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zeroth-order
The accuracy of hyperfine integrals in relativistic NMR computations based on the zeroth-order regular approximation
      
The accuracy of the hyperfine integrals obtained in relativistic NMR computations based on the zeroth-order regular approximation (ZORA) is investigated.
      
The dominant relativistic effects are treated by using the zeroth-order regular approximation.
      
From the hierarchical ordering of the natural orbitals, the zeroth-order orbital space is deduced, which generates the zeroth-order wavefunction, typically an MCSCF function in the full valence space.
      
The aromatic species were found to increase in concentration with pseudo zeroth-order kinetics, the PAH species rose from zero to some higher amount, whereas the saturate and the polar species remained essentially constant over the mileage period.
      
We present a complete derivation of the intrinsic viscosity up to first order in interbead distances (Oseen-type hydrodynamic interaction), finding that a term that belongs to the zeroth-order contribution is missing in the usual description.
      
It is demonstrated that the zeroth-order solution of this two-scale approach approximates the numerical solution of the model well, even if recombination rate is on the order of the selection coefficients.
      
Inclusion of these recoil corrections makes the MIT bag model, even in its zeroth-order version, very appealing, if the sum of many other corrections is not important by comparison.
      
In specular reflection direction, we show that the total radiation is partitioned into a term which is the zeroth-order counterpart to the higher-order diffraction and a term related only to the properties of two adjoining bulk media.
      
The focusing conditions deduced for an idealized configuration can serve as a zeroth-order approximation in a numerical optimization process.
      
The adsorption is characterized by a zeroth-order kinetic with a constant sticking probability of S0=0.0062 up to θ=0.25, followed by a Langmuir kinetic until the saturation coverage θs=0.5 is reached.
      
Composite right/left-handed coplanar waveguide band-pass filter using capacitively-coupled zeroth-order resonators
      
Design and performance of a coplanar waveguide (CPW) bandpass filter (BPF) using composite right/left-handed (CRLH) zeroth-order resonators have been studied.
      
The Bloch analysis is applied based on the S parameters to derive the characteristics of the eigen modes (Bloch modes), from which the right/left-handed frequency band and the zeroth-order resonant frequency are clearly determined.
      
When based on vorticity, this time scale significantly increased as expected when the tracking was computed with a second-order Lagrangian tracking technique as compared to a (zeroth-order) Taylor hypothesis approach.
      
The zeroth-order solution in which the convective terms are neglected is inserted into the governing equations which then can be integrated again.
      
The zeroth-order approximation allows only for rigid-body motions of the plate.
      
A comparison to a zeroth-order BEM, based on the same integral formulation is also included.
      
Consequently, tilted standing waves are formed by two-beam interference between zeroth-order and the other first-order on the image plane.
      
The resulting block-scale expressions can be written as a perturbation series of which the first term, or zeroth-order solution, coincides with the conventionally applied arithmetic and harmonic averages over the layers of the subsurface.
      
 

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