Sentence examples for be a given real from inspiring English sources

Let be a given real parameter.

Let be a given real number, satisfying.

(i) Let (aneqfrac{1}{2}) be a given real number.

Let (alphaneqfrac{1}{2}) be a given real number.

Let (T > 0) be a given real number.

Let any r > 0 be a given real number, and let x ∈ E be any point.

Let (f Itimes Rrightarrow R) be a given real-value function.

Let (c > 0) be a given real-valued constant and let lambda= -frac{alpha- 1}{2} quadtextit{and}quad mu= frac{1}{2} sqrt{4beta- (alpha- 1)^{2}}.

In particular, let (c > 0) be a given real-valued constant and let lambda= -frac{alpha- 1}{2} quadtextit{and}quad mu= frac{1}{2} sqrt{4beta- (alpha- 1)^{2}}.

(1.1) where (Ainmathbb{R}^{ntimes n}) and (qinmathbb{R}^{n}) are a given real matrix and a real vector, respectively.

We deal with a conditional functional inequality, where is a given orthogonality relation, is a given nonnegative number, and is a given real number.