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Least-squares Procedure (least-square + procedure)
Selected AbstractsAccurate prediction of thermodynamic properties of alkyl peroxides by combining density functional theory calculation with least-square calibrationJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 7 2009Cun-Xi Liu Abstract Owing to the significance in kinetic modeling of the oxidation and combustion mechanisms of hydrocarbons, a fast and relatively accurate method was developed for the prediction of ,fH of alkyl peroxides. By this method, a raw ,fH value was calculated from the optimized geometry and vibration frequencies at B3LYP/6-31G(d,p) level and then an accurate ,fH value was obtained by a least-square procedure. The least-square procedure is a six-parameter linear equation and is validated by a leave-one out technique, giving a cross-validation squared correlation coefficient q2 of 0.97 and a squared correlation coefficient of 0.98 for the final model. Calculated results demonstrated that the least-square calibration leads to a remarkable reduction of error and to the accurate ,fH values within the chemical accuracy of 8 kJ mol,1 except (CH3)2CHCH2CH2CH2OOH which has an error of 8.69 kJ mol,1. Comparison of the results by CBS-Q, CBS-QB3, G2, and G3 revealed that B3LYP/6-31G(d,p) in combination with a least-square calibration is reliable in the accurate prediction of the standard enthalpies of formation for alkyl peroxides. Standard entropies at 298 K and heat capacities in the temperature range of 300,1500 K for alkyl peroxides were also calculated using the rigid rotor-harmonic oscillator approximation. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009 [source] Modeling the hepatitis C virus epidemic in France using the temporal pattern of hepatocellular carcinoma deathsHEPATOLOGY, Issue 3 2002Jenny Griffiths Deuffic et al. developed a compartmentalized model that characterized the evolution and spread of the hepatitis C virus (HCV) within France. There were various parameters defining the age- and sex-dependent transition probabilities between chronic hepatitis and cirrhosis in need of determination to completely specify their model. These were estimated by means of a weighted least-squares procedure that was executed numerically. The objective function used was based on the distribution of the age at death from hepatocellular carcinoma (HCC) rather than the temporal pattern of deaths due to HCC from 1979 to 1995. In this report, we investigate the impact of using an objective function based on the temporal pattern of deaths. We show that the dynamics of the epidemic can be quite different, in particular, short-term prediction of HCC deaths by HCV infection and times to death from onset of disease. [source] Comparison of three second-order accurate reconstruction schemes for 2D Euler and Navier,Stokes compressible flows on unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2001N. P. C. Marques Abstract This paper reports an intercomparison of three second-order accurate reconstruction schemes to predict 2D steady-state compressible Euler and Navier,Stokes flows on unstructured meshes. The schemes comprise one monotone slope limiter (Barth and Jespersen, A1AA Paper 89-0366, 1989) and two approximately monotone methods: the slope limiter due to Venkatakrishnan and a data-dependent weighting least-squares procedure (Gooch, Journal of Computational Physics, 1997; 133:6,17). In addition to the 1D scalar wave problem, comparisons were performed under two inviscid test cases: a supersonic 10° ramp and a supersonic bump; and two viscous laminar compressible flow cases: the Blasius boundary layer and a double-throated nozzle. The data-dependent oscillatory behaviour is found to be dependent on a user-supplied constant. The three schemes are compared in terms of accuracy and computational efficiency. The results show that the data-dependent procedure always returns a numerical steady-state solution, more accurate than the ones returned by the slope limiters. Its use for Navier,Stokes flow calculations is recommended. Copyright © 2001 John Wiley & Sons, Ltd. [source] On accurate boundary conditions for a shape sensitivity equation methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2006R. Duvigneau