1、differential equations

differential equations发音

英：　　美：

differential equations中文意思翻译

常见释义：

微分方程

differential equations双语使用场景

1、The theory of the solution of partial differential equations remained to be fashioned.───偏微分方程解的理论还有待于形成.

2、In 1728 Euler gave differential equations for geodesics on surfaces.───1728年,奥伊勒绘出了曲面上测地线的微方程.

3、And let's not even talk about differential equations.───我们不再讨论微分方程序。

4、To some extent, his work pays dividends in differential equations.───他的工作在某种程度上给微分方程带来了好处.

5、Systems of linear differential equations can be handled by using the methods of linear algebra.───线性微分方程组可以应用线性代数中的方法求解.

6、His work remains mathematically in the realm of ordinary differential equations.───他的工作在数学上就停留在常微分方程的范围.

7、The generalization is quite similar to the corresponding one in the theory of differential equations.───这一推广和对应的微分方程中理论的推广相当类似.

8、His doctoral dissertation on differential equations connected itself with existence theorems.───他论述微分方程的博士论文涉及到存在理论.

9、Some of you may already have solved differential equations.───你们有些人也许已经，解出了微分方程。

10、The earliest work in differential equations was first disclosed in letters from one mathematician to another.───常微分方程最早的著作出现在数学家们彼此的通信中.

11、Solutions in this sense exist only for very few types of differential equations.───只有很少几类方程才存在这种意义下的解.

12、Couple of differential equations.───几个微分方程。

13、The more recent research on differential equations is concerned with the qualitative theory.───对微分方程更近代的研究是关于定性理论.

14、The overwhelming majority of nonlinear differential equations are not soluble analytically.───绝大多数非线性微分方程是不能用解析方法求解的.

15、This is called a normal system of differential equations.───这称为正规微分方程组.

16、As applications, a second order system of differential equations is considered.───作为应用, 考虑了二阶微分方程组,得到了新的结论.

17、The solution of the set of second - order linear differential equations depends on the eigenvalues of A.───二阶线性微分方程组(6.10)的解依赖于A的特征值.

18、Very general systems of differential equations can be reduced to the normal form.───形式很普通的微分方程组可以化为正规的形式.

differential equations相似词语短语

1、differential rates───差异运价

2、adjoint differential equations───[数]伴随微分方程；相关微分方程式

3、differential housings───差速齿轮箱；差速器壳

4、differential housing───差速齿轮箱；差速器壳

5、partial differential equations───偏微分方程式

6、differential equation───[数]微分方程

7、differential gearing───差速齿轮

8、differential tone───差分音

9、differential operators───[数]微分算子；微分算符

2、吴微的论文论著

1． 吴微,　解非线性分枝问题的扩展方程方法,

科学出版社, 北京, 1993.

2.　R. Li, Z. Chen and W. Wu, Generalized Difference Methods for

Differential Equations,

(美国）Marcel Dekker Inc., New York, 2000.

3.　吴微, 神经网络计算,

高等教育出版社, 北京, 2003.　(“十五”规划国家级教材) 1． 吴微,李荣华, 解一维二阶椭圆和抛物型微分方程的广义差分法,

数学年刊, 5A(1984)303-312.

2． 吴微, 系数与时间相关的二阶双曲方程的半离散有限元逼近,

吉大自然科学学报报, 1(1985)35-42.

3． 吴微, 与时间相关的二阶双曲方程的全离散有限元逼近,

吉大自然科学学报, 2(1985)46-54.

4． 吴微, 与时间相关的非自共轭抛物方程的全离散有限元逼近,

高校计算数学, 2(1985)113-120.

5． 倪平,吴微,　广义 Galerkin 方法的超收敛估计,

高校计算数学学报, 2(1986)154-158.

6． 吴微, 解双调和方程的混合广义差分法,

吉大自然科学学报, 3 (1986)14-22.

7． 吴微, The Calahan method for parabolic equations with time-

dependent coefficients,

计算数学(英文版), 5(1987)10-20.

