Related papers: Rotation properties of isotropic dilation matrices

We have introduce a new vision of stochastic processes through the geometry induced by the dilation. The dilation matrices of a given processes are obtained by a composition of rotations matrices, contain the measure information in a…

We investigate the invariance properties of general wavelet coorbit spaces and Besov-type decomposition spaces under dilations by matrices. We show that these matrices can be characterized by quasi-isometry properties with respect to a…

We characterize the d x d matrices whose numerical ranges are invariant by rotations of angle 2$\pi$/d.

The covariance matrix function is characterized in this paper for a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the compact two-point homogeneous space. Necessary and…

In the paper, we present a family of multivariate compactly supported scaling functions, which we call as elliptic scaling functions. The elliptic scaling functions are the convolution of elliptic splines, which correspond to homogeneous…

In this note, we generalize biharmonic equation for rotationally symmetric maps ([4], [16], [10]) to equivariant maps between model spaces and use it to give a complete classification of rotationally symmetric conformal biharmonic maps from…

We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…

This note deals with two topics of linear algebra. We give a simple and short proof of the multiplicative property of the determinant and provide a constructive formula for rotations. The derivation of the rotation matrix relies on simple…

This paper examines the properties of real symmetric square matrices with a constant value for the main diagonal elements and another constant value for all off-diagonal elements. This matrix form is a simple subclass of circulant matrices,…

In this work a symmetry of universal finite-size scaling functions under a certain anisotropic scale transformation is postulated. This transformation connects the properties of a finite two-dimensional system at criticality with…

Elliptical rotation is the motion of a point on an ellipse through some angle about a vector. The purpose of this paper is to examine the generation of elliptical rotations and to interpret the motion of a point on an elipsoid using…

In the present study an oscillator system formed by a seesaw connected to a simple pendulum coupled to a mobile platform with a certain slope, is analyzed. The observed properties of the system when faced with a possible displacement of the…

We present the reduction of the correlation functions of the Ising model on the anisotropic square lattice to complete elliptic integrals of the first, second and third kind, the extension of Kramers-Wannier duality to anisotropic…

Correlation functions of the two-dimensional Ising model on the periodic lattice can be expressed in terms of form factors - matrix elements of the spin operator in the basis of common eigenstates of the transfer matrix and translation…

A hermitian matrix can be parametrized by a set consisting of its determinant and the eigenvalues of its submatrices. We established a group of equations which connect these variables with the mixing parameters of diagonalization. These…

We estimate the second order linking invariants of Lipschitz maps from an n-dimensional ellipse. The estimate uses a new directionally-dependent version of the isoperimetric inequality for cycles inside the ellipse. Using this work, we…

We calculate the two-point correlation function and magnetic susceptibility in the anisotropic 2D Ising model on a lattice with one infinite and the other finite dimension, along which periodic boundary conditions are imposed. Using exact…

This article extends the study of the dynamical properties of the symmetric McMillan map, emphasizing its utility in understanding and modeling complex nonlinear systems. Although the map features six parameters, we demonstrate that only…

We determine when a matrix is similar to a partial isometry, refining a result of Halmos--McLaughlin.

Pillow boxes are surfaces used for gift boxes, packaging, and even architectural applications. By definition, a pillow box is isometric to a double rectangle consisting of two copies of a rectangle. If the crease pattern is allowed to…