Search results for "5R"

showing 10 items of 108 documents

The fixed angle scattering problem and wave equation inverse problems with two measurements

2019

We consider two formally determined inverse problems for the wave equation in more than one space dimension. Motivated by the fixed angle inverse scattering problem, we show that a compactly supported potential is uniquely determined by the far field pattern generated by plane waves coming from exactly two opposite directions. This implies that a reflection symmetric potential is uniquely determined by its fixed angle scattering data. We also prove a Lipschitz stability estimate for an associated problem. Motivated by the point source inverse problem in geophysics, we show that a compactly supported potential is uniquely determined from boundary measurements of the waves generated by exactl…

ScatteringApplied Mathematics010102 general mathematicsMathematical analysisPlane waveBoundary (topology)Inverse problemWave equationLipschitz continuity01 natural sciencesinversio-ongelmatComputer Science ApplicationsTheoretical Computer Science010101 applied mathematicsMathematics - Analysis of PDEs35R30Signal ProcessingInverse scattering problemReflection (physics)FOS: Mathematics0101 mathematicsMathematical PhysicsMathematicsAnalysis of PDEs (math.AP)
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The homotopy Leray spectral sequence

2018

In this work, we build a spectral sequence in motivic homotopy that is analogous to both the Serre spectral sequence in algebraic topology and the Leray spectral sequence in algebraic geometry. Here, we focus on laying the foundations necessary to build the spectral sequence and give a convenient description of its $E_2$-page. Our description of the $E_2$-page is in terms of homology of the local system of fibers, which is given using a theory similar to Rost's cycle modules. We close by providing some sample applications of the spectral sequence and some hints at future work.

Serre spectral sequencePure mathematicsHomotopy[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]K-Theory and Homology (math.KT)Leray spectral sequenceAlgebraic geometryHomology (mathematics)Mathematics::Algebraic TopologyMathematics - Algebraic GeometryLocal systemMathematics::K-Theory and HomologySpectral sequenceMathematics - K-Theory and HomologyFOS: MathematicsMSC 14F42 (14-06)Algebraic Topology (math.AT)Mathematics - Algebraic Topology14F42 55R20 19E15[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Algebraic Geometry (math.AG)Mathematics
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CCDC 263681: Experimental Crystal Structure Determination

2005

Related Article: D.Schollmeyer, R.Hoffmann, J.Mattay|2005|Acta Crystallogr.,Sect.E:Struct.Rep.Online|61|o290|doi:10.1107/S1600536805000140

Space GroupCrystallography(-)-(3a'S4'S9b'S1R2S5R)-4'-Ethyl-3a'4'5'7'8'9b'-hexahydro-2-isopropyl-5-methyl-2'-phenylspiro(cyclohexane-17'-dioxino(32-e)isoindole)-1'3'9'-trioneCrystal SystemCrystal StructureCell ParametersExperimental 3D Coordinates
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CCDC 1565150: Experimental Crystal Structure Determination

2018

Related Article: Mirella Wawryszyn, Paul F. Sauter, Martin Nieger, Martin R.Koos, Christine Koehler, Burkhard Luy, Edward A. Lemke, Stefan Bräse|2018|Eur.J.Org.Chem.|2018|4296|doi:10.1002/ejoc.201800602

Space GroupCrystallography(1R2R3R4R5R)-2-[(acetyloxy)methyl]-6-azido-5-(13-dioxo-13-dihydro-2H-isoindol-2-yl)oxane-34-diyl diacetateCrystal SystemCrystal StructureCell ParametersExperimental 3D Coordinates
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CCDC 639296: Experimental Crystal Structure Determination

2007

Related Article: J.Becker, R.Frohlich, K.Salorinne, D.Hoppe|2007|Eur.J.Org.Chem.|2007|3337|doi:10.1002/ejoc.200700219

Space GroupCrystallography(1R3S3(1R5R)3aR7aS)-3-(66-Dimethylbicyclo(3.1.1)hept-2-en-2-yl)-1-(naphthalen-2-yl)-hexahydroisobenzofuran-4(1H)-oneCrystal SystemCrystal StructureCell ParametersExperimental 3D Coordinates
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CCDC 133885: Experimental Crystal Structure Determination

2000

Related Article: S.Lochynski, B.Frackowiak, A.Siemieniuk, K.Piatkowski, Z.Ciunik, C.Wawrzenczyk|1999|Tetrahedron:Asymm.|10|1033|doi:10.1016/S0957-4166(99)00056-7

Space GroupCrystallography(1S2S3R5R2'R)-(+)-266-Trimethyl-3-hydroxy-3-(2-hydroxyprop-1-yl)-7-oxabicyclo(3.2.1)octaneCrystal SystemCrystal StructureCell ParametersExperimental 3D Coordinates
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CCDC 1972521: Experimental Crystal Structure Determination

2020

Related Article: Sami Kortet, Aurélie Claraz, Petri M. Pihko|2020|Org.Lett.|22|3010|doi:10.1021/acs.orglett.0c00772

Space GroupCrystallography(2R5R)-25-bis(35-bis(trifluoromethyl)phenyl)pyrrolidineCrystal SystemCrystal StructureCell ParametersExperimental 3D Coordinates
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CCDC 854401: Experimental Crystal Structure Determination

2012

Related Article: N.M.Friedemann, A.Harter, S.Brandes, S.Gross, D.Gerlach, W.Munch, D.Schollmeyer, U.Nubbemeyer|2012|Eur.J.Org.Chem.|2012|2346|doi:10.1002/ejoc.201200073

Space GroupCrystallography(3S4S5R)-3-(3-Methoxyphenethyl)-dihydro-4-(3-t-butyl(diphenyl)silyloxypropyl)-5-(iodomethyl)-5-methylfuran-2(3H)-oneCrystal SystemCrystal StructureCell ParametersExperimental 3D Coordinates
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CCDC 618136: Experimental Crystal Structure Determination

2006

Related Article: M.A.Gonzalez, M.J.Gil-Gimeno, A.J.Blake|2006|Acta Crystallogr.,Sect.E:Struct.Rep.Online|62|o3346|doi:10.1107/S1600536806026705

Space GroupCrystallography(4R5R9R10R)-713-Abietadien-18-yl p-bromobenzoateCrystal SystemCrystal StructureCell ParametersExperimental 3D Coordinates
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CCDC 1419794: Experimental Crystal Structure Determination

2016

Related Article: Marta Feliz and Francisco Estevan|2016|Eur.J.Inorg.Chem.||92|doi:10.1002/ejic.201501085

Space GroupCrystallography(Dihydrogen)-hydrido-bis(11'-(12-phenylene)bis((2R5R)-25-dimethylphospholane))-iron tetrafluoroborateCrystal SystemCrystal StructureCell ParametersExperimental 3D Coordinates
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