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1. Matrix refinement equations: continuity and smoothness

Creator:
He, Xing-Gang and Liu, Chun-Tai
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
matrix refinement equation, continuity, smoothness, iteration, and multi-wavelet
Language:
English
Description:
In this paper we give some criteria for the existence of compactly supported $C^{k+\alpha }$-solutions ($k$ is an integer and $0\le \alpha <1$) of matrix refinement equations. Several examples are presented to illustrate the general theory.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Recent progress in attractors for quintic wave equations

Creator:
Savostianov, Anton and Zelik, Sergey
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
damped wave equation, fractional damping, critical nonlinearity, global attractor, and smoothness
Language:
English
Description:
We report on new results concerning the global well-posedness, dissipativity and attractors for the quintic wave equations in bounded domains of R 3 with damping terms of the form (−∆x) θ ∂tu, where θ = 0 or θ = 1/2. The main ingredient of the work is the hidden extra regularity of solutions that does not follow from energy estimates. Due to the extra regularity of solutions existence of a smooth attractor then follows from the smoothing property when θ = 1/2. For θ = 0 existence of smooth attractors is more complicated and follows from Strichartz type estimates.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Smooth implications on a finite chain

Creator:
Su, Yong
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
finite chain, smoothness, and implications
Language:
English
Description:
Mas et al. adapted the notion of smoothness, introduced by Godo and Sierra, and discussed two kinds of smooth implications (a discrete counterpart of continuous fuzzy implications) on a finite chain. This work is devoted to exploring the formal relations between smoothness and other six properties of implications on a finite chain. As a byproduct, several classes of smooth implications on a finite chain are characterized.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public