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  • Articles: DFG German National Licenses  (856)
  • 1990-1994  (856)
  • 1994  (856)
  • Engineering General  (702)
  • crystal structure  (154)
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  • Articles: DFG German National Licenses  (856)
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Years
  • 1990-1994  (856)
Year
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Il nuovo cimento della Società Italiana di Fisica 16 (1994), S. 1671-1678 
    ISSN: 0392-6737
    Keywords: Effects of material synthesis ; crystal structure ; chemical composition ; Y-based compounds ; Conference proceedings
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Summary YBCO with high granulometric perfection and low dispersion can be obtained by a low-temperature reaction (≈800°C) of atomic-scale dispersed powders, produced through the thermal decomposition of liquid precursors. As reacted such powders are tetragonal and not superconducting, but they transform into the high-T c phase after optimized annealing treatments. We describe the method we developed and the characteristics of the materials we achieved, and we discuss the main features of the process in the light of the current know-how.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of chemical crystallography 24 (1994), S. 759-762 
    ISSN: 1572-8854
    Keywords: Sulfonamide ; methanesulfonanilide ; crystal structure ; molecular structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The title compound, crystallizes in the triclinic space group $$P\bar 1$$ witha=8.232(4),b=9.159(2),c=10.230(3)Å. α=74.07(3)°, β=72.50(4)°, γ=63.65(3)° andZ=2. The structure was solved by direct methods and refined by full matrix least squares methods toR=0.054 for 1817 observed reflections. The plane containing the nitrogen and sulfur atoms is perpendicular to the aromatic plane. One of the S−O bonds in each methanesulfonyl group is in nearly eclipsed conformation with the N−C bond.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of chemical crystallography 24 (1994), S. 437-440 
    ISSN: 1572-8854
    Keywords: Ca(C4H4O4)·H2O ; pentagonal pyramid ; calcium succinate ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The crystal structure of calcium succinate monohydrate, Ca(C4H4O4)·H2O, has been determined by single crystal X-ray diffraction. The crystals are monoclinic witha=11.952(2),b=9.691(2),c=11.606(2)Å, β=108.81(1)°, space group C2/c,Z=8,V=1272.49 Å3,d m =1.80, andd c =1.818 Mg m−3. The structure was refined by full-matrix least-squares techniques toR=0.027,R w =0.040, for 829 reflections with1≥3δ(I). Ca is coordinated to seven oxygen atoms, and the coordination polyhedron is best described as a pentagonal bipyramid. One carboxylate group in the succinate ion is bonded to three different Ca ions, forming a four-membered chelate ring with one Ca ion is bonded to three different Ca ions, forming a four-membered chelate ring with one Ca ion and unidentate bridge bonds to two other Ca ions. The other carboxylate group is bonded to two Ca ions through unidentate bonds. The structure is highly polymeric. The general structural features are nearly identical to those of calcium adipate monohydrate.
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  • 4
    ISSN: 1572-8854
    Keywords: Pyrimidine ; uracil ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A new and easy method for the preparation of 1,3,7,9-tetramethylpyrido-[2,3-d∶6,5-d′]-dipyrimidine-2,4,6,8-tetrone is described. The structure of this compound has been solved by means of X-ray diffraction methods. The chemical characterization by spectral (mass, ultraviolet, infrared, and proton nuclear magnetic resonance) and thermal (thermogravimetry and differential scanning calorimetry) method is also reported. The compound is monoclinic, space groupP21/c,a=12.720(5),b=13.688(7),c=8.079(2) Å, β=107.06(4)°,Z=4. The structure consists of discrete tricyclic molecules, stacking playing an important role in crystal packing.
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  • 5
    ISSN: 1572-8862
    Keywords: Tungsten ; isomeric forms ; crystal structure ; triple bonds ; interconversion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A thorough study of compounds with the formula W2Cl4(NHCMe3)2(PR3)2, withR 3=Me3, Et3, Prg n 3 Me2,Ph, is reported. In addition to the previously reported crystalline compounds, namely Ia,trans-W2Cl4(NHCMe3)2(PMe3)2 in space group Pmmn;3a,trans-W2Cl4(NHCM3)2(PEt3)2 in space group P21/a (or P21/c); and4,cis-W2Cl4(NHCMe3)2(PMe2Ph)2 in Pna21, we have obtained and structurally characterized the following new substances,1b,trans-W2Cl4,(NHCMe3)2(PMe2)2, space group P21/c,a= 12.233 (4) Å,b= 12.872 (4) Å,c=17.095 (5) Å,β=93.52 (2)°,Z=4,V=2687 (1) Å3 2,cis-W2Cl4(NHCMe3)2(PMe3)2, P21/c,a=9.673 (4) Å,b=17.249 (4) Å,c=16.244 (5) Å,β=99.63 (3),Z = 4 ,V=2669 (1) Å.3b,trans-W2Cl4(NHCMe3)2(PEt3)2, Pl,a=16.850 (3) Å,b=17.797 (3) Å,c= 11.459 (2)Å,α= 101.02 (1),β= 103.13°, y=84.23 (1)°,Z=4,V= 3279 (1) Å5,trans-W2Cl4(NHCM3)2(PMe2Ph)2, Fdd2,a=39.563 (8) Å at 20°C; 39.325 (10) Å at -6O°C,b = 57.543 (17) Å at 20°C; 57.186 (16) Å at -60°C,c= 8.810 (1) Å at 20°C; 8.770 (1) Å at - 60°C ,Z=24,V=20057 (7) Å3 (20°C), 19723 (8) Å3 ( - 60°C) .6,trans-W2Cl4(NHCMe3 2(PPrn 3)2, Pl,a= 17.287 (2) Å (20°C); 17.077 (5) Å (-60°C),b= 19.119 (2) Å (20°C); 18.952 (6) Å (-60°C),c= 12.713 (1) Å (20°C); 12.668 (4) Å (-60°C),Z=4,V= 3980 (1) Å3 (20°C), 3898 (2) ,Å3 ( - 60°C). In addition, the structure of3a was re-determined and refined so that the disorder ratio was a refined parameter, leading to a value of 0.520:0.480 instead of being arbitrarily fixed at 0.50:0.50. In all of the structures the molecules are held in eclipsed (but very distorted) rotational conformations and the W-W distances are all within the range of 2.305-2.330 Å. As will be shown in a later paper, for all phosphines, thecis andtrans isomers are of similar stability and an equilibrium mixture exists in solution. It is also shown that1a and3a do not contain unexpectedly short W-N bonds as previously reported.
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  • 6
    ISSN: 1572-8862
    Keywords: Mixed metal cluster ; alkyne ; diphenylacetylene ; platinum ; osmium ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The new platinum-osmium alkyne cluster complex Pt2Os4(CO)8(μ3-PhC2Ph)3 (μ 4-PhC2Ph),2, was obtained from the reaction of Pt2Os4(CO)18,1b, with PhC2Ph and was characterized by IR.1H NMR and single-crystal X-ray diffraction analyses. The cluster of compound2 consists of an osmium capped Pt2Os3 square pyramid. It aLso contains three triply bridging and one quadruply bridging diphenylacetylene ligands. Crystal data for2: space group PI,a = 12.530(2) Å,b = 21.565(4) Å,c = 11.284(2) Å,α = 100.31(2),β = 111.89(1),β = 76.78(2),Z = 2, 3879 reflections,R = 0.032.
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  • 7
    ISSN: 1572-8854
    Keywords: Centrosymmetric ; symmetry ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The title compound crystallizes in the centrosymmetric triclinic space group $$P\bar 1$$ (C 1 l ; No.2) witha=9.9143(10) Å,b=10.2616(11) Å,c=10.7715(10) Å, α=113.887(8)°, β=109.197(8)°, γ=90.699(9)°,V=932.78(17) Å3 andZ=1. A total of 4869 data were collected and merged to a set of 2450 independent reflections; the structure was solved and refined toR=1.42% andwR=1.94%. The molecule lies on a site of $$\bar 1$$ symmetry and is disordered, with obvious scrambling of carbonyl and chloride ligands. Resulting bond lengths include Ir−P=2.339(1) Å, Ir−Cl=2.398(4) Å and Ir−CO=1.808(15) Å.
