41 6 Vol 41 No 6 2017 11 Journal of Jiangxi Normal UniverityNatural Science Nov 2017 1000-5862201706-0637-04 Lagrange 1 2* 1 2150092 215009 Noether 1 Lagrange Lagrange Noether Lagrange Noether Noether Noether Lagrange O 316 A DOI10 16357 /j cnki in1000-5862 2017 06 16 Lagrange 0 Lagrange -Mill 1 1 1 2-3 Lagrange 4-5 16 Lagrange T R R Z N 6-14 Lagrange N 0 Noether 6 Lie T 6-9 Mei 6 i σ T T ρ 1988 Stefan Hilger T T σt = infp Tp > tρt = 15 upp Tp < tt Tinf = up T up = inf T ii μ T 0 2 μt= σt- t t T iiiσt> t σt= t ρt< t ρt= t ρt< t < σtt = σt= ρt t 16 17-21 20-27 Lagrange Noether T = Rt R σt = t μt = 0 T = Zt Z σt= t + 1 μt= 1 2017-09-20 11572212 11272227 KYLX15_0405 1987- E-mailongchuanjingun@ 126 com 1964- E-mailzhy@ mail ut edu cn
638 2017 delta f σ = f σ = f + μtf αf + βg t= αf t+ βg t fg t= f tg σ t+ ftg t= f σ tg t+ f tgt 2 Lagrange n q k k = 1 2 n Lagrange L = Lt q σ k q k b Sγ= a Ltqσ k t q k t t 1 Hamilton q σ k t= q k σ t q k tdelta t T LR R n R n R C 1 17 Lagrange t L q - L q σ = 0 = 1 2 n r + 1 r + 2 n 18 2 3 ft R t T κ aε > 0δ > 0 ω t - δ t + Lagrange Noether δ T fσt - fω- f t σt- ω Hamilton ε σt- ω f t f t delta Noether Noether bf ~ f t = t + - t q ~ t ~ = q t+ - q 4 C rd C 1 rd = ft R f C rd t ~ = t + εξ 0 t q k q t ~ = q t+ εξ t q k 5 T = Rdelta ε ξ 0 ξ - f t= f 'tt = Zdelta f t= ft + 1- ft 4 Hamilton ~ 1 Sγ ~ b = a ~ Lt~ q ~ σ ~ k t ~ q ~ k t ~ ~ ~ t - S Sγ ~ - Sγ ε 1 Hamilton 1 5 - S = 0 5Noether Lξ 0 - S = 0 20 + L t ξ 0 + L ξ σ q σ ξ σ t q k t = q k t = t ξ t q k t + L ξ q - ξ 0 q = 0 6 ξ σt q k σt ξ t 1 5 6 Lagrange 2 Hamilton 1 det ( 2 L ) = 0 5 q q k Lagrange - b S = - a t - Gt Lagrange 5Noether 2 r G = Gt q σ k q k n - r q i = α i t - b S = - q σ k q k i = 1 2 rβ j tq σ k q k = 0j = a t - Gt 20 Lξ 0 + L t ξ 0 + L ξ σ q σ + L ξ q - ξ 0 q = - G N 7 L - L t t μt = L t + L q σ q σ + L - G = εg q N G N q 3 3 Noether 2 5 7
6 Lagrange 639 Lagrange I NR = Lξ 0 + L ξ - q ξ 0 + G N = cont q 1 2 3 6 Lagrange 4 Lagrange q k 1 Lagrange 2 5 1 I N = Lξ 0 - L t ξ 0μt+ L ξ q - ξ 0 q = cont 2 Lagrange 2 5 2 I N = Lξ 0 - L t ξ 0μt+ L ξ q - ξ 0 q + G N = cont 2 2 3 7 t I N = L ξ σ t q + L ξ + L - L q t t μt ξ σ 0 + ( L - L t μt ξ ) 0 - L t( ξ q 0 q ) + G N = L ξ σ q σ + L ξ q + ( L t + L q σ + L q q σ q ξ ) σ 0 + ( L - L t μt ξ ) 0 - ( L ) ξ t q 0 q σ - L ξ q 0 q + G N = L ξ σ q σ + L ξ q + ( L t + L q σ + L q ) ξ σ 0 + q σ q 3 Lagrange Lξ 0 + L t ξ 0 + L q ξ + L q ξ - q ξ 0+ G N = 0 5 Lagrange L = t + q 1 q σ 2 - q 2 + a q σ 1 2 + q σ 2 2 a T = 2 n n N 0 3 Lagrange Noether t I Nt q k q σ k q k = 0 I N t q k q σ k 2 q 2 = aq σ 1 - q 2 /t q 1 + 2aq σ 2 = 0 r = 1 7 t + q 1 q σ 2 - q 2 + a q σ 1 2 + q σ 2 2 ξ 0 + ξ 0 + 2aq σ 1 ξ σ 1 + q 1 + 2aq σ 2 ξ σ 2 + q σ 2 ξ 1 - ξ 0 q 1 - ξ 2 - ξ 0 q 2 + G N = 0 8 ξ 0 = - 1ξ 1 = ξ 2 = 0 = t 8 2 G N I N = - a q σ 1 2 + q σ 2 2 +t = cont 6 Lagrange 1 2 Lagrange Noether 2 Lagrange Lagrange Lagrange Lie Mei Lagrange Hamilton L - L t μt ξ 0 - L ξ σ q σ 0 q σ - L ξ σ q 0 q - L ξ q 0 q + Hamilton 28 Hamilton G N = 0 1 T = R 2 28-30 Hamilton 31 32 -σ
640 2017 2003 274 316-319 14 Hojman III J 2004 281 36-38 15Hilger S Ein Makettenkalkül mit Anwendung auf Zentrummannigfaltigkeiten D Würzburg Univerity of Würzburg 1988 16Bohner M Peteron A Dynamic equation on time cale an introduction with application M Boton Birkhuer 2001 17Bohner M Calculu of variation on time cale J Dy- namic Sytem & Application 2004 1312 339-349 7 1 M 1993 2Luca W F Differential equation model M New YorkSpringer Verlag 1983 3 M cale J 1999 omy 2013 565 1017-1028 4Santilli R M Foundation of theoretical mechanic I M New YorkSpringer Verlag 1978 ytem on time cale J 5 M ic 2015 5610 102701 1988 22Bartoiewicz Z 6 M cale J 2004 tion 2008 3422 1220-1226 7Mei Fengxiang Zhu Haiping Lie ymmetrie and conerved quantitie for the