Sentence examples for required compactness from inspiring English sources
Then, by the Lions Aubin Lemma, we know that required compactness of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{\iota }}$$\end{document} ι ¯ holds.
Nb3Al and Nb3Sn superconducting strands with a high Cu/non-Cu ratio and NbTi strands with ∼10 μm diameter of filaments have been developed for the toroidal and poloidal superconducting coils requiring compactness and low AC losses.
The mentioned method is called a prior estimate method which does not require compactness of the operator and relaxing the conditions for existence and uniqueness of solutions of differential and integral equations.
The offshore operation of chemical plant requires the compactness of process equipments due to its harsh environment.
Compared with the results in [23 25], in this paper we do not require the compactness of the semigroup T ( t ) and Lipschitz continuity of f.
We present a general criterion for the existence and completeness of the wave operators in obstacle (or potential) scattering which does not require local compactness near the boundary of the obstacle.
Remark 4.4 Theorem 3.1 improves Theorem 3.1 of Zhou [20], Theorem 3.1 of Yao et al. [26] and Theorem 3.1 of Tang et al. [27] in the sense that our convergence requires neither compactness of T nor computation of closed and convex C n of C for each n ≥ 1. Below are the links to the authors' original submitted files for images.
Using Proposition 3.2, we therefore obtain that the compactness required in Assumption 3.5 holds.
Here we recall the principle of operation and the major features, mainly discussing the changes made in order to improve both the robustness of the system as well as its compactness, as required for a field instrument.
Even where compactness is required, it is rarely enforced by the courts.
As in the previous work by the first author with Gigli and Savaré in the Sobolev case, the proof requires neither local compactness nor doubling and Poincaré.
