For the 2-vortex interaction the generalized critical parameter determining qualitative character of interaction of vortices is introduced.
The intent of this qualitative and generalized quantitative review of project areas was to determine the extent and location of two invasive plant species populations: purple loosestrife and common reed (Phragmites australis (Cav).).
Using the fact that the set of minimizers is invariant by a wide class of monotone transformations, we prove that level sets of minimizers are generalized Cheeger sets and obtain qualitative properties of the minimizers: they are all bounded and all achieve their essential supremum on a set of positive measure.
In Section 2, we first analyze qualitative properties of the generalized neutral operator A which will be helpful for further studies of differential equations with this neutral operator; in Section 3, by Mawhin's continuation theorem, we obtain the existence of periodic solutions for the generalized neutral Rayleigh equation with variable parameter.
In Section 2, we first analyze qualitative properties of the generalized neutral operator A which will be helpful for further studies of differential equations with this neutral operator; in Section 3, we consider a third-order neutral differential equation as follows: ( x ( t ) − c ( t ) x ( t − δ ( t ) ) ) ‴ = a ( t ) x ( t ) − λ b ( t ) f ( x ( t − τ ( t ) ) ), (1.1).
We recently developed a general combinatorial approach, namely the generalized multifactor dimensionality reduction (GMDR) method, which can entertain both qualitative and quantitative phenotypes and allows for both discrete and continuous covariates to detect G × G and G × E interactions in a sample of unrelated individuals.
For other qualitative stability results on parametric generalized vector equilibrium problems, see [14 20] and the references therein.
In this paper, we establish some new generalized Gronwall-type inequalities suitable for the qualitative and quantitative analysis of the solutions to fractional differential equations.
To assess our success in improving not only context-specific qualitative understanding, but also more generalized numeracy, we compared precourse versus postcourse results for each student using the Quantitative Reasoning Quotient (QRQ) instrument (Sundre, 2003), a refinement of the earlier Statistical Reasoning Assessment instrument (Garfield, 1998, 2003).
The numerical results show that the new generalized hydrodynamic computational model yields the solutions in qualitative agreement with experimental data and DSMC results in the case of the problems studied.
