Related papers: Polarizing Anisotropic Heisenberg Groups
By decomposing the regular representation of a particular (Heisenberg-like) Lie supergroup into irreducible subspaces, we show that not all of them can be obtained by applying geometric quantization to coadjoint orbits with an even…
In this paper we extend the research on potential theory and its geometric applications from Euclidean spaces to homogeneous Carnot groups. We introduce a new approach to use the geometric completeness to estimate the Hausdorff dimension of…
We provide a new and elementary proof for the structure of geodesics in the Heisenberg group $\mathbb{H}^n$. The proof is based on a new isoperimetric inequality for closed curves in $\mathbb{R}^{2n}$. We also prove that the…
In this paper we establish the starshapedness of the level sets of the capacitary potential of a large class of fully-nonlinear equations for condensers in Carnot groups, once a natural notion of starshapedness has been introduced. Our main…
We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.
The class of all quasigroups is covered by six classes: the class of all asymmetric quasigroups and five varieties of quasigroups (commutative, left symmetric, right symmetric, semi-symmetric and totally symmetric). Each of these classes is…
We propose a simple cluster-based method with application to calculations of Compton profile anisotropies of ice. The convergence of the method is checked with respect to Crystal95 results. Increasing both basis-set quality and cluster…
The authors suggest a new powerful tool for solving group classification problems, that is applied to obtaining the complete group classification in the class of nonlinear Schr\"odinger equations of the form…
A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces…
In this paper, we establish a Reshetnyak type theorem for quasiregular values on the setting of Carnot group of $H$-type.
We provide a simple way to obtain the meromorphic extension of Eisenstein series and Scattering matrices under conditions which generalize the case of discrete groups acting convex cocompactly on hyperbolic spaces.
The factorization technique for superintegrable Hamiltonian systems is revisited and applied in order to obtain additional (higher-order) constants of the motion. In particular, the factorization approach to the classical anisotropic…
It is known that if an Abelian group operation is used in an Ar{\i}kan-style construction, we have multilevel polarization where synthetic channels can approach intermediate channels that are neither almost perfect nor almost useless. An…
We define the notion of affine Anosov representations of word hyperbolic groups into the affine group $\mathsf{SO}^0(n+1,n)\ltimes\mathbb{R}^{2n+1}$. We then show that a representation $\rho$ of a word hyperbolic group is affine Anosov if…
In this paper, we establish the theory of nilpotent hypergroups and study some properties of nilpotent hypergroups and provided some structural characterizations of nilpotent hypergroups.
A generalization of the polar coding scheme called mixed-kernels is introduced. This generalization exploits several homogeneous kernels over alphabets of different sizes. An asymptotic analysis of the proposed scheme shows that its…
In this paper we describe the factorization of the higher order polars of a generic branch in its equisingularity class. We generalize the results of Casas-Alvero and Hefez-Hernandes-Hern\'andez to higher order polars.
The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.
In this paper we classify Baumslag-Solitar groups up to commensurability. In order to prove our main result we give a solution to the isomorphism problem for a subclass of Generalised Baumslag-Solitar groups.
The anisotropic propagation of particles is a fundamental transport phenomenon in solid state physics. As for crystalline semiconductors, the anisotropic charge transport opens novel designing routes for electronic devices, where the…