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A basis is calledmonomial if each of its elements is the result of applying to a (fixed) highest weight vector a monomial in the Chevalley basis elementsYα, α a simple root, in the opposite Borel subalgebra.
      
The result generalizes and implies the classical "branching rules" that describe the restriction of an irreducible representation of the symmetric groupSn toSn-1.
      
Implementing this point of view, Poisson Summation Formulas are proved in several spaces including integrable functions of bounded variation (where the result is known) and elements of mixed norm spaces.
      
We use interpolation methods to prove a new version of the limiting case of the Sobolev embedding theorem, which includes the result of Hansson and Brezis-Wainger for Wnk/k as a special case.
      
The weighted inequalities allow us to transfer the result to the ergodic case, when the operator is induced by a mean bounded, invertible, positive groups.
      
The result of stability analysis shows that, under a specific bounded modelling error, the closed-loop system is BIBO stable in the presence of unmodelled dynamics.
      
Second, a characterization of convergence for L1-regular splittings of a singular Z-matrix is given, which improve the result of [3].
      
The result shows that most inverse network optimization problems with l∞ objective function can be solved in the polynomial time.
      
The result reduces the number of ovals in original Brauer's theorem in many cases.
      
The result is significant because the previous conclusions are only applied to open-loop stable plant (or model).
      
Recently the result has been extended to a group of equations with more general nonlinearities such as f(u)=u+-1+g(u) (Chen >amp;amp; McKenna, 1997).
      
Moreover the result in this paper improves, generalizes and summarizes some important and elegant recent results.
      
In this paper, the properties about how small are the increments of the fractional Levy-Wiener process are studied, and some interesting results are obtained, which extend the result of Lin and Choi in 2001.
      
And the result obtained extends those for ρ--mixing random fields, ρ*-mixing random fields and negatively associated fields.
      
From the result of simulations, it is manifest that the tracking speeds of these kinds of linear and nonlinear tracking-differentiators are very high, and their design procedures are simple.
      
The result is also true for ρ-mixing, φ-mixing, α-mixing, associated and negatively asosciated sequences under suitable conditions.
      
To obtain the result, some new techniques are used.
      
As the order is 1, the result here is simplified to that of first order differential equation.
      
The result of the note generalizes the W2,p estimate of Poisson equation in Lp(Ω).
      
In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment.
      
 

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