Self-dual Vortices in the Abelian Chern-Simons Model with Two Complex Scalar Fields
时间尺度上非迁移Birkhoff系统的Mei对称性定理
时间尺度上非迁移Birkhoff系统的Mei对称性定理*张毅†(苏州科技大学土木工程学院, 苏州 215011)(2021 年2 月25日收到; 2021 年9 月9日收到修改稿)研究并证明时间尺度上非迁移Birkhoff系统的Mei对称性定理. 首先, 建立任意时间尺度上Pfaff-Birkhoff原理和广义Pfaff-Birkhoff原理, 由此导出时间尺度上非迁移Birkhoff系统(包括自由Birkhoff系统、广义Birkhoff系统和约束Birkhoff系统)的动力学方程. 其次, 基于非迁移Birkhoff方程中的动力学函数经历变换后仍满足原方程的不变性, 给出了时间尺度上Mei对称性的定义, 导出了相应的判据方程. 再次, 建立并证明了时间尺度上非迁移Birkhoff系统的Mei对称性定理, 得到了时间尺度上Birkhoff系统的Mei守恒量.并通过3个算例说明了结果的应用.关键词：Birkhoff系统, Mei对称性定理, 时间尺度, 非迁移变分学PACS：45.20.Jj, 11.30.Na, 02.30.Xx DOI: 10.7498/aps.70.202103721 引 言Birkhoff力学起源于Birkhoff[1]的著作《动力系统》. Santilli[2]首次提出Birkhoff力学一词, 并详细地讨论了Birkhoff方程的构造、变换理论及其对强子物理的应用. 梅凤翔等[3]和Galiullin等[4]从各自角度分别独立地研究了Birkhoff系统动力学, 他们的研究各具特色且更侧重于分析力学. 文献[5]构建了广义Birkhoff系统动力学. 梅凤翔先生[6]指出Birkhoff力学是分析力学发展的第4个阶段. 近年来, Birkhoff力学在对称性理论[7−13]、几何动力学[14,15]、全局分析与稳定性[16,17]、数值计算[18−22]等研究方向上都取得了重要进展.时间尺度, 即实数集的任意非空闭子集, 最早是由Hilger博士[23]引进的. 由于实数集和整数集本身就是一类特殊的时间尺度, 因而在时间尺度上不仅可以统一地处理连续系统和离散系统, 而且可以处理既有连续又有离散的复杂动力学过程. 近20年来, 时间尺度分析理论不仅在理论上不断完善[24−26], 其应用领域也在不断拓广[27−34]. 文献[35]最早提出并研究了时间尺度上基于delta导数的自由Birkhoff系统动力学及其Noether对称性. 文献[36]利用对偶原理将文献[35]的结果拓展到nabla导数情形. 文献[37]给出了时间尺度上非迁移Birkhoff系统的Noether定理. 但是, 这些研究尚限于: 1)自由Birkhoff系统; 2) Noether对称性;3)守恒量是Noether型的. 文献[38, 39]初步研究了时间尺度上Birkhoff系统的Lie对称性和Mei 对称性, 但是其守恒量的证明基于第二Euler-La-grange方程, 而数值计算表明该方程并不成立[34].此外, 根据Bourdin[33]的研究, 在离散层面非迁移情形的结果是保变分结构及其相关性质的, 尽管迄今时间尺度上非迁移变分问题研究还很少. 本文研* 国家自然科学基金(批准号: 11972241, 11572212)和江苏省自然科学基金(批准号: BK20191454)资助的课题.† 通信作者. E-mail: zhy@© 2021 中国物理学会 Chinese Physical Society 究时间尺度上非迁移Birkhoff 系统的Mei 对称性,包括自由Birkhoff 系统、广义Birkhoff 系统和约束Birkhoff 系统, 建立并证明上述3类Birkhoff 系统的Mei 对称性定理, 给出时间尺度上新型守恒量, 称之为Mei 守恒量.2 时间尺度上非迁移Birkhoff 方程关于时间尺度上微积分及其基本性质, 读者可参阅文献[24, 25].2.1 Pfaff-Birkhoff 原理及其推广在时间尺度上, 非迁移Pfaff 作用量为R β:T ×R 2n →R B :T ×R 2n →R a ∆βa βC 1,∆rd(T )β,γ=1,2,···,2n a γσρ其中 是时间尺度上Birkhoff 函数组, 是时间尺度上Birkhoff 函数, 是Birkhoff 变量 对时间的delta 导数. 设所有函数都是 函数. .非迁移是指作用量(1)中的变量 没有经过前跳算子 或后跳算子 的作用而发生跃迁[33].等时变分原理且满足端点条件以及互易关系原理(2)称为时间尺度上非迁移Pfaff-Birkhoff 原理.等时变分原理(2)可推广为Φβ=Φβ(t,a γ)式中 表示附加项[5]. 原理(5)式可称为时间尺度上非迁移广义Pfaff-Birkhoff 原理.2.2 自由Birkhoff 系统由原理(2), 容易导出σ(t )δa ∆β其中 是前跳算子. 考虑到 的独立性,由时间尺度上Dubois-Reymond 引理[24], 得到C β其中 为常数. 因此有方程(8)为时间尺度上非迁移Birkhoff 方程.2.3 广义Birkhoff 系统由原理(5), 可导出类似于方程(8), 有方程(10)可称为时间尺度上非迁移广义Birkhoff-方程.2.4 约束Birkhoff 系统约束方程为将(11)式取变分, 得由(6)式和(12)式, 容易导出λj =λj (t,a β)λj 其中 为约束乘子. 假设约束(11)式相互独立, 则由(11)式和(13)式可解出 . 于是方程(13)可写成P β=λj∂f j∂a β其中 . 方程(14)可视作与约束Birk-hoff 系统(13)和(11)相应的自由Birkhoff 系统.只要初始条件满足约束方程(11), 那么方程(14)的解就给出约束Birkhoff 系统的运动.3 Mei 对称性3.1 自由Birkhoff 系统引进无限小变换t →ϑ(t )=t +υξ0+o (υ)C 1,∆rd υ∈R ϑ(t )¯T¯σ¯∆其中映射 是1个严格递增 函数, 是无限小参数, 是一个新的时间尺度 , 前跳算子为 , delta 导数为 .B R β¯B ¯Rβ在变换(15)下, 动力学函数 和 变换为 和 , 有υ=0将(16)式在 处Taylor 级数展开, 得到Y (0)=ξ0∂/∂t +ξβ∂/∂a β其中 .定义1 对于时间尺度上非迁移Birkhoff 系统(8), 如果成立, 则变换(15)称为Mei 对称性的.判据1 如果变换(15)满足如下判据方程:则变换相应于时间尺度上非迁移Birkhoff 系统(8)的Mei 对称性.3.2 广义Birkhoff 系统B R βΦβ¯B¯R β¯Φβ设时间尺度上动力学函数 , 和 经历变换(15)后, 成为 , 和 , 有于是有下述定义2和判据2.定义2 对于时间尺度上非迁移广义Birkhoff 系统(10), 如果成立, 则变换(15)称为Mei 对称性的.判据2 如果变换(15)满足如下判据方程:则变换相应于时间尺度上非迁移广义Birkhoff 系统(10)的Mei 对称性.3.3 约束Birkhoff 系统B R βP βf j ¯B ¯R β¯P β¯f j 设时间尺度上动力学函数 , 和 , 以及约束 经历变换(15)后, 成为 , , 和 , 有于是有下述定义3和判据3.定义3 对于时间尺度上与约束Birkhoff 系统(13)和(11)相应的自由Birkhoff 系统(14), 如果成立, 则变换(15)称为Mei 对称性的.判据3 如果变换(15)满足如下判据方程:则变换相应于时间尺度上相应自由Birkhoff 系统(14)的Mei 对称性.定义4 对于时间尺度上约束Birkhoff 系统(13)和(11), 如果方程(24)以及如下方程成立, 则变换(15)称为Mei 对称性的.判据4 如果变换(15)满足判据方程(25)和如下限制方程:则变换相应于时间尺度上约束Birkhoff 系统(13)和(11)的Mei 对称性.4 Mei 对称性定理4.1 自由Birkhoff 系统定理1 假设变换(15)满足判据方程(19), 则时间尺度上非迁移Birkhoff 系统(8)存在新型守恒量G M 其中 是规范函数, 满足因此, (28)式是系统的守恒量. 证毕.定理1可称为时间尺度上非迁移Birkhoff 系统(8)的Mei 对称性定理, (28)式称为Mei 守恒量.4.2 广义Birkhoff 系统定理2 假设变换(15)满足判据方程(22), 则时间尺度上非迁移广义Birkhoff 系统(10)存在新型守恒量G M 其中 是规范函数, 满足证明∇∇tI M =0将方程(22)和方程(33)代入(34)式, 得到, 于是(32)式是系统的守恒量.定理2可称为时间尺度上非迁移广义Birkhoff 系统(10)的Mei 对称性定理, (32)式称为Mei 守恒量. 证毕.4.3 约束Birkhoff 系统定理3 假设变换(15)满足判据方程(25), 则时间尺度上与约束Birkhoff 系统(13)和(11)相应的自由Birkhoff 系统(14)存在新型守恒量G M 其中 是规范函数, 满足G M 定理4 假设变换(15)满足判据方程(25)和限制条件(27)式, 则时间尺度上约束Birkhoff 系统(13)和(11)存在新型守恒量(35), 其中规范函数 满足方程(36).定理3为时间尺度上与约束Birkhoff 系统(13)和(11)相应的自由Birkhoff 系统(14)的Mei 对称性定理.定理4为时间尺度上非迁移约束Birkhoff 系统的Mei 对称性定理, (35)式是Mei 守恒量.5 算 例例1 研究时间尺度上Birkhoff 系统, 设Birk -hoff 函数和Birkhoff 函数组为试研究该系统的Mei 对称性与守恒量.由方程(8)得到T =R 如取 , 则方程(38)成为这是著名的Hojman-Urrutia 问题[3,4]. 该问题本质上不是自伴随的, 因此没有Lagrange 结构或Hami-lton 结构.下面来计算Mei 对称性. 经计算, 有取生成函数为则生成函数(41)满足判据方程(19), 因此它相应于系统的Mei 对称性. 将(41)式代入方程(29), 可解得由定理1, 系统有Mei 守恒量, 形如(44)式表明, 对于任意的时间尺度, (44)式都是Birkhoff 系统(37)的守恒量. 如取生成函数为那么生成函数(45)也是Mei 对称的, 由方程(29)得由定理1, 得到Mei 守恒量T =R σ(t )=t 对于守恒量(47), 如果系统是通常的Birkhoff 系统, 即取 , 则 , 从而(47)式给出T =h Z h>0σ(t )=t +h 这是通常意义下Hojman-Urrutia 问题的守恒量[3].如果是离散情形, 即取 , 这里 , 则 , 从而(47)式成为h 这是步长为 的离散版本的Mei 守恒量.例2 研究时间尺度上广义Birkhoff 系统的Mei 对称性与守恒量.广义Birkhoff 方程(10)给出计算Mei 对称性, 由于将(52)式代入判据方程(22), 有解(53)式和(54)式相应于系统的Mei 对称性. 将(53)式代入方程(33), 解得由定理2, 系统有Mei 守恒量, 形如G M =−2t 同理, 相应于生成函数(54), , 由定理2得(56)式和(57)式是由Mei 对称性(53)和(54)导致的Mei 守恒量.例3 研究时间尺度上约束Birkhoff 系统约束为g φ试研究其Mei 对称性与守恒量,其中 和 是常数.方程(13)给出由方程(59)和方程(60),解得因此有做计算取生成函数为则µ(t )=σ(t )−t ν(t )=t −ρ(t )其中 为向前互差函数, 为向后互差函数. 由判据4, 生成函数(64)相应于系统的Mei 对称性. 将(65)式代入方程(36),解得由定理4, 系统有Mei 守恒量, 形如6 讨 论T =R σ(t )=t µ(t )=0如果取时间尺度 , 则前跳算子 ,互差函数 , 因此上述结果退化为通常意义下Birkhoff 系统、广义Birkhoff 系统和约束Birkh-off 系统连续版本的变分原理、Birkhoff 方程和Mei 对称性定理.T =R 例如, 对于自由Birkhoff 系统, 当取 时,原理(2)成为方程(8)成为由判据方程(19)容易得到于是, 定理1退化为下述推论1.推论1 假设变换(15)满足判据方程(19),则自由Birkhoff 系统(69)的Mei 对称性导致如下G M 其中 是规范函数, 满足推论1是通常意义下自由Birkhoff 系统连续版本的Mei 对称性与守恒量定理[7]. 而方程(68)、方程(69)和方程(71)就是通常意义下自由Birk-hoff 系统连续版本的Pfaff-Birkhoff 原理、Birk-hoff 方程和Mei 守恒量.T =h Z h >0σ(t )=t +h µ(t )=h 如果取时间尺度 , 常数 , 则前跳算子 , 互差函数 . 此时, 原理(2)成为方程(8)成为则定理1退化为下述推论2.推论2 假设变换(15)满足判据方程(19), 则自由Birkhoff 系统(74)的Mei 对称性导致如下形式的守恒量:G M 其中 是规范函数, 满足h 推论2是通常意义下自由Birkhoff 系统离散版本的Mei 对称性与守恒量定理. 而方程(73)—(75)就是通常意义下自由Birkhoff 系统离散版本步长为 的Pfaff-Birkhoff 原理、Birkhoff 方程和Mei 守恒量.7 结 论对称性和守恒量一直是分析力学研究的一个重要方面. 