The Njiki’s Fundamental Theorem-Definition on Fractions in the Mathematical Set ℚ and by Extension in ℝ and ℂ, for the Purpose of Leading to the Construction of Some Algebraic Structures as Its Theoretical Applications and for the Practical Ones

The purpose of the research in the NJIKI’s fundamental THEOREM-DEFINITION on fractions in the mathematical set ℚand by extension in ℝand ℂand in order to construct some algebraic structures is about the proved EXISTENCE and the DEFINITION by NJIKI of two INNOVATIVE, IMPORTANT and TEACHABLE operations of addition or additive operations, in ℚ, marked ⊕and +α,β, and taken as VECTORIAL, TRIANGULAR, of THREE or PROPORTIONAL operations and in order to make THEM not be different from the RATIONAL ONE, +, but to bring much more and new information on fractions, and, by extension in ℝand ℂ. And the very NJIKI’s fundamental THEOREM-DEFINITION having many APPLICATIONS in the everyday life of the HUMAN BEINGS and without talking about computer sciences, henceforth being supplied with very interesting new ALGORITHMS. And as for the work done in the research, it will be waiting for its extension to be done after publication and along with the research results concerned.

k维单形上的广义余弦定理

将余弦定理推广到k维单形(三角形在高维空间的类似物)上去,旨在为余弦定理和作者的建立在四面体上的以面积为关注点的余弦定理(任何四面体的任一面的面积平方等于其余各面的面积平方和,再减去其中每两个面的面积与它们所成的内二面角的余弦之乘积的2倍)提供一揽子解决方案.以此证明:余弦定理从此不再是个初等几何问题.

用余弦的加法定理不同的证明来说明一题多解的重要性

用不同的方法证明余弦的加法定理说明一题多解很重要,它要求学生有很高的参与热情,能唤起学生的好奇心和求知欲,便于搞清问题的内涵和外延,而且可以提高数学能力。

两个与勾股定理有关的定理

本文给出了两个定理:从一个新的角度推广了勾股定理与余弦定理:另外我们还给出了这两个定理的若干简单应用。

勾股逆定理的推广

用导数方法对勾股逆定理进行了推广，得到了如下结果：在△ABC中，若△a^x＋b^x＝c^x，其中x∈R－［0，1」，则1）当x∈（－∞，0）∪（1，2］时，Cmax＝；2）当x∈［2，＋∞）时，Cmin＝．此外，给出了上述结果的两个推论及其应用．

一种激光共焦位移传感器倾角误差补偿方法

应用激光共焦位移传感器测量物体倾角时,易受到物体颜色、位置的影响,导致误差较大,提出一种激光共焦位移传感器倾角误差补偿方法。基于激光共焦位移传感器分析结果,结合朗伯定律,对散射光场产生的光强进行计算,获取激光光束光能质心线在接收透镜中的角位置,分析激光光束与物体表面间是否呈垂直关系,若垂直说明没有发生倾斜,无需补偿;若不垂直说明物体表面发生倾斜,利用余弦定理计算出倾角,以倾角与物面间位移变量作为误差补偿结果。在不同倾角误差的测试实验中,所提方法都能实现精准补偿,具有适用性和鲁棒性。

数据驱动型的维修任务分配方法

采用数据驱动方法来解决维修生产环境中复杂的任务分配问题。首先利用多种细致的量化方法制订一套详细而客观的评分系统,然后采用并行计算环境下的蒙特卡洛树搜索来快速搜寻各种有价值的分配组合方案,最后从探索的树结构中选择最佳的方案来完成任务的分配。该方法不仅使数据科学技术在实际生产过程中得到落地,而且还取得了不错的效果。