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  • 8
    ISSN: 1572-9605
    Keywords: High-Tc superconductivity ; La1.9Bi0.1CuO4+δ ; excess oxygen ; crystal structure ; superconducting transition temperature
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract We have investigated the relation between the crystal structure and superconductivity in La1.9Bi0.1CuO4+δ , in which the phase separation observed in La2CuO4+δ is suppressed. A phase diagram in theT−δ plane is given for La1.9Bi0.1CuO4+δ with excess oxygen. For very smallδ values, the crystal structure is orthorhombic, and an orthorhombic-tetragonal phase transition occurs markedly atδ ∼ 0.03 in the measured temperature range between 13 and 293 K. Superconductivity is observed in the range of 0.04〈δ〈0.11. This is clear evidence thathigh-T c superconductivity also appears in the tetragonal phase.
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  • 9
    ISSN: 1572-882X
    Keywords: cellulose I ; molecular mechanics ; crystal structure ; molecular ; modelling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract Energies for various trial packing arrangements of unit cells for the Iα and Iβ phases of native cellulose discovered by Sugiyamaet al. were evaluated. Both a rigid-ring method, PLMR, and the full-optimization, molecular mechanics program, MM3(90), were used. For both phases the models that had the lowest PLMR energy also had the lowest MM3 energy. Both calculated models have the chains packed ‘up’, O6s intg positions, and the same sheets of hydrogen-bonded chains. The Iβ structure model is essentially identical to that proposed previously for ramie cellulose by Woodcock and Sarko. It is also the same as the best parallel model previously proposed that was based on the X-ray data of Mann, Gonzalez and Wellard, once the various unit cell conventions are considered. Also, the energies from both methods for all three celluloses, Iα, Iβ and II, are in the order that rationalizes their relative stabilites.
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  • 10
    ISSN: 1573-904X
    Keywords: ephedrine ; pseudoephedrine ; salicylate ; chirality ; salt formation ; homochiral crystal ; racemic compound ; racemic conglomerate ; crystal structure ; conformation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The physicochemical properties and crystal structures of the crystalline salts formed by the interaction of an achiral anion, salicylate, with homochiral and racemic ephedrinium and pseudoephedrinium cations were determined. The interaction of ephedrinium or pseudoephedrinium with salicylate in aqueous solution yielded crystalline salts with the notable exception of homochiral ephedrinium. Evaporation of the solvent from solutions of homochiral ephedrine and salicyclic acid in various organic solvents, as well as grinding together solid homochiral ephedrine and solid salicylic acid, yielded viscous semisolids suggesting that homochiral ephedrinium salicylate has a low melting point and/or a high aqueous solubility. Mixing of the two viscous solids, obtained by grinding each of the opposite enantiomers of ephedrine with equimolar salicylic acid, resulted in the formation of racemic ephedrine and subsequently, upon heating, in the formation of racemic ephedrinium salicylate. While racemic ephedrinium salicylate exists as a crystalline compound (P21/n space group) with an equal number of opposite enantiomers in the unit cell, its diastereomer, racemic pseudoephedrinium salicylate, exists as a conglomerate, i.e. a physical mixture, of the homochiral crystals of the opposite enantiomers (each P21 space group). The inability of homochiral ephedrinium to exist as a crystalline salicylate salt at 20–25°C is attributed to its high energy conformation and/or to the poor packing of homochiral ephedrinium salicylate molecules in the crystal lattice.
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  • 11
    ISSN: 1572-9001
    Keywords: tris(pyrazol-1-yl)-s-triazine ; crystal structure ; electron diffraction ; AM1 semiempirical calculation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The conformation of the TPT molecule has been analyzed using experimental and computational techniques. The solid-state molecular structure shows similar conformational features to those in the 2-pyrimidine and phenyl derivatives although a different pattern of bond angles in the triazine ring was observed. The AM1 calculations predicted two conformations of comparable stability (ΔE=1.8 kcal/mol) differing in the orientation of one pyrazole ring. While the minimum energy conformation corresponds to a model displayingC 3h symmetry (φ 1=φ 2=φ 3=0°), the other minimum (φ 1=φ 2=0°,φ 3=180°) is close to that observed in the solid state. The electron diffraction results are consistent with a planar or nearly planar conformation in agreement with the preceding studies.
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  • 12
    ISSN: 1572-9001
    Keywords: Isocinchomeronic acid ; 2,5-pyridinedicarboxylic acid ; hydrogen isocinchomeronate ; manganese(II) complex ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The reactions between Mn(II), Co(II), Ni(II), and Zn(II) ions with isocinchomeronic acid (H2-isocin) afforded complexes of the general formula M(H-isocin)2-2H2O, whereas Fe(II) gives both red and deep red-brown products of the same formula. Various physical measurements suggest that the complexes of M = Co, Ni, Zn, and Fe (brown) are octahedrally coordinated by two aqua ligands and twotrans-N,O-bidentate H-isocin− anions with dimeric hydrogen bonding. Those for M = Mn and Fe (red) are the correspondingcis isomers. The structure of the manganese complex as determined by X-ray crystallography exhibitsC 2 molecular symmetry with Mn-N = 2.279(2), Mn-O(H-isocin)− = 2.196(2), and Mn-O(aqua) = 2.137(2) Å. Each aqua ligand forms two donor O-H ⋯ O hydrogen bonds with carboxy groups of different molecules in adjacent chains.
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  • 13
    Electronic Resource
    Electronic Resource
    Springer
    Journal of chemical crystallography 24 (1994), S. 731-737 
    ISSN: 1572-8854
    Keywords: Synthesis ; crystal structure ; IR data
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The synthesis, crystal structure and IR data are reported for Na2[Zn(CMA)4]·2EtOH·7H2O, where CMA− is the 9,10-dihydro-9-oxo-10-acridinacetate ion. The complex crystallizes in the monoclinic space group P2/n, with cell dimensionsa=17.335(9),b=8.440(5),c=21.875(12) Å, β=91.94(5)°,Z=2. The structure was solved by direct methods and refined to a finalR value of 0.0363 for 3022 non-zero reflections. The Zn2+ ion occupies twofold axis and is coordinated to four carboxylate ligands, the ZnO4 tetrahedron is considerably distorted with Zn−O distances of 1.978(3) and 1.961(3)Å. Each Na+ cation interacts with two water, one ethanol, and three carboxylate O atoms comprising distorted octahedron. The Zn2+ and Na+ cations are linked through monooxygen and syn-syn carboxylate bridges forming a trinuclear, mixed-metal cluster. The Zn...Na separation is 3.267(2)Å and Na...Na distance equals 3.520(2)Å. All oxygen bonded H-atoms are utilized in hydrogen bonds. The acridone rings overlap in the crystal with the 3.5 Å interlayer separations. The compound has been characterized by IR spectroscopy.
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  • 14
    ISSN: 1572-8862
    Keywords: Mixed metal ; platinum ; ruthenium ; alkyne ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstarct The ten metal cluster complex Pt2Ru8(CO)23(µ3−H)2, 1 was found to react with EtC2Et to form a new ten metal tris-alkyne complex Pt2Ru8(CO)18(µ3−EtC2Et)2 (µ4−EtC2Et),2 in 35% yield. Complex 2 was characterized by IR,1H NMR , and single crystalx-ray diffraction analyses. The cluster can be viewed as a dodecahedron of eight metal atoms capped with two ruthenium carbonyl groups, two triply bridging EtC2Et ligands and one quadruply bridging EtC2Et ligand. Application of the standard electron counting procedures indicate that this is an unusual complex in which the 18 electron rule applies and the polyhedral skeletal electron pair theory does not. Crystal Data for 2 2.0.5 CH2CI2: space group = P21,a = 12.759(2) A,b=18.438(2)Å,c = 20.197(3) Å,β = 91.59(1)°, Z. = 4, 6394 reflections,R = 0.037.
