We complete the classification of ruled real hypersurfaces with shape operator constant norm in nonflat complex space forms by showing existence a unique inhomogeneous example hyperbolic space.

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

In ‎the present ‎paper, ‎we ‎introduce the ‎two-wavelet ‎localization ‎operator ‎for ‎the square ‎integrable ‎representation ‎of a‎ ‎homogeneous space‎ with respect to a relatively invariant measure. ‎We show that it is a bounded linear operator. We investigate ‎some ‎properties ‎of the ‎two-wavelet ‎localization ‎operator ‎and ‎show ‎that ‎it ‎is a‎ ‎compact ‎operator ‎and is ‎contained ‎in‎ a...

Mathematical morphology (MM) is a theory for spatial structure analysis that was established by introducing fundamental operators applied to two sets [1]. A set is processed by another one having a carefully selected shape and size, known as the structuring element (SE). In the context of image processing, the SE acts as a probe for extracting or suppressing specific structures of the image obj...

A deformation invariant representation of surfaces, the GPS embedding, is introduced using the eigenvalues and eigenfunctions of the Laplace-Beltrami differential operator. Notably, since the definition of the GPS embedding completely avoids the use of geodesic distances, and is based on objects of global character, the obtained representation is robust to local topology changes. The GPS embedd...

We introduce a powerful method based on integral geometry and the Kac theorem for the spectrum of the Laplace operator to define the effective shape of an inclusion in a system made up of a distribution of arbitrarily shaped constituents. Reconstructing the microstructure using the effective inclusion shape leads to an excellent match to the percolation thresholds and to the mechanical and tran...

In this paper, we consider the well-known following shape optimization problem: λ2(Ω ∗) = min |Ω|=V0 Ω convex λ2(Ω), where λ2(Ω) denotes the second eigenvalue of the Laplace operator with homogeneous Dirichlet boundary conditions in Ω ⊂ R, and |Ω| is the area of Ω. We prove, under some technical assumptions, that any optimal shape Ω∗ is C 1 2 and is not C for any α > 1 2 . We also derive from o...

Data from 1006 pigs selected for breeding and subsequently scored at 22-24 weeks of age were used to estimate heritabilities for conformation traits. Front wrists, front pasterns, back hocks, back pasterns, front view, rear view and back shape were each subjectively scored by a single operator. For the individual traits heritability estimates ranged from high (0.42±0.09 for front pasterns) to n...

3-dimensional affine hypersurfaces admitting a pointwise SO(2)-or Z 3-symmetry Abstract In (equi-)affine differential geometry, the most important algebraic invariants are the affine (Blaschke) metric h, the affine shape operator S and the difference tensor K. A hypersurface is said to admit a point-wise symmetry if at every point there exists a linear transformation preserving the affine metri...

Computer vision needs suitable methods of shape representation and contour reconstruction. One of them, invented by the author and called method of Hurwitz-Radon Matrices (MHR), can be used in representation and reconstruction of shapes of the objects in the plane. Proposed method is based on a family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed o...