登录

双语推荐：几何代数

进入期刊文章
数形结合，实质是将抽象的数学语言与直观的图像结合起来，关键是代数问题与图形之间的相互转化，它可以使代数问题几何化，几何问题代数化。它在我们解题中扮演着重要的角色。
Symbolic-graphic combination is to combine abstract mathematical language with intuitive graphics, and the key is the mutual transformation between algebra problems and graphics, thus realizing the mutual transformation between algebra and ge-ometry. So it plays a pivotal role in our problem-solving process.

[ 可能符合您检索需要的词汇 ]

进入期刊文章
对二元多项式插值问题进行了研究与探讨，并把这个插值问题转化为代数几何问题．通过引进H-基的概念并使用代数几何中的基本定理，得到利用两个任意次代数曲线横截相交的方法来构造平面代数曲线的插值适定结点组的新方法，从而将以往该研究方向所得结果推广到了一般情形．在得到这些研究结果的同时，我们搞清了二元多项式插值适定结点组的几何结构和基本特征，为多元多项式插值在工业产品外形设计和有限元法中的实际应用提供了理论依据．
Through the use of the concept of H-bases we ,gets a new method which use the transverse intersection of two algebraic curves to construct the Properly Posed Set of Nodes on a plane curve . Thus we generalizes the obtained results in this field to the most general case ,gets a further under-standing of bivariate interpolation for the Properly Posed Set of Nodes geometry construction and es-sential characteristics ,and provides the theory basis for the practical application of the polynomial in-terpolation in manufactures industrial products design and finite element .

[ 可能符合您检索需要的词汇 ]

进入期刊文章
针对传统三角网求交计算方法逻辑结构复杂,维度不统一等不足,基于几何代数理论,从对象表达、关系运算相统一的角度,构建了基于meet算子的自适应三角网求交算法。利用共形几何代数中与Grassmann分级结构一致的对象外积表达,建立了三角网的几何代数表达。基于meet算子构建空间三角网求交算法,探讨该算法对几何对象及维度的自适应性。最后基于南极冰盖模拟数据对上述算法进行案例验证。结果显示,本算法可以很好地支撑三角网的求交运算,在简化算法结构的同时实现了不同维度对象的自适应求交,可为基于几何代数的多维融合空间分析算法构建提供借鉴。
Traditional triangulation intersection calculation methods are insufficient in complex logical structures and not unified in dimensions.To overcome these disadvantages,an adaptive algorithm, based on the geometric algebra,is proposed.It is founded on the meet operator and from the unified object expression and relation computation perspectives.The outer product expression in Conformal Geometric Algebra,which has a property of Grassmann structure consistency,is used for constructing the geometric algebra expression of the triangulation.The triangulation intersection algorithm is constructed based on the meet operator.The object and dimensional adaptive characteristics of this algorithm are discussed.Finally,case studies based on the Antarctic ice sheet simulation data are proposed to verify the algorithm.The result suggests the proposed algorithm can well support the com-plex triangulation intersection operations.The algorithm structure is simplified and can be adaptive for multidimensi

[ 可能符合您检索需要的词汇 ]

进入期刊文章
讨论了高等代数中的一些抽象概念的直观几何解释,用图形及例子说明了概念的理解和问题求解时几何直观意义的重要性.
The geometrical and intuitional explanation of some abstract concepts in linear algebra was discussed , and the importance of geometrical intuition in comprehension of concepts and solving questions in advanced algebra is illustrated by using graphs and examples.

[ 可能符合您检索需要的词汇 ]

进入期刊文章
数形结合是高中数学重要的思想方法。代数关系和几何关系之间的相互转换，往往能够使问题更加形象和直观。然而一些复杂的代数关系很难通过人工画图快速、准确地反映出来，而且人工画图难以体现变量变化、几何对象的动态变化时，我们需要借助动态数学软件。而动态数学软件 GeoGebra 拥有强大的作图功能，可以方便快捷地搭建起把“数”与“形”结合在一起的桥梁，实现代数问题的可视化。
Symbolic-graphic combination is an important think-ing method in mathematics for senior high school. The intercon-version between algebraic relations and geometrical relations can often make problems more visual and intuitive. However, some complicated algebraic relations can hardly be rapidly and accu-rately reflected through artificial drawings which can hardly re-flect the dynamic changes of geometric objects with the changes of variables, so we should draw support from dynamic mathemat-ical software in this case. The dynamic mathematical software GeoGebra possesses powerful functions of drawing, which can rapidly make algebraic problems visualized through symbol-ic-graphic combination.