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  • 15
    ISSN: 1573-1111
    Keywords: 12-Membered crown ethers ; ion-selective membrane electrodes ; complexes ; crystal structure ; X-ray analysis ; conformation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Lipophilic derivatives of benzo-12-crown-4 and naphtho-12-crown-4 have been synthesized. The behavior of the parent compounds and their derivatives in membrane ion-selective electrodes have been studied. Selectivity changes have been observed with the rise in lipophilicity. Crystal structures of the NaI and KI complexes of benzo-12-crown-4 (1 and2) have been determined by X-ray analysis. The alkali metal and iodide ions are in direct contact in2 but not in1. Compound1 [Na(benzo-12-crown-4)2]·I is triclinic, witha=13.368(8),b=10.727(7),c=10.325(4) Å; α=73.56(4),β=77.73(4), γ=108.70(5)°;Z=2, space group is $$P\bar 1$$ . Compound2 [K(benzo-12-crown-4)2·I] is monoclinic, witha=15.807(8),b=12.043(4),c=15.601(6) Å,β=117.74(3)°;Z=4, space groupC2/c. In both compounds the cations interact with all oxygen atoms of two crown ether molecules. Correlation of the crystal structures and behavior of the crown ethers in ion-selective membrane electrodes is discussed.
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  • 16
    Electronic Resource
    Electronic Resource
    Springer
    Journal of inclusion phenomena and macrocyclic chemistry 20 (1994), S. 53-71 
    ISSN: 1573-1111
    Keywords: Lithium ionophores ; podand ; dicyclohexylamides ; Li-complex ; crystal structure ; X-ray analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The influence of structure and lipophilicity of dicyclohexylamides on the lithium selectivity in membrane electrodes is discussed. The crystal structures of the triamide podand1 and its complex with LiBr1b has been determined by X-ray analysis. Crystal data for ligand1: C48H83O6N3, triclinic,P1,a=10.749(2),b=12.097(3),c=19.123(6)Å, α=95.76(2),β=80.06(2), γ=100.27(2)0,V=2403(1) Ã3,Z=2. Crystal data for the lithium complex1b: C48H83O6N3·LiBr·x C2H5OH, monoclinic,P2 1/c,a=21.297(6),b=16.316(8),c=19.450(4) Å,β=110.87(2)0,V=6315(3) Å3,Z=4. In the complex the ligand adopts a conformation in which oxygen binding sites surrounding the Li+ cation form a slightly distorted trigonal prism.
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  • 17
    Electronic Resource
    Electronic Resource
    Springer
    Journal of inclusion phenomena and macrocyclic chemistry 17 (1994), S. 137-148 
    ISSN: 1573-1111
    Keywords: Clathrate hydrate ; phase diagram ; crystal structure ; tetraisoamylammonium fluoride
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The phase diagram of the binary (i-C5H11)4NF-water system has been studied in the clathrate formation region. Three polyhydrates have been discovered, two of which (1∶38.9 and 1∶32.7) are the known orthorhombic and tetragonal phases:Pbmn,a=11.88,b=21.53,c=12.70 Å,ρ means=1.019 g cm-3 (0°C), m.p.=32.4°C andP42/m, a=23.729,c=12.466 Å,ρ means=1.062 g cm-3, (0°C), m.p.=31.2°C, respectively. A single crystal X-ray analysis of the novel clathrate hydrate (i-C5H11)4NF·27 H2O is reported. This new clathrate hydrate is tetragonal,I4I/a, witha=16.894(5),c=17.111(2) Å,Z=4, (−50°C), and m.p.=34.6°C. Each (i-C5H11)4N+ cation occupies a four-chamber cavity built of 15-hedra 71635942 (idealized description), with small vacant 5444 cavities filling the intervening space.
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  • 18
    Electronic Resource
    Electronic Resource
    Springer
    Journal of inclusion phenomena and macrocyclic chemistry 17 (1994), S. 187-201 
    ISSN: 1573-1111
    Keywords: β-Cyclodextrin ; sulfathiazole ; inclusion complex ; crystal structure ; thermal analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract An inclusion complex with the formula (β-cyclodextrin) (sulfathiazole) 8.3 H2O has been crystallized and characterized by physicochemical methods including single crystal X-ray analysis. The complex crystallizes in the monoclinic system, space group P21, witha=15.264(4),b= 16.500(6),c=15.559(5) Å,β=117.29(3)o andZ=2. The structure was solved using published co-ordinates forβ-cyclodextrin in an isomorphous complex. Refinement by block-diagonal leastsquares yieldedR=0.061 for 4706 unique observed reflections. Inclusion of sulfathiazole produces a slight ellipticity in the host conformation, but the guest adopts a conformation similar to that observed in its polymorphs. The guest is held in the macrocyclic cavity predominantly by hydrophobic forces, with the phenyl ring near the host primary hydroxyl side and the thiazole ring near the secondary hydroxyl side. The complex packs in layers parallel to theac-plane. Layers are linked by hydrogen bonding to water molecules which are located outside the cyclodextrin cavity. An extensive network of hydrogen bonds mediated chiefly by water molecules stabilizes the crystal structure.
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  • 19
    ISSN: 1573-1111
    Keywords: Gossypol ; complex ; crystal structure ; single crystal ; desolvation ; polymorph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The structures of gossypol complexes are extremely sensitive to the halogenomethane present as the guest; e.g. changing the number of Cl atoms in chloromethane derivatives changes the structure of the gossypol complex. The crystals of C30H30O8·CH2Cl2 are monoclinic, space groupC2/c,a=21.320(4),b=19.199(6),c=15.765(2)Å, β=113.05(2)o,V=5916(2)Å3,Z=8,D x=1.35 g/cm3,T=295 K. The structure has been solved by direct methods and refined to the finalR value of 0.084 for 1828 reflections. In the structure H-bonded gossypol molecules form columns, generating channels in the structure which are filled by guest molecules. After decomposition (desolvation) monocrystals of the complexes are conserved without destruction, in which there are rather wide and empty channels though slightly smaller than in the complex. An attempt is made to explain some peculiarities of the behavior of the gossypol polymorph formed on the basis of its structure with empty channels.
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  • 20
    Electronic Resource
    Electronic Resource
    Springer
    Journal of inclusion phenomena and macrocyclic chemistry 17 (1994), S. 365-376 
    ISSN: 1573-1111
    Keywords: Gossypol ; inclusion compounds ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The crystal structure of a compound obtained in a condensation reaction of (±)-gossypol with (R)-(+)-phenylethylamine has been determined by X-ray structure analysis. The crystals of C46H48O6N2·(C4H8O2)2 are monoclinic, space groupP21,a=21.243(3),b=8.666(1),c=28.651(4) Å, β=108.24(1)0,V=5009(3) β3,Z=4,D x=1.195 g cm−3, μ(CuK α)=0.66 mm−1,T=292 K. The structure has been solved by direct methods and refined to the finalR value of 0.091 for 4290 observed reflections and 1049 parameters. There are two diastereoisomeric molecules of the host and four solvent molecules in the asymmetric unit. The host molecules are H-bonded into chains with diastereoisomeric molecules alternating along the chain. The fact that the host prefers the association mode in which molecules with a different configuration of the 2,2′-binaphthyl moiety are H-bonded explains why separation of diastereoisomeric diaminogossypols by fractional crystallization has been unsuccessful. The 1,4-dioxane molecules are accommodated in infinite channels but only every second guest molecule in a channel is H-bonded to the host.
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  • 21
    ISSN: 1573-1111
    Keywords: D,L-hexapeptide ; cyclic ; crystal structure ; stacks ; tubular ; β-rings ; channels
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract An X-ray analysis of single crystals (from MeOH) of cyclo(-D-Leu-L-MeLeu-D-Leu-L-MeLeu-D-Leu-L-MeLeu-) has been carried out. The analysis reveals that the molecules of the cyclopeptide occur in the crystals with two slightly different, almost hexagonal backbone conformations of the β-type, and that pairs of molecules with the same conformation interact through their nonmethylated face, forming dimeric units (units A and B) with six interannular H-bonds. This kind of pairing reproduces well that expected for a two-ring element in a stack of antiparalleβ-rings. The X-ray analysis has also revealed the presence in the A units of two water molecules, each at one of two equivalent sites located on the 3-fold axis of the units and equidistant from the center of gravity, and the presence in the B units of one water molecule at the center of the units. This provides experimental support for the idea that stacks ofβ-rings can serve as molecular channels.