Abstract This paper studies the application of the continuous sensitivity equation method (CSEM) for the Navier,Stokes equations in the particular case of shape parameters. Boundary conditions for shape parameters involve flow derivatives at the boundary. Thus, accurate flow gradients are critical to the success of the CSEM. A new approach is presented to extract accurate flow derivatives at the boundary. High order Taylor series expansions are used on layered patches in conjunction with a constrained least-squares procedure to evaluate accurate first and second derivatives of the flow variables at the boundary, required for Dirichlet and Neumann sensitivity boundary conditions. The flow and sensitivity fields are solved using an adaptive finite-element method. The proposed methodology is first verified on a problem with a closed form solution obtained by the Method of Manufactured Solutions. The ability of the proposed method to provide accurate sensitivity fields for realistic problems is then demonstrated. The flow and sensitivity fields for a NACA 0012 airfoil are used for fast evaluation of the nearby flow over an airfoil of different thickness (NACA 0015). Copyright © 2005 John Wiley & Sons, Ltd. [source] Influence of response factors on determining equilibrium association constants of non-covalent complexes by electrospray ionization mass spectrometryJOURNAL OF MASS SPECTROMETRY (INCORP BIOLOGICAL MASS SPECTROMETRY), Issue 5 2003Valérie Gabelica Abstract A method for determining the equilibrium association constant of a complexation reaction A + B , AB by electrospray ionization mass spectrometry is described. The method consists in measuring the relative intensities of the peaks corresponding to A and to AB in equimolar A,B solutions at different concentrations C0. The results are fitted by a non-linear least-squares procedure, with the two variable parameters being the equilibrium association constant Ka and a factor R, defined by I(AB)/I(A) = R × [AB]/[A]. The factor R is the ratio between the response factors of AB and A, and corrects for the relative electrospray responses of the complex and the free substrate A, mass discrimination of instrumental origin and/or moderate in-source dissociation. The method is illustrated with the following two systems: complexes between a double-stranded 12-base pair oligonucleotide and minor groove binders, and cyclodextrin complexes with ,,,-dicarboxylic acids. For the oligonucleotide complexes, it is found that the response of the complex is not dramatically different to the response of the free oligonucleotide duplex, as the double helix conformation is disturbed by the drug only to a minor extent. In the case of cyclodextrin complexes, these complexes were found to have a much higher response than free cyclodextrin. This may be due to the fact that cyclodextrin is neutral in solution, whereas the complex is charged, but it can also stem from the fact that a significant proportion of the complex is in a non-inclusion geometry. The present method requires the exact determination of the concentrations of the reactants and is applicable to 1 : 1 complexes. Copyright © 2003 John Wiley & Sons, Ltd. [source] Scaling of one-shot oscillation images with a reference data setJOURNAL OF SYNCHROTRON RADIATION, Issue 1 2004Kunio Hirata By combining a least-squares procedure with the program MOSFLM, a program SCLONE has been developed which processes diffraction images that do not contain serial oscillation images and may have a few or no full reflections. After each image was processed by MOSFLM, the partialities and structure amplitudes of the reflections were estimated using a least-squares method to refine the scaling factor, the relative temperature factor, the mosaic spread, cell constants, and missetting angles for each independent image. The SCLONE calculation significantly improved the quality of the intensities from the reflections obtained by the initial MOSFLM calculation and crystal structural refinement confirmed the improvement. The SCLONE calculation indicated that the reflection of the present crystal had a rocking curve that was steeper at the middle of the profile and more gradual at both ends of the profile than that assumed in the program