1、differential equations

differential equations發(fā)音

英：　　美：

differential equations中文意思翻譯

常見(jiàn)釋義：

微分方程

differential equations雙語(yǔ)使用場(chǎng)景

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

2、In 1728 Euler gave differential equations for geodesics on surfaces.───1728年,奧伊勒繪出了曲面上測地線(xiàn)的微方程.

3、And let's not even talk about differential equations.───我們不再討論微分方程序。

4、To some extent, his work pays dividends in differential equations.───他的工作在某種程度上給微分方程帶來(lái)了好處.

5、Systems of linear differential equations can be handled by using the methods of linear algebra.───線(xiàn)性微分方程組可以應用線(xiàn)性代數中的方法求解.

6、His work remains mathematically in the realm of ordinary differential equations.───他的工作在數學(xué)上就停留在常微分方程的范圍.

7、The generalization is quite similar to the corresponding one in the theory of differential equations.───這一推廣和對應的微分方程中理論的推廣相當類(lèi)似.

8、His doctoral dissertation on differential equations connected itself with existence theorems.───他論述微分方程的博士論文涉及到存在理論.

9、Some of you may already have solved differential equations.───你們有些人也許已經(jīng)，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(zhù)作出現在數學(xué)家們彼此的通信中.

11、Solutions in this sense exist only for very few types of differential equations.───只有很少幾類(lèi)方程才存在這種意義下的解.

12、Couple of differential equations.───幾個(gè)微分方程。

13、The more recent research on differential equations is concerned with the qualitative theory.───對微分方程更近代的研究是關(guān)于定性理論.

14、The overwhelming majority of nonlinear differential equations are not soluble analytically.───絕大多數非線(xiàn)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.───這稱(chēng)為正規微分方程組.

16、As applications, a second order system of differential equations is considered.───作為應用, 考慮了二階微分方程組,得到了新的結論.

17、The solution of the set of second - order linear differential equations depends on the eigenvalues of A.───二階線(xiàn)性微分方程組(6.10)的解依賴(lài)于A(yíng)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組可以化為正規的形式.

differential equations相似詞語(yǔ)短語(yǔ)

1、differential rates───差異運價(jià)

2、adjoint differential equations───[數]伴隨微分方程；相關(guān)微分方程式

3、differential housings───差速齒輪箱；差速器殼

4、differential housing───差速齒輪箱；差速器殼

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

6、differential equation───[數]微分方程

7、differential gearing───差速齒輪

8、differential tone───差分音

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

2、吳微的論文論著(zhù)

1． 吳微,　解非線(xiàn)性分枝問(wèn)題的擴展方程方法,

科學(xué)出版社, 北京, 1993.

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

Differential Equations,

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

3.　吳微, 神經(jīng)網(wǎng)絡(luò )計算,

高等教育出版社, 北京, 2003.　(“十五”規劃國家級教材) 1． 吳微,李榮華, 解一維二階橢圓和拋物型微分方程的廣義差分法,

數學(xué)年刊, 5A(1984)303-312.

2． 吳微, 系數與時(shí)間相關(guān)的二階雙曲方程的半離散有限元逼近,

吉大自然科學(xué)學(xué)報報, 1(1985)35-42.

3． 吳微, 與時(shí)間相關(guān)的二階雙曲方程的全離散有限元逼近,

吉大自然科學(xué)學(xué)報, 2(1985)46-54.

4． 吳微, 與時(shí)間相關(guān)的非自共軛拋物方程的全離散有限元逼近,

高校計算數學(xué), 2(1985)113-120.

5． 倪平,吳微,　廣義 Galerkin 方法的超收斂估計,

高校計算數學(xué)學(xué)報, 2(1986)154-158.

6． 吳微, 解雙調和方程的混合廣義差分法,

吉大自然科學(xué)學(xué)報, 3 (1986)14-22.

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

dependent coefficients,

計算數學(xué)(英文版), 5(1987)10-20.

8． 包剛,吳微, 二階雙曲方程廣義差分法的誤差估計,

吉大自然科學(xué)學(xué)報, 2(1987)33-42.

9． 吳微, 非線(xiàn)性?huà)佄锓匠虖V義差分法的誤差估計,

計算數學(xué)(中文版), 2(1987)119-132.

