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四元数矩阵的行展开式与其行列式
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作者 吕洪斌 杨忠鹏 《北华大学学报(自然科学版)》 CAS 2001年第2期104-111,共8页
在注意到由谢邦杰定义的四元数矩阵的行展开式与陈龙玄定义的四元数矩阵的行列式之间联系与差异的基础上,给出了一个新的自共轭矩阵的行列式的展开定理,由此可得到四元数矩阵逆的新的显示公式及Cramer解式.
关键词 四元数矩阵 行展开 列式 自共轭矩阵 列式 逆矩阵 显示公式 Vramer解式
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行列式按行(列)展开定理的简单证法
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作者 周仲旺 《高等数学研究》 2023年第2期93-93,共1页
本文利用行列式定义,给出了行列式按行(列)展开定理的一个简单证法.
关键词 列式 代数余子式 列式按(列)展开
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一类特殊行列式的新算法 被引量:1
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作者 张盛 荆治宇 +4 位作者 徐波 刘诗雨 陈虹 曲虹烨 高佳齐 《渤海大学学报(自然科学版)》 CAS 2023年第1期58-65,共8页
行列式计算有许多方法,其中针对含参数的行列式时常需要进行分类讨论.给出右上角元素为α、左下角元素为β、主对角线上元素分别x_(1),x_(2),…,x_(n)的一类特殊行列式的多种算法,包括数学归纳法、拆分法、升阶法、按行(列)展开后迭代... 行列式计算有许多方法,其中针对含参数的行列式时常需要进行分类讨论.给出右上角元素为α、左下角元素为β、主对角线上元素分别x_(1),x_(2),…,x_(n)的一类特殊行列式的多种算法,包括数学归纳法、拆分法、升阶法、按行(列)展开后迭代法和按行(列)展开后直接计算法,从中得到这类行列式的一个具有一般性的公式.所采用的多种方法不但去掉了文献中基于两种不同情况进行分类计算的限制,而且得到的一般性公式,还统一了已知算法在两种分类情况下的不同结果,这对所考虑的行列式计算而言是新尝试. 展开更多
关键词 列式 数学归纳法 升阶法 拆分法 (列)展开
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浅谈“线性代数”学习中学生创新与应用能力的培养——以行列式的按行(列)展开法则为例
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作者 万前红 郑立景 《科教导刊》 2021年第29期144-146,共3页
线性代数的概念多且抽象,这是线性代数学习的难点之一。下功夫去探讨新概念和新知识的引入,寻找各个概念之间的联系是解决线性代数概念多且抽象问题的手段之一,同时可以提高学生数学思维、数学理解、数学应用等方面的创新能力。本文通... 线性代数的概念多且抽象,这是线性代数学习的难点之一。下功夫去探讨新概念和新知识的引入,寻找各个概念之间的联系是解决线性代数概念多且抽象问题的手段之一,同时可以提高学生数学思维、数学理解、数学应用等方面的创新能力。本文通过具体的教学实例来分享如何在线性代数教学中实现这个目标。 展开更多
关键词 列式按(列)展开法则 克拉姆法则 逆矩阵 伴随矩阵
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关于自共轭四元数矩阵的注记 被引量:1
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作者 张峥嵘 《南京师大学报(自然科学版)》 CAS CSCD 2002年第1期49-52,共4页
指出了文 [1]中的两处错误 ,并在文 [3]的基础上给出了文 [1]中部分定理的新证明 .