8． 包刚,吴微, 二阶双曲方程广义差分法的误差估计,

吉大自然科学学报, 2(1987)33-42.

9． 吴微, 非线性抛物方程广义差分法的误差估计,

计算数学(中文版), 2(1987)119-132.

10．吴微, 非线性转折点计算中的矩阵分裂技巧,

高校计算数学学报, 4 (1990)355-369.

11．P.J. Aston, A. Spence and W. WU, Bifurcation to rotating waves in

equations with O(2)-symmetry,

SIAM J. Apll. Math., 52(1992)792-809. （SCI)

12．P.J. Aston, A.Spence and W.Wu, Numerical investigation of the

bifurcation from travelling waves to modulated travelling waves,

Inter. Ser. Numer. Math., 104(1992)35-47.

13．Wei WU, Nondegeneracy of Hopf points emanating from a Z_2 symmetry-

breaking Takens-Bogdanov point,

Appl. Math. Lett., 6(1993)9-12. (SCI)

14．吴微,吴柏生,李荣华, Singular points near a double fold　point in

Z_2-symmetric nonlinear equations,

高校计算数学学报(英文版), 2(1993)101-115.

15．A. Spence, W. Wu, D. Roose and B. De Dier, Bifurcation analysis of

double Takens- Bogdanov points of nonlinear equations with $Z_2$-

symmetry,

Inter. J. Bifurcation and Chaos, 3(1993)1141-1153.

16．苏毅,吴微, 从双重折叠点分枝出的 Hopf 点的非退化性和稳定性,

吉大自然科学学报, 3(1993)1-8.

17．吴微, Galerkin methods for elliptic and parabolic convection-

diffusion problems,

东北数学, 9(4)(1993)525-538.

18．吴微, A Petrov-Galerkin method based on symmetrization for

convection-defusion problems,

东北数学, 10(1)(1994)59-70.

19．W. Wu and A. Spence, A pitchfork/fold interaction in nonlinear

equations with Z2-symmetry,

东北数学, 10(2)(1994)174-180.

20．W. Wu, Y. Zou and M. Huang, Heteroclinic cycles emanating from

local bifurcations,

manuscripta mathematika, 85(1994)381-392.(SCI)

21．W. Wu, P.J. Aston and A. Spence,

Rotating waves from Hopf bifurcations in equations with O(2)-

symmetry,

SIAM J. Sci. Comput., 15(3)(1994)495-510.(SCI)

22．W. Wu, A. Spence and K.A. Cliffe,

Steady-state/Hopf interaction at a symmetry-breaking Takens-

Bogdanove point,

IMA J. Numer. Anal., 14(1994)137-160.(SCI)

23．吴微, Stability of travelling waves,

数学研究与评论, 14(3)(1994)1-7.

24．苏毅,吴微, Singular points near an X0-breaking double singular fold

point in Z2-symmetric nonlinear equations,

东北数学, 10(3)(1994) 385-395.

25．W. Wu and Y. Su, Stability of periodic solutions generated by Hopf

points emanating from a Z_2-symmetry-breaking Takens-Bogdanov

point,

东北数学, 11(2)(1995)157-168.

26．吴微, Period-doubling bifurcation of travelling waves,

非线性动力学学报, 2(增刊)(1995)48-52.

27. 吴微，Bifurcation from steady-state to global dynamics,

Bull. Allahabad Math. Soc., 10/11(1995/96)85-94.

28．邹永魁,吴微,　Petrov-Galerkin method with linear trial and

quadratic test spaces for parabolic convection-diffusion problems,

东北数学, 12(2)(1996)207-216.

29．W.Wu,　On nondegeneracy of Hopf bifurcation points emanating from

TB point.

Nonlinear Analysis T.M.A., 26(6)(1996) 1161-1168.(SCI)

30．P.J. Aston, A. Spence and W. Wu, Hopf bifurcation near a double

singular point,

J. Computational and Applied Mathemetics, 80(1997)277-297.(SCI)

31．W. Wu and F.Y. Meng,　Mode interaction at a triple zero point of

O(2)-symmetric nonlinear systems with two parameters,

东北数学, 16(1)(2000)10-20.

