Sentence examples for be two real functions from inspiring English sources

Let and be two real functions, and let be a positive integer,.

Let and be two real functions, and let be a nonnegative integer and.

Let be a real number, and let and be two real functions, and and, where.

Let be a real number, and, and let and be two real functions, and and.

Let X:Ω→H be a continuous random variable with the distribution function F and let q 1 and q 2 be two real functions defined on H such that E[q 1(X)|X≥x]=E[q 2(X)|X≥x]η(x),x∈H, is defined with some real function η.

In this and the next sections we consider the nonlocal p(x -Laplacian-Neumann problem (P), where a and b are two real functions satisfying the following conditions.

The Chebyshev functional [2] is defined by T (f,g )=frac{1}{b-a}int_{a}^{b}f ( s ) g ( s ),mathrm{d}s -frac{1}{b-a}int_{a}^{b}f ( s ),mathrm{d}s cdot frac{1}{b-a}int_{a}^{b}g ( s ),mathrm{d}s, where (f,g: [a,b ] rightarrowmathbb{R} ) are two real functions such that (f, g, fcdot g in L^{1} [a,b ]).

Let f and g be two real positive integrable functions defined on ([a,infty)) such that 0< mleq f tau) leq M < infty quad textit{and}quad 0 < nleq g tau) leq N< infty quad bigl( tauin[a,t] (t>a) bigr), (2.9) where n, N, m, M are real constants.

Let F z) and G z) be two real, continuous and increasing functions for z ≥ 0 such that F 0) = G 0) = 0 and define F ̄ ( z ) = 1 - F ( z ), Ḡ ( z ) = 1 - G ( z ) for z ≥ 0. Definition 1.8.

Let (eta_{1}, eta_{2}in^{mathrm{c}}operatorname{Var}(0,a)) be two functions, and let (epsilon_{1}) and (epsilon_{2}) be two real numbers, and consider the new function of two parameters breve{y}=y+epsilon_{1}eta_{1}+ epsilon_{2}eta_{2}.

Let be two real-valued functions, and let be the Lebesgue measure on.