应用这个新结果获得了一个在G - FC -空间中相互等价的KK M型定理和极大极小元定理。
The new result is applied to obtain a KKM type theorem and maximal and minimal element theorems which are equivalent to each other on G-FC-spaces.
借助于四元数理论证明了任意顺序下刚体有限转动合成的可交换性定理。
With the help of the theory of quaternions the theorems of commutativity of composition for the finite rotation of rigid body are proved in the any order.
详细研究了一种一元非线性系统的BP算法，提出并证明了该算法的收敛性定理，给出了该算法的应用实例。
This paper traverses the BP arithmetic to solve non-linear system in one variable, presents and proves the convergence theorem of the arithmetic, shows the application example.
本文对四元数体上矩阵奇异值摄动定理给出了推广，且这些结果对复矩阵也是新的。
The quaternion matrix singular value perturbation theorem is generalized and these results are also new one for complex matrix.
由此，把复数域上矩阵论的若干重要定理推广到了四元数体。
Accordingly, we extended several important theorems of complex matrix theory to the quaternion field.
获得了内积空间关于弱闭凸集的最佳逼近元的存在性及其刻划定理。
In the inner product space, the existence theory of best approximation element was obtained and described.
本文给出了一个关于部分变元渐近稳定性的判定定理，推广了有关文献中的有关结果。
This paper gives one determining theorem for asymptotic stability of partial variables and develops the results recorded in the related papers.
利用区间数的分解和模糊分解定理，研究了一种结构模糊有限元平衡方程的求解方法。
Based on resolution of interval Numbers and fuzzy resolution theorem, we develop a method of solving the structural fuzzy finite element equilibrium equations.
利用数域上一元多项式环与整数环相似的性质，建立数域上一元多项式环中的孙子定理，并给出它的简单应用。
Using the similarity between polynomial ring and integer ring the paper establishes Sunse's Theorem in the polynomial ring in number field, and offers its brief learning and practice.
本方法既体现有限元方法处理问题的方便性，又反映了结构稳定理论在实际工程中切实可行的应用。
The approach embodies not only the convenience of employing finite element method, but also the feasibility of solving practical engineering problems.
通过对滤子积余弦算子函数及生成元谱性质的讨论，建立了局部等度连续余弦算子函数的谱映象定理。
By discussing the filter product cosine operator function and the spectrum of it 's generator, the spectral mapping theorem for the locally equicontinuous cosine operator function is established.
研究了在门德尔遗传定理和哈代-维恩伯格平衡假设下，三元家庭基因型数据的单体分型和单体型频率估计问题。
The problems of haplotyping and haplotype frequency estimation on trio genotype data under the Mendelian law of inheritance and the assumption of Hardy-Weinberg equilibrium are studied in this paper.
本文基于旋转矩阵单位四元数分解定理，提出一种由3D特征点空间位置估计运动参数的算法。
Based on the unit quaternion decomposition of rotation matrix, this paper puts forward an algorithm to estimate motion parameters from the space position vectors of 3d feature points.
应用结构塑性极限分析的上、下限定理及相应的有限元法分析重力坝的极限承载能力，以判断大坝的稳定性。
The upper bound and lower bound theorem of classical plasticity theory and corresponding FEM is applied to analyze the bearing capacity of gravity dam for judging the stability of the dam.
基于物元分析理论，建立了大型旋转机组故障诊断系统品质综合评定理论模型。
Based on the material element theory, a new model on quality evaluation for the fault diagnosis system of large rotating machines is proposed.
在一定的条件下，用黏性逼近法证明了序列逼近于这一公共元的强收敛定理。
It is shown that under suitable conditions by the viscosity approximation algorithms, some strong convergence theorems for approximating to this common elements are proved.
讨论了二元函数中值定理中间值的渐近性质，给出了一个相关反问题的解。
The asymptotic properties of mean value in the mean value of bivariate functions are discussed, a solution is presented for related inverse problem.
本文使用超维里定理与升降算符方法，导出了氢原子跃迁矩阵元与平均值计算的一些递推关系式。
Some recursive relations were derived for the radial matrix elements of Hydrogenic Atom using hypervirial Theorem and ladder operators.
本文的目的是要给出关于可列非齐次马尔可夫链M元状态序组出现频率的一类新形式的强极限定理，所得结论对任意可列非齐次马尔可夫链普遍成立。
The purpose of this paper is to present a class of new strong limit theorems on the frequency ofm-tuple of states for arbitrary countable non-homogeneous Markov chains.
讨论了广义V_-多项式的基本定理，可乘性、拓扑不变性的充要条件以及广义二元色多项式及其应用。
Some basic theorems, multiplicability and topological invariance of the extended V-functions as well as extended dichromatic polynomials are discussed.
本文利用拓扑矢量空间中的连续线性泛函导入最佳逼近定义，给出了最佳逼近元的特征定理、存在性定理和唯一性定理。
In this paper the author introduces the definition of the best approximation in topological vector Spaces by use of continuous linear functionals.
以中值定理为工具，给出了利用一阶偏导数判定二元函数极值的方法。
The criterion extreme value of binary function for first partial derivative is given by means of the mean value theorem. The two theorems are obtained.
利用功的互等定理，推出适用于有限元求解内力影响线的方法。
Based on the reciprocal theorem of work, the paper presented a method to calculate influence lines of internal forces with finite element.
本文将一元函数的罗尔定理推广到多元函数中，并给出了一个简洁、颖的证明。
In this paper, the Rolle's theorem of a variadle function is extended to multiple-variable functions. The paper, then, gives a new and simple proof.
按照耐奎斯特空间采样定理，阵元间距超过半波长将会带来方位估计的周期性模糊。
Extending the uniform intersensor spacing beyond a half-wavelength would lead to a set of cyclically ambiguous direction-of-arrival estimates, in accordance with the spatial Nyquist sampling theorem.
本文引进并研究了三元代数的相对乘子代数，建立了一个同构定理。
This paper given the definition of the relative double multiplier on a ternary algebra, and study the isomorphic problem of the relative multiplier algebra.
本研究每元生成的子半群成群的半群，得出这种半群的某些结构定理。
This paper discusses the semigroups, each of whose sub-semigroups generated by single element is a group and some structural theorems of these semigroups are derived.
应用函数列的极限与函数的极限交换次序定理，研究了二元函数的二重极限与它的两个累次极限的关系定理，研究了二元函数的两个二阶混合偏导数可交换次序定理。
By using the limits of functions and the exchange limit theorem, we considered the relationship between the double limit of function with two variables and its repeated limits.
对双基线系统余数定理解模糊原理作了分析，提出了虚拟阵元概念，清晰地解释了基线长度之比为互质数之比的多基线系统的相位解模糊能力。
The principle for resolving ambiguity in dual baseline system is analyzed by using theorem of remainder and the concept of imaginary array is presented.
文中表明用四元数方法证明该定理比矢量法更为简单。
The paper shows that the method of proving the commutative property of composition for the finite rotations by quaternions is simpler than that by vectors.
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