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Making pensions a claim on the private sector rather than the public purse does not change the problem.
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It stops the runny nose, but it doesn't change the problem".
So, yeah, this is a step in the right direction, but fundamentally it doesn't change the problems that the state of California faces and local governments face with huge, unfunded liabilities".
Note that the usage of the matrix U does not change the minimization problem in Eq. (6), but is there to improve the convergence.
Making the prediction certain to be accurate does not change the character of the problem.
Future problems in the industry would doubtless warrant another intervention that puts taxpayers and the broader economy at risk – and the fact that taxpayers made money on the interventions five years ago does not change the reality that the problems in money market mutual funds greatly compounded an already difficult situation in financial markets following the Lehman bankruptcy.
We note that adding dominated points to does not change the value of optimization problem (14), which allows us to consider problem (A.1)–(A.6) instead.
That does not change the dimensions of a problem that strains schools, medical services and families.
This simplification is to facilitate our description below and does not change the overall analysis of our problem.
This does not change the optimal solution of the dual problem (24) because we know that the optimizer satisfies μ ⋆>0.
Noticing that taking the square root of the objective function and both sides of the constraint does not change the solution set, we can rewrite problem (44) as min w ∥ R ~ 1 2 w ∥ s.t.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com