等价的

In the second chapter, the concept of an integrated abstract delay equation is introduced, and the equivalence of the well - posedness of an integrated delay equation and an associated integrated Cauchy problem is derived.

在第二章中，引入了积分抽象时滞方程的概念，并且得到积分抽象时滞方程的适定性与相应的积分柯西问题适定性等价。

This paper,using the method of differential equation,proves some characters properties of basic elementary function ,and then concludes an equivalent representation about basic elementary function .

运用微积分的方法，对基本初等函数的若干特征性质进行了证明，从而给出了基本初等函数的等价表征。

Based on the assessment of mycelial biomass, xylanase activity and content of xylose-equivalent reducing sugars in their liquid cultures, the isolate CY4786 was best for xylanase production in a basal medium containing birchwood xylan (10.0 g/L)as a sole carbon source, yeast extract (2.5 g/L) and sea salts (15.0 g/L) with initial pH 7.8. When assayed at the optimized regime of 50℃ and pH 4.6, the activity of xylanase produced by CY4786 in 7d liquid culture at 25℃ reached 1.07 × 104 unit/mL.

根据培养液中菌丝生物量、木聚糖酶活力和木糖等价还原糖含量等指标的测定，菌株CY4786在起始pH 7.8的木聚糖-酵母膏-海盐液体培养基中25℃下震荡(100r/min)培养7d产酶最佳；粗酶液在50q℃和pH 4.6的优化条件下进行测定，木聚糖酶活力达到1.07×104U/mL。

In this paper,a proof is made of the equivalence in three definitions of the integral of bounded function in finite set measure.

关于Lebesgue积分，文献有不同的定义，本文给出了测度有限集上有界函数 Lebesgue积分三种不同定义的等价性的一种证明。

Brown and Halmos [3] showed that the only compact Toeplitz operator on the Hardy space is the zero operator and a Toeplitz operator is bounded on the Hardy space if and only if its symbol is bounded.

Brown和Halmos[3]证明了经典Hardy空间上只有零算子才是紧的Toeplitz算子，并且证明了Toeplitz算子有界等价于它的符号是有界的。

It has been showed that the quantum PCII can be still valid for the general case Jacobi J 1, which is different from quantum Noether theorem. The equivalence between quantum canonical equation and PCII is deflved at the quantum level. The comparisons of these results in quantum level with those in classical theories are discussed in detail. The relationship of canonical transformation with quantum PCII is obtained.

结果表明，当变换的Jacobi行列式不为1时，量子PC积分不变量仍然存在，从而把PC积分不变量推广到了最一般情形；在量子水平上，证明了量子正则方程与该积分不变量之间的等价性；比较了经典与量子PC积分不变量以及PC积分不变量与Noether定理；给出正则变换与量子PC积分不变量间的关系。

There are assumptions about aircraft's ground motion; one of those widely used is "the center of simultaneous turning of the airframe is the same as the center of curvature of the mass center's track".

对飞机的地面运动一直沿用瞬时转动中心等价于质心轨迹的曲率中心的假设。

The algebraic and coalgebraic methods in computer science is investigated in general, including its basic ideas, the categorical properties of algebras and coalgebras, initial algebra and final coalgebra, bisimulation and behavior equivalence, coalgebraic specifications, and coalgebraic logics.

对代数方法与共代数方法的基本概念、代数与共代数范畴的性质、初始代数与终结共代数、双模拟与行为等价、共代数规范以及共代数逻辑进行了比较全面和深入的研究。

Schauengurg[2] considered more general case and found necessary and sufficient conditions for the cosmash product coalgebra H Q to be a Hopf algebra with a Hopf subalgebra H and a weak projection !

Schauenburg在文献[2]中把Radford的研究加以推广，给出了使余smash积HQ为Hopf代数，H为HQ的子Hopf代数，且具有弱投射π：HQ→H(即π是左模余代数同态，且π|_H=id_H)的等价条件。

We prove the equivalent conditions of completely monotone function, we also discuss the relationship of positive definite function, semi-positive definite function and completely monotone function when the function take values in a commutitive von Neumann algebras.

我们证明了完全单调函数的几个等价条件，并且讨论了取值于交换von Neumann代数的正定函数，半正定函数及完全单调函数之间的关系。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。