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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of geodesy 72 (1998), S. 101-106 
    ISSN: 1432-1394
    Keywords: Key words. Ellipsoidal Stokes problem ; Nullfield method ; Boundary integral equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. The ellipsoidal Stokes problem is one of the basic boundary-value problems for the Laplace equation which arises in physical geodesy. Up to now, geodecists have treated this and related problems with high-order series expansions of spherical and spheroidal (ellipsoidal) harmonics. In view of increasing computational power and modern numerical techniques, boundary element methods have become more and more popular in the last decade. This article demonstrates and investigates the nullfield method for a class of Robin boundary-value problems. The ellipsoidal Stokes problem belongs to this class. An integral equation formulation is achieved, and existence and uniqueness conditions are attained in view of the Fredholm alternative. Explicit expressions for the eigenvalues and eigenfunctions for the boundary integral operator are provided.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0044-2313
    Keywords: Rhenium complexes ; nitrido complexes ; thionitrosyl complexes ; nitrido bridges ; crystal structure ; Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Mixed-ligand Complexes of Rhenium. IX. Reactions on the Nitrido Ligand of [ReN(Me2PhP)(Et2dtc)2]. Synthesis, Characterization, and Structures of [Re(NBCl3)(Me2PhP)(Et2dtc)2], [Re(NGaCl3)(Me2PhP)(Et2dtc)2], and [Re(NS)Cl(Me2PhP)2(Et2dtc)]BCl3, GaCl3 and S2Cl2 react with the well-known [ReN(Me2PhP)(Et2dtc)2] by attack of the nucleophilic nitrido ligand. Final products of these reactions are [Re(NBCl3)-(Me2PhP)(Et2dtc)2], [Re(NGaCl3)(Me2PhP)(Et2dtc)2], and [Re(NS)Cl(Me2PhP)2Et2dtc)] which have been studied by mass spectrometry, IR spectroscopy and X-ray diffraction.[Re(NBCl3)(Me2PhP)(Et2dtc)2] crystallizes in the triclinic space group P1, Z = 2, a = 8.151(6), b = 9.935(8), c = 18.67(1) Å; α = 94.42(4), β = 97.09(1), γ = 101.35(4)°. The coordination geometry is a distorted octahedron. The equatorial coordination sphere is occupied by one phosphorus and three sulphur atoms. The fourth sulphur atom is in trans position to the Re≡N—B moiety. The almost linear Re≡N—B unit has an Re≡N—B angle of 170.5(3)° with a Re—N bond length of 1.704(3) Å.The analogous [Re(NGaCl3)(Me2PhP)(Et2dtc)2] crystallizes in P21/c with a = 8.138(3), b = 18.279(2), c = 19.880(6) Å; β = 99.81(2)°; Z = 4. Rhenium has a distorted octahedral environment. The Re—N—Ga bond is slightly bent with an angle of 154.5(4)° and a Re—N bond length of 1.695(6) Å.[Re(NS)Cl(Me2PhP)2(Et2dtc)] crystallizes in the triclinic space group P1, Z = 4, a = 9.514(2); b = 16.266(5); c = 18.388(3) Å; α = 88.75(2), β = 76.59(2), γ = 85.50(2)° with two crystallographically independent molecules in the asymmetric unit. Rhenium has a distorted octahedral environment with the chloro ligand in trans position to the almost linear thionitrosyl group. The Re=N bond lengths are 1.795(6) and 1.72(1) Å, respectively, and the N=S distances are 1.55(1) and 1.59(1) Å, respectively.
