Sentence examples for uniquely attained from inspiring English sources

Furthermore, we can deduce that the upper bound of (ABC (G) - r (G)) would be uniquely attained by the complete graph.

In the following, we will consider the lower bound of (ABC (G) - r (G)) for connected graphs G and show that this lower bound would be uniquely attained by the path.

Let (16a) be satisfied, then (bar lambda _{2,i}^{k + 1}) can be uniquely attained by solving the following convex problem: begin{aligned} bar lambda_{2,i}^{k + 1} &= mathop {arg min }limits_{{{bar lambda }_{2,i}} in {{mathbf{chi }}_{i}}} left{ {f_{i}}left({{{bar lambda }_{2,i}}} right) + frac{1}{{2rho left({{P_{i}} + {S_{i}}} right)}}right.

The simplex structure of the polyhedron implies that the optimum of any linear combination of metabolic fluxes involved in the model is either uniquely attained for one of these extreme points or attained by all flux distributions positioned on a face of the simplex.

Cardoso et al. [4] propose this problem and show that the minimum value of (kappa(G)) is attained uniquely in the unicyclic graph obtained from the cycle (C_{3}) by attaching a path at one of its end vertices.

In all their respective offices, functions, and capacities, those who have exercised and manipulated sacred power have attained a uniquely prestigious position as the spiritual and social leaders par excellence.

This paradox suggests the perfection of the kinase as an enzyme: a region ideally suited for the common function of catalysis, with another region(s) uniquely modifiable to attain substrate specificity without altering fold, compromising ligand binding or the subsequent reaction mechanism.

For the transcript data, maximal individual clustering was attained with ten PCs as shown, but eight individuals grouped uniquely with as few as five PCs, as well as with eight PCs (75.6 % VE).

Duplicate labels are eliminated in order to attain a uniquely labelled net, on which object-based behavioural specifications are obtained as projections.

Children already engage in pretend play and enjoy stories compulsively long before they attain a uniquely human, yet still imperfectly developed, level of ToM in their fifth year.

But he also thought that there was a special kind of technological beauty, uniquely realizable in the medium of computers, which itself verged on, and sometimes attained, the status of art.