Sentence examples for provided that I from inspiring English sources

L is said to be a Fredholm operator of index zero provided that: (i) ImL is a closed subset of Z,   (ii) dim Ker L = codim Im L < + ∞.  .

An edge in this network is weighted and represents the similarity relation s i,j between the two endnodes, i.e. molecules m i and m j provided that i ≠ j.

Y is said to be the Fredholm operator of index zero provided that: (i) ImL is a closed subset of Z;   (ii) (dim operatorname{Ker} L=operatorname{co}dim operatorname{Im} L<+infty).  .

Therefore, in this latter situation, the BRT predictions might be considered adequate without the need for geostatistical modelling, provided that i) care is exercised in model fitting and validating, and ii) the dataset does not allow for modelling of local spatial autocorrelations, as is the case for many national systematic sampling schemes.

Let, then and the inequality holds with a constant depending on, and, provided that (i)   if ; (ii)  ,.

L is said to be a Fredholm operator with index zero provided that (i) ImL is closed subset of Y,   (ii) dim ker L = codim Im L < + ∞.  .

If I can provide that, I'm happy, because I'm far too lazy to ever write about anything other than the things I'm enjoying at that moment.

Then, the following properties hold provided that ;. (i) ; are all composed -cyclic -contraction self-mappings which satisfy, in addition, ; (i.e., and ; ) and which possess common fixed points in, that is, ;.   (ii) There is a unique set satisfying the constraints, subject to, for any given and for any given.

I don't think it would be a violation of Article II, provided that -- I mean would -- if the first part of your question JUSTICE SOUTER.

Then T has at least one best proximity point in A provided that ((I-T)) is demiclosed.

I usually reflect on the care I have provided that day, often questioning if I could have done anything differently.