    Notes: BCl3, GaCl3 und S2Cl2 reagieren mit dem nukleophilen Nitridoliganden von [ReN(Me2PhP)(Et2dtc)2]. Als Endprodukte dieser Reaktionen konnten [Re(NBCl3)(Me2PhP)-(Et2dtc)2], [Re(NGaCl3)(Me2PhP)(Et2dtc)2] und [Re(NS)Cl-(Me2PhP)2(Et2dtc)] isoliert und spektroskopisch sowie strukturell charakterisiert werden.[Re(NBCl3)(Me2PhP)(Et2dtc)2] kristallisiert in der triklinen Raumgruppe P1, Z = 2, a = 8,151(6), b = 9,935(8); c = 18,67(1) Å; α = 94,42(4), β = 97,09(1); γ = 101,35(4)Å. Das Koordinationspolyeder um Rhenium ist ein verzerrtes Oktaeder. Die äquatoriale Koordinationssphäre wird von einem Phosphor- und drei Schwefelatomen besetzt. Das vierte Schwefelatom ist in trans-Stellung zur N—B-Einheit koordiniert. Re≡N—B ist mit einem Winkel von 170,5(3)Å und einem Re—N-Abstand von 1,704(3) Å gebunden.Die Bindungsverhältnisse in [Re(NGaCl3)(Me2PhP)(Et2dtc)2] sind analog. Raumgruppe P21/c mit a = 8,138(3), b = 18,279(2), c = 19,880(6) Å; β = 99,81(2)°; Z = 4. Rhenium ist wiederum verzerrt oktaedrisch koordiniert. Der Re—N—Ga-Winkel ist mit 154,5(4)° deutlich kleiner als im Bortrichlorid-Addukt. Der Bindungsabstand Re—N beträgt 1,695(6) Å.[Re(NS)Cl(Me2PhP)2(Et2dtc)] kristallisiert in der triklinen Raumgruppe P1, a = 9,514(2); b = 16,266(5); c = 18,388(3) Å; α = 88,75(2), β = 76,59(2), γ = 85,50(2)° mit zwei kristallographisch unabhängigen Molekülen in der asymmetrischen Einheit. Re ist nahezu ideal oktaedrisch koordiniert. Der Chloroligand befindet sich in trans-Position zur fast linearen Re=N=S-Gruppierung. Die Bindungsabstände Re=N betragen 1,795(9) bzw. 1,72(1) Å, die Abstände N=S 1,55(1) bzw. 1,59(1) Å.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 0044-2313
    Keywords: Technetium ; nitrido complexes ; crystal structure ; dithiolenes ; Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Mixed-Ligand Complexes of Technetiums. XVI Synthesis and Structure of (1,2-Dicyanoethene-1,2-dithiolato)bis(dimethylphenylphosphine)nitridotechnetium(V), [TcN(Me2PhP)2(mnt)][TcN(Me2PhP)2(mnt)] is formed from [TcNCl2(Me2PhP)3] and one equivalent of the sodium salt of 1,2-dicyanoethene-1,2-dithiolate (Na2mnt). The same reaction yields [TcN(mnt)2]2-, when a large excess of the ligand and long reaction periods are applied. The complex anion can be isolated as tetraalkylammonium or tetraphenylarsonium salts.[TcN(Me2PhP)2(mnt)] crystallizes in the triclinic space group P1 (a = 10.000(5), b = 14.182(6), c = 17.77(1) Å, α = 98.77(3), β = 103.77(3), γ = 104.55(3)°; Z = 4). The coordination sphere is a square pyramid with the sulfur and phosphorus atoms as basal plane. Tc is situated out of this plane by 0.56 Å towards the nitrido ligand.
    Notes: [TcN(Me2PhP)2(mnt)] entsteht bei der Reaktion von [TcNCl2(Me2PhP)3] mit dem Natriumsalz des 1,2-Dicyanoethen-1,2-dithiolats (Na2mnt), wenn ein äquivalent des Liganden eingesetzt wird. Bei Verwendung eines Na2mnt-überschusses und Reaktionszeiten von mehreren Stunden bildet sich das Komplexanion [TcN(mnt)2]2-, das in Form seiner Tetraalkylammonium- bzw. Tetraphenylarsoniumsalze isoliert werden kann.[TcN(Me2PhP)2(mnt)] kristallisiert triklin (Raumgruppe P1; a = 10,000(5); b = 14,182(6); c = 17,77(1) Å; α = 98,77(3); β = 103,77(3); γ = 104,55(3)°; Z = 4). Das Koordinationspolyeder ist eine quadratische Pyramide, in der das Metall um 0,56 Å über der durch die Schwefel- und Phosphoratome gebildeten Grundfläche angeordnet ist.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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