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  • 22
    ISSN: 1573-1111
    Keywords: Pentaborate ; boric acid ; clathrate ; diamond-related network ; hydrogen bonding ; tetrapropy-lammonium ; tetrabutylammonium ; crystal structure ; 11B MAS NMR ; 13C MAS NMR ; thermogravimetry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Single-crystal X-ray structure analyses of N(nPr)4[B5O6(OH)4][B(OH)3]2,1, and N(nBu)4 [B5O6(OH)4][B(OH)3]2,2, reveal that these materials are novel clathrates, the isotypic host structures of which are three-dimensional assemblies of hydrogen-bonded [B5O6(OH)4]− ionsand B(OH)3 molecules. The assembly of only the pentaborate anions is a distorted (i.e., along [102] elongated) fourconnected diamond-related network. The N(nPr) 4 + and N(nBu) 4 + ions are trapped within the complex three-dimensional channel systems of the host frameworks. Both1 and2 crystallize monoclinically with space groupP21/c andZ=4. The cell constants are:1:a=13.592(5),b=12.082(2),c=17.355(6) Å, β=106.60(2)° (298K);2:a=13.874(3),b=12.585(1),c=17.588(4) Å, β=107.04(1)° (238 K). The results obtained by both11B and13C MAS NMR spectroscopy are discussed. Thermogravimetric studies under a flowing inert-gas atmosphere suggest that water, stemming from polycondensation of the hydrous borate species, is released from the clathrates at ca. 443 K (1) and 398 K (2) before the decomposition of the organic cations starts at ca. 603 K (1) and 603 K (2).
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  • 23
    ISSN: 1573-1111
    Keywords: Calixarenes ; arenetricarbonylchromium ; crystal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The structures of three arene-tricarbonylchromium complexes prepared from cone and 1,3-alternate-25, 26,27,28-tetrapropoxycalix[4]arene(1) and Cr(CO)6 were determined by single crystal X-ray studies. Crystal data for 1,3-alternate-1·Cr(CO)3 are space groupP21/a,a=19.496(3)Å,b=11.118(2)Å,c=19.121(2)Å, β=109.95°(1) andV=3895Å3. The structure was refined toRw=0.068. Crystal data for cone-1·Cr(CO)3 are space groupP21/a,a=21.457(4)Å,b=12.184(1)Å,c=14.816(2)Å, β=91.61°(1) andV=3872Å3. The structure was refined toRw=0.077. Crystal data for cone-1·2Cr(CO)3 are space groupP21/a,a=18.019(3)Å,b=41.347(4)Å,c=11.743(2)Å, β=97.39°(1) andV=8676Å3. The single crystal included two similar but slightly different structures but the data were successfully refined toRw=0.092. The structure of 1,3-alternate-1·Cr(CO)3 differs only slightly from that of the regular 1,3-alternate calix[4]arene. In contrast, cone-1·Cr(CO)3 and cone-1·2Cr(CO)3 show an unusual conformation with a pair of faced gablelike roofs, which is considerbly distorted from the regular cone calix[4]arene. The origin of this distortion is discussed in combination with the spectral studies.
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  • 24
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    Proteins: Structure, Function, and Genetics 19 (1994), S. 4-13 
    ISSN: 0887-3585
    Keywords: trichosanthin ; ribosome-inactivating proteins ; crystal structure ; orthorhombic ; molecular replacement ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Trichosanthin (TCS) is one of the single chain ribosome-inactivating proteins (RIPs). The crystals of the orthorhombic form of trichosanthin have been obtained from a citrate buffer (pH 5.4) with KC1 as the precipitant. The crystal belongs to the space group P212121 with a = 38.31, b = 76.22, c = 79.21 Å. The structure was solved by molecular replacement method and refined using the programs XPLOR and PROLSQ to an R-factor of 0.191 for the reflections within the 6-1.88 Å resolution range. The bond length and bond angle in the protein molecule have root-mean-square deviations from ideal value of 0.013 Å and 3.3°, respectively. The refined model includes 247 residues and 197 water molecules. The TCS molecule consists of two structural domains. The large domain contains six α-helices, a six stranded sheet, and an antiparallel β-sheet. The small domain has a largest α-helix, which shows a distinct bend. The possible active site of the molecule located on the cleft between two domains was proposed. In the active site Arg-163 and Glu-160, Glu-189 and Arg-122 form two ion pairs, Glu-189 and Gln-156 are hydrogen bonded to each other. Three water molecules are bonded to the residues in the active site region. The structures of TCS molecule and ricin A-chain (RTA) superimpose quite well, showing that the structures of the two protein molecules are homologous. Comparison of the structures of the TCS molecule in this orthorhombic crystal with that in the monoclinic crystal indicates that there are no essential differences of the structures between the two protein crystals. © 1994 Wiley-Liss, Inc.
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  • 25
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    Proteins: Structure, Function, and Genetics 20 (1994), S. 149-166 
    ISSN: 0887-3585
    Keywords: crystal structure ; cold adaption ; catalytic efficiency ; protein stability ; anionic ; ectotherm ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: The crystal structure of an anionic form of salmon trypsin has been determined at 1.82 Å resolution. We report the first structure of a trypsin from a phoikilothermic organism in a detailed comparison to mammalian trypsins in order to look for structural rationalizations for the cold-adaption features of salmon trypsin. This form of salmon trypsin (T II) comprises 222 residues, and is homologous to bovine trypsin (BT) in about 65% of the primary structure. The tertiary structures are similar, with an overall displacement in main chain atomic positions between salmon trypsin and various crystal structures of bovine trypsin of about 0.8 Å. Intramolecular hydrogen bonds and hydrophobic interactions are compared and discussed in order to estimate possible differences in molecular flexibility which might explain the higher catalytic efficiency and lower thermostability of salmon trypsin compared to bovine trypsin. No overall differences in intramolecular interactions are detected between the two structures, but there are differences in certain regions of the structures which may explain some of the observed differences in physical properties. The distribution of charged residues is different in the two trypsins, and the impact this might have on substrate affinity has been discussed. © 1994 Wiley-Liss, Inc.
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  • 26
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    Numerical Linear Algebra with Applications 1 (1994), S. 105-105 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 27
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    Numerical Linear Algebra with Applications 1 (1994), S. 151-154 
    ISSN: 1070-5325
    Keywords: Linear systems ; Singular systems ; Iterative methods ; Convergent methods ; Index of the iteration operator ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Equivalence is shown between different conditions for convergence of iterative methods for consistent singular systems of linear equations on Banach spaces. These systems appear in many applications, such as Markov chains and Markov processes. The conditions considered relate the range and null spaces of different operators.
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  • 28
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    Numerical Linear Algebra with Applications 1 (1994), S. 211-212 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 29
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    Numerical Linear Algebra with Applications 1 (1994), S. 179-210 
    ISSN: 1070-5325
    Keywords: Linear system solvers ; Conjugate gradients ; Iteration number estimates ; Explicit preconditionings ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Instead of the standard estimate in terms of the spectral condition number we develop a new CG iteration number estimate depending on the quantity B = 1/ntr M/(det M)1/n, where M is an n × n preconditioned matrix. A new family of iterative methods for solving symmetric positive definite systems based on B-reducing strategies is described. Numerical results are presented for the new algorithms and compared with several well-known preconditioned CG methods.
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  • 30
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    Numerical Linear Algebra with Applications 1 (1994), S. 155-177 
    ISSN: 1070-5325
    Keywords: Preconditioning ; Diagonal compensation ; Eigenvalue bounds ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: When solving linear algebraic equations with large and sparse coefficient matrices, arising, for instance, from the discretization of partial differential equations, it is quite common to use preconditioning to accelerate the convergence of a basic iterative scheme. Incomplete factorizations and sparse approximate inverses can provide efficient preconditioning methods but their existence and convergence theory is based mostly on M-matrices (H-matrices). In some application areas, however, the arising coefficient matrices are not H-matrices. This is the case, for instance, when higher-order finite element approximations are used, which is typical for structural mechanics problems. We show that modification of a symmetric, positive definite matrix by reduction of positive offdiagonal entries and diagonal compensation of them leads to an M-matrix. This diagonally compensated reduction can take place in the whole matrix or only at the current pivot block in a recursive incomplete factorization method. Applications for constructing preconditioning matrices for finite element matrices are described.