经典的对称性主要有Noether 对称性和Lie对称性. Mei对称性是本质上不同于前两种对称性的一种不变性, 它可以导致Mei守恒量. Mei守恒量不同于Noether守恒量, 是一种新的守恒量. 本文提出并研究了时间尺度上非迁移Birkhoff系统的Mei对称性定理.一是提出了时间尺度上非迁移Pfaff-Birkhoff 原理和广义Pfaff-Birkhoff原理, 导出了时间尺度上Birkhoff系统, 包括自由Birkhoff系统、广义Birkhoff系统和约束Birkhoff系统的动力学方程.主要结果是原理(2)和(5), Birkhoff方程(8), (10)和(13).二是定义了时间尺度上非迁移Birkhoff系统的Mei对称性, 并导出了它的判据方程. 主要结果是4个定义和4个判据.三是提出并证明了时间尺度上非迁移Birkhoff 系统、非迁移广义Birkhoff系统和非迁移约束Birkhoff系统的Mei对称性定理. 主要结果是4个定理, Mei守恒量(28), (32)和(35).T=R T=h Z当取时间尺度和时, 文中定理给出通常意义下自由Birkhoff系统、广义Birkhoff 系统和约束Birkhoff系统的连续版本和离散版本的Mei对称性与守恒量定理. 由于除了实数集和整数集以外, 时间尺度还可以有很多选择, 因此时间尺度上Birkhoff系统的Mei对称性定理具有一般性.参考文献B irkhoff G D 1927 Dynamical Systems (Providence: AMSCollege Publ. ) pp59–96[1]S antilli R M 1983 Foundations of Theoretical Mechani cs II (New York: Springer-Verlag) pp1–280[2]M ei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoffian System (Beijing: Beijing Institute of Technology Press) pp1–228[3]G aliullin A S, Gafarov G G, Malaishka R P, Khwan A M1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow: UFN) pp118–226[4]M ei F X 2013 Dynamics of Generalized Birkhoffian Systems (Beijing: Science Press) pp1–206[5]M ei F X, Wu H B, Li Y M, Chen X W 2016 J. Theor. Appl.Mech. 48 263 (in Chinese) [梅凤翔, 吴惠彬, 李彦敏, 陈向炜2016 力学学报 48 263][6]M ei F X 2004 Symmetries and Conserved Quantities of [7]Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) pp1–482 (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量 (北京: 北京理工大学出版社) 第1—482页]W ang P, Xue Y, Liu Y L 2012 Chin. Phys. B 21 070203 [8]Z hang Y, Zhai X H 2015 Nonlinear Dyn. 81 469[9]Z hang H B, Chen H B 2017 J. Math. Anal. Appl. 456 1442 [10]Z hang Y 2018 Int. J. Non-Linear Mech. 101 36[11]X u X X, Zhang Y 2020 Acta Phys. Sin. 69 220401 (in Chinese) [徐鑫鑫, 张毅 2020 物理学报 69 220401][12]Z hang L J, Zhang Y 2020 Commun. Nonlinear Sci. Numer.Simul. 91 105435[13]G uo Y X, Liu C, Liu S X 2010 Commun. Math. 18 21[14]L iu S X, Liu C, Guo Y X 2011 Chin. Phys. B 20 034501[15]C hen X W, Li Y M 2013 Acta Mech. 224 1593[16]L uo S K, He J M, Xu Y L 2016 Int. J. Non-Linear Mech. 78 105[17]L iu S X, Liu C, Guo Y X 2011 Acta Phys. Sin. 60 064501 (in Chinese) [刘世兴, 刘畅, 郭永新 2011 物理学报 60 064501] [18]L iu S X, Liu C, Hua W, Guo Y X 2016 Chin. Phys. B 25 114501[19]K ong X L, Wu H B, Mei F X 2013 Appl. Math. Comput. 225 326[20]K ong X L, Wu H B 2017 Acta Phys. Sin. 66 084501 (in Chinese) [孔新雷, 吴惠彬 2017 物理学报 66 084501][21]H e L, Wu H B, Mei F X 2017 Nonlinear Dyn. 87 2325[22]H ilger S 1990 Results Math. 18 18[23]B ohner M, Peterson A 2001 Dynamic Equations on TimeScales (Boston: Birkhäuser) pp1–353[24]B ohner M, Georgiev S G 2016 Multivariable DynamicCalculus on Time Scales (Switzerland: Springer International Publishing AG) pp1–600[25]G eorgiev S G 2018 Fractional Dynamic Calculus andFractional Dynamic Equations on Time Scales (Switzerland: Springer International Publishing AG) pp1–357[26]A tici F M, Biles D C, Lebedinsky A 2006 Math. Comput.Modell. 43 718[27]B ohner M 2004 Dyn. Syst. Appl. 13 339[28]B artosiewicz Z, Torres D F M 2008 J. Math. Anal. Appl. 3421220[29]B enkhettou N, Brito da Cruz A M C, Torres D F M 2015Signal Process. 107 230[30]D ryl M, Torres D F M 2017 Springer Proceedings inMathematics & Statistics 195 223[31]H an Z L, Sun S R 2014 Oscillation Theory of DynamicEquations on Time Scales (Jinan: Shandong University Press) pp1–232 (in Chinese) [韩振来, 孙书荣 2014 时间尺度上动态方程振动理论 (济南: 山东大学出版社) 第1—232页][32]B ourdin L 2014 J. Math. Anal. Appl. 411 543[33]A nerot B, Cresson J, Belgacem K H, Pierret F 2020 J. Math.Phys. 61 113502[34]S ong C J, Zhang Y 2015 J. Math. Phys. 56 102701[35]S ong C J, Zhang Y 2017 J. Nonlinear Sci. Appl. 10 2268 [36]S ong C J, Cheng Y 2020 Appl. Math. Comput. 374 125086 [37]Z hang Y 2019 Chaos, Solitons Fractals 128 306[38]Z hang Y, Zhai X H 2019 Commun. Nonlinear Sci. Numer.Simul. 75 251[39]Mei’s symmetry theorems for non-migrated Birkhoffiansystems on a time scale*Zhang Yi †(College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China)( Received 25 February 2021; revised manuscript received 9 September 2021 )AbstractThe Mei symmetry and its corresponding conserved quantities for non-migrated Birkhoffian systems on a time scale are proposed and studied. Firstly, the dynamic equations of non-migrated Birkhoffian systems (including free Birkhoffian systems, generalized Birkhoffian systems and constrained Birkhoffian systems) on a time scale are derived based on the time-scale Pfaff-Birkhoff principle and time-scale generalized Birkhoff principle. Secondly, based on the fact that the dynamical functions in the non-migrated Birkhoff’s equations still satisfy the original equations after they have been transformed, the definitions of Mei symmetry on an arbitrary time scale are given, and the corresponding criterion equations are derived. Thirdly, Mei’s symmetry theorems for non-migrated Birkhoffian systems on a time scales are established and proved, and Mei conserved quantities of Birkhoffian systems on a time scale are obtained. The results are illustrated by three examples.Keywords: Birkhoffian system, Mei’s symmetry theorem, time scale, non-migrated variational calculus PACS: 45.20.Jj, 11.30.Na, 02.30.Xx DOI: 10.7498/aps.70.20210372* Project supported by the National Natural Science Foundation of China (Grant Nos. 11972241, 11572212) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20191454).† Corresponding author. E-mail: zhy@。
阿贡实验室RietveldRefinementwithGSAS
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Errors & parameters?
position – lattice parameters, zero point (not common)
- other systematic effects – sample shift/offset shape – profile coefficients (GU, GV, GW, LX, LY, etc. in GSAS) intensity – crystal structure (atom positions & thermal parameters)
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So how does Rietveld refinement work?
