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Observe that these coefficients may not necessarily be bounded from below by a positive bound which is independent of and.
We only need to prove that for sufficiently large k, (alpha_{k}) has a positive bound from below.
If (A2), (A3), and the conditions in Assumption 3.1 hold, then the sequence ({alpha_{k}}) generated by the line search (12) has a positive bound from below.
If (A4) and the conditions in Assumption 3.1 hold, then the sequence ({alpha_{k}}) generated by the line search (9) has a positive bound from below.
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Due to the character of the LDG method, there is no need of a strict positive bound of the absolute value of the convection term.
In particular, stability is guaranteed if the expression in Theorem 2 exceeds a certain positive bound that is close to zero if (f"_{a}) and (f"_{b}) are nearly constant across most of the range of variation of the firing rate.
Here for i∈{1,I}, h i,z (t) is a positive bounded measurable function with a strictly positive lower bound.
Let ( B_{i}^ ) be a dynamic universal interval of any period i with the most positive bound ( B_{i}^{*[LB]} ) and most negative bound ( B_{i}^{*[UB]} ) for which all fluctuating transitions take place (no transition swing value can exceed ( B_{i}^ )).
r is the positive bound of the search range.
Let S be a positive upper bound for the bounded sequence { ∥ x n ∥ }.
Then we have So, Thus, for any small ε > 0, (End of Proof) This theorem shows that when VQI is bounded above and EQI has a positive lower bound, a sufficiently long stream of evidence will very likely result in the refutation of false competitors of a true hypothesis.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com