We show local higher integrability of derivative a suitable weak solution to the surface growth model, provided scale-invariant quantity is locally bounded. If additionally our small, we prove smoothness solutions.

Surface treatment of titanium implants has been a new frontier in clinical dentistry. Usually it is based on additive and subtractive techniques that modify the surface topography of implants. It alters the roughness/smoothness of the implant surface which becomes more favourable to achieve osseointegration. This modified surface exhibits varied biological responses when the implant is placed i...

Cortical surface-based analysis of fMRI data has proven to be a useful method with several advantages over 3-dimensional volumetric analyses. Many of the statistical methods used in 3D analyses can be adapted for use with surface-based analyses. Operating within the framework of the FreeSurfer software package, we have implemented a surface-based version of the cluster size exclusion method use...

Shading is the variation in image intensity due to changes in surface shape, and has long been recognized as one of the most important visual cues to surface shape. Leonard0 Da Vinci, for instance, wrote in his notebooks: “Shading appears to me to be of supreme importance in perspective, because, without it opaque and solid bodies will be ill-defined.” Despite its importance, however, relativel...

This paper describes a method for melody detection in polyphonic musical signals. Our approach starts by obtaining a set of pitch candidates for each time frame, with recourse to an auditory model. Trajectories of the most salient pitches are then constructed. Next, note candidates are obtained by trajectory segmentation (in terms of frequency and pitch salience variations). Too short, low-sali...

We prove lower bounds for the approximation error of the variation-diminishing Schoenberg operator on the interval [0, 1] in terms of classical moduli of smoothness depending on the degree of the spline basis. For this purpose we use a functional analysis framework in order to characterize the spectrum of the Schoenberg operator and investigate the asymptotic behavior of its iterates.

Various authors have noted that in particular models, the upper bound on the axion decay constant may not hold. We point out that within supersymmetry, this is a generic issue. For large decay constants, the cosmological problems associated with the axion’s scalar partner are far more severe than those of the axion. We survey a variety of models, both for the axion multiplet and for cosmology, ...

When bivariate filter banks and wavelets are used for surface multiresolution processing, it is required that the decomposition and reconstruction algorithms for regular vertices derived from them have high symmetry. This symmetry requirement makes it possible to design the corresponding multiresolution algorithms for extraordinary vertices. Recently lifting-scheme based biorthogonal bivariate ...

The direct and inverse theorems are established for the best approximation in the weighted L space on the unit sphere of R, in which the weight functions are invariant under finite reflection groups. The theorems are stated using a modulus of smoothness of higher order, which is proved to be equivalent to a K-functional defined using the power of the spherical h-Laplacian. Furthermore, similar ...