Even though ADP is developed in this intuitive way, numerous proofs of both convergence and optimality have been developed for specific applications.
In the past few years, numerous proofs of the concept of in vitro biosystems containing complex enzyme mixtures from different groups worldwide have inspired the development of these platforms for biomanufacturing, these biosystems show advantages such as near-theoretical product yields, faster reaction rates, reduced interference from toxic compounds, and unprecedented level of engineering.
The comprehensive and systematic theology presented in this work reflects Milton's close engagement with Scripture, from which he draws numerous proof texts in order to buttress his concepts of the Godhead and of moral theology, among others.
In the same way, numerous proof-of-concept researchers have confirmed the increasing of cellular tolerances through increasing the production of ethanol and glucose (Liu et al. 2010; Tan et al. 2016).
The availability of inbred mouse strains and an easily identifiable population of CD4+CD25+ Tregs have enabled numerous proof-of-principle experiments demonstrating that, in mice, adoptively transferred natural Tregs can treat type 1 diabetes [44], prevent GVHD [45], [21], and increase the success of organ transplantation [12].
Inequality (4.5) has evoked the interest of several mathematicians and in numerous articles new proofs, extensions, refinements and various related results have been published [7].
Invariably, the generating function will be reported as a very effective device that facilitates proofs of numerous interrelationships between Legendre polynomials of various orders and/or their derivatives.
Meanwhile, punctuation is often awry and there are numerous examples of negligent proof reading.
A few trial runs, some careful proofing and numerous small adjustments later (a tiny piece of newsprint stuck onto the packing can make all the difference), the finished job emerges: crisp, tangibly different, immensely satisfying.
The declarations (and the "offers of proof") from numerous potential witnesses now before the court provide some insight as to how its various provisions might operate, but for the most part they are merely the predictions of purportedly knowledgeable people as to effects which may or may not ensue if the proposed final judgment is entered.
During numerous deployments, this feature proofed itself to be a unique tool to learn from an event and to improve crowd management related measures for future events.