32. 吴微，赵卫海，广义逆矩阵及其在神经网络计算中的应用，

大连理工大学学报，40(S1)(2000)9-11。

33. 吴微，陈维强，刘波，用BP神经网络预测股票市场涨跌，

大连理工大学学报，41(1)(2001)9-15。

34. 李正学，吴微，张宏伟，Convergence of on-line gradient methods for

two-layer feedforward neural networks，

数学研究与评论， 21(2)(2001)219-228。

35．孔俊，吴微，赵卫海，识别数学符号的神经网络方法，

吉大自然科学学报, 3(2001)11-16.

36. 吴微，陈维强，用于股市预测的BP算法的一些改进，

大连理工大学学报，41(5)(2001)518-522。

37. 孔俊，吴微，Online gradient methods with a punishing term for

nureul networks,

东北数学, 17(3)(2001)371-378.

38. Wei Wu and Yi Su, Hopf bifurcation near a singular point with Z2-

symmetry and X0-breaking,

J. Computational and Applied Mathematics, 144(1-2)(2002)335-347.

(SCI)

39. Wei Wu and Yuesheng Xu, Deterministic convergence of an online

gradient method for neural networks,

J. Computational and Applied Mathematics,　144(1-2)(2002)335-347

(SCI)

40. Wei Wu, Guori Feng and Xin Li, Training multiple perceptrons via

minimization of sum of ridge functions,

Advances in Computational Mathematics, 17(2002)331-347.

(SCI)

41．Zhengxue Li, Wei Wu and Weidong Gao, Predictions of stock market

by BP neural networks with technical indexes as input,

J. Mathematical Research and Exposition, 23(2003)83-97.

42．郭立宾，吴微，二维图像中交叉点的神经网络识别，

大连理工大学学报，43(2003)548-550。

43．Wei Wu and Zhiqiong Shao, Convergence of online gradient methods

for continuous perceptrons with linearly separable training

patterns,

Applied Mathematics Letters, 16(2003)999-1002.(SCI)

44．Zhengxue Li, Wei Wu and Yuelong Tian, Convergence of an online

gradient method for feedforward neural networks with stochastic

inputs，

Journal of Computational and Applied Mathematics, 163(1)(2004)

165-176.(SCI)

45．张玉林，吴微，用BP神经网络捕捉股市黑马初探，

运筹与管理，13(2)(12004)123-130.

46. Lijun Liu and Wei Wu, Finite convergence of MR1 neural networks

for linearly separable training patterns,

Lecture Notes in Computer Science, 3147(2004)282-295. (SCI)

47. Wei Wu et al., Recent developments in on convergence of online

gradient methods for neural network training,

Lecture Notes in Computer Science, 3147(2004)235-238. (SCI)

48. Liqing Zhang and Wei Wu, Online gradient methods with a penalty

term for neural networks with large training set,

J. of Nonlinear Dynamics in Science and Technology, 11(2004)53-58.

49. Hongmei Shao, Wei Wu and Feng Li, Convergence of online gradient

method with a penalty term for feedforward neural networks with

stochastic inputs, Numerical Mathematics, A journal Chinese

Universities, 14(2004)87-96.

50. Wu, W., Feng, G., Li, Z. and Xu, Y., Deterministic Convergence of

an Online Gradient Method for BP Neural Networks, IEEE

Transactions on Neural Networks, 16(2005)533- 540. (SCI)

51. Zhengxue Li, Wei Wu, Guorui Feng and Huifang Lu, Convergence of an

Online Gradient Method for BP Neural Networks with Stochastic

Inputs, Lecture Notes in Computer Science, 3610(2005)720-729.