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  • 31
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    Numerical Linear Algebra with Applications 1 (1994) 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 32
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    Numerical Linear Algebra with Applications 1 (1994), S. 237-245 
    ISSN: 1070-5325
    Keywords: Korovkin theorem ; Heat conduction equation ; Lax theorem ; Difference scheme ; Convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Sufficient conditions are obtained for the convergence of difference schemes for the numerical solution of the Cauchy problem for a heat conduction equation in two space variables. The sufficient conditions are derived in a form similar to those for the convergence of a sequence of linear positive operators in the Korovkin theorem. As an application it is shown that difference schemes that are widely used in practice can easily be checked for convergence by these conditions.
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  • 33
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    Numerical Linear Algebra with Applications 1 (1994), S. 213-236 
    ISSN: 1070-5325
    Keywords: Optimal order preconditioners ; Algebraic multilevel ; Chebyshev polynomial approximation ; Diagonal compensation ; Approximate inverses ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The numerical solution of elliptic selfadjoint second-order boundary value problems leads to a class of linear systems of equations with symmetric, positive definite, large and sparse matrices which can be solved iteratively using a preconditioned version of some algorithm. Such differential equations originate from various applications such as heat conducting and electromagnetics. Systems of equations of similar type can also arise in the finite element analysis of structures.We discuss a recursive method constructing preconditioners to a symmetric, positive definite matrix. An algebraic multilevel technique based on partitioning of the matrix in two by two matrix block form, approximating some of these by other matrices with more simple sparsity structure and using the corresponding Schur complement as a matrix on the lower level, is considered.The quality of the preconditioners is improved by special matrix polynomials which recursively connect the preconditioners on every two adjoining levels. Upper and lower bounds for the degree of the polynomials are derived as conditions for a computational complexity of optimal order for each level and for an optimal rate of convergence, respectively.The method is an extended and more accurate algebraic formulation of a method for nine-point and mixed five- and nine-point difference matrices, presented in some previous papers.
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  • 34
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    Numerical Linear Algebra with Applications 1 (1994) 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 35
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    Numerical Linear Algebra with Applications 1 (1994), S. 1-1 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 36
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    Numerical Linear Algebra with Applications 1 (1994), S. 33-44 
    ISSN: 1070-5325
    Keywords: Rank revealing QR factorization ; Column pivoting ; Numerical rank ; Subset selection ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Rank revealing factorizations are used extensively in signal processing in connection with, for example, linear prediction and signal subspace algorithms. We present an algorithm for computing rank revealing QR factorizations of low-rank matrices. The algorithm produces tight upper and lower bounds for all the largest singular values, thus making it particularly useful for treating rank deficient problems by means of subset selection, truncated QR, etc. The algorithm is similar in spirit to an algorithm suggested earlier by Chan for matrices with a small nullity, and it can also be considered as an extension of ordinary column pivoting.
    Additional Material: 1 Ill.
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  • 37
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    Numerical Linear Algebra with Applications 1 (1994), S. 571-581 
    ISSN: 1070-5325
    Keywords: GMRES ; GMRES(m) ; Large-scale nonsymmetric linear systems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The generalized minimal residual (GMRES) method is widely used for solving very large, nonsymmetric linear systems, particularly those that arise through discretization of continuous mathematical models in science and engineering. By shifting the Arnoldi process to begin with Ar0 instead of r0, we obtain simpler Gram-Schmidt and Householder implementations of the GMRES method that do not require upper Hessenberg factorization. The Gram-Schmidt implementation also maintains the residual vector at each iteration, which allows cheaper restarts of GMRES(m) and may otherwise be useful.
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  • 38
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    Numerical Linear Algebra with Applications 1 (1994), S. 555-570 
    ISSN: 1070-5325
    Keywords: Linear system of equations ; Iterative method ; Fast algorithm ; Arnoldi process ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new iterative scheme is described for the solution of large linear systems of equations with a matrix of the form A = ρU + ζI, where ρ and ζ are constants, U is a unitary matrix and I is the identity matrix. We show that for such matrices a Krylov subspace basis can be generated by recursion formulas with few terms. This leads to a minimal residual algorithm that requires little storage and makes it possible to determine each iterate with fairly little arithmetic work. This algorithm provides a model for iterative methods for non-Hermitian linear systems of equations, in a similar way to the conjugate gradient and conjugate residual algorithms. Our iterative scheme illustrates that results by Faber and Manteuffel [3,4] on the existence of conjugate gradient algorithms with short recurrence relations, and related results by Joubert and Young [13], can be extended.
    Additional Material: 3 Ill.
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  • 39
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    Numerical Linear Algebra with Applications 1 (1994), S. 583-587 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 40
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    Numerical Linear Algebra with Applications 1 (1994), S. 45-63 
    ISSN: 1070-5325
    Keywords: Conjugate gradients ; Convergence ; Linear systems ; Acceleration of conjugate gradients ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The solution of linear systems has considerable importance for the computation of problems resulting from engineering, physics, chemistry, computer science, mathematics, medicine and economics. The calculation of costly and time-consuming problems, e.g. crash tests, simulation of the human lung and skin, calculation of electrical and magnetical fields, thermal analysis and fluid dynamics, to name only a few, has become possible with the recent developments of advanced computer architectures and iterative solvers. Generalized conjugate gradient (CG) methods are the most important iterative solvers because they converge very quickly under certain conditions. Therefore they are widely used and in a rapid further development.The purpose of this paper is to present new results for the convergence of generalized CG methods. A convergence result for non-symmetric and non-positive definite matrices is given that includes the classical theory for symmetric, positive definite matrices as a special case.The norm of the residuals resulting from CG methods may oscillate heavily. Different remedies for smoothing this sequence have been proposed, for example by van der Vorst. Schönauer introduced in the 1980s a smoothing algorithm to get a norm nonincreasing function of the iteration index. For this algorithm a complete theoretical analysis is given. A surprising result is obtained showing that the smoothing algorithm is in a sense optimal. Convergence estimates are derived therefrom. A geometric interpretation of the smoothing algorithm is given showing the propagation of the errors.It should be stressed that a smooth convergence of the residuals is not equivalent to a smooth convergence of the errors which is the proper aim. A class of error minimizing methods can be easily derived from the theory.
    Additional Material: 6 Ill.
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  • 41
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    Numerical Linear Algebra with Applications 1 (1994), S. 107-128 
    ISSN: 1070-5325
    Keywords: Incomplete factorization ; Preconditioning ; Linear elasticity problems ; Displacement decomposition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Two preconditioning techniques for the numerical solution of linear elasticity problems are described and studied. Both techniques are based on spectral equivalence approach. The first technique consists in an incomplete factorization of the separate displacement component part of the stiffness matrix. The second technique uses an incomplete factorization of the isotropic approximation to the stiffness matrix. Results concerning existence, stability and efficiency of these preconditioning techniques are presented. The efficiency and robustness of the described techniques are illustrated by numerical experiments.
    Additional Material: 2 Ill.
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  • 42
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    Numerical Linear Algebra with Applications 1 (1994), S. 129-139 
    ISSN: 1070-5325
    Keywords: Conjugate gradient method ; Nonsymmetric linear system ; Krylov subspace method ; Conjugate residual method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Yserentant's and Bramble/Pasciak/Xu's hierarchical preconditioners only require the hierarchical node connection of a finite element grid. So they could be applied to nonsymmetric FE-systems too, having a symmetric preconditioner. We investigate the question whether this fact could be useful in the CG-like iterative methods. The main key is the consideration of an appropriate choice of the inner product defined in the N-vector space. It is shown, how the inner product influences the formulas of the methods, the rate of convergence and some other properties.
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  • 43
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    Numerical Linear Algebra with Applications 1 (1994), S. 141-150 
    ISSN: 1070-5325
    Keywords: Invariant manifolds ; Error estimates ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Many processes in the sciences and in engineering are modelled by dynamical systems and - in discretized version - by nonlinear maps. To understand the often complicated dynamical behaviour it is a well established tool to use the concept of invariant manifolds of the system. In this way it is often possible to reduce the dimension of the system considerably. In this paper we propose a new method to calculate numerically invariant manifolds near fixed points of maps. We prove convergence of our procedure and provide an error estimation. Finally, the application of the method is illustrated by examples.
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  • 44
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    Numerical Linear Algebra with Applications 1 (1994), S. 335-335 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 45
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    Numerical Linear Algebra with Applications 1 (1994), S. 369-386 
    ISSN: 1070-5325
    Keywords: GMRES ; Unsymmetric linear systems ; Iterative solver ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed per iteration step by a suitable approximation process, e.g., by GMRES itself. Our numerical experiments indicate that this may lead to considerable savings in CPU-time and memory requirements in typical CFD applications.
