无穷积分

Energy density and particle density in high energy heavy-ion collisions are calculated with infinite series expansion method and Gauss-Laguerre formulas in numerical integration separately, and the results of these two methods are compared, the higher terms and linear terms in series expansion are also compared.

分别用无穷级数展开方法和数值积分计算中的高斯拉盖尔求积法对高能重离子碰撞中能量密度和粒子密度数值进行计算，并对结果及级数展开中的高次项和一次项的大小进行了比较。

Further, with the help of Riccati equations, an infinite number of conservation laws for the solton hierarchy are deduced. For the sake of simplicity, taking the general TD hierarchy as an illustrative example, we prove that its 2×2 Lenard pair of operators forms a Hamiltonian pair. Thus the isospectral evolution TD hierarchy is the general Hamiltonian system and possesses the Bi-Hamiltonian structures and Multi-Hamiltonian structures. By using the method of derivation of functional under some constraint condition, a complete one-to-one correspondence between the Hamiltonian functions of the hierarchy and its conservation density functions can be built. These results can also be applied to the isospectral evolution soliton hierarchy of this paper. Finally, there's a gauge transformation between the spectral problem of this paper and the AKNS system. Moreover, the potentials in these spectral problems satisfy the general Miura transformation, the corresponding relationship between the two soliton hierarchies is also given.

进一步本文还通过特征函数的组合关系所满足的Riccati方程，得到了该等谱方程族的无穷多个守恒律；为简便起见，本文以广义TD族为例，由它的2×2 Lenard算子对的性质证明了此算子对为Hamilton算子对，这说明广义TD族是广义Hamilton系统且具有Bi-Hamilton结构和Multi-Hamilton结构；进而利用它的依赖于谱参数的一般守恒密度的积分在约束条件下求泛函导数的方法，得到了广义TD族的Hamilton函数与守恒密度之间的对应关系，这些性质对于由本文提出的2×2谱问题所导出的等谱孤子族仍成立；另外此谱问题与AKNS系统存在着规范变换，位势之间有广义Miura变换，而孤子方程之间也满足一定的等价关系。

Let be continuous on ,and .If the limit exists and have finite value , the value is the improper integral of on ,which is denoted by,that is

定义1 设函数在区间上连续，取，如果极限存在且为有限值，则此极限为函数在无穷区间上的反常积分，记作，即

Thus we available defined a fuzzy Henstock integral on infinite interval.

基于这种考虑，定义了无穷区间上的模糊Henstock积分。

However, due to the oscillation and singularity of the integrand of Green's function and that integral interval is infinite, it is difficult to compute the function and to control the accuracy.

而格林函数中被积函数的振荡性，奇异性和积分区间为无穷使得该函数的计算较为困难，精度不易控制。

-integrals of vector valued functions on infinite interval

无穷区间上n维模糊数值函数的积分：背景，定义及刻划

In this paper, we will introduce the weighted modulus of smoothness and the weighted K-functional to discuss the direct and the converse theorems, the local saturation results on the simultaneous approximation on an infinite interval with Jacobi-weight by the integral operator, the lin...

本文利用带权光滑模与带权K--泛函讨论定义在无穷区间上的积分型算子Gamma算子线性组合对空间L_∞(0，∞)中函数的带Jacobi权同时逼近的正逆定理以及局部饱和结果，还讨论了Gamma算子的强逆不等式。

Integral comparison criterion, product of absolutely convergence series.

积分判别法；无穷乘积

In Chapter 4 and Chapter 5, complete researches have been done respectively on the center conditions and center integral of a quintic system and a septic system.

在第四章和第五章，分别对一类五次系统和七次系统的无穷远点的中心条件和中心积分进行了完整研究。

This article investigates the two-point boundary value problem to a coupled system of nonlinear fractional differential equations. By applying growth conditions on the nonlinear terms, we obtain an existence result of solutions. Our analysis relies on the Schauder fixed-point theorem and the reduction of the considered problem to the equivalent coupled system of integral equations.

本文讨论非线性分数阶微分方程耦合系统的两点边值问题，应用Green函数，将其转化为等价的积分方程耦合系统，并设非线性项在无穷远处有增长条件，应用Schauder不动点定理证明解而非限于正解的存在性。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。