关键词 自共轭四元数矩阵 行展开 展开 展开定理 半正定矩阵 四元数体
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矩阵左半张量积的一些重要性质
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作者 李东方 《科教导刊》 2013年第31期215-216,共2页
文章对矩阵的一种新的乘法运算——左半张量积,进行了探讨,获得了一些新的性质,得到了一些重要的结论。
关键词 左半张量积 换位矩阵 行展开 展开
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Application of Modified G'/G-Expansion Method to Traveling Wave Solutions for Whitham-Broer-Kaup-Like Equations 被引量:5
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作者 ZHOU Yu-Bin LI Chao 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第4期664-670,共7页
A modified G′/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham -Broer- Kaup-Like equations. As a result, the hyperbolic functio... A modified G′/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham -Broer- Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained. 展开更多
关键词 Whitham-Brover-Kaup-like equations G′/G-expansion solitary wave solution
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关于代数余子式若干注记
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作者 徐国静 《大学数学》 2019年第4期104-107,共4页
把一个行列式的每个元素都加一个任意常数之后,得到一个新的行列式,这两个行列式的所有元素的代数余子式之和保持不变.现利用行列式的性质、行列式的按行(列)展开和加边法,给出这个结论的几种证明方法.
关键词 列式性质 列式按(列)展开 代数余子式 加边法
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条形统计图的整理与复习
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作者 周玲娇 《基础教育论坛》 2017年第9期34-36,共3页
文章尝试从“形”(条形统计图的基本知识)与“行”(数据的分析与推测)两个方面开展教学,以提高学生综合运用条形统计图解决实际问题的能力。
关键词 数据分析 “形”的回顾 ”的展开 整理复习
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Creating Regional Tourism Standards in the Yangtze River Dalta Region
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作者 Zhang Chen 《China Standardization》 2009年第1期30-33,共4页
With the strategicdevelopment of regionaltourism cooperation in theYangtze River Delta region,acceleratingthe creation oftourism standards becomesparamount.Which organizationcould best develop tourismstandards and the... With the strategicdevelopment of regionaltourism cooperation in theYangtze River Delta region,acceleratingthe creation oftourism standards becomesparamount.Which organizationcould best develop tourismstandards and the principles oftourism standards are discussedin this paper.Thelong-term and short-term plansfor the creation of regionaltourism standards in theYangtze River Delta region arealso presented. 展开更多
关键词 STANDARDIZATION Yangtze River Delta re-gional tourism cooperation
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Electricity Sector Transitions in an after War Country: A Review of Afghanistan's Electricity
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作者 Mir Sayed Shah Danish Najib Rahman Sabory +4 位作者 Sayed Mir Shah Danish Tomonobu Senjyu Gul Ahmad Ludin Ahmad Samim Noorzad Atsushi Yona 《Journal of Energy and Power Engineering》 2017年第7期491-496,共6页
Afghanistan electricity sector has experienced many ups and downs of transitions from 1893 to date. With the growing global interest in Afghanistan rehabilitation, this paper presents an over view of Afghanistan elect... Afghanistan electricity sector has experienced many ups and downs of transitions from 1893 to date. With the growing global interest in Afghanistan rehabilitation, this paper presents an over view of Afghanistan electricity sector which includes the historical development trends, power generation potential, sustainable energy exploitation, electricity policy transition and immature policies experiences, and the legacy of the war. The lack of access to the basic information about Afghanistan power sector was one of the serious concerns of international donors and investors. Still, this information somehow has been kept in official documents wrap up. In this collection, the Afghanistan's electricity sector is pictured as a reference for Afghanistan electricity. It can be opening toward primary sources of Afghanistan electricity sector of the lessons learned and asset for researchers interesting in this topic. 展开更多
关键词 Afghanistan electricity electricity sector development Afghanistan renewable energy
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A Research on QFD-"House of Brand" in Fashion Industry
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作者 Evrim Kabukcu 《Chinese Business Review》 2016年第4期207-213,共7页