10．吳微, 非線(xiàn)性轉折點(diǎn)計算中的矩陣分裂技巧,

高校計算數學(xué)學(xué)報, 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．吳微,吳柏生,李榮華, Singular points near a double fold　point in

Z_2-symmetric nonlinear equations,

高校計算數學(xué)學(xué)報(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．蘇毅,吳微, 從雙重折疊點(diǎn)分枝出的 Hopf 點(diǎn)的非退化性和穩定性,

吉大自然科學(xué)學(xué)報, 3(1993)1-8.

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

diffusion problems,

東北數學(xué), 9(4)(1993)525-538.

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

convection-defusion problems,

東北數學(xué), 10(1)(1994)59-70.

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

equations with Z2-symmetry,

東北數學(xué), 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．吳微, Stability of travelling waves,

數學(xué)研究與評論, 14(3)(1994)1-7.

24．蘇毅,吳微, Singular points near an X0-breaking double singular fold

point in Z2-symmetric nonlinear equations,

東北數學(xué), 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,

東北數學(xué), 11(2)(1995)157-168.

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

非線(xiàn)性動(dòng)力學(xué)學(xué)報, 2(增刊)(1995)48-52.

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

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

28．鄒永魁,吳微,　Petrov-Galerkin method with linear trial and

quadratic test spaces for parabolic convection-diffusion problems,

東北數學(xué), 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,

東北數學(xué), 16(1)(2000)10-20.

32. 吳微，趙衛海，廣義逆矩陣及其在神經(jīng)網(wǎng)絡(luò )計算中的應用，

大連理工大學(xué)學(xué)報，40(S1)(2000)9-11。

33. 吳微，陳維強，劉波，用BP神經(jīng)網(wǎng)絡(luò )預測股票市場(chǎng)漲跌，

大連理工大學(xué)學(xué)報，41(1)(2001)9-15。

34. 李正學(xué)，吳微，張宏偉，Convergence of on-line gradient methods for

two-layer feedforward neural networks，

數學(xué)研究與評論， 21(2)(2001)219-228。

35．孔俊，吳微，趙衛海，識別數學(xué)符號的神經(jīng)網(wǎng)絡(luò )方法，

吉大自然科學(xué)學(xué)報, 3(2001)11-16.

36. 吳微，陳維強，用于股市預測的BP算法的一些改進(jìn)，

大連理工大學(xué)學(xué)報，41(5)(2001)518-522。

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

nureul networks,

東北數學(xué), 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．郭立賓，吳微，二維圖像中交叉點(diǎn)的神經(jīng)網(wǎng)絡(luò )識別，

大連理工大學(xué)學(xué)報，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．張玉林，吳微，用BP神經(jīng)網(wǎng)絡(luò )捕捉股市黑馬初探，

運籌與管理，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，吳微，邵紅梅，帶動(dòng)量項的線(xiàn)性輸出BP網(wǎng)絡(luò )收斂性, 高校計算數學(xué)學(xué)

報，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. 吳微，侯利昌， 基于LL（1）文法的印刷體數學(xué)公式結構分析方法， 大連理

工大學(xué)學(xué)報，46（2006）454-459

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

neural networks with linearly separable training patterns, 數學(xué)研究

與評論，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. 陳兵，吳微，基于SOFM和最短路徑法的粘連字符分割，儀器儀表學(xué)報, 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. 國際會(huì )議論文集

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,

工程與科學(xué)中的非線(xiàn)性問(wèn)題國際會(huì )議文集, 肖竹鐵,胡向忱主編, 科學(xué)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, 吳微, 版面分析中基于可并行化局部操作序列的局部極大成分標記,

第六屆全球智能控制與自動(dòng)化大會(huì ) (WCICA’06), 大連, 中國, 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.　李正學(xué)，吳微, 引入技術(shù)指標的BP網(wǎng)絡(luò )在滬市綜合指數漲跌預測中的應用,

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

2.　吳微，陳維強，劉播，用BP神經(jīng)網(wǎng)絡(luò )預測股票市場(chǎng)漲跌，

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

3.　吳微, Generalized Difference Methods for Partial Differential

Equations,

The Third International Workshop on Scientific Computing and

Applications, Hongkong, 2003, 國際會(huì )議特邀報告.

4.　吳微，Monotone and deterministic convergence of online gradient

methods for feedforward neural networks，

第二屆中韓數值分析及其應用研討會(huì )，北京，2003, 國際會(huì )議特邀報告.

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

neural networks，

The Second International Symposium on Computing Science,

Guangzhou, 2002, 國際會(huì )議特邀報告.

6.　吳微，Some recent developments on convergence online gradient

methods for neural networks,

第七屆中日計算數學(xué)研討會(huì ),張家界,2004, 國際會(huì )議特邀報告.