中文翻译与英英解释

【数学】广义积分，非正常积分。

improper:    adj. 1.不适当的，不合适的，非正常的。 2.不正确 ...

integral:    adj. 1.完全的；缺一不可的，主要的。 2.【数学】 ...

In calculus, an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number or ∞ or ?∞ or, in some cases, as both endpoints approach limits. Such an integral is often written symbolically just like a standard definite integral, perhaps with infinity as a limit of integration.

例句与用法

Chapter 4, omitting the section on the existence of the integral but including improper integrals .
第四章略去了关于积分存在性那一节，且包括广义积分。

A new class of nonlinear inequalities involving improper integrals
一类新的含反常积分的非线性不等式

Some nonlinear inequalities involving improper integrals and their discrete analogues
涉及广义积分及其离散模型的某些非线性不等式

Comparison of convergences on regular integral two kinds of improper integral and infinite series
求无穷级数和以及多重积分极限的概率方法

These new improper integral inequalities are closely related with some integral inequalities proved by the present author in an earlier paper
这类含反常积分的非线性不等式与笔者以前证明的某些非线性积分不等式密切相关。

A priori point - wise estimations are established for bounded functions satisfying a new class of nonlinear inequalities involving improper integrals
摘要对满足一类新的含反常积分非线性不等式的有界函数建立了先验逐点估计。