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zeroth-order
The zeroth-order general Randi? index of a graph is defined as $$R_{\alpha}^0(G)=\sum_{v\in V(G)}{d_{v}}^{\alpha}$$ where α is an arbitrary real number.
      
Firstly, we build up a zeroth-order model and analyse the effects produced by a potential coronal field or a constant-α force-free field.
      
In the zeroth-order approximation, the dispersion coefficient is calculated using the convection-dispersion-reaction equation with constant parameters, that is, perturbation corrections to the local equation are ignored.
      
This zeroth-order dispersion coefficient is a linear function of the variance of the Damk?hler number, ?(ΔDa)2?.
      
The zeroth-order approximation does not give accurate predictions of mixing or spreading of a plume when Damk?hler numbers, Da ? 1 and its variance, ?(ΔDa)2? >amp;gt; 0.25 ?Da2?.
      
The rate of disappearance of [CeIV] shows a first-order dependence on both [Os]T and [DMSO]T and zeroth-order kinetics with respect to [CeIV].
      
The kinetics are first-order in each of the hydrogen ion, selenomethionine and ferrate ion concentrations over the pH range 8.53 to 10.13, but zeroth-order in hydrogen ion concentration at lower pH values.
      
It is striking to note that the uncatalysed path shows a second-order dependence on [H+], while the PA-catalysed path shows a zeroth-order dependence on [H+].
      
In this paper, we are concerned with the nonoverlapping domain decomposition method with Lagrange multiplier for three-dimensional second-order elliptic problems with no zeroth-order term.
      
Mating inDrosophila is precisely characterized by an exponential phase based on second-order kinetics coupled with an initial lag phase based on zeroth-order kinetics.
      
The process has a significantly lower activation energy (14±1 kJ/mol compared to 26±2 kJ/mol on alumina-supported catalysts) and different reaction orders for both CO (zeroth-order compared to -1) and 02 (0.40 to 0.46 compared to first-order).
      
Similar to the hydrogenation kinetics of butenes, 1,3-butadiene hydrogenation exhibits near zeroth-order dependence on hydrocarbon and near first-order dependence on hydrogen pressure.
      
Approximate first- and zeroth-order kinetics with respect to the hydrocarbon and oxygen concentrations, respectively, was observed in all cases.
      
Applying the dual operator formalism to derive the zeroth-order boundary function of the plasma-sheath equation
      
The second-order differential equation describing the behavior of the zeroth-order boundary function is investigated using the dual operator formalism - an analog of the conjugate operator in the linear theory.
      
Numerical solution of the differential equation describing the behavior of the zeroth-order boundary function
      
A numerical algorithm is considered for the solution of the second-order differential equation describing the behavior of the zeroth-order boundary function.
      
A second-order differential equation is derived describing the behavior of the zeroth-order boundary functions.
      
Zeroth-order correlations distinguished the self-critical perfectionism variables (i.e., socially prescribed perfectionism, self-criticism, and the solitude subscale of autonomy) from self-oriented perfectionism.
      
The zeroth-order field equations are exactly the classical field equations for matter fields on Minkowski space subject to local action of an internal symmetry group (classical gauge theory).
      
 

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