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The essential dimension is a numerical invariant of the group; it is often equal to the minimal number of independent parameters required to describe all algebraic objects of a certain type.
      
We show that the structure of a block outside the critical hyperplanes of category O over a symmetrizable Kac-Moody algebra depends only on the corresponding integral Weyl group and its action on the parameters of the Verma modules.
      
Quantitative parameters in an analog of the Beurling-Pollard theorem differ from those for A.
      
Quantitative parameters in an analog of the Beurling-Pollard theorem differ from those for A.
      
In this article we consider the question when one can generate a Weyl- Heisenberg frame for l2(?) with shift parameters N, M-1 (integer N, M) by sampling a Weyl-Heisenberg frame for L2(?) with the same shift parameters at the integers.
      
We briefly indicate when and how one can generate a Weyl-Heisenberg frame for the space of K-periodic sequences, where K=LCM (N, M), by periodization of a Weyl-Heisenberg frame for ?2? with shift parameters N, M-1.
      
We estimate ∥f∥p from above by C∥f∥p,n and give an explicit value for C depending only on p, τ, and characteristic parameters of the sequence {tn}n∈?.
      
Finally, we consider the spline of order 2; we investigate numerically the region of the time-frequency plane where it generates a frame and we compute the dual function for some values of the parameters.
      
Such sets need not exist even when the parameters involved are rational, but they do exist if in addition all the slopes are powers of 2.
      
The resulting Taylor series can be evaluated far outside their radii of convergence-by means of appropriate methods of analytic continuation in the domain of complex perturbation parameters.
      
These schemes use 2 or 7 parameters respectively depending on whether Hermite data involve only first derivatives or include second derivatives.
      
Statistically significant correlation (r>amp;gt;0.905) was obtained between the physicochemical parameters and biological activity.
      
In the present study, the effect of picroliv, an irridoid glycosidic fraction of Picrorhiza kurroa, on the above said parameters of these alcoholic rats was studied.
      
Picroliv significantly reverted most of the above said altered blood and hepatic parameters in the alcohol-fed male and female rats to almost normal levels.
      
The results indicate that thermodynamic and electronic parameters are major contributors to the activity.
      
The results indicate that electronic and thermodynamic parameters are major contributors to the activity.
      
The 2D QSAR studies revealed that the activity is mainly influenced by electronic parameters where the contribution of field effect and Hammet constant is positive while that of resonance is negaitive.
      
The denaturation data are analyzed based on the effective Gibbs free energy (ΔG°eff) approach and the chemical denaturation parameters including ΔG°eff, m value and equilibrium unfolding constant (KU) were obtained.
      
The developed model was validated by standard QSAR parameters and through a detailed structural analysis of how it reproduces and explains the differences in the experimentally known activity data.
      
In this paper, a mathematical model with respect to the optimal identification of the thermodynamic parameters is established.
      
 

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