    Additional Material: 10 Tab.
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  • 46
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    Numerical Linear Algebra with Applications 1 (1994), S. 337-368 
    ISSN: 1070-5325
    Keywords: Local refinement ; Preconditioning ; Two-grid method ; Cell-centered grids ; Finite differences ; Elliptic problem ; Optimal rate of convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Two preconditioning techniques for solving difference equations arising in finite difference approximation of elliptic problems on cell-centered grids are studied. It is proven that the BEPS and the FAC preconditioners are spectrally equivalent to the corresponding finite difference schemes, including a nonsymmetric one, which is of higher-order accuracy. Numerical experiments that demonstrate the fast convergence of the preconditioned iterative methods (CG and GCG-LS in the nonsymmetric case) are presented.
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  • 47
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    Numerical Linear Algebra with Applications 1 (1994), S. 421-425 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 48
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    Numerical Linear Algebra with Applications 1 (1994), S. 403-420 
    ISSN: 1070-5325
    Keywords: Quasi-minimal residual iteration ; Non-Hermitian matrix ; Singular linear system ; Markov chain modeling ; Krylov-subspace method ; Convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Recently, Freund and Nachtigal proposed the quasi-minimal residual algorithm (QMR) for solving general nonsingular non-Hermitian linear systems. The method is based on the Lanczos process, and thus it involves matrix - vector products with both the coefficient matrix of the linear system and its transpose. Freund developed a variant of QMR, the transpose-free QMR algorithm (TFQMR), that only requires products with the coefficient matrix. In this paper, the use of QMR and TFQMR for solving singular systems is explored. First, a convergence result for the general class of Krylov-subspace methods applied to singular systems is presented. Then, it is shown that QMR and TFQMR both converge for consistent singular linear systems with coefficient matrices of index 1. Singular systems of this type arise in Markov chain modeling. For this particular application, numerical experiments are reported.
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    Numerical Linear Algebra with Applications 1 (1994) 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 50
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    Numerical Linear Algebra with Applications 1 (1994), S. 387-402 
    ISSN: 1070-5325
    Keywords: Preconditioning ; Incomplete LU ; Threshold strategies ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we describe an Incomplete LU factorization technique based on a strategy which combines two heuristics. This ILUT factorization extends the usual ILU(O) factorization without using the concept of level of fill-in. There are two traditional ways of developing incomplete factorization preconditioners. The first uses a symbolic factorization approach in which a level of fill is attributed to each fill-in element using only the graph of the matrix. Then each fill-in that is introduced is dropped whenever its level of fill exceeds a certain threshold. The second class of methods consists of techniques derived from modifications of a given direct solver by including a dropoff rule, based on the numerical size of the fill-ins introduced, traditionally referred to as threshold preconditioners. The first type of approach may not be reliable for indefinite problems, since it does not consider numerical values. The second is often far more expensive than the standard ILU(O). The strategy we propose is a compromise between these two extremes.
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    Numerical Linear Algebra with Applications 1 (1994), S. 427-447 
    ISSN: 1070-5325
    Keywords: Nonsymmetric linear systems ; Conjugate gradient type iterative methods ; GMRES ; Restarting ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The solution of nonsymmetric systems of linear equations continues to be a difficult problem. A main algorithm for solving nonsymmetric problems is restarted GMRES. The algorithm is based on restarting full GMRES every s iterations, for some integer s〉0. This paper considers the impact of the restart frequency s on the convergence and work requirements of the method. It is shown that a good choice of this parameter can lead to reduced solution time, while an improper choice may hinder or preclude convergence. An adaptive procedure is also presented for determining automatically when to restart. The results of numerical experiments are presented.
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  • 52
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    Communications in Numerical Methods in Engineering 10 (1994) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 53
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    Communications in Numerical Methods in Engineering 10 (1994), S. 1-9 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative method is introduced for computing second-order partial derivatives (sensitivities) of eigenvalues and eigenvectors of matrices which depend on a number of real design parameters. Numerical tests confirm the viability of the method and support our theoretical analysis. Alternative methods are reviewed briefly and compared with the one proposed here.
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  • 54
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    Communications in Numerical Methods in Engineering 10 (1994), S. 11-19 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the formulation of the semi-Loof element the rotation of the tangent plane is derived from the interpolation of the transverse displacement, while the rotation of the normal is interpolated separately by another set of shape functions. The geometric stiffness matrix can be formulated by use of either of the two rotation representations. It is demonstrated that the use of the tangent plane representation in the geometric stiffness matrix is far superior to the common form at present.
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  • 55
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    Communications in Numerical Methods in Engineering 10 (1994), S. 21-32 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient solution to boundary-value problems may be based on the application of a suitably truncated T-complete set of Trefftz functions over individual subdomains and on linking the fields by a least-squares procedure. Although it yields a symmetric system of linear equations, this approach as originally presented by Zielinski and Zienkiewicz is not suited for implementation into FE codes. The present paper presents two equivalent formulations, which take respectively the form of the finite (FE) and non-conventional boundary-element (BE) approach. Both allow the resulting simultaneous equations to be assembled following the standard direct stiffness methods and can readily be implemented into existing FE codes.As in the conventional p-method, the accuracy may be controlled within large limits without increasing the number of elements. The present approach allows substantial saving in computer time in comparison with the so-called hybrid-Trefftz (HT) elements, though the assumed displacement fields are identical. The practical efficiency of the new T-element approach is assessed on the problem of stress concentration in a symmetrically compressed perforated panel.
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  • 56
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    Communications in Numerical Methods in Engineering 10 (1994), S. 43-58 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented for the solution of elliptical problems defined on general-shape multiconnected three-dimensional domains approximated by means of polyhedra. The boundary conditions may be of the Neumann type. The differential operator and the normal derivative are discretized by generalized finite-difference (GFD) methods using an orthogonal non-uniform Cartesian grid. The convergence properties are analysed and the solutions of some Poisson and biharmonic problem are presented.
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  • 57
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    Communications in Numerical Methods in Engineering 10 (1994), S. 59-65 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A heuristic optimization design methodology based on redesign rules for composite laminated plates is presented. It is modelled on the cyclic approach to the design process observed in designers of structural components using composites. In comparison with a simple weight minimization algorithm it gives quasioptimal ply thicknesses, but takes under ten iterations. It is thereby shown to be most suitable for initial design studies. Multiaxial combinations of in-plane loads and bending moments are considered in the design procedure.
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  • 58
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    Communications in Numerical Methods in Engineering 10 (1994), S. 33-42 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Reduction of reheating time saves on energy input and increases the production rate in the steel-making process. Reductions can be achieved by allowing the centre temperature of a steel bar to be lower than the surface temperature by a small margin, before starting with the hot rolling process. This can only be done if the temperature difference does not adversely affect the quality of the final product or the rolling equipment. The paper presents numerical simulations to investigate the savings that can be obtained for various temperature differences between surface and centre temperatures to evaluate the feasibility of the concept. The results presented include the cross-sectional temperature distribution in a typical steel bar during reheating at hourly intervals as well as the effect of various differences between centre and surface temperatures on reheating time. The reheating time predicted for various steel bar sizes as well as for various differences between surface and centre temperatures are then compared against measured reheating times. To indicate the practical applicability of the concept to the hot rolling process the detailed temperature distribution in a typical steel bar, with an initial temperature difference between the surface and centre of the bar, was simulated numerically. This was compared to a similar simulation for a well soaked steel bar for which experimental measurements are also available. The numerical method used to obtain the simulations is also presented. Boundary conditions account for radiation, convection and conduction inside the steel bar. It is concluded that the concept of allowing differences between surface and centre temperatures of a steel bar during reheating holds great potential for energy savings in the steel-making process.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 73-80 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Standard isoparametric finite elements can be used as singular crack-tip elements in fracture mechanical computations by placing the middle nodes in the neighbourhood of the crack tip. Such elements have already been applied to several plane and three-dimensional problems, so this method can be considered as commonly well accepted. The paper shows that singularity of order r(1 - m)/m is obtained with an nth-order isoparametric element.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 67-71 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an iterative method of statistic linearization (IMSL) is presented to solve non-linear stochastic vibration equations. This method represents an improvement over the classical linearization method. The method uses the solution of the corresponding linear vibration equation as an initial value in an iterative procedure. To obtain information about essential statistical average values, the method uses a ‘boot-strapping’ procedure, which defines a pseudorandom process based on the statistical characteristics of the linear solution and then uses samples from the process to estimate them. For Gaussian input excitation, the statistical average values are obtained by theoretical analysis.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 89-91 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    Communications in Numerical Methods in Engineering 10 (1994), S. 81-87 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Dynamic stress intensity factors of cracked linear viscolastic solids under conditions of plane stress are computed by the boundary-element method in conjunction with the numerical Laplace transform and the correspondence principle of linear viscoelasticity. Quadratic isoparametric conventional and quarter-point boundary elements are employed. The multidomain approach is used in cases where symmetry cannot be invoked. Dynamic stress intensity factors are computed for cracked viscoelastic rectangular plates subjected to suddenly applied loads, and comparisons are made against results obtained by other numerical methods.
