For example, in Fagaceae it is derived from a highly modified and reduced branch system with its associated modified leaves or bracts, at least in the genus Quercus; and in Betulaceae the husks are thought to be made up of several modified bracts.
Some properties of the associated modified equations are proven and then extended to the semi-discrete case.
In order to prove our results via variational approach, inspired by the methods of [27, 28], first, we need to modify and extend f to an appropriate f̃ and to show for the associated modified functional the existence of solutions.
By making use of a recently introduced block tridiagonal partitioning of the collocation matrix, which yields faster rates of convergence, and its associated modified red-black ordering of unknowns and equations, we succeeded to increase the scalability of the problem.
Based on the flow resistivity, the frequency-dependent acoustic absorption coefficient of the needled nonwovens was predicted using the empirical model of Delany and Bazley (1970) and its associated modified models.
We will modify and extend W to an appropriate W̃ and show for the associated modified functional I the existence of a sequence of homoclinic solutions converging to zero in (L^{infty}) norm, and therefore we obtain infinitely many homoclinic solutions for the original problem.
Undoubtedly, the activity-related receptor mislocalisation and the associated modified signalling characteristics represent a general phenomenon and influence the oncogenic potential of mutant RTKs.
They designed a software to select the patients' data changes and to automatically modify medical reports associated to modified patients' identities without impact on results, and to present for biological re-interpretation reports with potential impact of those modifications (date of birth, gender, etc). in order to meet the expectations of the Cofrac.
By removing any liability associated with modifying the first mortgage, the banks that own the second liens can expose investors to losses or reduced income while keeping their own interests in the second lien intact.
By examining heatmaps of portfolio characteristics derived by perturbing constraints with commensurable elasticities, it offers insights into trade-offs associated with modifying constraint bounds.
