Later, with R.J. DiPerna, Lions rigorously demonstrated the existence of solutions to Boltzmann's equation for the density of colliding hard spheres, given general initial data.
First Cantor rigorously demonstrated that the set of rational numbers (fractions) is the same size as the counting numbers; hence, they are called countable, or denumerable.
Although doctors assume that the treatments are more or less equivalent to prostate surgery, that has not been rigorously demonstrated, nor has it been shown that these treatments prevent prostate cancer deaths.
Further, studies for heterologous expression, purification, and biochemical characterization of other genes are currently underway to rigorously demonstrate involvement of both the pathways.
In its ideal form metaphysics would be presented in a manner analogous to Euclid's Elements, where propositions are rigorously demonstrated on the basis of definitions and axioms.
Many potential strategies for CSC-directed thavepy have been proposed, but few studies have rigorously demonstrated their efficacy using in vivo models.
The second additional criticism is that Alexander's documentation also fails to rigorously demonstrate the fundamental premise that beautiful environments are comprised of greater numbers of patterns than the contemporary designs which are allegedly destroying the world [9].
In this paper, we rigorously demonstrate that the continuous neuronal model can be reduced to the discrete model if the intrinsic and synaptic properties of the cells are chosen appropriately.
Despite the accumulating knowledge on the role of cytoplasmic PNGase in the ERAD and the conservation of its structural features in species from yeast to mammals [17], [18], [19], [20], [21]), the biological significance of this protein has not yet been rigorously demonstrated in any system.
9 10 While the value of such measures has been rigorously demonstrated, they have limitations.
