Sentence examples for there exist limits from inspiring English sources

Namely, if we consider an upper bound, say (resp., a lower bound ) as a function of, then there exist limits (1.38).

Then there exist limits lim_{ntoinfty} x_{i}(n)=c_{i}neq0, quad c_{i} inmathbb{R} cup {-infty, +infty}, i=2,3,4.

Thus, there exist limits (as real numbers or −∞) L_{0}:= lim_{k toinfty} w_{mk}, qquad L_{1}:= lim_{k toinfty} w_{mk + 1},qquad ldots, qquad L_{m-1} := lim_{k to infty} w_{mk + m - 1}.

Although research has proven that early-strength is achievable, there exist limited published durability data for these systems.

Within the context of this study, there exists limited published local information regarding the average number of drugs that a patient older than fifty years gets prescribed.

We find that with fundamental-based rules, there exist limited information equilibria that are stable under learning.

Although there exist limited sex- and age-disaggregated data on roles in rangeland/dryland management activities (FAO 2003), women are demanding more equality in access and control to land and participation in decision-making at various levels (IFAD 2006).

However, there exist limited information on the implications of rangeland enclosures on gender roles, responsibilities and decision-making power in the management and utilization of private enclosures as observed by Nedessa et al. (2005).

hold, and we also have that (Delta tilde {g}_{t}) converges to 0. Hence (tilde {g}_{t}) converges to a finite value, so that there exist limit points for the sequence {x t }.

While there exists limited data on enforcement, it appears unvigorous (National Highway Traffic Safety Administration 2004; Borglund et al. 1999).

Let and let be a mapping. is called Gateaux differentiable at if for any, there exists limit (3.28).