Rietveld Minimize
MR w(Io Ic )2
Io
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Study of B - rho pi decays at Belle
a r X i v :h e p -e x /0207007v 1 1 J u l 2002BELLEBelle Prerpint 2002-18KEK Preprint 2002-59Study of B →ρπdecays at BelleBelle Collaboration A.Gordon u ,Y.Chao z ,K.Abe h ,K.Abe aq ,N.Abe at ,R.Abe ac ,T.Abe ar ,Byoung Sup Ahn o ,H.Aihara as ,M.Akatsu v ,Y.Asano ay ,T.Aso aw ,V.Aulchenko b ,T.Aushev ℓ,A.M.Bakich an ,Y.Ban ag ,A.Bay r ,I.Bedny b ,P.K.Behera az ,jak m ,A.Bondar b ,A.Bozek aa ,M.Braˇc ko t ,m ,T.E.Browder g ,B.C.K.Casey g ,M.-C.Chang z ,P.Chang z ,B.G.Cheon am ,R.Chistov ℓ,Y.Choi am ,Y.K.Choi am ,M.Danilov ℓ,L.Y.Dong j ,J.Dragic u ,A.Drutskoy ℓ,S.Eidelman b ,V.Eiges ℓ,Y.Enari v ,C.W.Everton u ,F.Fang g ,H.Fujii h ,C.Fukunaga au ,N.Gabyshev h ,A.Garmash b ,h ,T.Gershon h ,B.Golob s ,m ,R.Guo x ,J.Haba h ,T.Hara ae ,Y.Harada ac ,N.C.Hastings u ,H.Hayashii w ,M.Hazumi h ,E.M.Heenan u ,I.Higuchi ar ,T.Higuchi as ,L.Hinz r ,T.Hokuue v ,Y.Hoshi aq ,S.R.Hou z ,W.-S.Hou z ,S.-C.Hsu z ,H.-C.Huang z ,T.Igaki v ,Y.Igarashi h ,T.Iijima v ,K.Inami v ,A.Ishikawa v ,H.Ishino at ,R.Itoh h ,H.Iwasaki h ,Y.Iwasaki h ,H.K.Jang a ℓ,J.H.Kang bc ,J.S.Kang o ,N.Katayama h ,Y.Kawakami v ,N.Kawamura a ,T.Kawasaki ac ,H.Kichimi h ,D.W.Kim am ,Heejong Kim bc ,H.J.Kim bc ,H.O.Kim am ,Hyunwoo Kim o ,S.K.Kim a ℓ,T.H.Kim bc ,K.Kinoshita e ,S.Korpar t ,m ,P.Krokovny b ,R.Kulasiri e ,S.Kumar af ,A.Kuzmin b ,Y.-J.Kwon bc ,nge f ,ai ,G.Leder k ,S.H.Lee a ℓ,J.Li ak ,A.Limosani u ,D.Liventsevℓ,R.-S.Lu z,J.MacNaughton k,G.Majumder ao, F.Mandl k,D.Marlow ah,S.Matsumoto d,T.Matsumoto au,W.Mitaroffk,K.Miyabayashi w,Y.Miyabayashi v,H.Miyake ae,H.Miyata ac,G.R.Moloney u,T.Mori d,T.Nagamine ar,Y.Nagasaka i,T.Nakadaira as,E.Nakano ad, M.Nakao h,J.W.Nam am,Z.Natkaniec aa,K.Neichi aq, S.Nishida p,O.Nitoh av,S.Noguchi w,T.Nozaki h,S.Ogawa ap, T.Ohshima v,T.Okabe v,S.Okuno n,S.L.Olsen g,Y.Onuki ac, W.Ostrowicz aa,H.Ozaki h,P.Pakhlovℓ,H.Palka aa,C.W.Park o,H.Park q,L.S.Peak an,J.-P.Perroud r, M.Peters g,L.E.Piilonen ba,J.L.Rodriguez g,F.J.Ronga r, N.Root b,M.Rozanska aa,K.Rybicki aa,H.Sagawa h,S.Saitoh h,Y.Sakai h,M.Satapathy az,A.Satpathy h,e,O.Schneider r,S.Schrenk e,C.Schwanda h,k,S.Semenovℓ,K.Senyo v,R.Seuster g,M.E.Sevior u,H.Shibuya ap,V.Sidorov b,J.B.Singh af,S.Staniˇc ay,1,M.Stariˇc m,A.Sugi v, A.Sugiyama v,K.Sumisawa h,T.Sumiyoshi au,K.Suzuki h,S.Suzuki bb,S.Y.Suzuki h,T.Takahashi ad,F.Takasaki h, K.Tamai h,N.Tamura ac,J.Tanaka as,M.Tanaka h,G.N.Taylor u,Y.Teramoto ad,S.Tokuda v,S.N.Tovey u,T.Tsuboyama h,T.Tsukamoto h,S.Uehara h,K.Ueno z, Y.Unno c,S.Uno h,hiroda h,G.Varner g,K.E.Varvell an,C.C.Wang z,C.H.Wang y,J.G.Wang ba,M.-Z.Wang z,Y.Watanabe at,E.Won o,B.D.Yabsley ba,Y.Yamada h, A.Yamaguchi ar,Y.Yamashita ab,M.Yamauchi h,H.Yanai ac,P.Yeh z,Y.Yuan j,Y.Yusa ar,J.Zhang ay,Z.P.Zhang ak,Y.Zheng g,and D.ˇZontar aya Aomori University,Aomori,Japanb Budker Institute of Nuclear Physics,Novosibirsk,Russiac Chiba University,Chiba,Japand Chuo University,Tokyo,Japane University of Cincinnati,Cincinnati,OH,USAf University of Frankfurt,Frankfurt,Germanyg University of Hawaii,Honolulu,HI,USAh High Energy Accelerator Research Organization(KEK),Tsukuba,Japani Hiroshima Institute of Technology,Hiroshima,Japanj Institute of High Energy Physics,Chinese Academy of Sciences,Beijing,PRChinak Institute of High Energy Physics,Vienna,Austria ℓInstitute for Theoretical and Experimental Physics,Moscow,Russiam J.Stefan Institute,Ljubljana,Slovenian Kanagawa University,Yokohama,Japano Korea University,Seoul,South Koreap Kyoto University,Kyoto,Japanq Kyungpook National University,Taegu,South Korear Institut de Physique des Hautes´Energies,Universit´e de Lausanne,Lausanne,Switzerlands University of Ljubljana,Ljubljana,Sloveniat University of Maribor,Maribor,Sloveniau University of Melbourne,Victoria,Australiav Nagoya University,Nagoya,Japanw Nara Women’s University,Nara,Japanx National Kaohsiung Normal University,Kaohsiung,Taiwany National Lien-Ho Institute of Technology,Miao Li,Taiwanz National Taiwan University,Taipei,Taiwanaa H.Niewodniczanski Institute of Nuclear Physics,Krakow,Polandab Nihon Dental College,Niigata,Japanac Niigata University,Niigata,Japanad Osaka City University,Osaka,Japanae Osaka University,Osaka,Japanaf Panjab University,Chandigarh,Indiaag Peking University,Beijing,PR Chinaah Princeton University,Princeton,NJ,USAai RIKEN BNL Research Center,Brookhaven,NY,USAaj Saga University,Saga,Japanak University of Science and Technology of China,Hefei,PR ChinaaℓSeoul National University,Seoul,South Koreaam Sungkyunkwan University,Suwon,South Koreaan University of Sydney,Sydney,NSW,Australiaao Tata Institute of Fundamental Research,Bombay,Indiaap Toho University,Funabashi,Japanaq Tohoku Gakuin University,Tagajo,Japanar Tohoku University,Sendai,Japanas University of Tokyo,Tokyo,Japanat Tokyo Institute of Technology,Tokyo,Japanau Tokyo Metropolitan University,Tokyo,Japanav Tokyo University of Agriculture and Technology,Tokyo,Japanaw Toyama National College of Maritime Technology,Toyama,Japanay University of Tsukuba,Tsukuba,Japanaz Utkal University,Bhubaneswer,Indiaba Virginia Polytechnic Institute and State University,Blacksburg,VA,USAbb Yokkaichi University,Yokkaichi,Japanbc Yonsei University,Seoul,South KoreaB events collected with the Belle detector at KEKB.Thebranching fractions B(B+→ρ0π+)=(8.0+2.3+0.7−2.0−0.7)×10−6and B(B0→ρ±π∓)=(20.8+6.0+2.8−6.3−3.1)×10−6are obtained.In addition,a90%confidence level upper limitof B(B0→ρ0π0)<5.3×10−6is reported.Key words:ρπ,branching fractionPACS:13.25.hw,14.40.Nd1on leave from Nova Gorica Polytechnic,Nova Gorica,Sloveniamodes are examined.Here and throughout the text,inclusion of charge con-jugate modes is implied and for the neutral decay,B0→ρ±π∓,the notation implies a sum over both the modes.The data sample used in this analysis was taken by the Belle detector[9]at KEKB[10],an asymmetric storage ring that collides8GeV electrons against3.5GeV positrons.This produces Υ(4S)mesons that decay into B0B pairs.The Belle detector is a general purpose spectrometer based on a1.5T su-perconducting solenoid magnet.Charged particle tracking is achieved with a three-layer double-sided silicon vertex detector(SVD)surrounded by a central drift chamber(CDC)that consists of50layers segmented into6axial and5 stereo super-layers.The CDC covers the polar angle range between17◦and 150◦in the laboratory frame,which corresponds to92%of the full centre of mass(CM)frame solid angle.Together with the SVD,a transverse momen-tum resolution of(σp t/p t)2=(0.0019p t)2+(0.0030)2is achieved,where p t is in GeV/c.Charged hadron identification is provided by a combination of three devices: a system of1188aerogelˇCerenkov counters(ACC)covering the momentum range1–3.5GeV/c,a time-of-flight scintillation counter system(TOF)for track momenta below1.5GeV/c,and dE/dx information from the CDC for particles with very low or high rmation from these three devices is combined to give the likelihood of a particle being a kaon,L K,or pion, Lπ.Kaon-pion separation is then accomplished based on the likelihood ratio Lπ/(Lπ+L K).Particles with a likelihood ratio greater than0.6are identified as pions.The pion identification efficiencies are measured using a high momentum D∗+data sample,where D∗+→D0π+and D0→K−π+.With this pion selection criterion,the typical efficiency for identifying pions in the momentum region0.5GeV/c<p<4GeV/c is(88.5±0.1)%.By comparing the D∗+data sample with a Monte Carlo(MC)sample,the systematic error in the particle identification(PID)is estimated to be1.4%for the mode with three charged tracks and0.9%for the modes with two.Surrounding the charged PID devices is an electromagnetic calorimeter(ECL) consisting of8736CsI(Tl)crystals with a typical cross-section of5.5×5.5cm2 at the front surface and16.2X0in depth.The ECL provides a photon energy resolution of(σE/E)2=0.0132+(0.0007/E)2+(0.008/E1/4)2,where E is in GeV.Electron identification is achieved by using a combination of dE/dx measure-ments in the CDC,the response of the ACC and the position and shape of the electromagnetic shower from the ECL.Further information is obtained from the ratio of the total energy registered in the calorimeter to the particle momentum,E/p lab.Charged tracks are required to come from the interaction point and have transverse momenta above100MeV/c.Tracks consistent with being an elec-tron are rejected and the remaining tracks must satisfy the pion identification requirement.The performance of the charged track reconstruction is studied using high momentumη→γγandη→π+π−π0decays.Based on the relative yields between data and MC,we assign a systematic error of2%to the single track reconstruction efficiency.Neutral pion candidates are detected with the ECL via their decayπ0→γγ. Theπ0mass resolution,which is asymmetric and varies slowly with theπ0 energy,averages toσ=4.9MeV/c2.The neutral pion candidates are selected fromγγpairs by requiring that their invariant mass to be within3σof the nominalπ0mass.To reduce combinatorial background,a selection criteria is applied to the pho-ton energies and theπ0momenta.Photons in the barrel region are required to have energies over50MeV,while a100MeV requirement is made for photons in the end-cap region.Theπ0candidates are required to have a momentum greater than200MeV/c in the laboratory frame.Forπ0s from BE2beam−p2B and the energy difference∆E=E B−E beam.Here, p B and E B are the momentum and energy of a B candidate in the CM frame and E beam is the CM beam energy.An incorrect mass hypothesis for a pion or kaon produces a shift of about46MeV in∆E,providing extra discrimination between these particles.The width of the M bc distributions is primarily due to the beam energy spread and is well modelled with a Gaussian of width 3.3MeV/c2for the modes with a neutral pion and2.7MeV/c2for the mode without.The∆E distribution