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    Communications in Numerical Methods in Engineering 10 (1994) 
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    Keywords: Engineering ; Engineering General
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  • 64
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    Communications in Numerical Methods in Engineering 10 (1994), S. 93-110 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach to constructing monotonous second-order-accurate schemes for time-dependent Navier-Stokes equations in the compressible case is suggested. Flows with shock waves and thin viscous boundary layers are considered. The approach joins two different schemes while each of them is appropriate for its own type of flow. The resulting scheme is constructed as a splitting one, and the approach is applied at the stage governed by the Euler equations in Lagrangian variables. The approach turns out to be fruitful also for parabolic equations with ‘viscous’ terms. The method is illustrated by the problem on compression of deuterium in a conical solid-body target with viscous heating of deuterium.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 111-119 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
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    Topics: Mathematics , Technology
    Notes: A new eigensolution reanalysis method for modified structures is developed and presented based on the usual first-order perturbation scheme and the Rayleigh quotients. By this method, the accuracies of the eigensolutions of the modified structures computed by perturbation methods are improved. A numerical example is presented and the accuracies of the usual first-order perturbation method, second-order perturbation method, William B. Bickford method and the proposed method are compared.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 121-134 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this study a perturbation method for computing the upper and lower bounds of eigenvalues of structural vibration systems with interval parameters is presented. The eigenproblem of the uncertain (interval) structure is expressed by equations consisting of the uncertainties. If the uncertainity is small in parameters, the eigensolutions of uncertain structures can be obtained efficiently by the perturbation method presented. A numerical example is given to demonstrate the validity of the method.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 135-148 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performance of the univariant finite element Q1P0 and the multivariant finite elements Q1+P0 and R2+P0 are compared for simulation of three-dimensional incompressible viscous flows. Incompressible flow vortices for the R2+P0 element are presented. For the two flows simulated, the R2+P0 element is found to be not only the most accurate but also computationally the most efficient of the three types of finite element used. For one of the two flows simulated, the pressure distribution obtained by using the Q1P0 element is found to be afflicted with the checker-board spurious pressure mode. For the uniform finite-element mesh used, the checker-board pressure mode is eliminated by taking a weighted average of the pressure over the neighbouring Q1P0 elements.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 179-181 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    Communications in Numerical Methods in Engineering 10 (1994), S. 149-154 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper the use of a truncated envelope technique is discussed as a preconditioning for the conjugate gradient method for solving large linear systems of equations with symmetric positive-definite matrices. An algorithm to generate a truncated envelope is introduced. Computational experience with systems of linear equations from the Harwell-Boeing collection is presented to highlight the efficiency of this approach.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 167-178 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A sixth-order polynomial shape function is developed for BIE analysis. The function is applied over only three-noded elements, but with the support for the function extending over adjacent elements. This avoids the oscillations near the ends of the range which otherwise are characteristic of high-order polynomial interpolation. Various test problems are explored, and it is shown that results as accurate as those from conventional quadratic elements are obtained with larger nodal spacings, and thus giving the potential for significant reductions in matrix storage requirements and solution times.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 155-166 
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    Keywords: Engineering ; Engineering General
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    Notes: A finite element formulation based on superposition is proposed for a lifting aerofoil in incompressible potential flow. An accuracy improvement technique for the singularity at the aerofoil trailing edge is discussed. It is shown that the quarter-node quadrilateral element can be readily employed to simulate this singularity. It is also demonstrated that the circulation in the flow field can be easily represented by a single constraint equation rather than introducing an artificial cut line in the mesh. The influence of finite-element mesh size on solution accuracy and the correct form of the boundary condition have been investigated as well. Numerical examples are given for both steady and quasisteady Joukowski aerofoils of various thicknesses and at a range of incidences. In all test cases, good agreement is observed between the analytical solution and the numerical result.
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    Communications in Numerical Methods in Engineering 10 (1994) 
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    Communications in Numerical Methods in Engineering 10 (1994), S. 183-194 
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    Topics: Mathematics , Technology
    Notes: An 8-node element (HMITC) for 3D non-linear analysis of solids is presented. The new element is based on an element developed by Wilson and Ibrahimbegovic, that incorporates incompatible modes, and on the method of mixed interpolation of tonsorial components. The HMITC element does not contain spurious zero energy modes and satisfies Irons' Patch Test. The numerical experimentation indicates that the HMITC has good performance even with distorted meshes.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 203-215 
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    Notes: In this paper we consider an explicit finite-element method, with elements adaptively oriented in space-time, for the solution of one-dimensional conservation laws, extending previous work dealing with linear convection-diffusion and incompressible flow. In particular we consider Burgers' equation and the compressible Euler equations.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 195-201 
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    Keywords: Engineering ; Engineering General
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    Notes: A numerical method, based on neural-network-based functions, for solving partial differential equations is reported in the paper. Using a ‘universal approximator’ based on a neural network and point collocation, the numerical problem of solving the partial differential equation is transformed to an unconstrained minimization problem. The method is extremely easy to implement and is suitable for obtaining an approximate solution in a short period of time. The technique is illustrated with the aid of two numerical examples.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 217-225 
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    Notes: An efficient algorithm for consideration of axial and cyclic symmetry in the boundary-element method is presented. The appropriate transformation relationships was derived. The algorithm is then implemented in a boundary element program for the analysis of 2D elastostatic problems. Through analysis of typical problems the validity of the algorithm and its implementation is verified. A high level of accuracy and substantial reduction in computer time and storage was achieved.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 227-235 
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    Topics: Mathematics , Technology
    Notes: The diffusion of oxygen into an absorbing medium as an example of an implicit moving boundary problem has been dealt with by a number of authors using various numerical techniques, and, where appropriate, approximate analytical expressions. To evaluate the time for complete absorption, extrapolation is usually employed. An unconditionally stable explicit numerical scheme that avoids the limitations of such methods is presented and tested herein. Unlike existing schemes this method is fully numerical; it avoids the large array size, generally required for existing methods, by using a variable-length time step. The time for complete absorption emerges from the final step in the normal computing procedure with no recourse to extrapolation. Furthermore, owing to the implicit condition prevailing at the moving boundary, no iterations are needed to evaluate the time step required for the moving boundary to move a single space increment. The numerical results obtained compare very favourably with those due to earlier authors.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 237-248 
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    Notes: In the paper we have developed a new formulation for solution of structural-acoustic coupling problems by boundary elements using the multiple reciprocity method. It is assumed that the structure is composed of plate components and is excited by the external or the internal noise source. The efficiency of the proposed formulation becomes especially remarkable if the boundary-value problem is to be solved repeatedly for different values of frequency. The accuracy of the numerical computations has been compared with the analytical solution in a test example.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 257-265 
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    Notes: Techniques for stress- and strain-controlled in situ homogenization of inelastic periodic composites are presented. The results of homogenization computations on a specific elastoplastic composite solid are then employed to validate the form of an orthotropic elastoplasticity model with a tensorial kinematic hardening law.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 249-255 
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    Notes: An algorithm for evaluation of friction in general contact-impact interfaces is described. The algorithm is based on an explicit finite-element method. Coulomb's friction law is assumed. The defence node algorithm is used such that the sticking condition can be imposed with the Lagrange multiplier method even in explicit dynamic analysis. The algorithm is supposed to be applicable in general situations, including large deformations of the contact-impact bodies and large relative sliding between the contact-impact boundaries. Numerical results are presented to demonstrate the performance of the algorithm.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 275-277 
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    Communications in Numerical Methods in Engineering 10 (1994), S. 267-273 
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    Notes: A generalization of the r(1-m)/m strain singularity of higher-order isoparametric elements is presented. It is shown that, by variable placement of the side nodes between their original and singular positions, the point of singularity sensed by the element can be controlled. The transition elements have a strain singularity outside their domain. The singular and non-singular elements are elements are special cases of the general mapping. The transition elements, together with the singular isoparametric elements, can be used for solving crack problems.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 279-290 
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    Notes: In the design of members with flaws, it is necessary to keep the stress intensity factor K of any sharp crack below the fracture toughness Kcr of the materials. Stress-intensity factor equations for the more common basic specimen geometries and various loading conditions are available in the literature. The application of these equations to complex structures involves geometric problems such as the identification of the outline of each member and the sizing of the equivalent specimen for each flaw. The paper gives a response to such difficulties.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 303-312 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A simple, yet storage-effective ‘linear’ programming code is given. The assumption of non-negative variables is bypassed without increasing the size of the problem. Furthermore, the objective is allowed to be summed over not just linear, but also concave, functions. A specific truss topology optimization example is shown.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 291-296 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We propose in this paper a nine-point, fourth-order difference method for the numerical solution of the quasilinear Poisson equation \documentclass{article}\pagestyle{empty}\begin{document}$$ Au_{zz} + \frac{1}{r}u_r + Bu_{rr} = f\left({r,z,u,u_r,u_z} \right) $$\end{document} with appropriate boundary conditions. The method is based on five evaluations of f. The numerical results of four problems obtained using this method are listed. The results demonstrate the fourth-order accuracy of the method.
