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When one expands a Schur function in terms of the irreducible characters of the symplectic (or orthogonal) group, the coefficient of the trivial character is 0 unless the indexing partition has an appropriate form.
      
Asymptotic Behavior of Variable-Coefficient Toeplitz Determinants
      
The partial autocorrelation coefficient matrices are computed directly from Levinson's recursions.
      
Further the PLS coefficient contour maps from CoMFA and CoMSIA, well explain the structural variation of the PPARα inhibitors.
      
1) for R isomers with correlation coefficient r =0.9, chance= 0.05 and match= 0.47 has four biophoric sites and three secondary sites while the best model for S isomers (model no.
      
2) with correlation coefficient r =0.86, chance =0.01 and match = 0.45 has three biophoric sites and two secondary sites.
      
QSAR reveals that if partition coefficient, connectivity index, and shape index of these molecules are altered, the activity is likely to increase.
      
The model showed a good correlative and predictive ability, with a cross-validated correlation coefficient of 0.594.
      
Empirical Bayes estimation of the parameter vector θ=(β',σ2)' in a multiple linear regression modelY=Xβ+ε is considered, where β is the vector of regression coefficient, ε∽N(0,σI with σ2 unknown.
      
Inverse scattering transformation for the variable coefficient Sine-Gordon type equation
      
In this paper, the variable coefficient Sine-Gordon type equation
      
Zhu and gives the variance and its estimation of the squared sample correlation coefficient ?n2.
      
Pinning of vortices for the ginzburglandau functional with variable coefficient
      
In this paper, the asymptotic behavior as ε→O of the minimizers u,of the Ginzburg-Landau functional with variable coefficient is discussed.
      
The singularities are found to be located at the points which globally minimize the coefficient.
      
Let α(M) = sup{∥P1MP∥:P is a projection in the diagonal algebra} and then call K(M) = d(M)/α(M) the distance-coefficient of M.
      
Exact solutions of the variable coefficient kdV and sg type equations
      
In this paper,the variable cofficient KdV equation with dissipative loss and nonuniformity terms and the variable coefficient SG equation with nonuniformity term are studied.
      
The non-parametric estimation of contaminated coefficient ε and regression parameter β are established, and the strong consistency and convergence rate almost surely of the estimators are obtained.
      
Functional-coefficient regression model and its estimation
      
 

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