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研究一个包含数论函数的方程的可解性。The solvability of an equation involving the arithmetical function is studied.

菱镁矿和白云石同属于碳酸盐类矿物，二者具有较大的溶解度和较快的溶解速度。Magnesite and dolomite are two salt type minerals. They have high solubility and fast solvability.

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讨论不确定离散广义系统的因果性鲁棒控制问题。The solvability problem of robust non causality elimination is discussed by using feedback control.

将这些应用于微分方程组，证明微分方程组具有正确能解性。Positive results are obtained in the application of the normal solvability to differential equations.

讨论了线性离散周期奇异系统初值问题的可解性和渐近稳定性问题。The notion of solvability and stability for linear discrete periodic singular systems is investigated.

由此得出了判别重特征线性偏微分算子亚椭园性和局部可解性的若干充分条件。From this, we obtain some sufficient conditions for hypoellipticity and local solvability of those operators.

本文利用某些幂零子群的半正规性，讨论有限群的可解性，所得结果统一推广了王品超、赵耀庆的若干结果。In this paper, we investigate the solvability of finite groups by using some semi normal nilpotent subgroups.

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从矩阵李代数可解性角度，推导出新的简单的延迟独立稳定性判据。In terms of solvability of a matrix Lie algebra, new simple delay-independent stability criteria are presented.

建立了以有限群的极大子群的指数复合刻划可解性的两个新定理。Two new theorems on the solvability of finite groups are proved by means of index complex of maximal subgroups.

在弹性梁方程满足渐近非一致非共振条件时，讨论了方程解的存在性。This paper discusses the solvability of an elastic beam equation under asymptotic nonuniform nonresonance condition.

玻尔兹曼机可避免陷入局部极小的问题，最后对二种算法的性能和运行情况进行了分析。Boltzmann machine can avoid the local solvability. The performance and running of the two algorithms are also analysed.

给出了有限群的幂零性、超可解性和可解性的一些新的刻画。By using NE- subgroup, some new criteria are given for the nilpotency and solvability and supersolvability of finite groups.

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讨论了一类非线性项含一阶和二阶导数的三阶三点边值问题的可解性。The solvability is considered for a class of third-order three-point boundary value problem with first and second derivatives.

本文不仅给出了可解性的数学表达式条件，而且给出了等效的拓扑条件。The results presented would be not only a mathematical conditions, but also a topological conditions for subnetwork solvability.

本文研究有源网络的故障诊断问题，着重研究其可解性与可诊断性。The fault diagnosis problem of active network is studied in this paper with the emphasis upon its solvability and diagnosability.

研究复平面单位圆域内一类非线性二维奇异积分方程的可解性。In this paper, the solvability for a class of nonlinear two-dimensional singular integral equation is considered in unit circular.

讨论了四元数量子力学中带有谱约束的最小二乘解反问题，得到了此问题有解的充分条件。The inverse least square problem with spectral constraints is also studied and a sufficient condition is given for its solvability.

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文中利用正规指数的概念刻画有限群的可解性，给出了有限群可解的几个充分条件。In this paper some sufficient conditions for solvability of finite groups are obtained by using the normal indexes of maximal subgroups.

通过定义对称系统的导出分布族的新概念，我们得出了问题可解的条件。The concept of derived distributions is firstly defined for system with symmetry. Condition for the solvability of our problem is given.

本文研究波动方程边值问题当非线性项满足强共振条件或为周期函数时的可解性和非平凡解的存在性。The solvability and the existence of solution for a wave equation with periodic condition under strong resonance are studied in the paper.