is found to be asymmetric with a small tail on the lower side for the modes with aπ0.This is due toγinteractions withmaterial in front of the calorimeter and shower leakage out of the calorimeter. The∆E distribution can be well modelled with a Gaussian when no neutral particles are present.Events with5.2GeV/c2<M bc<5.3GeV/c2and|∆E|< 0.3GeV are selected for thefinal analysis.The dominant background comes from continuum e+e−→qB events and jet-like qi,j|p i||p j|P l(cosθij)i,k|p i||p k|,r l=),where L s and L qqD0π+ decays.By comparing the yields in data and MC after the likelihood ratiorequirement,the systematic errors are determined to be4%for the modes with aπ0and6%for the mode without.Thefinal variable used for continuum suppression is theρhelicity angle,θh, defined as the angle between the direction of the decay pion from theρin the ρrest frame and theρin the B rest frame.The requirement of|cosθh|>0.3 is made independently of the likelihood ratio as it is effective in suppressing the background from B decays as well as the qB events is used[14].The largest component of this background is found to come from decays of the type B→Dπ;when the D meson decays via D→π+π−,events can directly reach the signal region while the decay D→K−π+can reach the signal region with the kaon misidentified as a pion.Decays with J/ψandψ(2S) mesons can also populate the signal region if both the daughter leptons are misidentified as pions.These events are excluded by making requirements on the invariant mass of the intermediate particles:|M(π+π−)−M D0|>0.14 GeV/c2,|M(π+π0)−M D+|>0.05GeV/c2,|M(π+π−)−M J/ψ|>0.07GeV/c2 and|M(π+π−)−Mψ(2S)|>0.05GeV/c2.The widest cut is made around the D0mass to account for the mass shift due to misidentifying the kaons in D0 decays as pions.Fig.1shows the∆E and M bc distributions for the three modes analysed after all the selection criteria have been applied.The∆E and M bc plots are shown for events that lie within3σof the nominal M bc and∆E values,respectively. The signal yields are obtained by performing maximum likelihoodfits,each using a single signal function and one or more background functions.The signal functions are obtained from the MC and adjusted based on comparisons of B+→B0are assumed to be equal.The M bc distribution for all modes isfitted with a single Gaussian and an ARGUS background function[15].The normalization of the ARGUS function is left tofloat and shape of the function isfixed from the∆E sideband:−0.25 GeV<∆E<−0.08GeV and5.2GeV/c2<M bc<5.3GeV/c2.For the mode with only charged pions in thefinal state,the∆E distribution isfitted with a single Gaussian for the signal and a linear function withfixed shape for the continuum background.The normalization of the linear function is left to float and the slope isfixed from the M bc sideband,5.2GeV/c2<M bc<5.26GeV/c2,|∆E|<0.3GeV.There are also other rare B decays that are expected to contaminate the∆E distribution.For the mode without aπ0,these modes are of the type B0→h+h−(where h denotes aπor K),B→ρρ(including all combinations of charged and neutralρmesons,where the polarizations of theρmesons are assumed to be longitudinal)and B→Kππ(including the decays B+→ρ0K+,B+→K∗0π+,B+→K∗0(1430)0π+,B+→f0(980)K+ and B+→f0(1370)K+)[16].These background modes are accounted for by using smoothed histograms whose shapes have been determined by combining MC distributions.The three B→ρρmodes are combined into one histogram. The normalization of this component is allowed tofloat in thefit due to the uncertainty in the branching fractions of the B→ρρmodes.Likewise,the B→hh and all the B→Kππmodes are combined to form one hh and one Kππcomponent.The normalizations of these components arefixed to their expected yields,which are calculated using efficiencies determined by MC and branching fractions measured by previous Belle analyses[16,17].The∆Efits for the modes with aπ0in thefinal state have the signal compo-nent modelled by a Crystal Ball function[18]to account for the asymmetry in the∆E distribution.As for the B+→ρ0π+mode,the continuum background is modelled by a linear function withfixed slope.Unlike the B+→ρ0π+mode, a component is included for the background from the b→c transition.The pa-rameterization for rare B decays includes one component for the B→Kππ0 modes(B0→ρ+K−and B0→K∗+π−)[19]and one for all the B→ρρmodes.The normalization of the B→ρρcomponent is left tofloat while the other components from B decays arefixed to their expected yields.Table1summarizes the results of the∆Efits,showing the number of events, signal yields,reconstruction efficiencies,statistical significance and branching fractions or upper limits for eachfit.The statistical significance is defined assystematic error in thefitted signal yield is estimated by independently varying eachfixed parameter in thefit by1σ.Thefinal results are B(B+→ρ0π+)=(8.0+2.3+0.7−2.0−0.7)×10−6and B(B0→ρ±π∓)=(20.8+6.0+2.8−6.3−3.1)×10−6where thefirst error is statistical and the second is systematic.For theρ0π0mode,one standard deviation of the systematic error is added to the statistical limit to obtain a conservative upper limit at90%confidence of5.3×10−6.The possibility of a nonresonant B→πππbackground is also examined.To check for this type of background,the M bc and∆E yields are determined for differentππinvariant mass bins.Byfitting the M bc distribution inππinvariant mass bins with B→ρπand B→πππMC distributions,the nonresonant contribution is found to be below4%.To account for this possible background, errors3.7%and3.2%are added in quadrature to the systematic errors of the ρ+π−andρ0π+modes,respectively.Theππinvariant mass distributions are shown in Fig.2.Two plots are shown for theρ+π−andρ0π+modes,one with events from the M bc sideband superimposed over the events from the signal region(upper)and one with events from signal MC superimposed over events from the signal region with the sideband subtracted(lower).Fig.3 shows the distribution of the helicity variable,cosθh,for the two modes with all selection criteria applied except the helicity condition.Events fromρπdecays are expected to follow a cos2θdistribution while nonresonant and other background decays have an approximately uniform distribution.The helicity plots are obtained byfitting the M bc distribution in eight helicity bins ranging from−1to1.The M bc yield is then plotted against the helicity bin for each mode and the expected MC signal distributions are superimposed.Both the ππmass spectrum and the helicity distributions provide evidence that the signal events are consistent with being fromρπdecays.The results obtained here can be used to calculate the ratio of branching frac-tions R=B(B0→ρ±π∓)/B(B+→ρ0π+),which gives R=2.6±1.0±0.4, where thefirst error is statistical and second is systematic.This is consistent with values obtained by CLEO[20]and BaBar[21,22]as shown in Table2. Theoretical calculations done at tree level assuming the factorization approx-imation for the hadronic matrix elements give R∼6[3].Calculations that include penguin contributions,off-shell B∗excited states or additionalππres-onances[4–8]might yield better agreement with the the measured value of R.In conclusion,statistically significant signals have been observed in the B→ρπmodes using a31.9×106BWe wish to thank the KEKB accelerator group for the excellent operation of the KEKB accelerator.We acknowledge support from the Ministry of Ed-ucation,Culture,Sports,Science,and Technology of Japan and the Japan Society for the Promotion of Science;the Australian Research Council and the Australian Department of Industry,Science and Resources;the National Science Foundation of China under contract No.10175071;the Department of Science and Technology of India;the BK21program of the Ministry of Education of Korea and the CHEP SRC program of the Korea Science and Engineering Foundation;the Polish State Committee for Scientific Research under contract No.2P03B17017;the Ministry of Science and Technology of the Russian Federation;the Ministry of Education,Science and Sport of the Republic of Slovenia;the National Science Council and the Ministry of Education of Taiwan;and the U.S.Department of Energy.References[1] A.E.Snyder and H.R.Quinn,Phys.Rev.D48,2139(1993).[2]I.Bediaga,R.E.Blanco,C.G¨o bel,and R.M´e ndez-Galain,Phys.Rev.Lett.81,4067(1998).[3]M.Bauer,B.Stech,and M.Wirbel,Z.Phys.C34,103(1987).[4] A.Deandrea et al.,Phys.Rev.D62,036001(2000).[5]Y.H.Chen,H.Y.Cheng,B.Tseng and K.C.Yang,Phys.Rev.D60,094014(1999).[6] C.D.Lu and M.Z.Yang,Eur.Phys.J C23,275(2002).[7]J.Tandean and S.Gardner,SLAC-PUB-9199;hep-ph/0204147.[8]S.Gardner and Ulf-G.Meißner,Phys.Rev.D65,094004(2002).[9]Belle Collaboration,A.Abashian et al.,Nucl.Instr.and Meth.A479,117(2002).[10]E.Kikutani ed.,KEK Preprint2001-157(2001),to appear in Nucl.Instr.andMeth.A.[11]G.C.Fox and S.Wolfram,Phys.Rev.Lett.41,1581(1978).[12]This modification of the Fox-Wolfram moments wasfirst proposed in a seriesof lectures on continuum suppression at KEK by Dr.R.Enomoto in May and June of1999.For a more detailed description see Belle Collaboration,K.Abe et al.,Phys.Lett.B511,151(2001).[13]CLEO Collaboration,D.M.Asner et al.,Phys.Rev.D53,1039(1996).[14]These MC events are generated with the CLEO group’s QQ program,see/public/CLEO/soft/QQ.The detector response is simulated using GEANT,R.Brun et al.,GEANT 3.21,CERN Report DD/EE/84-1,1984.[15]The ARGUS Collaboration,H.Albrecht et al.,Phys.Lett.B241,278(1990).[16]Belle Collaboration,A.Garmash et al.,Phys.Rev.D65,092005(2002).[17]Belle Collaboration,K.Abe et al.,Phys.Rev.Lett.87,101801(2001).[18]J.E.Gaiser et al.,Phys.Rev.D34,711(1986).[19]Belle Collaboration,K.Abe et al.,BELLE-CONF-0115,submitted as acontribution paper to the2001International Europhysics Conference on High Energy Physics(EPS-HEP2001).[20]CLEO Collaboration,C.P.Jessop et al.,Phys.Rev.Lett.85,2881(2000).