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The needed properties of the half-linear trigonometric functions for our purpose are the validity of the half-linear Pythagorean identity |sin_{p} y|^{p}+|cos_{p} y|^{p}=1,quad y inmathbb{R}, (2.13) and the boundedness of these functions given by (see (2.13)) |cos_{p} y|^{p} le1, qquadbiglvert Phi( cos_{p} y)sin_{p} y bigrvert le1,qquad |sin_{p} y|^{p} le1,quad y inmathbb{R}.
Strengths of this study are the validity of the HADS and the Short Form-36 and the large changes in these measures after surgery.
The strengths of our study are the validity of the registers, the linkage methods, the large sample size and the 11-year time frame.
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It is the validity of that policy that is before us...
And what is the validity of the verdict, considering Hanna was unable to defend herself adequately?
It is the validity of that test that is at issue in the case, KSR International Co. v. Teleflex Inc., No. 04-1350.
At issue in the case, United States v. Playboy Entertainment Group, No. 98-1682, was the validity of Section 505 of the Telecommunications Act of 1996.
Unfortunately, one thing theatergoers are also discovering is the validity of Harlem residents' longtime complaints about the difficulty of getting a cab.
One is the validity of a regulation issued by the Equal Employment Opportunity Commission that interpreted a defense that the statute made available to employers.
The key issue before Gordon is the validity of the marital property agreement — or agreements — the couple signed in 2004.
And, pretty as they were, the validity of transparent trousers remains questionable, at least to this critic.
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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