在分析多个理论模型的基础上，采用贝叶斯定理证明了前提概率原则，并将此原则与人类心理过程相结合，将归纳推理分解为连续进行的三步过程。
After analyzing several theory models of inductive reasoning, we use the Bayes Theorem to prove the premise probability principle, and integrate this theory with human mental process.
然后引入拓扑直和的概念，利用它和商空间给出一个归纳极限表示定理。
We introduce the notion of topological direct sum, and get a representative theorem of inductive limit by topological direct sum and quotient space.
二是“试验机制无差别原则”，用以为主观主义概率归纳逻辑的意见收敛定理进行辩护。
The other is the Indifference Principle of Trial Setup, with which the Theorem of Opinions' Convergence in the subjective probability theory is justified.
通过典型例题，归纳出用高斯定理求解场强问题的四种类型。
Do sum up four types using Gauss law to solute the Field strength problems by typical instances.
揭示了海涅定理的内涵，分别给出了不同函数极限的海涅定理，归纳总结了它的应用并举出实例。
This paper is intended to give a definition of Heine theorem in different functions limits and summarize its application through illustrating examples.
当代概率归纳逻辑的一个重要学派即主观主义或私人主义对待休谟问亦即归纳合理性问题的态度，密切地依赖于他们提出的大弃赌定理。
The solution of Hume's problem by the subjective or personalistic theory of probability induction relies heavily on Dutch Book theorem, which is divided into two parts, static and dynamic.
类比关于数式的二项式定理，导出关于矩阵的二项式定理，并用数学归纳法予以证明，最后举例说明关于矩阵的二项式定理的应用。
Compared to digital binomial function, matrix binomial function is derived and proved with induction method and the application of it is illustrated with examples.
常见的图像分割方法归纳为基于边界检测和边缘连接的方法、基于区域的分割方法和结合特定理论工具的分割方法三大类。
Common methods of image segmentation can be summarized as follow: methods based on boundary detection and edge linking, methods based on region, methods based on special theory.
通过对两个求导例题的分析，归纳出求函数在某些特殊点导数的新的解法定理及推论，并举例说明它们的应用，最后对此求导方法进行总结。
Through analyzing two examples of seeking derivative, new theorem and deduction for solution to some functions derivation under the special condition are concluded, and examples are shown.
同时我指出了希伍德对顶点数套用数学归纳法的格式来证明“五色定理”的方法是错误的，从而否定了希伍德证明的“五色定理”。
I is pointed out that Heawood applied the mathematical induction for the vertex number to prove 'The Five Color theorem' is incorrect.
同时我指出了希伍德对顶点数套用数学归纳法的格式来证明“五色定理”的方法是错误的，从而否定了希伍德证明的“五色定理”。
I is pointed out that Heawood applied the mathematical induction for the vertex number to prove 'The Five Color theorem' is incorrect.
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