In this paper, combining some special eigenvalue inequalities of matrix’s product and sum with the equivalent form of the continuous coupled algebraic Riccati equation (CCARE), we construct linear inequalities. Then,...
In this paper, combining some special eigenvalue inequalities of matrix’s product and sum with the equivalent form of the continuous coupled algebraic Riccati equation (CCARE), we construct linear inequalities. Then, in terms of the properties of M-matrix and its inverse matrix, through solving the derived linear inequalities, we offer new upper matrix bounds for the solution of the CCARE, which improve some of the recent results. Finally, we present a corresponding numerical example to show the effectiveness of the given results.
Two-level additive preconditioners are presented for edge element discretizations of time-harmonic Maxwell equations. The key is to construct a special “coarse mesh” space, which adds the kernel of the curl -operato...
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Two-level additive preconditioners are presented for edge element discretizations of time-harmonic Maxwell equations. The key is to construct a special “coarse mesh” space, which adds the kernel of the curl -operator in a fine space to a coarse mesh space, to solve the original problem, and then uses the fine mesh space to solve the H ( curl ) -elliptic problem. It is shown that the generalized minimal residual (GMRES) method applied to the preconditioned system converges uniformly provided that the coarsest mesh size is reasonably small (but independent of the fine mesh size) and the parameter for the “coarse mesh” space solver is sufficiently large. Numerical experiments show the efficiency of the proposed approach.
We discuss the cubic spline collocation method with two parameters for solving the initial value problems (IVPs) of fractional differential equations (FDEs). Some results of the local truncation error, the convergence...
In this paper,a new numerical algorithm for solving the time fractional Fokker-Planck equation is *** analysis of local truncation error and the stability of this method are *** analysis and numerical experiments show...
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In this paper,a new numerical algorithm for solving the time fractional Fokker-Planck equation is *** analysis of local truncation error and the stability of this method are *** analysis and numerical experiments show that the proposed method has higher order of accuracy for solving the time fractional Fokker-Planck equation.
We propose some new weighted averaging methods for gradient recovery,and present analytical and numerical investigation on the performance of these weighted averaging *** is shown analytically that the harmonic averag...
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We propose some new weighted averaging methods for gradient recovery,and present analytical and numerical investigation on the performance of these weighted averaging *** is shown analytically that the harmonic averaging yields a superconvergent gradient for any mesh in one-dimension and the rectangular mesh in *** results indicate that these new weighted averaging methods are better recovered gradient approaches than the simple averaging and geometry averaging methods under triangular mesh.
Two anti-2,4-bis（3-R-phenyl）pentane-2,4-diols （1, R = Me; 2, R = SMe） have been synthesized and were characterized by X-ray diffraction, IR and UV spectra. X-ray diffractions indicate that intra- and intermolecula...
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Two anti-2,4-bis（3-R-phenyl）pentane-2,4-diols （1, R = Me; 2, R = SMe） have been synthesized and were characterized by X-ray diffraction, IR and UV spectra. X-ray diffractions indicate that intra- and intermolecular hydrogen bonding interactions form one-dimensional （ID） ribbons. The adjacent infinite I D ribbons result in 3D supramolecular structures. The dihedral angles between every two benzene rings in the two diols are 31.61（12） and 31.80（7）°, respectively. UV absorption spectra of the title compounds were recorded in MeOH, C2H5OH, CH3CN, n-BuOH and cyclohexane solvents with different dielectric constants.
2,4-diphenylpentane- and 2,4-di-p-tolylpentane-2,4-diols were investigated employing experimental and density functional theory （DFT） method at B3LYP/6-31G （d） level. The structure of syn-2,4-di-p-tolylpentane-2,4...
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2,4-diphenylpentane- and 2,4-di-p-tolylpentane-2,4-diols were investigated employing experimental and density functional theory （DFT） method at B3LYP/6-31G （d） level. The structure of syn-2,4-di-p-tolylpentane-2,4-diol （2b） was characterized by X-ray diffraction and compared with the crystal structures of anti- and syn-2,4-diphenylpentane-2,4-diols （la and lb）. X-ray diffraction indicates that inter and intra-molecular hydrogen bonds are formed in the crystal structures. There is n-n staking interaction in lb and 2b. Good linear correlations and similar results are found between the experimental 1H and 13C NMR chemical shifts （6~exp） and GIAO （Gauge Independent Atomic Orbital） method calculated magnetic isotropic shielding tensors （acalc）. HOMO and LUMO molecular orbitals were calculated at the same levels with the different results. UV-vis absorption spectra of the compounds were recorded in EtOH, MeCN, n-BuOH and cyclohexane with different dielectric constants. It is found that the solvent effect is obvious when e is 24.85（EtOH）, 35.69（MeCN） and it is weak when e is decreased to 17.33（n-BuOH）, 1.18 （cyclohexane）.
High quality mesh plays an important role for finite element methods in science computation and numerical *** the mesh quality is good or not,to some extent,it determines the calculation results of the accuracy and **...
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High quality mesh plays an important role for finite element methods in science computation and numerical *** the mesh quality is good or not,to some extent,it determines the calculation results of the accuracy and *** from classic Lloyd iteration algorithm which is convergent slowly,a novel accelerated scheme was presented,which consists of two core parts:mesh points replacement and local edges Delaunay *** using it,almost all the equilateral triangular meshes can be generated based on centroidal Voronoi tessellation(CVT).Numerical tests show that it is significantly effective with time consuming decreasing by 40%.Compared with other two types of regular mesh generation methods,CVT mesh demonstrates that higher geometric average quality increases over 0.99.
It is well known that the aggregation of amyloid-β peptide (Aβ) induced by Cu2+ is related to incubation time, solution pH, and temperature. In this work, the aggregation of Aβ1–42 in the presence of Cu2+ under ac...
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It is well known that the aggregation of amyloid-β peptide (Aβ) induced by Cu2+ is related to incubation time, solution pH, and temperature. In this work, the aggregation of Aβ1–42 in the presence of Cu2+ under acidic conditions was studied at different incubation time and temperature (e.g. 25 and 37°C). Incubation temperature, pH, and the presence of Cu2+ in Aβ solution were confirmed to alter the morphology of aggregation (fibrils or amorphous aggregates), and the morphology is pivotal for Aβ neurotoxicity and Alzheimer disease (AD) development. The results of atomic force microscopy (AFM) indicated that the formation of Aβ fibrous morphology is preferred at lower pH, but Cu2+ induced the formation of amorphous aggregates. The aggregation rate of Aβ was increased with the elevation of temperature. These results were further confirmed by fluorescence spectroscopy and circular dichroism spectroscopy and it was found that the formation of β-sheet structure was inhibited by Cu2+ binding to Aβ. The result was consistent with AFM observation and the fibrillation process was restrained. We believe that the local charge state in hydrophilic domain of Aβ may play a dominant role in the aggregate morphology due to the strong steric hindrance. This research will be valuable for understanding of Aβ toxicity in AD.
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