[ 可能符合您检索需要的词汇 ]

进入期刊文章
运用几何的形象思维和代数的逻辑推理，以及反函数性质给出了中值定理几个新的证明。
Gave some new proof of mean value theorem by using of the geometric image thinking,algebraic logical reasoning and the properties of inverse function.

[ 可能符合您检索需要的词汇 ]

进入期刊文章
地理数据获取、建模手段的进步使得地理现象、地理过程的表达、建模方法得到了快速发展。随着GIS的发展,其研究对象已从早期的地表简单几何对象发展为如今的复杂三维地理空间对象,并从静态对象研究发展为时空动态对象的研究。本文从几何代数的理论入手,分析了当前时空数据模型中存在的主要问题,针对这些问题,探讨了基于几何代数的时空统一表达,并结合全省车辆通行数据进行分析。
The development of methods of spatial data acquisition and modelling promotes the rapid development of methods of geographic object description and modelling .With the development of GIS ,great changes have taken place on its object of study .Based on the theory of algebraic geometry ,aiming at the problems of the current spatio-temporal data model ,this paper focus on the unified expression of space time ,and take the provincial vehicle data as an example .

[ 可能符合您检索需要的词汇 ]

进入期刊文章
借助几何画板探究了椭圆轨迹形成的四种方法：定义法、压缩法、参数方程法、代数法。
With the help of geometric sketchpad,the author explores the four methods of the ellipse trajectory formation:definition method,compression method,the parametric equation method,the algebraic method.

[ 可能符合您检索需要的词汇 ]

进入期刊文章
利用几何代数的多维统一性与运动表达的简明性特征,设计了用几何代数向量场拟合进行地表坡向表达和提取的新算法。基于高斯合成曲面模型模拟的多尺度格网DEM数据,对坡向计算的正确性、抗噪性及空间整体性进行验证和统计分析,显示几何代数向量场拟合方法能正确提取地表坡向,且较之三阶反距离平方权算法具有更强的抗噪性;选取5类典型的不同地貌类型数据进行最优窗口和坡向提取试验,黄土丘陵,梁、峁、塬和风沙地貌的最优窗口大小分别为13、11、11、11、17,所提取的坡向可以较好地反映不同地貌类型的结构特征。
Based on the multidimension-unified and simple expression of movement characteristics of geometric algebra ,a new algorithm for expressing and extracting slope of surface multi-dimensional vector fields with the geometric algebra-based vector field matching method was proposed . The correctness , noise immunity and statistical spatial integrity of the slope extraction of our method was tested with multi-scale simulated grid DEMs generated with Gaussian composite surface . The results suggested the geometric algebra-based vector field matching method could correctly extract the slope of the surface ,and the algorithm had stronger noise immunity than three-order inverse distance square weight algorithm .The optimized window size finding and slope extraction experiments were constructed with five different real world data reflecting different terrain morphology . The optimized window sizes for loess hills ,loess ridge ,loess knolls ,loess plateau ,and loess sand geomorphology are 13 ,11 ,

[ 可能符合您检索需要的词汇 ]

进入期刊文章
通过构造一个新的Lie代数,利用它相应的Loop代数设计等谱Lax对,根据其相容性条件,得到了一族Lax可积方程族,其一种约化形式为著名的AKNS族.根据迹恒等式得到该方程族的Hamilton结构.利用该可积方程族可以进一步研究它的达布变换、对称、代数几何解等相关性质.
By constructing a new Lie algebra and its corresponding Loop algebra, an isospectral Lax pair is established whose compatibility condition gives rise to a Lax integrable hierarcy, whose reduced form is the well-known AKNS hierarchy. Its Hamilton structure is obtained by the use of the trace identity. Then, its Darboux transformations, symmetry, algebro-geometric solutions, and so on will be investigated further.

[ 可能符合您检索需要的词汇 ]