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Reductive group actions on affine quadrics with 1-dimensional quotient: Linearization when a linear model exists
      
A linear model for a given action is a linear orthogonal action with the same orbit types and equivalent slice representations.
      
We prove that if a reductive group action on an affine quadric with a 1-dimensional quotient has a linear model, then the action is linearizable.
      
Using the path model and the theory of crystals, we generalize the concept of patterns to arbitrary complex semi-simple algebraic groups.
      
In the model situationD is the Siegel disc,S is the manifold of Lagrangian subspaces andG is the symplectic group.
      
All parabolic geometries, i.e., Cartan geometries with homogeneous model a real
      
The mathematical theory usually addresses this problem in infinite dimensions (typically in L2 (?) or ?2(?)), whereas numerical methods have to operate with a finite-dimensional model.
      
Further we investigate under which conditions one can replace the discrete model of the finite section method by the periodic discrete model, which is used in many numerical procedures.
      
The Arov-Grossman Model and the Burg Multivariate Entropy
      
In this article we deal with the Arov-Grossman functional model to describe all the solutions of the Covariance Extension Problem for q-variate stationary stochastic processes and we find the density that maximizes the Burg Multivariate Entropy.
      
Also, from the information that the Arov-Grossman functional model provides we obtain a version of the Levinson algorithm.
      
We review here spherical wavelet analyses of the CMB that test the standard cosmological concordance model.
      
Convolution Estimates and Model Surfaces of Low Codimension
      
Among several models, one model has been identified with the statistical criteria r≥0.9, chance>amp;lt;0.02, superimposition match>amp;gt;0.67.
      
The model with three common biophoric sites such as center of triazole ring for A, center of phenyl ring for B, and charge heteroatom for C.
      
The regression analysis has shown that equalized electronegativity is a good parameter which in combination with topological indices and an indicator parameter gave excellent model.
      
For the GFA model, thirty molecules were used as training set and eight as test set to evaluate the external predictability of the equations generated using GFA.
      
In the CoMSIA model, steric, electrostatic, hydrophobic and hydrogen bond donating factors were correlated to the activity and later the favorable and unfavorable regions of interaction were obtained.
      
The training set was derived using twenty-eight compounds and six were used as test sets to evaluate external predictability of the model.
      
The CoMFA model was evaluated for both internal and external predictabilities having r2cv=0.456 and r2pred=0.519 respectively.
      
 

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