Ei Compedex (05439427415), SCI (BDA22)

52. Yang, J; Wu, W; Shao, ZQ, A new training algorithm for a fuzzy

perceptron and its convergence, Lecture Notes in Computer Science,

3496(2005) 609-614, Ei Compendex (05399382279), SCI (BCN38)

53. 曲笛，吴微，邵红梅，带动量项的线性输出BP网络收敛性, 高校计算数学学

报，27（2005）增刊，368—372.

54. Naimin Zhang; Wei Wu; Gaofeng Zheng, Convergence of gradient

method with momentum for two-Layer feedforward neural networks,

IEEE Transactions on Neural Networks, vol.17, no.2, 2006, 522-

525, Ei Compendex (06129763934), SCI (026SD)

55. Wei Wu, Feng Li, Jun Kong, Lichang Hou, and Bingdui Zhu，A Bottom-

Up OCR System for Mathematical Formulas Recognition，D.-S. Huang,

K. Li, and G.W. Irwin (Eds.): ICIC 2006, Lecture Notes in Computer

Science, 4113（2006）274–279, Ei Compendex（064210172616），SCI

56. 吴微，侯利昌， 基于LL（1）文法的印刷体数学公式结构分析方法， 大连理

工大学学报，46（2006）454-459

57. SHAO Zhiqiong, WU Wei, YANG Jie, Finite convergence of On-line BP

neural networks with linearly separable training patterns, 数学研究

与评论，26（2006）451-456

58. Wei Wu, Hongmei Shao, and Zhengxue Li，Convergence of Batch BP

Algorithm with Penalty for FNN Training， I. King et al. (Eds.):

ICONIP 2006, Part I, Lecture Notes in Computer Science 4232, 562–

569, 2006. SCI (BFG80)

59. Lichang Hou, Wei Wu, Bingdui Zhu, Feng Li, A Segmentation Method

for Merged Characters Using Self-Organizing Map Neural Networks,

Journal of Information and Computational Science, 3:2(2006)219-

226. EI Compendex

61. Hongmei Shao, Wei Wu, Lijun Liu， Convergence and Monotonicity of

an Online Gradient Method with Penalty for Neural Networks， WSEAS

TRANSACTIONS on MATHEMATICS，6:3（2007）469-476. EI Compendex

62. 陈兵，吴微，基于SOFM和最短路径法的粘连字符分割，仪器仪表学报, 2006

年第6期增刊，2090-2106

63. Lijun Liu and Wei Wu，Dynamical System for Computing Largest

Generalized Eigenvalue，J. Wang et al. (Eds.): ISNN 2006, Lecture

Notes in Computer Science 3971, 399-404, 2006. SCI

64. Huifang Lu, Wei Wu, Chao Zhang, Yanxiong, Convergence of Gradient

Descent Algorithm for Pi-Sigma Neural Networks, Journal of

information and Computational Science, 3:3(2006)503-509. EI

Compendex

三. 国际会议论文集

1． Wei Wu, E. Suli and K.W. Morton,

Optimal order estimates for linear Galerkin methods for convection-

diffusion problems,

MAFLAP 87, London,　Academic Press, 1988.

2． A. Spence, P.J. Aston and W. Wu,

Bifurcation and stability analysis in nonlinear equations using

symmetry-breaking in extended systems,

Numerical Analysis, Dundee, 89, eds. D.F Griffiths at. al.,

Longman, 1990, 243-256.

3． W. Wu,　K.A. Cliffe and A. Spence,

Steady-state/steady-state mode interaction in nonlinear equations

with Z2-symmetry,

Continuation and Bifurcation: Numerical Techniques and

Applications, eds. D. Roose, De D. Dier and A. Spence, Leuvon,

Belgium, 89.　Kluwer Academic Press, 1990, Series C: Mathematical

and Physical Science, Vol. 313., 89-104.

4． Wei Wu and A. Spence,

Hopf points emanating from a double singular fold point,

工程与科学中的非线性问题国际会议文集, 肖竹铁,胡向忱主编, 科学出版

社, 北京,1992, 267-269.