ingular Lagrange ytem J Journal of Beijing Intitute of Technology 2009 91 11-14 24Malinowka A B 8 M on time cale J 1999 20131 /2675127 9 Lie 25Malinowka A B J 2002 51 10 2186-2190 10 Lie 12 Hojman I J 2003 273 193-195 13 Hojman II J 18Bartoiewicz Z Martin N Torre D F M The econd Euler-Lagrange equation of variational calculu on time cale J European Journal of Control 2011 171 9-18 19Hilcher RZeidan V Calculu of variation on time caleweaklocal piecewie olution with variable endpoint J Journal of Mathematical Analyi and Application 2004 2891 143-166 20Cai Pingping Fu Jingli Guo Yongxin Noether ymmetrie of the nonconervative and nonholonomic ytem on time Science ChinaPhyic Mechanic & Atron- 21Song Chuanjing Zhang Yi Noether theorem for Birkhoffian Journal of Mathematical Phy- Torre D F M Noether' theorem on time Journal of Mathematical Analyi and Applica- 23Martin N Torre D F M Noether' ymmetry theorem for nabla problem of the calculu of variation J Applied Mathematic Letter 2010 2312 1432-1438 Martin N The econd Noether theorem Abtract and Applied Analyi 2013 Ammi M R S Noether' theorem for control problem on time cale J International Journal of Difference Equation 2014 91 87-100 26Peng Keke Luo Yiping Dynamic ymmetrie of Hamiltonian ytem on time cale J Journal of Mathematical J 2007 42 9 30-35 Phyic 2014 554 42702 11 27 Hamilton Noether J J 2003 27 1 2016 372 214-224 1-3 28Dirac P A M Lecture on quantum mechanic M New YorkYehiva Univerity Pre 1964 29 Hamiltonian M 1999 30Li Ziping Jiang Jinhuan Symmetrie in contrained canonical ytem M BeijingScience Pre 2002 31Liu Xinya Theoretical tudy of deflection of reflected and refracted of electromagnetic wave from incident plane J Communication in Theoretical Phyic 1996 25 3 361-364 32Wilczek F Quantum mechanic of fractional-pin particle J Phyical Review Letter 1982 4914 957-959 655
6 655 The Study on Licene Plate Location Technology by Pixel Connection DENG Hong 1 2 LI Shuiquan 3 PENG Yingqiong 1 2 1 School of Software Jiangxi Agricultural Univerity Nanchang Jiangxi 330045 China 2 Key Laboratory of Agricultural Information Technology of Jiangxi College Nanchang Jiangxi 330045 China 3 College of Computer Science & Software Engineering Shenzhen Univerity Shenzhen Guangdong 518060 China AbtractLicene plate location i regaded a the guide part of the licene plate recognition it accuracy determine the licene plate recognition ytem reliability The exiting licene plate locating algorithm ha the following two problem which i the fuion image morphological operation the ize of tructural element controland if the body ha a licene and the ame color and morphological dilation i likely to caue both connected In view of the above problem the method of licene plate location baed on pixel connection ha been propoed to achieve the better edge detection reult of the licene plate recognition ytem Key wordlicene plate locationpixel connectionedge detection 640 The Symmetry and Conerved Quantity for Singular Lagrangian Sytem on Time Scale SONG Chuanjing 1 ZHANG Yi 2* 1 School of Mathematic & Phyic Suzhou Univerity of Science and TechnologySuzhou Jiangu 215009 China 2 College of Civil EngineeringSuzhou Univerity of Science and TechnologySuzhou Jiangu 215009 China AbtractNoether ymmetry and conerved quantity for ingular Lagrangian ytem on time cale are tudied Firtly the differential equation of motion on time cale for ingular Lagrangian ytem are preented Secondly the definition and criteria of Noether ymmetry and Noether quai-ymmetry for thi ytem are tudied Latly conerved quantitie deduced from Noether ymmetry and Noether quai-ymmetry are obtained for ingular Lagrangian ytem on time cale And an example i given to illutrate the reult Key wordymmetryconerved quantityingular Lagrangian ytemtime cale