    Additional Material: 4 Tab.
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  • 87
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    Communications in Numerical Methods in Engineering 10 (1994), S. 297-302 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Singularly perturbed second-order elliptic equations with boundary layers are considered. These may be considered as model problems for the advection of some quantity such as heat or a pollutant in a flow field or as linear approximations to the Navier-Stokes equations for fluid flow. Numerical methods composed of central-difference operators on special piece-wise-uniform meshes are constructed for the above problems. Numerical results are obtained which show that these methods give approximate solutions with error estimates that are independent of the singular perturbation parameter. An open theoretical problem is posed.
    Additional Material: 2 Ill.
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  • 88
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    Communications in Numerical Methods in Engineering 10 (1994), S. 313-320 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions.
    Additional Material: 7 Ill.
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  • 89
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    Communications in Numerical Methods in Engineering 10 (1994), S. 321-331 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach to developing serendipity quadrilateral infinite elements is presented. Using these elements universal matrices for quasiharmonic equation are developed. For a particular member of the family these matrices are independent of the size and shape of the element. Using these matrices the element stiffness matrix can be generated in a simpler manner by taking into account the size and shape of the element.
    Additional Material: 4 Ill.
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  • 90
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    Communications in Numerical Methods in Engineering 10 (1994), S. 333-338 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new global secant relaxation (GSR)-method-based improvement procedure is used to improve the overall convergency performance of the modified Newton-Raphson iteration in carrying out the solution of discrete systems resulting from the finite-element discretization of a certain class of structural problems involving non-linear deformation behaviour.
    Additional Material: 4 Ill.
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  • 91
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    Communications in Numerical Methods in Engineering 10 (1994), S. 339-353 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Theoretical and experimental analysis of free-surface electrohydrodynamic flow is fragmented and incomplete. Simulation studies of this phenomenon are further limited by the inherent complexities in the modelling process. In this note a mathematical model is developed to analyse free-surface electrohydrodynamic flow in two dimensions, and preliminary results of the simulation are described. The configurations examined include electrified conducting surfaces, the dielectrophoretic forces, and a conducting jet. The simulation is compared with analytical results in the first two investigations and is shown to be quite accurate. In the last simulation it is demonstrated that in the initial formation of a conducting jet, a 10 per cent increase in applied voltage results in about a 10 per cent increase in fluid velocity.
    Additional Material: 7 Ill.
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  • 92
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    Communications in Numerical Methods in Engineering 10 (1994), S. 355-357 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 93
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    Communications in Numerical Methods in Engineering 10 (1994), S. 359-360 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 94
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    Communications in Numerical Methods in Engineering 10 (1994) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 95
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    Communications in Numerical Methods in Engineering 10 (1994), S. 361-371 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dual reciprocity boundary element method, first proposed by Nardini and Brebbia (1982, 1985), is a powerful technique for solving elliptic partial differential equations. Adopting this approach, a singular volume integral, which needs to be evaluated with a traditional boundary element method, can be converted into a boundary integral. However, when the governing equation is of a certain type, this conversion fails due to the singularities being introduced inside the physical domain and on the boundary arising by differentiating distance functions. We avoid these artificially created singularities by constructing a transformation which leads to improved numerical results.
    Additional Material: 5 Ill.
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  • 96
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    Communications in Numerical Methods in Engineering 10 (1994), S. 373-384 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper demonstrates an approach to generate three-dimensional boundary-fitted computational meshes efficiently. One basic idea underlying the present study is that often similar geometries have to be meshed, and therefore an efficient mesh-adaption method, which allows adaptation of the topological mesh to the specific geometry, would be more efficient than generating all new meshes. On the other hand the mesh generation for Cartesian topologies has been shown to be a very simple task. It can be executed by connecting and removing brick elements to a basic cube. In connection with a so-called ‘Macro Command Language’, a high degree of automation can be reached when adapting topologically defined meshes to a surface. Furthermore, a high mesh quality has proved to be the key to good simulation results. During the mesh generation it is important to provide the possibility of modifiying the mesh quality and also the mesh density at any time of the meshing process. Using this generation method the meshing time is reduced - e.g. a computational mesh for a two-valve cylinder head can be generated within a few hours.
    Additional Material: 11 Ill.
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  • 97
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    Communications in Numerical Methods in Engineering 10 (1994), S. 393-401 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we present numerical experiments made to investigate the behaviour of the Newmark time-stepping scheme applied to non-linear dynamic systems. Our attention is focused on the instability and chaos in the Newmark scheme when it is applied to the equation ü + P(u) = 0, representing a non-linear elastic spring. Some unusual modes of behaviour, which are of substantial interest, have been observed. In the first case, a stable but chaotic solution is found. In the second case, while a stable solution is obtained with a certain time step, an unstable solution is found by decreasing the time step. In the third case, instability is triggered by neglecting the initial acceleration. A simple modification of the Newmark scheme is proposed which keeps the energy constant for the equation ü + P(u) = 0 and thereby guarantees unconditional stability. Numerical examples in support of such an energy-conserving scheme are presented.
    Additional Material: 6 Ill.
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  • 98
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    Communications in Numerical Methods in Engineering 10 (1994), S. 385-392 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical problem which features prominently in the implementation of the boundary-element method (BEM) for the solution of heat-conduction problems arises from double-valued heat fluxes at boundary corners. This problem is readily dealt with by explicitly treating nodal heat fluxes as double-valued prior to assembly of the nodal equations. This formulation is very flexible as it also permits imposing discontinuous thermal conditions at any boundary node. However, at corner nodes where temperature only is prescribed, the scheme leads to two unknowns, while only one nodal BEM equation is available there. An additional equation which closely follows the previous work of Walker and Fenner is derived for these nodes, and this provides sufficient information to resolve the upstream and downstream values of the heat flux at the temperature node. The additional equation is general, is free of heuristic constraints, and is applicable through the wide range of acute, shallow, obtuse and re-entrant angles encountered in practice. Numerical examples are used to compare the present method with the Walker and Fenner approach and with analytical solutions. Results indicate both improved accuracy and generality, thus validating the present method.
    Additional Material: 3 Ill.
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  • 99
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    Communications in Numerical Methods in Engineering 10 (1994), S. 403-412 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive refinement/derefinement algorithm of nested meshes is presented. Some definitions are introduced. The main properties of the derefinement algorithm are remarked upon and its efficiency is shown through two numerical examples: a time-dependent convection-diffusion problems with dominant convection and a quasistationary problem.
    Additional Material: 5 Ill.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 425-426 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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