[21]Babar Collaboration,B.Aubert et al.,submitted as a contribution paper tothe20th International Symposium on Lepton and Photon Interactions at High Energy(LP01);hep-ex/0107058.[22]BaBar Collaboration,B.Aubert et al.,submitted as a contribution paper tothe XXXth International Conference on High Energy Physics(ICHEP2000);hep-ex/0008058.Table1∆Efit results.Shown for each mode are the number of events in thefit,the signal yield,the reconstruction efficiency,the branching fraction(B)or90%confidence level upper limit(UL)and the statistical significance of thefit.Thefirst error in the branching fraction is statistical,the second is systematic.ρ0π+15424.3+6.9−6.29.68.0+2.3+0.7−2.0−0.74.4σρ+π−30144.6+12.8−13.46.820.8+6.0+2.8−6.3−3.13.7σρ0π0116−4.4±8.58.5<5.3-Experiment B(B0→ρ±π∓)×10−6B(B+→ρ0π+)×10−6RE v e n t s /16 M e VE v e n t s /3 M e V /c2(b) ρ0π+Signal backgrd02.557.51012.51517.52022.55.25.225 5.25 5.2755.3E v e n t s /18 M e VE v e n t s /2 M e V /c2(d) ρ+π-Signal backgrd051015202530355.25.225 5.25 5.2755.3∆E(GeV)E v e n t s /18 M e V(e) ρ0π024681012-0.2-0.10.10.2(GeV/c 2)E v e n t s /2 M e V /c2M bc (f) ρ0πSignal backgrd02468101214165.25.225 5.25 5.2755.3Fig.1.The ∆E (left)and M bc (right)fits to the three B →ρπmodes:ρ0π+,ρ+π−and ρ0π0.The histograms show the data,the solid lines show the total fit and the dashed lines show the continuum component.In (a)the contribution from the B →ρρand B →hh modes is shown by the cross hatched component.In (c)the cross hatched component shows the contribution from the b →c transition and B →ρρmodes.102030405060+0(GeV/c 2)E v e n t s /0.1 G e V /c2M(π+π0)(GeV/c 2)E v e n t s /0.1 G e V /c2(GeV/c 2)E v e n t s /0.1 G e V /c2+-(GeV/c 2)E v e n t s /0.1 G e V /c2M(π+ π-)510152025Fig.2.The M (ππ)distributions for B 0→ρ±π∓(left)and B +→ρ0π+(right)events in the signal region.Plots (a)and (b)show sideband events superimposed;plots (c)and (d)show the sideband subtracted plots with signal MC superimposed.-1-0.500.51M b c y i e l d (E v e n t s )cos θh-1-0.500.51M b c y i e l d (E v e n t s )cos θhFig.3.The ρmeson helicity distributions for B 0→ρ±π∓(a)and B +→ρ0π+(b).Signal MC distributions are shown superimposed.。
21925065_榴辉岩中单斜辉石-石榴子石镁同位素地质温度计评述
１０００ ０５６９／２０２０／０３６（０６） １７０５ １８ＡｃｔａＰｅｔｒｏｌｏｇｉｃａＳｉｎｉｃａ 岩石学报ｄｏｉ：１０ １８６５４／１０００ ０５６９／２０２０ ０６ ０４榴辉岩中单斜辉石 石榴子石镁同位素地质温度计评述黄宏炜１ 杜瑾雪１ 柯珊２ＨＵＡＮＧＨｏｎｇＷｅｉ１，ＤＵＪｉｎＸｕｅ１ ａｎｄＫＥＳｈａｎ２１ 中国地质大学地球科学与资源学院，北京 １０００８３２ 中国地质大学地质过程与矿产资源国家重点实验室，北京 １０００８３１ ＳｃｈｏｏｌｏｆＥａｒｔｈＳｃｉｅｎｃｅｓａｎｄＲｅｓｏｕｒｃｅｓ，ＣｈｉｎａＵｎｉｖｅｒｓｉｔｙｏｆＧｅｏｓｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８３，Ｃｈｉｎａ２ ＳｔａｔｅＫｅｙＬａｂｏｒａｔｏｒｙｏｆＧｅｏｌｏｇｉｃａｌＰｒｏｃｅｓｓｅｓａｎｄＭｉｎｅｒａｌＲｅｓｏｕｒｃｅｓ，ＣｈｉｎａＵｎｉｖｅｒｓｉｔｙｏｆＧｅｏｓｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８３，Ｃｈｉｎａ２０１９ １１ １４收稿，２０２０ ０４ ０８改回ＨｕａｎｇＨＷ，ＤｕＪＸａｎｄＫｅＳ ２０２０ Ｒｅｖｉｅｗｏｎｔｈｅｃｌｉｎｏｐｙｒｏｘｅｎｅ ｇａｒｎｅｔｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓｆｏｒｅｃｌｏｇｉｔｅｓ ＡｃｔａＰｅｔｒｏｌｏｇｉｃａＳｉｎｉｃａ，３６（６）：１７０５－１７１８，ｄｏｉ：１０ １８６５４／１０００ ０５６９／２０２０ ０６ ０４Ａｂｓｔｒａｃｔ Ｔｈｅｒｅｍａｒｋａｂｌｅｅｑｕｉｌｉｂｒｉｕｍｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｆｒａｃｔｉｏｎａｔｉｏｎｂｅｔｗｅｅｎｃｌｉｎｏｐｙｒｏｘｅｎｅａｎｄｇａｒｎｅｔｏｂｓｅｒｖｅｄｉｎｅｃｌｏｇｉｔｅｓｍａｋｅｓｉｔａｐｏｔｅｎｔｉａｌｈｉｇｈ ｐｒｅｃｉｓｉｏｎｇｅｏｔｈｅｒｍｏｍｅｔｅｒ Ｔｈｅｒｅｆｏｒｅ，ｔｈｉｓｐａｐｅｒｓｅｌｅｃｔｓ６４ｐａｉｒｓｏｆｃｌｉｎｏｐｙｒｏｘｅｎｅ ｇａｒｎｅｔｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｄａｔａｏｆｅｃｌｏｇｉｔｅｓｉｎｔｈｅＣｈｉｎｅｓｅｓｏｕｔｈｗｅｓｔｅｒｎＴｉａｎｓｈａｎｏｒｏｇｅｎ，ｉｎｔｈｅＤａｂｉｅ ＳｕｌｕｏｒｏｇｅｎａｎｄｉｎｔｈｅＫａａｐｖａａｌｃｒａｔｏｎｉｎｔｈｅＳｏｕｔｈＡｆｒｉｃａｆｒｏｍｌｉｔｅｒａｔｕｒｅｓ Ｔｈｅｎ，ｗｅｓｃｒｅｅｎｅｄ５０ｐａｉｒｓｏｆｄａｔａｔｈａｔｒｅａｃｈｔｈｅｅｑｕｉｌｉｂｒｉｕｍｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｆｒａｃｔｉｏｎａｔｉｏｎｂｙｔｈｅδ２６ＭｇＣｐｘ δ２６ＭｇＧｒｔｄｉａｇｒａｍ Ｕｓｉｎｇｔｈｅｓｅｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｅｑｕｉｌｉｂｒｉｕｍｆｒａｃｔｉｏｎａｔｉｏｎｄａｔａ，ｗｅｃａｌｃｕｌａｔｅｄｐｅａｋｔｅｍｐｅｒａｔｕｒｅｓｏｆｅｃｌｏｇｉｔｅｓｂｙｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓｏｆＨｕａｎｇｅｔａｌ （２０１３）ｔｈｒｏｕｇｈｆｉｒｓｔ ｐｒｉｎｃｉｐｌｅｓｃａｌｃｕｌａｔｉｏｎａｎｄＷａｎｇｅｔａｌ （２０１２）ａｎｄＬｉｅｔａｌ （２０１６）ｔｈｒｏｕｇｈｅｍｐｉｒｉｃａｌｅｓｔｉｍａｔｉｏｎ，ａｎｄｃｏｍｐａｒｅｄｔｈｅｍｗｉｔｈｔｈｅｐｅａｋｔｅｍｐｅｒａｔｕｒｅｓｇｉｖｅｎｂｙｏｔｈｅｒｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓ Ｂｙａｎａｌｙｚｉｎｇｔｈｅｃａｌｃｕｌａｔｉｏｎｒｅｓｕｌｔｓ，ｉｔｉｓｆｏｕｎｄｔｈａｔｆｏｒｏｒｏｇｅｎｉｃｅｃｌｏｇｉｔｅｓ，ｔｈｅｃａｌｃｕｌａｔｉｏｎｒｅｓｕｌｔｓｏｆｔｈｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｏｆＨｕａｎｇｅｔａｌ （２０１３）ａｒｅｃｏｎｓｉｓｔｅｎｔｗｉｔｈｔｈｏｓｅｐｒｅｖｉｏｕｓｌｙｏｂｔａｉｎｅｄｂｙｔｒａｄｉｔｉｏｎａｌｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓａｎｄｐｈａｓｅｅｑｕｉｌｉｂｒｉａｍｏｄｅｌｉｎｇ，ｗｈｉｌｅｔｈｅｃａｌｃｕｌａｔｉｏｎｒｅｓｕｌｔｓｏｆｔｈｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓｏｆＷａｎｇｅｔａｌ （２０１２）ａｎｄＬｉｅｔａｌ （２０１６）ａｒｅｓｉｇｎｉｆｉｃａｎｔｌｙｌｏｗｅｒ Ｆｏｒｔｈｅｃｒａｔｏｎｅｃｌｏｇｉｔｅｓ，ｔｈｅｃａｌｃｕｌａｔｉｏｎｒｅｓｕｌｔｓｏｆａｌｌｔｈｅｔｈｒｅｅｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓａｒｅｓｉｇｎｉｆｉｃａｎｔｌｙｄｉｆｆｅｒｅｎｔｆｒｏｍｒｅｓｕｌｔｓｏｆｔｒａｄｉｔｉｏｎａｌｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓｂｙｍｏｒｅｔｈａｎ５０℃，ｗｈｉｃｈｉｓｍｏｓｔｐｒｏｂａｂｌｙｃａｕｓｅｄｂｙｒｅ ｅｑｕｉｌｉｂｒｉｕｍｏｆｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｄｕｒｉｎｇｅａｒｌｙｒｅｔｒｏｇｒａｄｅｍｅｔａｍｏｒｐｈｉｓｍａｔｈｉｇｈｔｅｍｐｅｒａｔｕｒｅｓ Ｔｈｉｓｉｎｄｉｃａｔｅｓｔｈａｔｔｈｅｓｅｔｈｒｅｅｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓａｒｅｎｏｔａｐｐｌｉｃａｂｌｅｆｏｒｔｈｅｃｒａｔｏｎｅｃｌｏｇｉｔｅｓ Ｂａｓｅｄｏｎｔｈｅａｂｏｖｅｄａｔａ，ｔｈｅｍｅｔｈｏｄｏｆｅｍｐｉｒｉｃａｌｅｓｔｉｍａｔｉｏｎｉｓｕｓｅｄｔｏｃａｌｉｂｒａｔｅａｎｅｗｃｌｉｎｏｐｙｒｏｘｅｎｅ ｇａｒｎｅｔｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒ，ｗｈｉｃｈｉｓΔ２６ＭｇＣｐｘ Ｇｒｔ＝１ １１×１０６／［Ｔ（Ｋ）］２（Ｒ２＝０ ９２）．Ｉｎａｄｄｉｔｉｏｎ，ｔｈｉｓｐａｐｅｒａｌｓｏｂｒｉｅｆｌｙｄｉｓｃｕｓｓｅｓａｐｐｌｉｃａｔｉｏｎｐｒｏｓｐｅｃｔｏｆｔｈｅｃｌｉｎｏｐｙｒｏｘｅｎｅ ｇａｒｎｅｔｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒｓａｎｄｔｈｅｐｒｏｂｌｅｍｓｔｈａｔｓｈｏｕｌｄｂｅｐａｉｄａｔｔｅｎｔｉｏｎｔｏｄｕｒｉｎｇａｐｐｌｉｃａｔｉｏｎ Ｋｅｙｗｏｒｄｓ Ｅｃｌｏｇｉｔｅｓ；Ｉｓｏｔｏｐｅｇｅｏｔｈｅｒｍｏｍｅｔｅｒ；Ｍａｇｎｅｓｉｕｍｉｓｏｔｏｐｅ；Ｃｌｉｎｏｐｙｒｏｘｅｎｅ ｇａｒｎｅｔ摘 要 榴辉岩中单斜辉石和石榴子石之间显著的镁同位素平衡分馏，使其成为一种具有潜力的高精度地质温度计。
12-多物理场、多尺度计算力学建模-摘要
1)
给出了非等温的纤维悬浮聚合物熔体领域的多尺度模型，该多尺度模型建立在聚合物大分子尺 度、增韧纤维尺度和宏观流场尺度的耦合上。 通过对4:1平板收缩流的数值模拟，验证了该多尺度 模型在纤维增韧聚合物复合材料加工过程中的有效性。 最后得到了各个尺度上的应力分布信息， 其中宏观流场的法向应力差和剪应力分别关于拐角平分线大致呈对称和反对称分布，而纤维产生的 法向应力差和剪应力则由于纤维的旋转取向运动而在下游产生逆序应力结构，聚合物哑铃大分子则 由于其黏性远小于基体溶液黏性，故而产生层状的法向应力差和剪应力分布。 对于对复合材料性 能影响很大的增韧纤维情况，也得到了其运动规律和取向分布，纤维大体沿流动方向取向，在壁面 处受到强剪切作用而沿壁面取向，在对称线上沿单轴拉伸，在下游区域，由于拐角效应纤维出现旋 转取向运动。 由温度影响聚合物熔体应力的数值结果可知，即使在流动阶段，较低的温度仍有助 于提升熔体的黏弹性。 关键词 纤维取向，黏弹性，多尺度
*
徐鉴君*,+,2)
(天津城市建设学院基础学科部, 天津 300384)
(南开大学数学科学学院, 天津 300071)
+
**
(麦吉尔大学数学与统计学系, H3A2K6)
液态粒子的固化成型是自然界与工业生产领域普遍存在的重要现象。 本文在平均场的概念下 对雾化液粒的凝固过程提出了一个简化的液-固-气-雾(LSGF)数学模型，并在小过冷度的条件下，求 出了有关初值问题的一致有效渐近解。 结果表明：整个动力学过程可以分为两个相互联结的时间 阶段。 （1）液粒初始温度分布的瞬态过渡阶段。 在这个阶段，凝固尚未正式启动，只是系统内 的温度从任意给定的初始分布迅速调整到某一特定空间分布。 （2）液粒向固粒转变阶段。 在这一 阶段，液－固两相开始分离，相界面逐渐向液粒中心传播，直至液相完全消失。 进而以铜为例， 讨论了液态粒子在不同生长条件与一些重要物理参数下的凝固时间与凝固过程中的温度分布的演化 规律。 关键词 Gibbs-Thomson 公式, 过冷度, 无量纲化, 界面条件, 渐近展开, 零级近似解, 内解, 外 解, 一致有效渐近解
C.parvum全基因组序列
DOI: 10.1126/science.1094786, 441 (2004);304Science et al.Mitchell S. Abrahamsen,Cryptosporidium parvum Complete Genome Sequence of the Apicomplexan, (this information is current as of October 7, 2009 ):The following resources related to this article are available online at/cgi/content/full/304/5669/441version of this article at:including high-resolution figures, can be found in the online Updated information and services,/cgi/content/full/1094786/DC1 can be found at:Supporting Online Material/cgi/content/full/304/5669/441#otherarticles , 9 of which can be accessed for free: cites 25 articles This article 239 article(s) on the ISI Web of Science. cited by This article has been /cgi/content/full/304/5669/441#otherarticles 53 articles hosted by HighWire Press; see: cited by This article has been/cgi/collection/genetics Genetics: subject collections This article appears in the following/about/permissions.dtl in whole or in part can be found at: this article permission to reproduce of this article or about obtaining reprints Information about obtaining registered trademark of AAAS.is a Science 2004 by the American Association for the Advancement of Science; all rights reserved. The title Copyright American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. 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critical word.This was done in order tonormalize for individual differences in EEG power anddifferences in baseline power between different fre-quency bands.Two relevant time-frequency compo-nents were identified:(i)a theta component,rangingfrom4to7Hz and from300to800ms after wordonset,and(ii)a gamma component,ranging from35to45Hz and from400to600ms after word onset.20.C.Tallon-Baudry,O.Bertrand,Trends Cognit.Sci.3,151(1999).tner et al.,Nature397,434(1999).22.M.Bastiaansen,P.Hagoort,Cortex39(2003).23.O.Jensen,C.D.Tesche,Eur.J.Neurosci.15,1395(2002).24.Whole brain T2*-weighted echo planar imaging bloodoxygen level–dependent(EPI-BOLD)fMRI data wereacquired with a Siemens Sonata1.5-T magnetic reso-nance scanner with interleaved slice ordering,a volumerepetition time of2.48s,an echo time of40ms,a90°flip angle,31horizontal slices,a64ϫ64slice matrix,and isotropic voxel size of3.5ϫ3.5ϫ3.5mm.For thestructural magnetic resonance image,we used a high-resolution(isotropic voxels of1mm3)T1-weightedmagnetization-prepared rapid gradient-echo pulse se-quence.The fMRI data were preprocessed and analyzedby statistical parametric mappingwith SPM99software(http://www.fi/spm99).25.S.E.Petersen et al.,Nature331,585(1988).26.B.T.Gold,R.L.Buckner,Neuron35,803(2002).27.E.Halgren et al.,J.Psychophysiol.88,1(1994).28.E.Halgren et al.,Neuroimage17,1101(2002).29.M.K.Tanenhaus et al.,Science268,1632(1995).30.J.J.A.van Berkum et al.,J.Cognit.Neurosci.11,657(1999).31.P.A.M.Seuren,Discourse Semantics(Basil Blackwell,Oxford,1985).32.We thank P.Indefrey,P.Fries,P.A.M.Seuren,and M.van Turennout for helpful discussions.Supported bythe Netherlands Organization for Scientific Research,grant no.400-56-384(P.H.).Supporting Online Material/cgi/content/full/1095455/DC1Materials and MethodsFig.S1References and Notes8January2004;accepted9March2004Published online18March2004;10.1126/science.1095455Include this information when citingthis paper.Complete Genome Sequence ofthe Apicomplexan,Cryptosporidium parvumMitchell S.Abrahamsen,1,2*†Thomas J.Templeton,3†Shinichiro Enomoto,1Juan E.Abrahante,1Guan Zhu,4 Cheryl ncto,1Mingqi Deng,1Chang Liu,1‡Giovanni Widmer,5Saul Tzipori,5GregoryA.Buck,6Ping Xu,6 Alan T.Bankier,7Paul H.Dear,7Bernard A.Konfortov,7 Helen F.Spriggs,7Lakshminarayan Iyer,8Vivek