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These results are quite remarkable since these algebras do not admit appropriate sl2-triples.
      
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.
      
It is shown that this is possible when the window g ε L2(?) generating the Weyl-Heisenberg frame satisfies an appropriate regularity condition at the integers.
      
In particular, the results in this article show that the oscillations of a function at large scale are comparable to the oscillations of its samples on an appropriate discrete set of points.
      
Under the appropriate definition of sampling density D?, a function f that belongs to a shift invariant space can be reconstructed in a stable way from its non-uniform samples only if D?≥1.
      
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.
      
The multiplier result for $\mathfrak{M}_{q}\left( \mathbb{R}\right) $ shown at the outset of this process expands the scope of the weighted Marcinkiewicz multiplier theorem from $q=1$ to appropriate values of $q >amp;gt; 1$
      
For the Fejer means on $L_p(R), 1\le p\le\infty$ an equivalence between the rate of its convergence and an appropriate
      
A physical implication is that the corresponding wave function ψ(t, x) = e-itHf(x) admits appropriate time decay in the Besov space scale.
      
In the present investigation, 4-hydroxy-3-methylacetophenone, on condensation with appropriate aldehydes in methanolic potassium hydroxide solution, yielded the corresponding chalcones (CI-XI).
      
A series of 1-[(sub)]-6-fluoro-3- [(sub)]-1, 3, 4-oxadiazol-2-yl-7-piperazino-1, 4-dihydro 4-quinolinones were synthesized by the reaction between ciprofloxacin and norfloxacin with an appropriate acid hydrazide in phosphorous oxychloride.
      
It is shown that the system is permanent under some appropriate conditions, and sufficient conditions are obtained for the local asymptotic stability of a positive equilibrium of the system.
      
Under appropriate hypotheses, the global existence and blow-up in finite time of positve solutions are obtained.
      
It is shown that the system can be made persistent under some appropriate conditions.
      
Under appropriate assumptions, existence and uniqueness of solutions are obtained by using upper and lower solutions method.
      
By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.
      
The notions of fuzzy dot ideals and fuzzy dot H-ideals in BCH-algebras are introduced, several appropriate examples are provided, and their some properties are investigated.
      
Catalyst with appropriate specific surface area and narrow pore size distribution was obtained.
      
The appropriate doping of Fe3+ can markedly increase the catalytic activity of TiO2 under visible light irradiation.
      
Tetraacetylene intermediates with complex structures were constructed rapidly via quadruple Hagihara coupling of monoprotected bisacetylenes to appropriate tetraiodides and subsequent desilylation.
      
 

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