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Boniface Nkemzi 《Mathematical Methods in the Applied Sciences》2006,29(9):1053-1080
This paper is concerned with the structure of the singular and regular parts of the solution of time‐harmonic Maxwell's equations in polygonal plane domains and their effective numerical treatment. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that the solution of the boundary value problem does not belong locally to H2 when the boundary of the domain has non‐acute angles. A splitting of the solution into a regular part belonging to the space H2, and an explicitly described singular part is presented. For the numerical treatment of the boundary value problem, we propose a finite element discretization which combines local mesh grading and the singular field methods and derive a priori error estimates that show optimal convergence as known for the classical finite element method for problems with regular solutions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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Ian K. Boddy J. Boniface Richard C. Cambie Peter A. Craw David S. Larsen Hamish McDonald Peter S. Rutledge Paul D. Woodgate 《Tetrahedron letters》1982,23(42):4407-4408
Gentle heating of allyloxyanthraquinones with sodium dithionite in dimethylformanide - water effects a rapid and controlled rearrangement to give high yields of 2-allyanthraquinones. 相似文献
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Eu8(NCN)4.95I6.10 is the first compound with discrete tritetrahedral Eu8 clusters which are interconnected by coordinating NCN2- carbodiimide anions on their triangular faces to form separated layers, the latter being bridged by iodide and carbodiimide anions. 相似文献
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Eunsoo Lee Hyounmyung Park Hyunkeun Joo Boniface P. T. Fokwa 《Angewandte Chemie (International ed. in English)》2020,59(29):11774-11778
Transition‐metal borides (TMBs) have recently attracted attention as excellent hydrogen evolution (HER) electrocatalysts in bulk crystalline materials. Herein, we show for the first time that VB and V3B4 have high electrocatalytic HER activity. Furthermore, we show that the HER activity (in 0.5 m H2SO4) increases with increasing boron chain condensation in vanadium borides: Using a ?23 mV overpotential decrement derived from ?0.296 mV (for VB at ?10 mA cm?2 current density) and ?0.273 mV (for V3B4) we accurately predict the overpotential of VB2 (?0.204 mV) as well as that of unstudied V2B3 (?0.250 mV) and hypothetical “V5B8” (?0.227 mV). We then derived an exponential equation that predicts the overpotentials of known and hypothetical VxBy phases containing at least a boron chain. These results provide a direct correlation between crystal structure and HER activity, thus paving the way for the design of even better electrocatalytic materials through structure–activity relationships. 相似文献
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Ludwig Stork Xiaohui Liu Boniface P. T. Fokwa Richard Dronskowski 《Acta Crystallographica. Section C, Structural Chemistry》2009,65(8):i54-i56
Green single crystals of trans‐tetraamminedibromidochromium(III) trans‐diamminetetrabromidochromate(III), [CrBr2(NH3)4][CrBr4(NH3)2], are found to contain two symmetry‐independent sixfold coordinated CrIII cations on centres of inversion. The structure is composed of octahedral trans‐[CrBr2(NH3)4]+ cations and octahedral trans‐[CrBr4(NH3)2]− anions, and adopts a distorted CsCl‐type lattice. The cations and anions are linked by N—H...Br interactions. This is the first example in which both ions are mixed ammine–bromide CrIII complexes. 相似文献
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Powder samples and single crystals of the borides M0.5Ru6.5B3 (M = Cr, Mn, Co, Ni) were synthesized by arc‐melting the elements in a water‐cooled copper crucible under argon. The new phases were structurally characterized by single‐crystal and powder X‐ray diffraction as well as EDX‐Analyses. They crystallize in the hexagonal Th7Fe3 structure type (space group P63mc, no. 186, Z = 2) and a pronounced site preferential M/Ru substitution is observed. Magnetic properties of the compounds were investigated and Pauli paramagnetism was observed in all cases. However, a strong temperature dependency is subsequently observed in Mn0.5Ru6.5B3 below 250 K, but no hint of magnetic ordering was found. 相似文献
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Boniface Nkemzi Michael Jung 《Numerical Methods for Partial Differential Equations》2021,37(1):836-853
Solutions of boundary value problems in three‐dimensional domains with edges may exhibit singularities which are known to influence both the accuracy of the finite element solutions and the rate of convergence in the error estimates. This paper considers boundary value problems for the Poisson equation on typical domains Ω ? ?3 with edge singularities and presents, on the one hand, explicit computational formulas for the flux intensity functions. On the other hand, it proposes and analyzes a nonconforming finite element method on regular meshes for the efficient treatment of the singularities. The novelty of the present method is the use of the explicit formulas for the flux intensity functions in defining a postprocessing procedure in the finite element approximation of the solution. A priori error estimates in H1(Ω) show that the present algorithm exhibits the same rate of convergence as it is known for problems with regular solutions. 相似文献
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Crystal and molecular structures of the title compound have been determined from a three-dimensional X-ray analysis using diffractometer data. The crystals are monoclinic, space group P21/c, with Z = 4 in a unit cell of dimensions a = 10.5876(9), b = 31.518(10), c = 16.2164(5) Å, β = 92.521(1)°. The observed and calculated densities are 1.38 and 1.374 g cm-1 respectively. The crystals decompose under X-rays, and three crystals were required to complete data collection. The structure was solved and refined by convetional methods to final residuals R and Rw of 0.087 and 0.107 respectively.The crystals contain monomeric cations, and BF4 anions. The iridium atom is in a distorted trigonal bipyramidal environment consisting of the two sulphur atoms (one axial, one equatorial) of a bidentate triphenylphosphoniodi-thiocarboxylate ligand, two triphenylphosphine groups (equatorial) and the carbonyl ligand (axial). The non-equivalent Ir-s distances are 2.377 and 2.307(5) Å, the Ir-P distances are 2.334, 2.331(5) Å. Within the zwitterion, the C-S distances are 1.66 and 1.70(2) Å, while P-C is 1.78(2) Å. The condensation of PPh3 and CS2 to form the PH3P+-CS2 zwitterion is in contrast to that predicted previously.It is probable that the other complexes of iridium and rhodium prepared in a similar manner [2] should now be reformulated as containing Ph3P+-CS2- ligands. 相似文献