Sentence examples for operators section from inspiring English sources

Our aim in this paper is to pursue this line of research by obtaining new fixed point theorems, valid not only for non-decreasing (Section 3) but also for non-increasing operators (Section 2).

We consider adaptive FEM for strongly monotone operators (Section  10), the p -Laplace problem (Section  10.2), and an elliptic eigenvalue problem (Section  10.3).

The points in the i th image are computed from the final segmentation validated by the operator (Section 4.3.3).

The parameters of the apparent contours of the tomatoes in the left and right images are provided by the segmentation procedure, after validation by an operator (Section 4.3.3).

The important step is a proof of a transversality (Remark 2.3 and Lemmas 5.1 and 5.2), which makes possible a construction of a continuous operator (Section 6) whose fixed point leads to a solution of our original impulsive problem (Section 7).

In summary, the main result of this paper is a non-isothermal strongly non-local model formulation for the dynamics of the GENERIC variables (10), including a split of the phase fields into conservative and non-conservative parts, as discussed in the "Decomposition of the friction operator" section.

In view of the goal of formulating models that are spatially strongly non-local in nature, the weakly non-local relation (the "Decomposition of the friction operator" section) between the thermodynamic fluxes ((boldsymbol {j}_{varepsilon }^) and (text{textit{textsf{textbf{j}}}}_{boldsymbol {varrho }}^)) and the corresponding irreversible dynamics (of ε and ϱ) may seem inappropriate.

The formulations of the reversible (the "Poisson operator and reversible dynamics" section) and irreversible (the "Friction operator and irreversible dynamics" and "Decomposition of the friction operator" sections) dynamics did not make use of the same set of variables.

For related spectral asymptotics for a family of commuting operators, see Section 6.1 of [14].

The paper is organized as follows: we start by reviewing some edge detection operators in Section 2.

In the context of affine parameter dependence, in which the operator is expressible as the sum of Q products of parameter-dependent functions and parameter-independent operators (see Section 3), the Offline-Online idea is quite self-apparent and has been naturally exploited [16, 25] and extended more recently in order to obtain efficient a posteriori error estimation.