Anantharaman,8L.Aravind,8Vivek Kapur2,9The apicomplexan Cryptosporidium parvum is an intestinal parasite that affects healthy humans and animals,and causes an unrelenting infection in immuno-compromised individuals such as AIDS patients.We report the complete ge-nome sequence of C.parvum,type II isolate.Genome analysis identifies ex-tremely streamlined metabolic pathways and a reliance on the host for nu-trients.In contrast to Plasmodium and Toxoplasma,the parasite lacks an api-coplast and its genome,and possesses a degenerate mitochondrion that has lost its genome.Several novel classes of cell-surface and secreted proteins with a potential role in host interactions and pathogenesis were also detected.Elu-cidation of the core metabolism,including enzymes with high similarities to bacterial and plant counterparts,opens new avenues for drug development.Cryptosporidium parvum is a globally impor-tant intracellular pathogen of humans and animals.The duration of infection and patho-genesis of cryptosporidiosis depends on host immune status,ranging from a severe but self-limiting diarrhea in immunocompetent individuals to a life-threatening,prolonged infection in immunocompromised patients.Asubstantial degree of morbidity and mortalityis associated with infections in AIDS pa-tients.Despite intensive efforts over the past20years,there is currently no effective ther-apy for treating or preventing C.parvuminfection in humans.Cryptosporidium belongs to the phylumApicomplexa,whose members share a com-mon apical secretory apparatus mediating lo-comotion and tissue or cellular invasion.Many apicomplexans are of medical or vet-erinary importance,including Plasmodium,Babesia,Toxoplasma,Neosprora,Sarcocys-tis,Cyclospora,and Eimeria.The life cycle ofC.parvum is similar to that of other cyst-forming apicomplexans(e.g.,Eimeria and Tox-oplasma),resulting in the formation of oocysts1Department of Veterinary and Biomedical Science,College of Veterinary Medicine,2Biomedical Genom-ics Center,University of Minnesota,St.Paul,MN55108,USA.3Department of Microbiology and Immu-nology,Weill Medical College and Program in Immu-nology,Weill Graduate School of Medical Sciences ofCornell University,New York,NY10021,USA.4De-partment of Veterinary Pathobiology,College of Vet-erinary Medicine,Texas A&M University,College Sta-tion,TX77843,USA.5Division of Infectious Diseases,Tufts University School of Veterinary Medicine,NorthGrafton,MA01536,USA.6Center for the Study ofBiological Complexity and Department of Microbiol-ogy and Immunology,Virginia Commonwealth Uni-versity,Richmond,VA23198,USA.7MRC Laboratoryof Molecular Biology,Hills Road,Cambridge CB22QH,UK.8National Center for Biotechnology Infor-mation,National Library of Medicine,National Insti-tutes of Health,Bethesda,MD20894,USA.9Depart-ment of Microbiology,University of Minnesota,Min-neapolis,MN55455,USA.*To whom correspondence should be addressed.E-mail:abe@†These authors contributed equally to this work.‡Present address:Bioinformatics Division,Genetic Re-search,GlaxoSmithKline Pharmaceuticals,5MooreDrive,Research Triangle Park,NC27009,USA.R E P O R T S SCIENCE VOL30416APRIL2004441o n O c t o b e r 7 , 2 0 0 9 w w w . s c i e n c e m a g . o r g D o w n l o a d e d f r o mthat are shed in the feces of infected hosts.C.parvum oocysts are highly resistant to environ-mental stresses,including chlorine treatment of community water supplies;hence,the parasite is an important water-and food-borne pathogen (1).The obligate intracellular nature of the par-asite ’s life cycle and the inability to culture the parasite continuously in vitro greatly impair researchers ’ability to obtain purified samples of the different developmental stages.The par-asite cannot be genetically manipulated,and transformation methodologies are currently un-available.To begin to address these limitations,we have obtained the complete C.parvum ge-nome sequence and its predicted protein com-plement.(This whole-genome shotgun project has been deposited at DDBJ/EMBL/GenBank under the project accession AAEE00000000.The version described in this paper is the first version,AAEE01000000.)The random shotgun approach was used to obtain the complete DNA sequence (2)of the Iowa “type II ”isolate of C.parvum .This isolate readily transmits disease among numerous mammals,including humans.The resulting ge-nome sequence has roughly 13ϫgenome cov-erage containing five gaps and 9.1Mb of totalDNA sequence within eight chromosomes.The C.parvum genome is thus quite compact rela-tive to the 23-Mb,14-chromosome genome of Plasmodium falciparum (3);this size difference is predominantly the result of shorter intergenic regions,fewer introns,and a smaller number of genes (Table 1).Comparison of the assembled sequence of chromosome VI to that of the recently published sequence of chromosome VI (4)revealed that our assembly contains an ad-ditional 160kb of sequence and a single gap versus two,with the common sequences dis-playing a 99.993%sequence identity (2).The relative paucity of introns greatly simplified gene predictions and facilitated an-notation (2)of predicted open reading frames (ORFs).These analyses provided an estimate of 3807protein-encoding genes for the C.parvum genome,far fewer than the estimated 5300genes predicted for the Plasmodium genome (3).This difference is primarily due to the absence of an apicoplast and mitochondrial genome,as well as the pres-ence of fewer genes encoding metabolic functions and variant surface proteins,such as the P.falciparum var and rifin molecules (Table 2).An analysis of the encoded pro-tein sequences with the program SEG (5)shows that these protein-encoding genes are not enriched in low-complexity se-quences (34%)to the extent observed in the proteins from Plasmodium (70%).Our sequence analysis indicates that Cryptosporidium ,unlike Plasmodium and Toxoplasma ,lacks both mitochondrion and apicoplast genomes.The overall complete-ness of the genome sequence,together with the fact that similar DNA extraction proce-dures used to isolate total genomic DNA from C.parvum efficiently yielded mito-chondrion and apicoplast genomes from Ei-meria sp.and Toxoplasma (6,7),indicates that the absence of organellar genomes was unlikely to have been the result of method-ological error.These conclusions are con-sistent with the absence of nuclear genes for the DNA replication and translation machinery characteristic of mitochondria and apicoplasts,and with the lack of mito-chondrial or apicoplast targeting signals for tRNA synthetases.A number of putative mitochondrial pro-teins were identified,including components of a mitochondrial protein import apparatus,chaperones,uncoupling proteins,and solute translocators (table S1).However,the ge-nome does not encode any Krebs cycle en-zymes,nor the components constituting the mitochondrial complexes I to IV;this finding indicates that the parasite does not rely on complete oxidation and respiratory chains for synthesizing adenosine triphosphate (ATP).Similar to Plasmodium ,no orthologs for the ␥,␦,or εsubunits or the c subunit of the F 0proton channel were detected (whereas all subunits were found for a V-type ATPase).Cryptosporidium ,like Eimeria (8)and Plas-modium ,possesses a pyridine nucleotide tran-shydrogenase integral membrane protein that may couple reduced nicotinamide adenine dinucleotide (NADH)and reduced nico-tinamide adenine dinucleotide phosphate (NADPH)redox to proton translocation across the inner mitochondrial membrane.Unlike Plasmodium ,the parasite has two copies of the pyridine nucleotide transhydrogenase gene.Also present is a likely mitochondrial membrane –associated,cyanide-resistant alter-native oxidase (AOX )that catalyzes the reduction of molecular oxygen by ubiquinol to produce H 2O,but not superoxide or H 2O 2.Several genes were identified as involved in biogenesis of iron-sulfur [Fe-S]complexes with potential mitochondrial targeting signals (e.g.,nifS,nifU,frataxin,and ferredoxin),supporting the presence of a limited electron flux in the mitochondrial remnant (table S2).Our sequence analysis confirms the absence of a plastid genome (7)and,additionally,the loss of plastid-associated metabolic pathways including the type II fatty acid synthases (FASs)and isoprenoid synthetic enzymes thatTable 1.General features of the C.parvum genome and comparison with other single-celled eukaryotes.Values are derived from respective genome project summaries (3,26–28).ND,not determined.FeatureC.parvum P.falciparum S.pombe S.cerevisiae E.cuniculiSize (Mbp)9.122.912.512.5 2.5(G ϩC)content (%)3019.43638.347No.of genes 38075268492957701997Mean gene length (bp)excluding introns 1795228314261424ND Gene density (bp per gene)23824338252820881256Percent coding75.352.657.570.590Genes with introns (%)553.9435ND Intergenic regions (G ϩC)content %23.913.632.435.145Mean length (bp)5661694952515129RNAsNo.of tRNA genes 454317429944No.of 5S rRNA genes 6330100–2003No.of 5.8S ,18S ,and 28S rRNA units 57200–400100–20022Table parison between predicted C.parvum and P.falciparum proteins.FeatureC.parvum P.falciparum *Common †Total predicted proteins380752681883Mitochondrial targeted/encoded 17(0.45%)246(4.7%)15Apicoplast targeted/encoded 0581(11.0%)0var/rif/stevor ‡0236(4.5%)0Annotated as protease §50(1.3%)31(0.59%)27Annotated as transporter 69(1.8%)34(0.65%)34Assigned EC function ¶167(4.4%)389(7.4%)113Hypothetical proteins925(24.3%)3208(60.9%)126*Values indicated for P.falciparum are as reported (3)with the exception of those for proteins annotated as protease or transporter.†TBLASTN hits (e Ͻ–5)between C.parvum and P.falciparum .‡As reported in (3).§Pre-dicted proteins annotated as “protease or peptidase”for C.parvum (CryptoGenome database,)and P.falciparum (PlasmoDB database,).Predicted proteins annotated as “trans-porter,permease of P-type ATPase”for C.parvum (CryptoGenome)and P.falciparum (PlasmoDB).