...STRUCTURAL ORGANIC CHEMISTRY. THE SHAPES OF MOLECULES. FUNCTIONAL GROUPS I n this chapter we first briefly review the most important types of covalent bonds encountered in organic substances and the ways in which these bonds are represented in structural formulas. Next we consider the sizes and shapes of organic molecules and how structural formulas written in two dimensions can be translated into three-dimensional models that show the relative positions of the atoms in space. We also discuss models that reflect the relative sizes of the atoms and the way in which the atoms may interfere with each other when in close quarters (steric hindrance). Then we go on to further important aspects of structure-the functional group concept and position isomerism. Our aim is to have you become more familiar with the various kinds of organic compounds and begin to see how the practicing organic chemist visualizes molecules and correlates the diverse kinds of structures that he has to deal with in his work. 2-1 STRUCTURAL FORMULAS The building block of structural organic chemistry is the tetravalent carbon atom. With few exceptions, carbon compounds can be formulated with four 2-1 Structural Fbrmulas 31 covalent bonds to each carbon, regardless of whether the combination is with carbon or some other element. The two-electron bond, which is illustrated by the carbon-hydrogen bonds in methane or ethane and the carbon-carbon bond in ethane, is called a single...
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...ﺟﺎﻣﻌﺔ اﻟﻤﻮﺻﻞ آﻠﻴﺔ اﻟﺘﺮﺑﻴﺔ ﻣﺤﺎآﺎة ﺣﺎﺳﻮﺑﻴﺔ ﺟﺪﻳﺪة ﻷﻧﻤﻮذج اﻟﺒﻮزوﻧﺎت اﻟﻤﺘﻔﺎﻋﻠﺔ )1- (IBMﻟﺪراﺳﺔ اﻻﻧﺤﻨﺎء اﻟﺨﻠﻔﻲ ﻓﻲ ﻧﻈﺎﺋﺮ 120-126Xeاﻟﺰوﺟﻴﺔ - اﻟﺰوﺟﻴﺔ ﻣﺸﺘﺎق ﻋﺒﺪ داؤد اﻟﺠﺒﻮري رﺳﺎﻟﺔ ﻣﺎﺟﺴﺘﻴﺮ اﻟﻔﻴﺰﻳﺎء ﺑﺈﺷﺮاف ﻋﻤﺎد ﻣﻤﺪوح اﺣﻤﺪ أﺳﺘﺎذ ﻣﺴﺎﻋﺪ 8002م 9241هـ ﳏﺎﻛﺎﺓ ﺣﺎﺳﻮﺑﻴﺔ ﺟﺪﻳﺪﺓ ﻷﳕﻮﺫﺝ ﺍﻟﺒﻮﺯﻭﻧﺎﺕ ﺍﳌﺘﻔﺎﻋﻠﺔ 621-021 )1- (IBMﻟﺪﺭﺍﺳﺔ ﺍﻻﳓﻨﺎء ﺍﳋﻠﻔﻲ ﰲ ﻧﻈﺎﺋﺮ Xe ﺍﻟﺰﻭﺟﻴﺔ - ﺍﻟﺰﻭﺟﻴﺔ ﺭﺳﺎﻟﺔ ﺗﻘﺪﻡ ﲠﺎ ﻣﺸﺘﺎﻕ ﻋﺒﺪ ﺩﺍﺅﺩ ﺍﳉﺒﻮﺭﻱ ﺇﱃ ﳎﻠﺲ ﻛﻠﻴﺔ ﺍﻟﱰﺑﻴﺔ ﰲ ﺟﺎﻣﻌﺔ ﺍﳌﻮﺻﻞ ﻭﻫﻲ ﺟﺰﺀ ﻣﻦ ﻣﺘﻄﻠﺒﺎﺕ ﻴﻞ ﺷﻬﺎﺩﺓ ﻣﺎﺟﺴﺘﲑ ﻋﻠﻮﻡ ﰲ ﺍﻟﻔﻴﺰﻳﺎﺀ ﺑﺈﺷﺮﺍﻑ ﻋﻤﺎﺩ ﳑﺪﻭﺡ ﺍﲪﺪ ﺃﺳﺘﺎﺫ ﻣﺴﺎﻋﺪ 8002 م 9241 هـ ﺑﺴﻢ ﺍ ﺍﻟﺮﲪﻦ ﺍﻟﺮﺣﻴﻢ ﻧﺮﻓﻊ ﺩﺭﺟـﺖ ﻣﻦ ﻧﺸﺂﺀ ُ ﹶ ٍ ٰ ﻭﻓﻮﻕ ﻛ ﹼ ِﺫﻯ ﻋﻠﻢ ﻋﻠِﻴﻢ ﹶ ﹸﻞ ِ ِ ﹾ ٍ ﺻﺪﻕ ﺍﷲ ﺍﻟﻌﻈﻴﻢ )ﺳﻮﺭﺓ ﻳﻮﺳﻒ :ﻣﻦ ﺍﻵﻳﺔ 67 ( ﺍﻹﻫﺪﺍء إﻟﻰ ﻣﻦ أﺿﺎء اﻟﻄﺮﻳﻖ ﻧﻮرا ﻓﻲ ﺳﺒﻴﻞ ﻣﺒﺘﻐﺎي وﻣﺪ ﻟﻲ ﻳﺪ اﻟﻤﺴﺎﻋﺪة واﻟﺪي إﻟﻰ ﻣﻦ ذرﻓﺖ اﻟﺪﻣﻊ ﺳﺒﻴﻼ ﻟﺮﻋﺎﻳﺘﻲ وهﻲ ﻣﺼﺪر ﻗﻮﺗﻲ وﻋﻮﻧﻲ ﻓﻲ اﻟﺤﻴﺎة وﺟﻌﻠﺖ ﻟﻲ ﻓﻲ هﺬﻩ اﻟﺪﻧﻴﺎ ﻣﻘﺎﻣﺎ واﻟﺪﺗﻲ إﻟﻰ ﻣﻦ أﺣﺒﻬﻢ ﺑﻜﻞ ﻣﺎ ﺧﻠﻖ اﷲ ﻣﻦ ﺣﺐ إﺧﻮﺗﻲ وأﺧﻮاﺗﻲ إﻟﻰ آﻞ ﻣﻦ ﻋﻠﻤﻨﻲ آﻞ ﺣﺮف ﺑﺈﺗﻘﺎن إﻟﻰ ﻣﻦ ﺻﻘﻞ اﻟﻔﻜﺮ ﻋﻠﻤﺎ ﻓﻲ ﺳﺒﻴﻞ ﻧﺠﺎﺣﻲ أﺳﺎﺗﺬﺗﻲ إﻟﻰ ﺗﻠﻚ اﻟﻜﻠﻤﺔ اﻟﺘﻲ ﺗﻨﻤﻮ ﻓﻲ أﺳﻤﺎﻋﻲ وﺗﻔﻴﺾ ﺑﻌﻄﺮهﺎ ﻓﻲ ﻧﻔﺴﻲ زﻣﻼﺋﻲ وزﻣﻴﻼﺗﻲ ﺍﻟﺤﻤﺩ ﷲ ﺍﻟﺫﻱ ﻫﺩﺍﻨﺎ ﺍﻟﻰ ﻁﺭﻴﻕ ﺍﻟﻌﻠﻡ ﻭﻤﺎ ﻜﻨﺎ ﻟﻨﻬﺘﺩﻱ ﻟﻭﻻ ﺍﻥ ﻫﺩﺍﻨﺎ ﺍﷲ ﻭﺍﻟﺼﻼﺓ ﻭﺍﻟـﺴﻼﻡ ﻋﻠﻰ ﻤﻌﻠﻡ ﺍﻟﺒﺸﺭﻴﺔ ﺍﻷﻭل ﺴﻴﺩﻨﺎ ﻤﺤﻤﺩ )ﺼﻠﻰ ﺍﷲ ﻋﻠﻴﻪ ﻭﺴﻠﻡ( ﻭﻋﻠﻰ ﺍﻟـﻪ ﻭﺍﺼـﺤﺎﺒﻪ ﺃﺠﻤﻌـﻴﻥ ﻭﺒﻌﺩ: ﻴﻁﻴﺏ ﻟﻲ ﻭﺍﻨﺎ ﺃﻨﻬﻲ ﻫﺫﺍ ﺍﻟﺠﻬﺩ ﺍﻟﻤﺘﻭﺍﻀﻊ ﺍﻥ ﺍﺘﻭﺠﻪ ﺒﻭﺍﻓﺭ ﺍﻟﺸﻜﺭ ﻭﺍﻟﺘﻘﺩﻴﺭ ﻷﺴﺘﺎﺫﻱ ﺍﻟﻔﺎﻀل ﺍﻟﺴﻴﺩ ﻋﻤﺎﺩ ﻤﻤﺩﻭﺡ ﺃﺤﻤﺩ ﻷﻗﺘﺭﺍﺤﻪ ﻤﻭﻀﻭﻉ ﺍﻟﺒﺤﺙ...
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...arXiv:math.DG/0207039 v1 3 Jul 2002 Exterior Differential Systems and Euler-Lagrange Partial Differential Equations Robert Bryant Phillip Griffiths July 3, 2002 Daniel Grossman ii Contents Preface Introduction 1 Lagrangians and Poincar´-Cartan Forms e 1.1 Lagrangians and Contact Geometry . . . . . . . . . 1.2 The Euler-Lagrange System . . . . . . . . . . . . . . 1.2.1 Variation of a Legendre Submanifold . . . . . 1.2.2 Calculation of the Euler-Lagrange System . . 1.2.3 The Inverse Problem . . . . . . . . . . . . . . 1.3 Noether’s Theorem . . . . . . . . . . . . . . . . . . . 1.4 Hypersurfaces in Euclidean Space . . . . . . . . . . . 1.4.1 The Contact Manifold over En+1 . . . . . . . 1.4.2 Euclidean-invariant Euler-Lagrange Systems . 1.4.3 Conservation Laws for Minimal Hypersurfaces 2 The 2.1 2.2 2.3 2.4 2.5 Geometry of Poincar´-Cartan Forms e The Equivalence Problem for n = 2 . . . . . . . Neo-Classical Poincar´-Cartan Forms . . . . . . e Digression on Affine Geometry of Hypersurfaces The Equivalence Problem for n ≥ 3 . . . . . . . The Prescribed Mean Curvature System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v vii 1 1 7 7 8 10 14 21 21 24 27 37...
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