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If is a ?2-grading of a simple Lie algebra, we explicitly describe a-module Spin0 () such that the exterior algebra of is the tensor square of this module times some power of 2.
      
The operation adj on matrices arises from the (n - 1)st exterior power functor on modules; the analogous factorization question for matrix constructions arising from other functors is raised, as are several other questions.
      
Let q be a power of p and let G(q) be the finite group of Fq-rational points of G.
      
We prove a Tauberian theorem of the form $\phi * g (x)\sim p(x)w(x)$ as $x \to \infty,$ where p(x) is a bounded periodic function and w(x) is a weighted function of power growth.
      
A new C*-algebra of strong limit power functions is proposed.
      
As applications of this, Fourier analysis and the Bochner-Fejér approximation are carried out for a strong limit power function.
      
We develop a method to estimate the power spectrum of a stochastic process on the sphere from data of limited geographical coverage.
      
In this note, we propose a direct proof, and extend the range allowed for the power of the nonlinearity to the set of all short range nonlinearities.
      
However, whatever method is used, real industrial applications need to establish well-defined and widely accepted protocols for validating the models and defining their robustness, prediction power and applicability domain.
      
The multiple antioxidant activity of the polysaccharides was evidenced by significant reducing power, superoxide scavenging ability, inhibition of mice erythrocyte hemolysis mediated by peroxyl free radicals, and also ferrous ion chelating potency.
      
The proposed superaugmented eccentric connectivity indices exhibited high sensitivity towards branching, exceptionally high discriminating power, and extremely low degeneracy.
      
The superaugmented eccentric connectivity index-3 (SAξc3) exhibited an exceptionally high discriminating power of >amp;gt; 4000 for all possible structures containing only five vertices.
      
Multiple linear regression analysis was performed to derive QSAR models, which were further evaluated for statistical significance and predictive power by internal and external validation.
      
If a collection of subsets are chosen at random from the power set of a finite setX, we give the probability that the collection is a tree of subsets ofX.
      
Using the Bayesian method, for certain choices of the prior distribution, several forms of estimators of the parameters in the normal stress Weibull distribution and the inverse power law model are derived.
      
In addition, the weighted weak type (1,1) estimates of the Littlewood-Paley function g?(f) with power weights is also proved.
      
This paper analyses the local behavior of the simple off-diagnonal bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin.
      
Numerical examples compare the obtained results with the approximation power of diagonal Chisholm approximant and Taylor polynomial approximant.
      
Approximate power of heteroscedasticity test in nonlinear models with arima (0,1,0) errors
      
This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives.
      
 

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