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High Order (high + order)
Selected AbstractsConvergence radii of the polarization expansion of intermolecular potentialsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2009William H. Adams Abstract A new method is presented to evaluate convergence radii of the polarization expansion of interaction energies for pairs of atoms or molecules. The method is based on an analysis of the variation of the perturbed state vector as a function of the coupling constant , and does not require a calculation of perturbation corrections to high order. The convergence radii at infinite interatomic/intermolecular distances R, as well as a remarkably accurate representation of the R dependence of the convergence radii are obtained from simple calculations involving only monomer wave functions. For the interaction of the lithium and hydrogen atoms, the obtained convergence radii agree well with those obtained previously from the large-order calculations of Patkowski et al. (Patkowski et al., J Chem Phys, 2002, 117, 5124), but are expected to be considerably more accurate. Rigorous upper bounds and reasonable approximations to the convergence radii at R = , are obtained for the pairs of lithium, beryllium, boron, neon, and sodium atoms, as well as for the dimer consisting of two LiH molecules. For all the systems studied, the convergence radii are significantly smaller than the unity and rapidly decrease with the increase of the nuclear charge. It is hoped that the results of this investigation will help to analyze and eventually to compute the convergence radii of the symmetry-adapted perturbation theories which utilize the same partitioning of the Hamiltonian as the polarization expansion. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Unavoidable parallel minors of 4-connected graphsJOURNAL OF GRAPH THEORY, Issue 4 2009Carolyn Chun A parallel minor is obtained from a graph by any sequence of edge contractions and parallel edge deletions. We prove that, for any positive integer k, every internally 4-connected graph of sufficiently high order contains a parallel minor isomorphic to a variation of K4,k with a complete graph on the vertices of degree k, the k -partition triple fan with a complete graph on the vertices of degree k, the k -spoke double wheel, the k -spoke double wheel with axle, the (2k+1)-rung Möbius zigzag ladder, the (2k)-rung zigzag ladder, or Kk. We also find the unavoidable parallel minors of 1-, 2-, and 3-connected graphs. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 313-326, 2009 [source] Nondipolar Content of T Wave Derived from a Myocardial Source Simulation with Increased Repolarization InhomogeneityANNALS OF NONINVASIVE ELECTROCARDIOLOGY, Issue 2 2009Milos Kesek M.D., Ph.D. Background: Several conditions with repolarization disturbances are associated with increased level of nondipolar components of the T wave. The nondipolar content has been proposed as a measure of repolarization inhomogeneity. This computer simulation study examines the link between increased nondipolar components and increased repolarization inhomogeneity in an established model. Methods: The simulation was performed with Ecgsim software that uses the equivalent double-layer source model. In the model, the shape of transmembrane potential is derived from biological recordings. Increased repolarization inhomogeneity was simulated globally by increasing the variance in action potential duration and locally by introducing changes mimicking acute myocardial infarction. We synthesized surface ECG recordings with 12, 18, and 300 leads. The T-wave residue was calculated by singular value decomposition. The study examined the effects of the number of ECG leads, changes in definition of end of T wave and random noise added to the signal. Results: Normal myocardial source gave a low level of nondipolar content. Increased nondipolar content was observed in the two types of increased repolarization inhomogeneity. Noise gave a large increase in the nondipolar content. The sensitivity of the result to noise increased when a higher number of principal components were used in the computation. Conclusions: The nondipolar content of the T wave was associated with repolarization inhomogeneity in the computer model. The measure was very sensitive to noise, especially when principal components of high order were included in the computations. Increased number of ECG leads resulted in an increased signal-to-noise ratio. [source] 4432: Comparison of the two domains of visual optics: the aberrometric domain and the straylight domainACTA OPHTHALMOLOGICA, Issue 2010TJTP VAN DEN BERG Purpose The ocular point-spread-function defines the functional problem originating from optical defects in the eye. Aberrations as well as scatter degrade the psf. How do these two types of defect differ with respect to their effect on the psf, and on functional measures? Methods Literature models for different aspects of the optical irregularities in the eye media, in particular Thibos et al. JOSA A 2002 for the aberration structure and Van den Berg et al. VR 1999 for small particle scattering, were used to delineate their effects on the psf. The Thibos et al. model was extrapolated to allow inclusion of the high orders of aberration not normally included in aberrometry, but potentially visible with double pass. With respect to the visual function counterparts, straylight (C-Quant from Oculus) outcomes were compared to visual acuity and contrast sensitivity in 2400 subjects. Results As a reference the full scale psf standard model of Vos et al. CIE 1999 was used. The modeled aberration structures of the eye proved to predict the central part of the psf up till about 0.3 degrees if extreme high orders were included. For angles >1 degree predicted values were far below the actual values of the psf. Small particle scattering was essential to predict the psf for angles above 1 degree. Conclusion In the assessment of disturbances to the optical media two domains must be discriminated: the aberration domain and the small particle domain, with corresponding parts (small angle vs large angle) to the psf. Straylight typically originates from irregularities of size 10 micrometer and below, as opposed to aberrations originating from refractile humps and bumps extending over 100 micrometer and more. Straylight has independent value. [source] | ||||||||||