The phrase "a minimal sum for" is correct and usable in written English.
It can be used when discussing the least amount of money required for a particular purpose or transaction.
Example: "The project can be completed with a minimal sum for the initial investment."
Alternatives: "a small amount for" or "a basic cost for".
"We got it after a battle, and we won by a minimal sum of money," said Frank Kenny, chief executive of Willett.
It may prove to be a case of allowing Rooney's contract to run down and taking the hit on losing him for a minimal sum in 2015, if it means having him around for a "comeback" season.
The constitution restricted the franchise to "active" citizens who paid a minimal sum in taxes, with higher property qualifications for eligibility for public office (a direct-tax payment equivalent to 3 days' wages for voters and 10 days' wages for electors and officeholders).
It may not ensure that someone's problems will be fixed, but even a minimal sum can offer a reprieve, a little extra time to sort things out.
FC measures the effective separation between normal random variables X ∼ n (μ1 σ1) and Y ∼ n (μ2 σ2) using the following measuref ([ 20, 21]): (16) FC (X, Y ) = | μ 1 − μ 2 | σ 1 2 + σ 2 2. We use FC to measure the separability of the distance sum corresponding to the true split (which should be the minimal sum for consistent SR functions) from the two remaining sums.
The minimal sum of isomirs for either EM or HT was set at 10 tpm miRNAs with BH-FDR p-values ≤ 0.05 were considered to be significantly differentially expressed between EMs and HTs groups.
Furthermore, the largest weight will increase as the number of imputations increases and the MNAR estimate will become unstable (because the chance of observing an imputed dataset with the minimal sum of the imputed values (for δ > 0), or with a maximal sum of imputed values (for δ < 0) increases as m increases).
The Beatles' manager, Brian Epstein, contacted Fred Brienien from the Students Union and offered him the chance of a Liverpool Art College dance concert (featuring the Beatles for the minimal sum of as recompense), but was turned down.
A parameter estimation routine, also performed by COPASI, allowed a search for Vh, Kh, Vk, and Kk values to produce an optimal fit (defined as minimal sum over all squared differences between experimental and predicted concentrations).
It was shot in New York City for the rather minimal sum of $2.8 million.
