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Similarly, a version of the Dedekind construction of the real numbers can be carried out, in which many important instances of the least upper bound axiom will be provable.
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CCA has been widely applied in many important fields, for instance, facial expression recognition [2, 3], detection of neural activity in functional magnetic resonance imaging (fMRI) [4, 5], machine learning [6, 7] and blind source separation [8, 9].
And there are many important adjustable features, for instance for the humidifier and the rate at which the air pressure increases.
Remark 3.3 Differential algebraic equations (DAE) arise in many important problems; see, for instance [10, 12].
Among the different notions of generalized convexity, quasiconvexity and arcwise connected convexity have found many important applications; see for instance [1 13].
Sun, for instance, has created many important technologies in-house, including a family of microprocessors based on an original design and the Java language, popular with programmers.
This problem contains many important problems as special cases, for instance, optimization, Nash equilibrium, complementarity, and fixed-point problems (see [1 3] and the references therein).
The classes (mathcal{F}(1,M)) contain many important types of domains in (mathbb{R}^{n}), for instance, balls, cubes, and John domains (cf. [11, 13, 14]).
Note that fractional calculus holds many important and interesting properties, which were described for instance in [3 5].
Many important problems have reformulations which require finding zero points, for instance, evolution equations, complementarity problems, mini-max problems, variational inequalities and fixed point problems.
Many important problems have reformulations which require finding zero points, for instance, evolution equations, complementarity problems, mini-max problems, variational inequalities and optimization problems.
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