¶Bidirectional BLAST hit (e Ͻ–15)to orthologs with assigned Enzyme Commission (EC)numbers.Does not include EC assignment numbers for protein kinases or protein phosphatases (due to inconsistent annotation across genomes),or DNA polymerases or RNA polymerases,as a result of issues related to subunit inclusion.(For consistency,46proteins were excluded from the reported P.falciparum values.)R E P O R T S16APRIL 2004VOL 304SCIENCE 442 o n O c t o b e r 7, 2009w w w .s c i e n c e m a g .o r g D o w n l o a d e d f r o mare otherwise localized to the plastid in other apicomplexans.C.parvum fatty acid biosynthe-sis appears to be cytoplasmic,conducted by a large(8252amino acids)modular type I FAS (9)and possibly by another large enzyme that is related to the multidomain bacterial polyketide synthase(10).Comprehensive screening of the C.parvum genome sequence also did not detect orthologs of Plasmodium nuclear-encoded genes that contain apicoplast-targeting and transit sequences(11).C.parvum metabolism is greatly stream-lined relative to that of Plasmodium,and in certain ways it is reminiscent of that of another obligate eukaryotic parasite,the microsporidian Encephalitozoon.The degeneration of the mi-tochondrion and associated metabolic capabili-ties suggests that the parasite largely relies on glycolysis for energy production.The parasite is capable of uptake and catabolism of mono-sugars(e.g.,glucose and fructose)as well as synthesis,storage,and catabolism of polysac-charides such as trehalose and amylopectin. Like many anaerobic organisms,it economizes ATP through the use of pyrophosphate-dependent phosphofructokinases.The conver-sion of pyruvate to acetyl–coenzyme A(CoA) is catalyzed by an atypical pyruvate-NADPH oxidoreductase(Cp PNO)that contains an N-terminal pyruvate–ferredoxin oxidoreductase (PFO)domain fused with a C-terminal NADPH–cytochrome P450reductase domain (CPR).Such a PFO-CPR fusion has previously been observed only in the euglenozoan protist Euglena gracilis(12).Acetyl-CoA can be con-verted to malonyl-CoA,an important precursor for fatty acid and polyketide biosynthesis.Gly-colysis leads to several possible organic end products,including lactate,acetate,and ethanol. The production of acetate from acetyl-CoA may be economically beneficial to the parasite via coupling with ATP production.Ethanol is potentially produced via two in-dependent pathways:(i)from the combination of pyruvate decarboxylase and alcohol dehy-drogenase,or(ii)from acetyl-CoA by means of a bifunctional dehydrogenase(adhE)with ac-etaldehyde and alcohol dehydrogenase activi-ties;adhE first converts acetyl-CoA to acetal-dehyde and then reduces the latter to ethanol. AdhE predominantly occurs in bacteria but has recently been identified in several protozoans, including vertebrate gut parasites such as Enta-moeba and Giardia(13,14).Adjacent to the adhE gene resides a second gene encoding only the AdhE C-terminal Fe-dependent alcohol de-hydrogenase domain.This gene product may form a multisubunit complex with AdhE,or it may function as an alternative alcohol dehydro-genase that is specific to certain growth condi-tions.C.parvum has a glycerol3-phosphate dehydrogenase similar to those of plants,fungi, and the kinetoplastid Trypanosoma,but(unlike trypanosomes)the parasite lacks an ortholog of glycerol kinase and thus this pathway does not yield glycerol production.In addition to themodular fatty acid synthase(Cp FAS1)andpolyketide synthase homolog(Cp PKS1), C.parvum possesses several fatty acyl–CoA syn-thases and a fatty acyl elongase that may partici-pate in fatty acid metabolism.Further,enzymesfor the metabolism of complex lipids(e.g.,glyc-erolipid and inositol phosphate)were identified inthe genome.Fatty acids are apparently not anenergy source,because enzymes of the fatty acidoxidative pathway are absent,with the exceptionof a3-hydroxyacyl-CoA dehydrogenase.C.parvum purine metabolism is greatlysimplified,retaining only an adenosine ki-nase and enzymes catalyzing conversionsof adenosine5Ј-monophosphate(AMP)toinosine,xanthosine,and guanosine5Ј-monophosphates(IMP,XMP,and GMP).Among these enzymes,IMP dehydrogenase(IMPDH)is phylogenetically related toε-proteobacterial IMPDH and is strikinglydifferent from its counterparts in both thehost and other apicomplexans(15).In con-trast to other apicomplexans such as Toxo-plasma gondii and P.falciparum,no geneencoding hypoxanthine-xanthineguaninephosphoribosyltransferase(HXGPRT)is de-tected,in contrast to a previous report on theactivity of this enzyme in C.parvum sporo-zoites(16).The absence of HXGPRT sug-gests that the parasite may rely solely on asingle enzyme system including IMPDH toproduce GMP from AMP.In contrast to otherapicomplexans,the parasite appears to relyon adenosine for purine salvage,a modelsupported by the identification of an adeno-sine transporter.Unlike other apicomplexansand many parasitic protists that can synthe-size pyrimidines de novo,C.parvum relies onpyrimidine salvage and retains the ability forinterconversions among uridine and cytidine5Ј-monophosphates(UMP and CMP),theirdeoxy forms(dUMP and dCMP),and dAMP,as well as their corresponding di-and triphos-phonucleotides.The parasite has also largelyshed the ability to synthesize amino acids denovo,although it retains the ability to convertselect amino acids,and instead appears torely on amino acid uptake from the host bymeans of a set of at least11amino acidtransporters(table S2).Most of the Cryptosporidium core pro-cesses involved in DNA replication,repair,transcription,and translation conform to thebasic eukaryotic blueprint(2).The transcrip-tional apparatus resembles Plasmodium interms of basal transcription machinery.How-ever,a striking numerical difference is seenin the complements of two RNA bindingdomains,Sm and RRM,between P.falcipa-rum(17and71domains,respectively)and C.parvum(9and51domains).This reductionresults in part from the loss of conservedproteins belonging to the spliceosomal ma-chinery,including all genes encoding Smdomain proteins belonging to the U6spliceo-somal particle,which suggests that this par-ticle activity is degenerate or entirely lost.This reduction in spliceosomal machinery isconsistent with the reduced number of pre-dicted introns in Cryptosporidium(5%)rela-tive to Plasmodium(Ͼ50%).In addition,keycomponents of the small RNA–mediatedposttranscriptional gene silencing system aremissing,such as the RNA-dependent RNApolymerase,Argonaute,and Dicer orthologs;hence,RNA interference–related technolo-gies are unlikely to be of much value intargeted disruption of genes in C.parvum.Cryptosporidium invasion of columnarbrush border epithelial cells has been de-scribed as“intracellular,but extracytoplas-mic,”as the parasite resides on the surface ofthe intestinal epithelium but lies underneaththe host cell membrane.This niche may al-low the parasite to evade immune surveil-lance but take advantage of solute transportacross the host microvillus membrane or theextensively convoluted parasitophorous vac-uole.Indeed,Cryptosporidium has numerousgenes(table S2)encoding families of putativesugar transporters(up to9genes)and aminoacid transporters(11genes).This is in starkcontrast to Plasmodium,which has fewersugar transporters and only one putative ami-no acid transporter(GenBank identificationnumber23612372).As a first step toward identification ofmulti–drug-resistant pumps,the genome se-quence was analyzed for all occurrences ofgenes encoding multitransmembrane proteins.Notable are a set of four paralogous proteinsthat belong to the sbmA family(table S2)thatare involved in the transport of peptide antibi-otics in bacteria.A putative ortholog of thePlasmodium chloroquine resistance–linkedgene Pf CRT(17)was also identified,althoughthe parasite does not possess a food vacuole likethe one seen in Plasmodium.Unlike Plasmodium,C.parvum does notpossess extensive subtelomeric clusters of anti-genically variant proteins(exemplified by thelarge families of var and rif/stevor genes)thatare involved in immune evasion.In contrast,more than20genes were identified that encodemucin-like proteins(18,19)having hallmarksof extensive Thr or Ser stretches suggestive ofglycosylation and signal peptide sequences sug-gesting secretion(table S2).One notable exam-ple is an11,700–amino acid protein with anuninterrupted stretch of308Thr residues(cgd3_720).Although large families of secretedproteins analogous to the Plasmodium multi-gene families were not found,several smallermultigene clusters were observed that encodepredicted secreted proteins,with no detectablesimilarity to proteins from other organisms(Fig.1,A and B).Within this group,at leastfour distinct families appear to have emergedthrough gene expansions specific to the Cryp-R E P O R T S SCIENCE VOL30416APRIL2004443o n O c t o b e r 7 , 2 0 0 9 w w w . s c i e n c e m a g . o r g D o w n l o a d e d f r o mtosporidium clade.These families —SKSR,MEDLE,WYLE,FGLN,and GGC —were named after well-conserved sequence motifs (table S2).Reverse transcription polymerase chain reaction (RT-PCR)expression analysis (20)of one cluster,a locus of seven adjacent CpLSP genes (Fig.1B),shows coexpression during the course of in vitro development (Fig.1C).An additional eight genes were identified that encode proteins having a periodic cysteine structure similar to the Cryptosporidium oocyst wall protein;these eight genes are similarly expressed during the onset of oocyst formation and likely participate in the formation of the coccidian rigid oocyst wall in both Cryptospo-ridium and Toxoplasma (21).Whereas the extracellular proteins described above are of apparent apicomplexan or lineage-specific in-vention,Cryptosporidium possesses many genesencodingsecretedproteinshavinglineage-specific multidomain architectures composed of animal-and bacterial-like extracellular adhe-sive domains (fig.S1).Lineage-specific expansions were ob-served for several proteases (table S2),in-cluding an aspartyl protease (six genes),a subtilisin-like protease,a cryptopain-like cys-teine protease (five genes),and a Plas-modium falcilysin-like (insulin degrading enzyme –like)protease (19genes).Nine of the Cryptosporidium falcilysin genes lack the Zn-chelating “HXXEH ”active site motif and are likely to be catalytically inactive copies that may have been reused for specific protein-protein interactions on the cell sur-face.In contrast to the Plasmodium falcilysin,the Cryptosporidium genes possess signal peptide sequences and are likely trafficked to a secretory pathway.The expansion of this family suggests either that the proteins have distinct cleavage specificities or that their diversity may be related to evasion of a host immune response.Completion of the C.parvum genome se-quence has highlighted the lack of conven-tional drug targets currently pursued for the control and treatment of other parasitic protists.On the basis of molecular and bio-chemical studies and drug screening of other apicomplexans,several putative Cryptospo-ridium metabolic pathways or enzymes have been erroneously proposed to be potential drug targets (22),including the apicoplast and its associated metabolic pathways,the shikimate pathway,the mannitol cycle,the electron transport chain,and HXGPRT.Nonetheless,complete genome sequence analysis identifies a number of classic and novel molecular candidates for drug explora-tion,including numerous plant-like and bacterial-like enzymes (tables S3and S4).Although the C.parvum genome lacks HXGPRT,a potent drug target in other api-complexans,it has only the single pathway dependent on IMPDH to convert AMP to GMP.The bacterial-type IMPDH may be a promising target because it differs substan-tially from that of eukaryotic enzymes (15).Because of the lack of de novo biosynthetic capacity for purines,pyrimidines,and amino acids,C.parvum relies solely on scavenge from the host via a series of transporters,which may be exploited for chemotherapy.C.parvum possesses a bacterial-type thymidine kinase,and the role of this enzyme in pyrim-idine metabolism and its drug target candida-cy should be pursued.The presence of an alternative oxidase,likely targeted to the remnant mitochondrion,gives promise to the study of salicylhydroxamic acid (SHAM),as-cofuranone,and their analogs as inhibitors of energy metabolism in the parasite (23).Cryptosporidium possesses at least 15“plant-like ”enzymes that are either absent in or highly divergent from those typically found in mammals (table S3).Within the glycolytic pathway,the plant-like PPi-PFK has been shown to be a potential target in other parasites including T.gondii ,and PEPCL and PGI ap-pear to be plant-type enzymes in C.parvum .Another example is a trehalose-6-phosphate synthase/phosphatase catalyzing trehalose bio-synthesis from glucose-6-phosphate and uridine diphosphate –glucose.Trehalose may serve as a sugar storage source or may function as an antidesiccant,antioxidant,or protein stability agent in oocysts,playing a role similar to that of mannitol in Eimeria oocysts (24).Orthologs of putative Eimeria mannitol synthesis enzymes were not found.However,two oxidoreductases (table S2)were identified in C.parvum ,one of which belongs to the same families as the plant mannose dehydrogenases (25)and the other to the plant cinnamyl alcohol dehydrogenases.In principle,these enzymes could synthesize protective polyol compounds,and the former enzyme could use host-derived mannose to syn-thesize mannitol.References and Notes1.D.G.Korich et al .,Appl.Environ.Microbiol.56,1423(1990).2.See supportingdata on Science Online.3.M.J.Gardner et al .,Nature 419,498(2002).4.A.T.Bankier et al .,Genome Res.13,1787(2003).5.J.C.Wootton,Comput.Chem.18,269(1994).Fig.1.(A )Schematic showing the chromosomal locations of clusters of potentially secreted proteins.Numbers of adjacent genes are indicated in paren-theses.Arrows indicate direc-tion of clusters containinguni-directional genes (encoded on the same strand);squares indi-cate clusters containingg enes encoded on both strands.Non-paralogous genes are indicated by solid gray squares or direc-tional triangles;SKSR (green triangles),FGLN (red trian-gles),and MEDLE (blue trian-gles)indicate three C.parvum –specific families of paralogous genes predominantly located at telomeres.Insl (yellow tri-angles)indicates an insulinase/falcilysin-like paralogous gene family.Cp LSP (white square)indicates the location of a clus-ter of adjacent large secreted proteins (table S2)that are cotranscriptionally regulated.Identified anchored telomeric repeat sequences are indicated by circles.(B )Schematic show-inga select locus containinga cluster of coexpressed large secreted proteins (Cp LSP).Genes and intergenic regions (regions between identified genes)are drawn to scale at the nucleotide level.The length of the intergenic re-gions is indicated above or be-low the locus.(C )Relative ex-pression levels of CpLSP (red lines)and,as a control,C.parvum Hedgehog-type HINT domain gene (blue line)duringin vitro development,as determined by semiquantitative RT-PCR usingg ene-specific primers correspondingto the seven adjacent g enes within the CpLSP locus as shown in (B).Expression levels from three independent time-course experiments are represented as the ratio of the expression of each gene to that of C.parvum 18S rRNA present in each of the infected samples (20).R E P O R T S16APRIL 2004VOL 304SCIENCE 444 o n O c t o b e r 7, 2009w w w .s c i e n c e m a g .o r g D o w n l o a d e d f r o m。
2024届北京市西城区高三二模语文试题含答案
2024届北京市西城区高三二模语文试题（答案在最后）2024.5本试卷共10页，共150分。
考试时长150分钟。
考生务必将答案写在答题卡上，在试卷上作答无效。
一、本大题共5小题，共18分。
阅读下面材料，完成小题。
材料一2023年是人工智能领域爆炸式发展的一年，OpenAI公司推出的ChatGPT便是其中的代表。
一年多的时间里，ChatGPT的版本从3.5升级到4.0，进步明显：专门训练它的硬件设备升级，其中央处理器（CPU）内核和专用图形处理器（GPU）分别增加到28万个和1万个；它有1万亿个参数，知识的获取从检索固定的数据库发展到可以自行上网寻找资料；它不但可以解读用户发送的图片，还可以根据文字描述生成图像……人工智能产品研发领域的竞争非常激烈。
ChatGPT展示出人工智能应用的巨大价值，OpenAI公司的估值因此一飞冲天，最大的外部投资者微软公司更因此获利巨大。
其他几家科技巨头不可能对此视而不见，尤其是谷歌公司，多年来一直被认为在人工智能研究领域处于世界领先位置，如今被OpenAI抢了先机，谷歌只能寻机后发制人。
果然，谷歌在2023年底推出了“双子座”（Gemini）。
这款多模态大模型人工智能产品在32项功能的评测中有30项的表现超过了ChatGPT。
除了在文字方面的输出看上去与ChatGPT不相上下，它还对图片和视频有着超强的理解和推理能力，同时可以针对提问给出混合文字和图像的多模态输出——这是ChatGPT 尚不具备的。
2024年初，谷歌的聊天机器人Bard已融合了Gemini的能力，升级版Bard的表现完全不逊于ChatGPT。
而与此同时，OpenAI又发布了文生视频大模型Sora，它能根据提示词生成60秒的连贯视频，这预示着一个新的视觉叙事时代的到来。
差不多同时，DeepMind公司和斯坦福大学的研究人员合作开发的Mobile ALOHA机器人问世。
它是一对可以使用锅碗瓢盆、操作家用电器乃至洗衣叠被的机器臂，精细程度不输人类。
磁性测量中ZFC和FC数据的获得与解释
1957年，χ－T低温极大值（CuMn，AgMn）
J. Owen & M. E. Browne, V. Arp & A. F. Kip, J. Phys. Chem. Solids, 2 (1957) 85
统一理论
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EA
Ising、Heisenberg、XY、 Bethe Lattice、Mattis、SK、 Random Bond…
单个Fe、Mn原子的各向异性
Science, 315 (2007.08.31) 1199-1203
三、Fe原子（团）更分叉
混磁性、自旋玻璃（SG）
非线性磁化率的实验 1979年～1980年，（Y. Miyako, et al） J. Phys. Soc. Japan, 46 (1979) 1951 J. Phys. Soc. Japan, 47 (1979) 335 J. Phys. Soc. Japan, 48 (1980) 329 综述： K. Binder & A. P. Young, Rev. Mod. Phys., 58 (1986) 801 Magnetic Susceptibility of Superconductor and Other Spin Systems Eds. R. A. Hein, T. L. Francavilla & D. H. Liebenberd, 1991, New York
三、Fe原子（团）更分叉
临界浓度、交换相互作用
近藤效应：稀释磁性合金电阻率－温度曲线极小值 1964年，始作俑者不是Jun Kondo（近藤 淳） J. Kondo, Prog. Theor. Phys., 32 (1964) 37 1931年，AuFe（J. W. Shih） Phys. Rev., 38 (1931) 2051 1951年，R－T低温极大值（AgMn）
Constructions of Mutually Unbiased Bases
Indeed, the right hand side equals 0 when κ = λ because the argument k + α ranges through all values of Fq ; and equals 1 when κ = λ. √ Note that all components of the sequence bλ,α have absolute value 1/ q , hence the basis Bα and the standard basis are mutually unbiased, for any α ∈ Fq . By computing the inner product | bκ,α , bλ,β | for α = β , we see that the terms cubic in k cancel out and, moreover, that the exponent is given by the trace of a quadratic polynomial in k . By Lemma 1 the inner product evaluates to q −1/2 , hence Bα and Bβ are mutually unbiased. 2 Remark 1. A remarkable feature of the previous construction is that knowledge of one basis Bα is sufficient because shifting the indices by adding a field element yields the other bases. The construction does not work in characteristic 2 and 3 because in these cases the sets Bα and Bβ , with α = β , are not mutually unbiased. Ivanovi´ c gave a fresh impetus to the field in 1981 with his seminal paper [14]. Among other things, he gave explicit constructions of p + 1 mutually unbiased bases of Cp , for p a prime. His construction was later generalized in the influential paper by Wootters and Fields [22], who gave the first proof of the following theorem. This proof was recently rephrased by Chaturvedi [9], and an alternate proof was given by Bandyopadhyay et al. [3]. We give a particularly short proof by taking advantage of Weil sums. Theorem 2. Let Fq be a finite field with odd characteristic p. Denote by Ba = {va,b | b ∈ Fq } the set of vectors given by
Tube Model for Light-Front QCD
For instance, some of the zero modes that were otherwise constrained become dynamical. In light-front field theory, equations of motion are typically of the form ∂+(∂− + igV )φ = U(φ), where U(φ) is the potential term. When V = 0 it is clear why zero modes ∂−φ = 0 are not dynamical: they have no conjugate momentum. However, note that when V is nonzero, the associated kinetic term is small (since V is small) relative to the kinetic term of any non-zero mode. Thus, one may just as well treat these zero modes as non-dynamical (that is, as a solution of a constraint equation).
1 The gauge zero mode
Before we begin, we must discuss the “gauge zero mode,” V ≡ dx− A−. As has been noticed by several authors in the context of both light-front [5] and equal time [6] quantization, one cannot set V = 0 by choice of gauge because it is a genuine dynamical degree of freedom. Only the gauge choice ∂−A− = 0 is allowed.