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Lower degree bounds for modular invariants and a question of I.
      
Lower bounds for Kazhdan-Lusztig polynomials from patterns
      
We give a lower bound for the values Px,w(1) in terms of "patterns".
      
Our lower bound comes from applying a decomposition theorem for "hyperbolic localization" [Br] to this torus action.
      
An important property of this matrix is that the maximum and minimum eigenvalues are equal (in some sense) to the upper and lower frame bounds.
      
As an application we give lower bounds for convolutions ? ? f, where ? is a radially decreasing function.
      
Lower frame bounds for sequences of exponentials are obtained in a special version of Avdonin's theorem on "1/4 in the mean" [1] and in a theorem of Duffin and Schaeffer [4].
      
This includes an explicit lower frame bound in a famous theorem of Duffin and Schaeffer.
      
Optimality in terms of upper and lower rates of convergence is established.
      
We derive a sharp lower bound for this product in the class of filters with so-called finite effective length and show the absence of minimizers.
      
In search of lower dimensional nonspectral tiles we were led to investigate the Universal Spectrum Conjecture (USC) of Lagarias and Wang [14].
      
This fact causes considerable difficulties in producing lower dimensional examples of tiles which have no spectra.
      
We find lower bounds for linear and Alexandrov's cowidths of Sobolev's classes on Compact Riemannian homogeneous manifolds $M^{d}$.
      
aureus in lower concentration of chloroform extract.
      
The formed intermediate showed a lower thermal transition temperature (Tm) by a magnitude of 10°C in relation to the native DNA.
      
Discriminant analysis and cluster analysis generally discerned association of these 17 compounds on a basis of higher and lower formula weight criteria.
      
We show that when there is strong dependence between the variates, the generalized variance of moment estimators is much lower than the stepwise estimators.
      
We further illustrate how to use these inequalities to determine the lower bound of relative efficiency of the parameter estimate in linear model.
      
In this paper, the existence and uniqueness of solutions for boundary value problemx?=f(t, x, x', x″),x(0)=A,x'(0)=B,g(x'(1),x″(1))=0 are studied by using Volterra type operator and upper and lower solutions.
      
We investigate the fractal interpolation functions generated by such a system and get its differentiability, its box dimension, its packing dimension, and a lower bound of its Hausdorff dimension.
      
 

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