Sentence examples for be defined on some from inspiring English sources
Let a real function f be defined on some nonempty interval I of a real line ℝ.
Let the continuously differentiable functions l i ( t, y ), i = 1, 2, …, p and m j ( t, y ), j = 1, 2, …, q, p 2 + q 2 > 0 be defined on some open set.
For, let the function be defined on as follows: (2.11).
Fixed point theory focuses on the strategies for solving nonlinear equations of kind T x = x, where the function T is defined on some abstract space X.
A noncommutative Poisson transform associated to a certain class of sequences of operators on Hilbert spaces, with property (P), is defined on some universalC*-algebras (resp. nonselfadjoint algebras) generated by isometries.
2 ∼' stands for asymptotically equal, i.e., f(x)∼g(x)⇔f(x)/g(x)→1 as x→a, x∈M where the functions f(x) and g(x) are defined on some set M, and a is a limit point of M. f(x)=o(g(x)) means ({lim }_{xto a}f(x)/g(x)=0).
Without further mention, we will assume throughout that every solution (x t)) of (1.1) under consideration here is continuable to the right and nontrivial, i.e., (x t)) is defined on some ray ([t_{x},infty)_{mathbb{T}}), for some (t_{x}geq t_{0}), and (sup { vert x t) vert :tgeq T_{1} } >0) for every (T_{1}geq t_{x}). Moreover, we tacitly assume that (1.1) possesses such solutions.
This season, the C.I.A. will largely be defined on television by "The Agency".
Let (0<alphaleq1) and f be defined on (mathbb{N}_{0}).
Let a σ-additive measure μ be defined on X.
