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The list goes on.Citi's biggest contribution, though, is its belief that microfinance can become a valid, profit-making business.
The longitudinal work of Reef et al. suggests "that children displaying high levels of externalizing behavior … run a larger risk to have poor outcomes in adult life …" and that different trajectories (they found four types) reflect different possibilities of disturbances along the lifespan and consequently different chances to profit from valid interventions.
Disappointment over a significant profit shortfall was valid – disappointment over sales was not.
Generally, most of the well known results arising in a market where firms maximize profit are also valid when considering that firms have extended, and possibly more realistic, goal functions.
So it's a valid question: If you're profiting more by reserving less capacity, how much are you actually keeping for us?
Dr Steve Collins is also unpaid director of Valid Nutrition, a not-for-profit company established to research and manufacture ready-to-use therapeutic food in developing countries.
This assumption lies in the linear relationship between the moments of profit and production function valid under price-taker individuals.
We construct an instance (G, p, c) of PCST by setting the vertex profits to p v)= w v)− w′ for all v∈ V and the edge costs to c e)=− w′ for all e∈ E. Clearly, this is a valid PCST instance since all vertex profits and edge costs are positive.
Having a valid patent in place can protect a profit stream.
However, there are still valid concerns that the company is planning to profit by selling access to the hidden negative reviews left on its platform.
It confessed that its profits guidance for this year is "no longer valid".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com