Fashion continues to be an area that reflects the increasing popularity of different theoretical and practical approaches of researchers from different disciplines. Due to the rapid cycles of fashion, sustainable prod... Fashion continues to be an area that reflects the increasing popularity of different theoretical and practical approaches of researchers from different disciplines. Due to the rapid cycles of fashion, sustainable products and processes in terms of technical creativity and innovative approach are needed. In this context, fashion marketing emerges as an integrative marketing application with its both technical and social aspects by taking potential customers center that symbolize rapid change and creativity of fashion products. In this study, QFD-House of Brand was designed with Quality Function Deployment (QFD) approach. In this context, the experts (focus group) in Fashion Industry evaluated the selected fashion brand and its selected products by prioritizing the criteria. These evaluations were used in QFD-House of Brand. Thus, technical and social aspects of fashion industry were analysed together. By this technique, QFD-House of Brand established in relation to products and brand was interpreted and optimization suggestions were presented in accordance with the findings of the research. In addition, suggestions on sustainability and optimization of brand equity in fashion industry were provided. 展开更多
关键词 brand equity fashion industry PRODUCT quality function deployment SUSTAINABILITY
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Analysis on Problems and Countermeasures of China's Digital Animation Industry
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作者 Hu Jia 《International Journal of Technology Management》 2014年第3期101-103,共3页
Since the reform and opening up,with the digital network science change rapidly development,China' s digital animation industry has been rapid development of corresponding.Effects of digital animation industry of Ch... Since the reform and opening up,with the digital network science change rapidly development,China' s digital animation industry has been rapid development of corresponding.Effects of digital animation industry of China' s national economy is more and more strong,and in the entire national economy proportion is also growing.Digital animation industry as one of the most promising future industry, its development potential is very great,and it should cause our enough attention,which must not regard as unimportant.The development of digital industry can drive software and hardware technology, telecommunications industry and other industries progress.However, at present our country digital animation industry development is not satisfactory, and there are still many problems,also,the problems existed in the development of China's digital animation industry problem for detailed analysis,and it puts forward some countermeasures to solve the problem. 展开更多
关键词 Digital Animation PROBLEMS COUNTERMEASURES
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Abundant Exact Traveling Wave Solutions of Generalized Bretherton Equation via Improved (G′/G)-Expansion Method 被引量:10
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作者 M.Ali Akbar Norhashidah Hj.Mohd.Ali E.M.E.Zayed 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第2期173-178,共6页
In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presen... In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves. 展开更多
关键词 improved (G'/G)-expansion method travelling wave solutions the Bretherton equation nonlinearevolution equations
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The effective propagation constants of SH wave in composites reinforced by dispersive parallel nanofibers 被引量:2
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作者 QIANG FangWei WEI PeiJun LI Li 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2012年第7期1172-1177,共6页
In the present paper, the effective propagation constants of elastic SH waves in composites with randomly distributed parallel cylindrical nanofibers are studied. The surface stress effects are considered based on the... In the present paper, the effective propagation constants of elastic SH waves in composites with randomly distributed parallel cylindrical nanofibers are studied. The surface stress effects are considered based on the surface elasticity theory and non-classical interfacial conditions between the nanofiber and the host are derived. The scattering waves from individual nanofibers embedded in an infinite elastic host are obtained by the plane wave expansion method. The scattering waves from all fibers are summed up to obtain the multiple scattering waves. The interactions among random dispersive nanofibers are taken into account by the effective field approximation. The effective propagation constants are obtained by the configurational average of the multiple scattering waves. The effective speed and attenuation of the averaged wave and the associated dynamical effective shear modulus of composites are numerically calculated. Based on the numerical results, the size effects of the nanofibers on the effective propagation constants and the effective modulus are discussed. 展开更多
关键词 multiple scattering averaged wave NANOFIBER surface elasticity size effects
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New Exact Solutions and Dynamics in(3+1)-Dimensional Gross–Pitaevskii Equation with Repulsive Harmonic Potential 被引量:1
