Nerve injury induces the expression of syndecan-1 heparan sulfate proteoglycan
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This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations on nonsmooth domains. In particular, we study the smoothness in the specific scale $\ B^r_{\tau,\tau}, \ \frac{1}{\tau}=\frac{r}{d}+\frac{1}{p}\ $ of Besov spaces. The regularity in these spaces determines the approximation order that can be achieved by adaptive and other nonlinear approximation schemes. We show that for all cases under consideration the Besov regularity is high enough to justify the use of adaptive algorithms.
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This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations on nonsmooth domains. In particular, we study the smoothness in the specific scale B^r_{\tau,\tau}, \frac{1}{\tau}=\frac{r}{d}+\frac{1}{p} $ of Besov spaces. The regularity in these spaces determines the approximation order that can be achieved by adaptive and other nonlinear approximation schemes. We show that for all cases under consideration the Besov regularity is high enough to justify the use of adaptive algorithms.
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This paper deals with Besov spaces of logarithmic smoothness $B_{p,r}^{0,b}$ formed by periodic functions. We study embeddings of $B_{p,r}^{0,b}$ into Lorentz–Zygmund spaces $L_{p,q}(\log L)_{\beta }$. Our techniques rely on the approximation struc
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We give several characterizations of holomorphic mean Besov-Lipschitz space on the unit ball in $\cn $ and appropriate Besov-Lipschitz space and prove the equivalences between them. Equivalent norms on the mean Besov-Lipschitz space involve different types of $L^p$-moduli of continuity, while in characterizations of Besov-Lipschitz space we use not only the radial derivative but also the gradient and the tangential derivatives. The characterization in terms of the best approximation by polynomials is also given.
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Previous research has shown that wavelet method can be used to estimate the Besov smoothness of a function (signal). This paper describes an algorithm that is based on the magnitudes of the wavelet coefficients and linear regression model to estimate the smoothness of different signals of one and two-dimensional in the Hölder spaces. Computational results show that the Holder smoothness of the general two-dimensional image is between 0.2 and 0.7. We compare our results with those in Besov smoothness spaces and discuss the smoothness relations between these two function spaces.
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Abstract We present characterizations of the Besov spaces of generalized smoothness $ B^{\sigma,N}_{p,q} $ (ℝ n ) via approximation and by means of differences. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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We show that the zero smoothness Besov space $B_{p,q}^{0,1}$ does not embed into the Lorentz space $L_{p,q}$ unless $p=q$; here $p,q\in (1,\infty)$. This answers negatively a question proposed by O. V. Besov.
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