Sentence examples for bound proved from inspiring English sources

The inequality on the left hand side of (2) follows taking (d_{i}=d_{j}=n-1) in the general bound proved in [26] R_{ij} gefrac{d_{i}+d_{i}-2}{d_{i}d_{j}-1}, (8) where ((i,j) in E) and (d_{i}) denotes the degree of vertex i.

Then, we deduce the signal reconstruction error bound, proving that it is effective for improving signal reconstruction performance.

This error bound proves that the approximate function f m ( x ) converges to f ( x ) based on shifted Jacobi polynomials.

It should not come as a surprise that the upper bound proves to be a much better predictor of VMT and emissions than does the lower bound.

We deduce the signal reconstruction error bound, proving that appropriate selection of the stretching factor and smoothness order guarantees low reconstruction error.

We see that both balanced and brute force codes reach the bound, proving thus their optimality in terms of level of interference.

The lower bound is proved in the same way.

Our bound is proved by analyzing the price of stability restricted to Nash equilibria that minimize the potential function of the game.

The first bound was proved by Faure Sjöstrand [84] and it holds for general Anosov flows on compact manifolds: for any ( gamma > 0 ), begin{aligned} N left( left[ r - r^{frac{1}{2}}, r + r^{frac{1}{2}} right] - i [ 0, gamma ] right) = o left( r^{ n - frac{1}{2}} right).

end{aligned} (4.47 For Anosov contact flows a sharp bound was proved by Datchev Dyatlov Zworski and it says that begin{aligned} N left( [ r - 1, r + 1 ] - i [ 0, gamma ] right) = mathcal {O} left( r^{frac{n-1}{2}} right), end{aligned} (4.48 which improves (4.47), giving ( N ( [ r - r^{frac{1}{2}}, r + r^{frac{1}{2}} ] - i [ 0, gamma ] ) = O ( r^{ frac{n}{2} } ) ), in the contact case.

But it is clear that the zero nominal interest rate bound has proven costly.