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作者 王晓丽 武振华 《Communications in Theoretical Physics》 SCIE CAS CSCD 2014年第5期583-589,共7页
Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic pot... Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential. 展开更多
关键词 Gross-Pitaevskii equation exact solution solitory wave periodic wave F-expansion
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Exact Interaction Solutions of an Extended(2+1)-Dimensional Shallow Water Wave Equation 被引量:5
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作者 王云虎 王惠 +1 位作者 张洪生 特木尔朝鲁 《Communications in Theoretical Physics》 SCIE CAS CSCD 2017年第8期165-169,共5页
Applying the consistent Riccati expansion method, the extended(2+1)-dimensional shallow water wave equation is proved consistent Riccati solvable and the exact interaction solutions including soliton-cnoidal wave solu... Applying the consistent Riccati expansion method, the extended(2+1)-dimensional shallow water wave equation is proved consistent Riccati solvable and the exact interaction solutions including soliton-cnoidal wave solutions,solitoff-typed solutions are obtained. With the help of the truncated Painlev′e expansion, the corresponding nonlocal symmetry is also given, and furthermore, the nonlocal symmetry is localized by prolonging the related enlarged system. 展开更多
关键词 soliton-cnoidal wave solutions consistent Riccati expansion nonlocal symmetry
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Stability of proteins with multi-state unfolding behavior 被引量:5
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作者 YANG BinSheng SONG Zhen +1 位作者 ZHENG XiaoYan ZHAO YaQin 《Science China Chemistry》 SCIE EI CAS 2012年第7期1351-1357,共7页
A new model used to calculate the free energy change of protein unfolding is presented. In this model, proteins are considered to be composed of structural elements. The unfolding of a structural element obeys a two-s... A new model used to calculate the free energy change of protein unfolding is presented. In this model, proteins are considered to be composed of structural elements. The unfolding of a structural element obeys a two-state mechanism and the free energy change of the element can be obtained by a linear extrapolation method. If a protein consists of the same structural elements, its unfolding will displays a two-state process, and only the average structural element free energy change 〈△G0 element(H2O)〉 can be measured. If protein consists of completely different structural elements, its unfolding will show a multi-state behavior. When a protein consists of n structural elements its unfolding will shows a (n+1)-state behavior. A least-squares fitting can be used to analyze the contribution of each structural element to the protein and the free energy change of each structural element can be obtained by using linear extrapolation to zero denaturant concentration, not to the start of each transition. The measured △Gn protein(H2O) is the sum of the free energy change for each structural element. Using this new model, we can not only analyze the stability of various proteins with similar structure and similar molecular weight, which undergo multi-state unfolding processes, but also compare the stability of proteins with different structures and molecular weights using the average structural element free energy change 〈△G0 element(H2O)〉. Although this method cannot completely provide the exact free energy of proteins, it is better than current methods. 展开更多
关键词 new model protein stability multi-state unfolding CopC
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A Note on Exact Traveling Wave Solutions of the Perturbed Nonlinear Schrdinger's Equation with Kerr Law Nonlinearity 被引量:3
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作者 张再云 甘向阳 +2 位作者 余德民 张映辉 李新平 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第5期764-770,共7页
In this paper,we investigate nonlinear the perturbed nonlinear Schrdinger's equation (NLSE) with Kerr law nonlinearity given in [Z.Y.Zhang,et al.,Appl.Math.Comput.216 (2010) 3064] and obtain exact traveling soluti... In this paper,we investigate nonlinear the perturbed nonlinear Schrdinger's equation (NLSE) with Kerr law nonlinearity given in [Z.Y.Zhang,et al.,Appl.Math.Comput.216 (2010) 3064] and obtain exact traveling solutions by using infinite series method (ISM),Cosine-function method (CFM).We show that the solutions by using ISM and CFM are equal.Finally,we obtain abundant exact traveling wave solutions of NLSE by using Jacobi elliptic function expansion method (JEFEM). 展开更多
关键词 exact solutions NLSE with Kerr law nonlinearity infinite series method (ISM) Cosine-function method (CFM) Jacobi elliptic function expansion method (JEFEM)
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