Sentence examples for existence of functions from inspiring English sources
By using the estimate (2.25), we deduce the existence of functions, such that in and in.
Relative to a model M this ESO sentence asserts the existence of functions f and g and an element t such that f = g (implication from left to right), this function is injective (implication from right to left), and its domain is the whole domain of M but the element t does not appear in its range.
Let us show the existence of functions (y_{s}=e^{omegalambda x}q_{s} x,lambda)), (s=1,2,ldots,m), satisfying the system of equations (15) for the operators (L=L_{lambda}), (L^{ k)}=L_{lambda}^{ k)}), (k=1,2,ldots,m).
Due to a result of Ozawa [15] (he proved that for any given ρ ∈ [ 1, ∞ ), there exists a periodic entire function of order ρ), Chen and Yi [9] and Li and Gao [12] gave some examples to show the existence of functions satisfying the conditions of Theorem B and Theorem C respectively.
The best strategy, therefore, is to assume the existence of function and purpose until one is finally forced to conclude that none exists.
With the help of Lemma 2.4 we can now deduce the existence of function u 0 ∈ K ∩ Ω ¯ r 2 ∗ ∖ Ω r 1 such that F u 0 = u 0. Hence, the problem (1.1 - 1.2 1.1 - 1.2east one solution.
The computational and visual observations together suggest the existence of function-related morphology traits that describe the continuum of LPA values.
ABF family members might have specificity in their role under different stresses apart from existence of function redundancy, in which ABF3 and ABF4 played essential roles in germination control and ABA/stress response, whereas ABF2 was more closely implicated in seedling growth regulation and glucose response [ 8, 13].
Here we shall mention that since the existence of amplifications function and behaved functions in model (1.1), thus there are some difficulties in dealing with the exponential stability.
We also might want to require the existence of choice functions.
Necessary and sufficient LMI conditions for the existence of these functions are presented.
