Sentence examples for which is invalid from inspiring English sources

Therefore, μ A ( x y ) ≥ 1 − k 2 and γ A ( x y ) ≤ 1 − k 2, which is invalid.

The different structure leads to a Kelvin transform used in [5 12] to obtain the decay estimate of (1.7), which is invalid for the system (1.1).

However, it will also return a total of four PubChem CID, one of which is invalid as it refers to a generic disaccharide (PubChem CID 294).

Therefore, μ A ( x y z ) ≥ 1 − k 2 and γ A ( x y z ) ≤ 1 − k 2, which is invalid.

If normal-shear interaction is ignored, separated normal and shear constitutive laws are usually used in fibre beam elements, which is invalid to simulate shear failure in beam/column members with small or medium shear span-to-depth ratios.

The proof of his result depends on cos π ρ theorem which is invalid for μ ( G 1 ) ≥ 1 2. In this paper, we consider some more general cases.

Board officials said that workers would continue their review of the registrations through the weekend to determine which are invalid by Tuesday's meeting.

The Board of Elections rejected about 3,500 of the 4,407 signatures the councilmen collected on their petitions but could not say which were invalid or why, according to the decision.

Many experimental systems employ centralized localization mechanisms, which are invalid for a fully distributed robotic system.

Unless we are 100% certain of the premises, the arguments above which are invalid on Adams's criterion guarantee nothing about what you are entitled to think about the conclusion.

The improvements in the algorithm were obtained from formalizing implicit assumptions made in the VPH+ algorithm regarding the sensor and the robot model, both of which were invalid for the Scorpio robot.