Related papers: Affine transformations of circle and sphere
The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical)…
We show that a $3-$dimensional paracontact manifold on which $Q\varphi =\varphi Q$ is either a manifold with $trh^2=0$, flat or of constant $\xi-$sectional curvature $k\neq-1$ and constant $\varphi$-sectional curvature $-k\neq 1$.
In this article we give a sufficient condition for a morphism $\varphi$ from a smooth variety $X$ to projective space, finite onto a smooth image, to be deformed to an embedding. This result puts some theorems on deformation of morphisms of…
The object of this study is an integral operator $\mathcal{S}$ which averages functions in the Euclidean upper half-space $\mathbb{R}_{+}^{n}$ over the half-spheres centered on the topological boundary $\partial \mathbb{R}_{+}^{n}$. By…
Any function from a round $n$-dimensional sphere of radius $r$ into $n$-dimensional Euclidean space must distort the metric additively by at least $\displaystyle \frac{\pi r}{1 + \sqrt{1 - \frac{2}{n+2}}}$ if $n$ is even and $\displaystyle…
The 3D compressible and incompressible Euler equations with a physical vacuum free boundary condition and affine initial conditions reduce to a globally solvable Hamiltonian system of ordinary differential equations for the deformation…
Three-dimensional central symmetric bodies different from spheres that can float in all orientations are considered. For relative density rho=1/2 there are solutions, if holes in the body are allowed. For rho different from 1/2 the body is…
We establish sensitivity analysis on the sphere. We present formulas that allow us to decompose a function $f\colon \mathbb S^d\rightarrow \mathbb R$ into a sum of terms $f_{\boldsymbol u,\boldsymbol \xi}$. The index $\boldsymbol u$ is a…
We study the spherical slice transform which assigns to a function on the $n$-dimensional unit sphere the integrals of that function over cross-sections of the sphere by $k$-dimensional affine planes passing through the north pole. These…
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple…
We study infinitesimal conformal deformations of a triangulated surface in Euclidean space and investigate the change in its extrinsic geometry. A deformation of vertices is conformal if it preserves length cross-ratios. On one hand,…
In this work we compute the universal framed deformation functor for a reducible Galois representation $\rho$ given by direct sum of 2-dimensional representations $\rho_i$ coming from p-divisible groups. We impose the local conditions of…
A nonlinear transformation in the momentum space is constructed which converts the deformed action of Lorentz and Weyl generators on momenta into the standard one.
A nonrigid rotor model is developed from the two-parameter quantum algebra $U_{qp}({\rm u}_2)$. [This model presents the $U_{qp}({\rm u}_2)$ symmetry and shall be referred to as the qp-rotor model.] A rotational energy formula as well as a…
Given an elliptic curve $E$ defined over the rational numbers and a prime $p$ at which $E$ has good reduction, we consider the Galois deformation ring parametrizing lifts of the residual representation on the $p$-torsion group $E[p]$. For a…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
A skew-morphism $\varphi$ of a finite group $A$ is a permutation on $A$ such that $\varphi(1)=1$ and $\varphi(xy)=\varphi(x)\varphi^{\pi(x)}(y)$ for all $x,y\in A$ where $\pi:A\to\mathbb{Z}_{|\varphi|}$ is an integer function. A…
We study the vertical and conical square functions defined via elliptic operators in divergence form. In general, vertical and conical square functions are equivalent operators just in $L^2$. But when this square functions are defined…
We compute the universal deformation ring of an odd Galois two dimensional representation of Gal$(M/Q)$ with an upper triangular image, where $M$ is the maximal abelian pro-$p$-extension of $F_{\infty}$ unramified outside a finite set of…
In this paper, we first characterize the polar decomposition of unbounded weighted composition operator pairs $\textbf{C}_{\phi,\omega}$ in an $L^2$-space. Based on this characterization, we introduce the $\lambda$-spherical mean transform…