In this paper we first introduce quermassintegrals for free boundary hypersurfaces in the $(n+1)$-dimensional Euclidean unit ball. Then solve some related isoperimetric type problems convex hypersurfaces, which lead to new Alexandrov–Fenchel inequalities. particular, $n = 2$ obtain a Minkowski-type inequality and 3$ an optimal Willmore-type inequality. To prove these estimates, employ specifica...

It is shown that the kernels for mean value representations of points in R in terms of the integrals over piecewise smooth hypersurfaces are divergence free vector fields defined by homogeneous functions of degree −(n+1), whose restrictions to the unit sphere are positive and orthogonal to the first harmonics. By Minkowski problem, such a function is the reciprocal of the composition of the Gau...

LetX be a compact, strictly convex C-hypersurface in the (n+1)-dimensional Euclidean space R. The Gauss map ofX maps the hypersurface one-to-one and onto the unit n-sphere S. One may parametrize X by the inverse of the Gauss map. Consequently, the Gauss curvature can be regarded as a function on S. The classical Minkowski problem asks conversely when a positive function K on S is the Gauss curv...

bstract. A comprehensive survey of 48 filters for impulsive noise emoval from color images is presented. The filters are formulated sing a uniform notation and categorized into 8 families. The perforance of these filters is compared on a large set of images that over a variety of domains using three effectiveness and one effiiency criteria. In order to ensure a fair efficiency comparison, a fas...

The classical Minkowski problem lead to the Lp Minkowski problem and now to the Orlicz-Minkowski problem. Existence is demonstrated for the even Orlicz-Minkowski problem. A byproduct is a new approach to the solution of the classical Minkowski problem.

We present a derivation of relativistic spacetime largely untethered from specific physical considerations, in constrast to the many physically-based derivations that have appeared in the last few decades. The argument proceeds from the inherent magma (groupoid) existing on the union of spacetime frame components [Formula: see text] and Euclidean [Formula: see text] which is consistent with an ...

A new approach to the inverse scattering problem proposed by Schroer, is applied to two-dimensional integrable quantum field theories. For any two-particle S-matrix S2 which is analytic in the physical sheet, quantum fields are constructed which are localizable in wedge-shaped regions of Minkowski space and whose two-particle scattering is described by the given S2. These fields are polarizatio...

A mapping between the operators of the bosonic oscillator and the Lorentz rotation and boost generators is presented. The analog of this map in the qdeformed regime is then applied to q-deformed bosonic oscillators to generate a q-deformed Lorentz algebra, via an inverse of the standard chiral decomposition. A fundamental representation, and the co-algebra structure, are given, and the generato...

The periodic Jacobi inverse eigenvalue problem concerns the reconstruction of a matrix from prescribed spectral data. In Minkowski spaces, with given signature operator H=diag(1,1,…,1,?1), corresponding is pseudo-Jacobi matrix. for such matrices consists in matrices, same order and H. this paper we solve by applying Sylvester’s identity Householder transformation. solution number algorithm are ...