This paper is devoted to the partial null controllability issue of parabolic linear systems with n equations. Given a bounded domain Ω in RN (N ∈ N∗), we study the effect of m localized controls in a nonempty open subset ω only controlling p components of the solution (p,m 6 n). The first main result of this paper is a necessary and sufficient condition when the coupling and control matrices ar...

Let Λ be a minimal Kac–Moody group of rank 2 defined over the finite field Fq , where q = pa with p prime. Let G be the topological Kac–Moody group obtained by completing Λ. An example is G = SL2(K), where K is the field of formal Laurent series over Fq . The group G acts on its Bruhat–Tits building X, a tree, with quotient a single edge. We construct new examples of cocompact lattices in G, ma...

Let g be a finite-dimensional simple Lie algebra over C of type An, and let U be the q-analogue of its universal enveloping algebra defined by Drinfel’d [4] and Jimbo [6]. According to [9, 3.5.6, 6.2.3 & 6.3.4], for each dominant weight λ in the weight lattice of g there is an irreducible, finite-dimensional highest weight U -module V (λ) with highest weight λ. Kashiwara [7] and Lusztig [8] hav...

a subgroup $h$ is said to be $nc$-supplemented in a group $g$ if there exists a subgroup $kleq g$ such that $hklhd g$ and $hcap k$ is contained in $h_{g}$, the core of $h$ in $g$. we characterize the supersolubility of finite groups $g$ with that every maximal subgroup of the sylow subgroups is $nc$-supplemented in $g$.

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...

We study the generalized Whittaker models for G = GSp(2,R) associated with indefinite binary quadratic forms when they arise from two standard representations of G: (i) a generalized principal series representation induced from the non-Siegel maximal parabolic subgroup and (ii) a (limit of) large discrete series representation. We prove the uniqueness of such models with moderate growth propert...

We determine explicitly the structure of the automorphism group of a parabolic Inoue surface. We also describe the quotients of the surface by typical cyclic subgroups of the automorphism group. 1. Statement of Results In this note we determine the automorphism group AutS of a parabolic Inoue surface S. The corresponding result for a hyperbolic Inoue surface (Inoue-Hirzebruch surface) was obtai...

Let $U$ be a regular connected affine semi-local scheme over field $k$. $G$ reductive group $U$. Assuming that has an appropriate parabolic subgroup scheme, we prove the following statement. Given $k$-scheme $W$, principal $G$-bundle $W\times_kU$ is trivial if it generic fiber of projection $W\times_kU\to U$. We also simplify proof Grothendieck-Serre conjecture: let A point generalize some othe...

All parabolic geometries, i.e. Cartan geometries with homogeneous model a real generalized flag manifold, admit highly interesting classes of distinguished curves. The geodesics of a projective class of connections on a manifold, conformal circles on conformal Riemannian manifolds, and Chern– Moser chains on CR–manifolds of hypersurface type are typical examples. We show that such distinguished...

Given a class of compact spaces, we ask which groups can be maximal parabolic subgroups of a relatively hyperbolic group whose boundary is in the class. We investigate the class of 1-dimensional connected boundaries. We get that any non-torsion infinite f.g. group is a maximal parabolic subgroup of some relatively hyperbolic group with connected one-dimensional boundary without global cut point...