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The rancorous ending to the debt discussions on Friday means that leaders of the House and Senate now have only days to find a debt limit solution that has eluded them for months, gaming out ways to get a debt increase through a Republican-controlled House packed with conservatives demanding deep cuts and no new revenues.
"I find it hard to believe that even if some critics have a beef with Boehner on how the final debt limit solution will look (and surely some will), that they will have the courage or the inclination to try to oust him," John Feehery, a party strategist who served as a top aide to Speaker J. Dennis Hastert, wrote on his blog on Wednesday.
Theoretically, the homogenized result corresponds to the limit solution when the size of the basic cell tends to be infinitely small.
A small displacement limit solution with an elastic-perfectly plastic material model overestimated the collapse load by more than 40% and could not reproduce the buckling behaviour.
Obviously, the limit solution ( p 0 e − i ( a t − 2 θ ), q 0 e − i ( a t − 2 θ ), b 0 ) is an exact plane-wave solution of (1.1).
Note that Theorem 5, although being able to prove convergence of both sequences {x t } and {z t }, cannot guarantee that the limit solution is feasible, i.e., it satisfies A x t =z t.
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We prove that such limit solutions solve a free boundary problem of Hele Shaw type.
The brute-force approach contrasts drastically from examination of fine bifurcation structure of limit solutions of the system.
In earlier works a kind of limit solutions x was considered (i.e. x is a limit of approximated solutions x n for problems driven by measures μ n tending, in some sense, to μ - cf. [52]).
Notches and cracks are usually treated as two-dimensional problems in most structural design and analysis applications, employing 2D limit solutions from plane elasticity theories to evaluate highly localized stress/strain concentration effects around their tips.
If the initial transcription factor and morphogen patters are unimodal, we find two stable, non-zero stationary limit solutions.
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