta, Gamma Variables are Meijer's G-funcfions which are expressible in closed analytical forms. When parameters F, S of Beta-distribution β(F,S ) and parameter Z of Gamma-distribution T ( Z,T ) are positive integral numbers, these results can applied to the problems of statistical estimation for the environmental factors of the tests of exponential-failure and pass/fail types.

本文推导了独立的Beta,Gamma变量之商的概率密度函数,它们可表为Meijer的G-函数。这两个Meijer G-函数有精确的解析表达式。当β-分布β(F,S)的参数F,S及Γ-分布Γ(z,τ)的参数z为正整数时,上述结果可直接用于解决寿命为指数分布及二项试验时的环境因子的统计估计问题。

Density distribution,vertical component g of gravitational field of a complex form object and second derivative w_(xy),w_(yy) of gravitational po- tential can be calculated by finite element method, Taking a sufficient large area that is surrounding the density body, the boundary value of g can be expressed as follows ■▽~2g=-4πK(■ρ)/(■y) within the area (■g)/(■n)+(sin(θ-α))/(rsinθ)g=0 at the boundary The calculus of variations corresponding to the above boundary value will be to get the extreme value by functional...

Density distribution,vertical component g of gravitational field of a complex form object and second derivative w_(xy),w_(yy) of gravitational po- tential can be calculated by finite element method, Taking a sufficient large area that is surrounding the density body, the boundary value of g can be expressed as follows ■▽~2g=-4πK(■ρ)/(■y) within the area (■g)/(■n)+(sin(θ-α))/(rsinθ)g=0 at the boundary The calculus of variations corresponding to the above boundary value will be to get the extreme value by functional analysis F(g)=■[1/2(▽g)~2+4πK(■g)/(■y)ρ]ds+■1/2(sin(θ-α))/(rsinθ)g~2dl When the calculus of varions described above is solved by finite ele- ment method,the area Ω is seperated into triangular elements and second functional interpolation is performed in element e.F_e(g)of each element is calculated first,then added together to get total F(g)which is the function of g to be calculated for each node.Taking the extreme value of F(g),a linear algebraic equation is derived;g of each node can be de- rived by solving the equation;after taking numerical derivative for g, second derivative of gravitational potential can be obtained.

有限元法可以计算密度分布、形态复杂物体的重力场垂直分量 g 及重力位二阶导数 W_x■、W_(yy)。取一个包围密度体的足够大的区域,求解 g 的边值问题可表为▽~2g=-4πK(■ρ)/(■y) 在区域内 (■)g)/(■n)+(sin(θ-α))/(r sin θ)g=0 在边界上与上述边值问题相应的变分问题是泛函F(g)=■[(1)/(2)(▽g)~2+4πK(■g)/(■y)ρ]dS+■_Γ(1)/(2)(sin(θ-α))/(r sin θ)g~2dl取极值。用有限元解上述变分问题时,将区域Ω剖分为三角单元,在单元 e 内进行二次函数插值。首先计算各单元的 F_e(g),然后相加组成总体的 F(g),它是各节点待求的 g 的函数。对 F(g)求极值,得一线性代数方程组。解方程组可得各节点的 g。对 g 进行微商,即可得重力位二阶导数。

 
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