Additionally, these results do not provide any insight as to whether academic equivalence, or positive social learning experiences, would be retained throughout multiple, consecutive, distributed courses.
And in fact, in Dedekind's Nachlass explicit sketches of two now familiar constructions can be found: that of the positive and negative integers as (equivalence classes of) pairs of natural numbers; and that of the rational numbers as (equivalence classes of) pairs of integers (Sieg & Schlimm 2005, earlier Dugac 1976).
Let us denote the asymptotic equivalence of two positive functions and as.
The symbol ∼ denotes the asymptotic equivalence of two positive functions, i.e., f(t)sim g(t), quad ttoinfty quad Longleftrightarrowquad lim_{ttoinfty } frac{g(t)}{f(t)}=1.
Combining the results above with Theorem 2.4, we have, for positive Volterra difference equations, the equivalence among the uniform asymptotic stability of the zero solution of (1.1) and (1.2), the summability of the fundamental solution and the invertibility of the operator outside the unit disk.
Huang et al. [9] established some equivalence results between the positive vector complementarity problem and the vector extremum problem and also sufficient conditions for the existence of a solution of the vector extremum problem.
Let (mathbf{D}_{A}:= ( sqrt{ ( epsilon2^{2vert lambda vert }+b2^{vert lambda vert }+c) }delta_{lambda,mu} ) ) be the diagonal matrix, ϵ, b, c be positive constants and let the norm equivalences (3) hold for (gamma>1).
Even though we do not resolve the general Shift Equivalence Problem, we obtain a positive answer for the class of imprimitivity bimodules.
No further axillary surgery even for one to two positive nodes [ 205] and the equivalence of axillary clearance to axillary radiotherapy for local disease recurrence (despite the differing morbidities) in the presence of a low disease burden [ 206] demonstrate further progress in this surgical setting.
Since equivalence was seen as a positive outcome in this study, it was important to carefully analyze protocol violators and perform both intention to treat and per protocol analyses [ 35].