5． Wei Wu,

Mode interaction at a triple zero point of O(2)-symmetric

nonlinear systems with two parameters,

World Congress of Nonlinear Analysts'92, Florida, ed. V.

Lakshmikantham, Walter de ruyter, Berlin, New York, 1996,2011-2022.

6． Wei Wu, Heteroclinic and Hopf points bifurcating from local

singular points,

Bifurcation Theory and Its Numerical Analysis, eds. Z. Chen, S.

Chow, K. LI, Xi’an, China, 1998, Springer, 194-202.

7.　Wei Wu，Convergence of an online gradient method,

Abstracts of short communications and poster sessions,

International　Congress of Mathematicians, Beijing, 2002, Higher

Education Press, p353.

8.　Wei Wu and Yuesheng Xu, Convergence of online gradient method for

neural networks, in Numeriacal Liner Algebra and Optimization,

edited by Ya-xiang Yuan, (Proceedings of 2001’ International

Conference on Numerical Optimization and Numerical Algebra,

Dunhuang, China, ) Science Press, Beijing/New York, 2003, 52-67,

(Invited lecture)

9.　Hongmei Shao, Wei Wu, Feng Li and Gaofeng Zheng, Convergence of

gradient algorithm for feedforward neural network training, The

Proceedings of International symposium on Computing and

Information (ISC&I 2004), Edited by Renhong Wang and Xiaonan Luo,

CIC Media Ltd., 2004, pp. 627-631

10. Wei Wu, Hongmei Shao and Di Qu, Strong convergence for gradient

methods for BP networks training, Proceedings of 2005

International Conference on Neural Networks & Brains (ICNN&B’05),

Edited by Mingsheng Zhao and Zhongzhi Shi, Beijing, China, 2005,

IEEE Press. pp. 332-334.

11. 李峰, 吴微, 版面分析中基于可并行化局部操作序列的局部极大成分标记,

第六届全球智能控制与自动化大会 (WCICA’06), 大连, 中国, 2006, IEEE

Press. pp. 10512-10516. (ISBN:1-4244-0331-6) EI

12. HONGMEI SHAO, WEI WU，LIJUN LIU，Convergence of an Online Gradient

Algorithm with Penalty for Two-layer Neural Networks，Proceedings

of the 10th WSEAS International Conference on APPLIED MATHEMATICS,

Dallas, Texas, USA, November 1-3, 2006. Edited by G. R.

Dattatreya, WSEAS, (ISSN: 1790-5117, ISBN: 960-8457-55-6)

13. Wei Wu, Liqing Zhang and Naimin Zhang, Online gradient method with

a penalty term for BP neural networks, in Proceedings of the

Seventh China-Japan Seminar on Numerical Mathematics, Zhangjiajie,

2005, Edited by Zhong-Ci Shi and Hisashi Okamoto, pp.179-192,

Science Press, Beijing, 2006. 1.　李正学，吴微, 引入技术指标的BP网络在沪市综合指数涨跌预测中的应用,

CCAST-WL Workshops Series, Beijing, Aug. 2001, Vol. 142, 161-176.

2.　吴微，陈维强，刘播，用BP神经网络预测股票市场涨跌，

CCAST-WL Workshops Series, Beijing, Aug. 2000, Vol. 127, 1-22.

3.　吴微, Generalized Difference Methods for Partial Differential

Equations,

The Third International Workshop on Scientific Computing and

Applications, Hongkong, 2003, 国际会议特邀报告.

4.　吴微，Monotone and deterministic convergence of online gradient

methods for feedforward neural networks，

第二届中韩数值分析及其应用研讨会，北京，2003, 国际会议特邀报告.

5.　吴微，Deterministic convergenceof an online gradient method for BP

neural networks，

The Second International Symposium on Computing Science,

Guangzhou, 2002, 国际会议特邀报告.

6.　吴微，Some recent developments on convergence online gradient

methods for neural networks,

第七届中日计算数学研讨会,张家界,2004, 国际会议特邀报告.