Vol. 41 No Journal of Jiangxi Normal University Natural Science Nov. 2017

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Ἰαρέδ Ζάνος
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1 41 6 Vol 41 No Journal of Jiangxi Normal UniverityNatural Science Nov Lagrange 1 2* Noether 1 Lagrange Lagrange Noether Lagrange Noether Noether Noether Lagrange O 316 A DOI /j cnki in Lagrange 0 Lagrange -Mill Lagrange 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 Lagrange Noether T = Rt R σt = t μt = 0 T = Zt Z σt= t + 1 μt= KYLX15_ ongchuanjingun@ 126 com zhy@ mail ut edu cn

2 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 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 S = 0 5Noether Lξ 0 - S = 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 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

3 6 Lagrange 639 Lagrange I NR = Lξ 0 + L ξ - q ξ 0 + G N = cont q Lagrange 4 Lagrange q k 1 Lagrange I N = Lξ 0 - L t ξ 0μt+ L ξ q - ξ 0 q = cont 2 Lagrange I N = Lξ 0 - L t ξ 0μt+ L ξ q - ξ 0 q + G N = cont 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 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 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 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 Hamilton σ

4 Hojman III J Hilger S Ein Makettenkalkül mit Anwendung auf Zentrummannigfaltigkeiten D Würzburg Univerity of Würzburg Bohner M Peteron A Dynamic equation on time cale an introduction with application M Boton Birkhuer Bohner M Calculu of variation on time cale J Dy- namic Sytem & Application M Luca W F Differential equation model M New YorkSpringer Verlag M cale J 1999 omy Santilli R M Foundation of theoretical mechanic I M New YorkSpringer Verlag 1978 ytem on time cale J 5 M ic Bartoiewicz Z 6 M cale J 2004 tion Mei Fengxiang Zhu Haiping Lie ymmetrie and conerved quantitie for the ingular Lagrange ytem J Journal of Beijing Intitute of Technology Malinowka A B 8 M on time cale J / Lie 25Malinowka A B J Lie 12 Hojman I J 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 Hilcher RZeidan V Calculu of variation on time caleweaklocal piecewie olution with variable endpoint J Journal of Mathematical Analyi and Application Cai 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 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 Peng Keke Luo Yiping Dynamic ymmetrie of Hamiltonian ytem on time cale J Journal of Mathematical J Phyic Hamilton Noether J J Dirac P A M Lecture on quantum mechanic M New YorkYehiva Univerity Pre Hamiltonian M Li Ziping Jiang Jinhuan Symmetrie in contrained canonical ytem M BeijingScience Pre Liu Xinya Theoretical tudy of deflection of reflected and refracted of electromagnetic wave from incident plane J Communication in Theoretical Phyic Wilczek F Quantum mechanic of fractional-pin particle J Phyical Review Letter

5 6 655 The Study on Licene Plate Location Technology by Pixel Connection DENG Hong 1 2 LI Shuiquan 3 PENG Yingqiong School of Software Jiangxi Agricultural Univerity Nanchang Jiangxi China 2 Key Laboratory of Agricultural Information Technology of Jiangxi College Nanchang Jiangxi China 3 College of Computer Science & Software Engineering Shenzhen Univerity Shenzhen Guangdong 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 China 2 College of Civil EngineeringSuzhou Univerity of Science and TechnologySuzhou Jiangu 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

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