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As a consequence the mass of at least one neutrino has to be different from zero and it becomes imperative to determine its absolute value.
Theorem 3 Let conditions of Theorem 1 be realized, and let the value D ( b, 0 ) + ω 2 D ( 0, b ) be different from zero.
For the risk-averse households, the term would be different from zero and would measure deviations from the risk neutrality position.
Even for data with zero mean, the final residue can be different from zero; for data with a trend the final residue is the trend.
By combining the data symbol X q and its complex conjugate, we force the pseudo-covariance matrix to be different from zero.
In all other cases, the value of mutual information will be different from zero reaching a maximum value when the two variables are completely dependent variables (such as, for instance, linearly dependent (Y = aX+b)).
Similar(36)
It is safe to say that all these pieces will be different from one another.
The CR-V Super Bowl commercial will be different from five other spots in the "leap list" campaign, Mr. Peyton said.
However, the effects of exposure and engaged activity may be different from one another.
IRC chat rooms will be different from one another, depending what rules and regulations are set for each channel.
Stress can make sensory processing more difficult, and their needs might be different from one day to the next.
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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