# boundedness

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## Synonyms for boundedness

### the quality of being finite

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Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
References in periodicals archive ?
Next, let us introduce a criterion that deals with the boundedness of the commutators of the operators satisfying [L.sup.P] [right arrow] [L.sup.q] off-diagonal estimates, which can be proved in .
The bound for (6.14c) follows from the boundedness of [mathematical expression not reproducible] (6.14b) is a telescopic sum, so we do not lose a [tau] by summation.
In this paper, the relationship between uniform continuity of a function and the boundedness of its fractional derivative will be built, then a fractional order Barbalat's Lemma described by fractional derivative will be proposed.
Vanualailai, Some stability and boundedness criteria for a class of Volterra integrodifferential systems, Electronic Journal of Qualitative Theory of Differential Equations 12 (2002) 1-20.
(1) Assumption 3 means that the disturbances induced by winds, waves, and currents have finite energy; (2) Assumption 4 indicates that the proposed control law relies just on a directed communication topology, which reduces the complexity of the communication among ships; (3) the boundedness of the first derivatives and second derivatives of the leaders will be introduced to analyze the stability of the closed-loop system.
then the boundedness of all the signals in the closed-loop switched system can be ensured and the state [xi](k) can track the reference signal [[xi].sup.d](k) and the system output can follow the desired trajectory [y.sup.d](k).
Considering the kinematic dynamic model of the trajectory tracking ship with three degrees of freedom satisfies the assumptions, there are adaptive disturbance observers as (3) and (4), first-order filter as (11), and control laws as (15) and (16) which can guarantee the global uniform ultimate boundedness of the tracking system.
Using a linearization method, sufficient conditions of existence and boundedness are established.
As for [M.sup.p](U) with p =1, Kim described some characterizations of boundedness (see ).
For [I.sup.1], [L.sup.2] boundedness of [S.sub.L] and the size condition of atom tell us
To this end, this special issue pays a special attention to the discretization of continuous fractional systems that preserve important characteristics including the positivity, boundedness, convexity, monotonicity, and energy of the underlying systems.
The proposed security measure evaluates the similarity between two vague sets of cover images and stego images in terms of n-order Markov chain for capturing the interpixel correlation and has been shown to have the properties of boundedness, commutativity, and unity.
Crucial in our analysis is the definition of proper norms for which we prove that the constants in the related boundedness and inf-sup conditions do not depend on any of the model parameters.
In this section, we establish the existence, positivity, and boundedness of solutions of problem (2)-(4) because this model describes the evolution of a cell population.
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