The phrase "a fails" is not correct in standard written English.
It may be intended to refer to a failure in a specific context, but it lacks clarity and grammatical structure.
Example: "In this project, a fails to meet the required standards."
Alternatives: "an error" or "a failure".
Fourth, for HS54, HS75, HS85 and HS117, Algorithm A fails to produce an invertible coefficient matrix after some iterations, then it cannot obtain the optimal objective value, so they are not listed in Table 2.
end{aligned}Please be warned that, since (Q = S + A) fails to be real-valued on (W_mathbb {R},), the intersection (mathfrak {osp}(W) cap mathrm {End}(W_mathbb {R})) is not a real form of the complex Lie superalgebra (mathfrak {osp}(W)).
However, perhaps there is another reason why the Langley Large Aerodrome "A" fails to put in an appearance... the notorious 1914 "tests" that Curtiss conducted using a substantially altered, rebuilt and strengthened Langley Large Aerodrome "A" in order to demonstrate that the Wrights weren't the first to fly.
When he was done making his presentation, according to people in the room, someone asked: "What happens if Plan A fails?
If plan A fails, well, just junk it all and adopt a completely different set of direct football tactics for about 10 minutes at the end.
Theorem A fails since (3.22).