MOSFLM. [source] Crystal structure of a ternary mononuclear copper (II) complex: 4-chloro-3-methyl-6[(N-2-picolyl)-1,-iminomethyl]phenolato copper(II)perchlorateCRYSTAL RESEARCH AND TECHNOLOGY, Issue 5 2006S. M. Malathy Sony Abstract The complex crystallizes in monoclinic space group P21/n with unit cell parameters a = 7.295(4), b = 19.627(5), c = 12.770(4) Å, , = 101.25(4)º, V = 1793.2(12) Å3, Z = 4, , = 1.684 Mg/m3 at T = 293(2)K. The structure was solved by Patterson method and refined by full-matrix least-squares procedures to final R = 0.0387 using 2906 observed reflections. The asymmetric unit of the complex contains a mononuclear tridentate ligand, a perchlorate group and a methanol molecule. The compound crystallizes as parallel layers of polymeric complex bridged through perchloarate groups. The molecular CuN2OO,O,,2 chromophore involves an elongated rhombic octahedral structure and the Cu-ligand bond shows greater disparity. The five-membered chelate ring and the pyridine ring lie in the same plane while the six membered chelate ring assumes sofa conformation. A strong O-H,O inter molecular interaction plays a key role in the formation of dimer along b-axis. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Crystal structures of two acridinedione derivativesCRYSTAL RESEARCH AND TECHNOLOGY, Issue 3 2005K. Palani Abstract The crystal structures of two acridinedione derivatives, namely 10-(3,4-Dichloro-5-hydroxyphenyl)-3,4,6,7,9,10-hexahydro-1,8(2H, 5H) acridinedione (DHHA, CCDC 206440) and 10-(3,5-Dihydroxy-4-nitrophenyl)-3,4,6,7,9,10-hexahydro-1,8(2H, 5H) acridinedione (DHNA, CCDC206441) are reported here. Both the structures were solved by direct methods and refined by full-matrix least-squares procedures to final R- values of 0.073 and 0.076 respectively. In both the crystal structures, the central pyridine ring in the acridinedione moiety tends to be planar while the outer two rings adopt half-chair (sofa) conformation. The buckling angles 2.2(2)° and 11.0(1)° for DHHA and DHNA show the degree of planarity of the acridinedione moiety. The C-H,O types of hydrogen bonds help to stabilize the molecules in the unit cell in addition to van der Waals forces. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Structure and conformation of a nickel complex: {2-Hydroxo-3-piperidine-1-yl-methyl-N,N,(bis-5-bromobenzylpropylenediimine)nickel(II)perchlorate}CRYSTAL RESEARCH AND TECHNOLOGY, Issue 2 2004S. M. Malathy Sony Abstract The title compound, a nickel complex [C23H26N3O2Br2Ni.(ClO4)] (CCDC 199520) crystallizes in triclinic space group P with the cell parameters a = 10.2560(4), b = 10.8231(4), c = 12.0888(5)Å, , = 99.404(1), , = 99.780(1), , = 92.252(1)° and V = 1301.49(9)Å3. The structure was solved by Patterson method and refined by full-matrix least-squares procedures to a final R = 0.0497 using 6287 observed reflections. In the complex, the piperidine ring takes chair conformation and the geometry around the Ni ion is slightly distorted square planar. The dihedral angle between the planes [N-Ni-N and O-Ni-O] is 9.4(1)°. The chelate ring containing both the nitrogen atoms adopts twisted boat conformation. The molecules in the crystal are stabilized by N-H,O and C-H,O types of hydrogen bonds in addition to a C-H,, interaction. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Crystal structure of ,-phenoxo bridged dicopper complex: {N-[(2-hydroxylato-5-methyl)benzyl-(2,-hydroxylato-3,,5,-dimethylbenzyl)]ethyl amine dicopper(II)}CRYSTAL RESEARCH AND TECHNOLOGY, Issue 12 2002S. M. Malathy Sony Abstract The title compound crystallizes in monoclinic space group C2/c with cell parameters a = 21.404(2), b = 13.962(1), c = 17.917(1)Å, , = 124.394(2)°, V = 4418.3(6)Å3, Z = 8, Dcal = 1.193Mg/m3 and T = 293 K. The structure was solved by Patterson method and refined by full-matrix least-squares procedures to final R = 0.0882 using 5253 observed reflections. The tetra coordinated copper atom have a slight distorted square planar geometry with the Cu-Cu distance of 2.987(1)Å. The two six membered rings containing copper atom assume distorted sofa conformation. C-H,, and C-H,O type of intermolecular interactions play a role in stabilizing the crystal packing in addition to van der Waals forces. [source] | |||||||||||||