The phrase "a certain weighted" is not correct in standard written English.
It may be intended to describe something that has a specific weight or importance, but it lacks clarity and proper grammatical structure.
Example: "In the analysis, we considered a certain weighted factor that influenced the outcome."
Alternatives: "a specific weight" or "a particular weighting".
The lower bound is given in terms of the complexity of a certain weighted integration problem.
By constructing a Lyapunov function for each isolated subsystem, a certain weighted sum of them was considered as the Lyapunov function of the original system.
For each such flow, we construct a generalized coherent state transform (CST), which is a unitary isomorphism between L2(K) and a certain weighted L2-space of holomorphic functions.
Indeed, for the functional (1.6) we deal with the integrals over (mathbb{R}^{N}) and, actually, with the functional setting over a certain weighted Sobolev space,1 instead of (W_{0}^{2,2}(Omega)) as assumed in [1].
Moreover, GM calculates the difference between the functional road class (FRC) of the source edge and the FRC of a candidate edge, and then integrates this difference with a certain weight into a weighted sum for the candidate rating [26], see also the next section, Section 3.3.
The proofs invoke Moser iteration to prove sublinearity of the corrector in pointwise sense; a key additional input is a conversion of certain weighted energy norms to ordinary ones.
To be precise, (A_{q}) is a Banach algebra with respect to the convolution, expressed as a union of certain weighted (L_{q}) spaces; the space (B_{q'}) is expressed as the intersection of the corresponding weighted (L_{q'}) spaces.
We obtain this result as a consequence of certain weighted L2 Sobolev inequalities on the d-torus.
We consider a scattering map that arises in the ¯∂ approach to the scattering theory for the Davey Stewartson II equation and show that the map is an invertible map between certain weighted L2 Sobolev spaces.
In the process we also find an interesting connection between the difference operator and certain weighted composition operators answering a question raised in Saukko (2011) [18].
Despite their seemingly different problem formulation, it is shown that both methods can be reduced to the same mathematical kernel problem, i.e. finding the closest (in a certain sense) weighted low rank matrix approximation where the weight is derived from the distribution of the errors in the data.
