A Polish group G is called a group of quasi-invariance or a QI-group, if there exist a locally compact group X and a probability measure μ on X such that 1) there exists a continuous monomorphism of G to X, and 2) for each g ∈ X either g ∈ G and the shift μg is equivalent to μ or g 6∈ G and μg is orthogonal to μ. It is proved that G is a σ-compact subset of X. We show that there exists a quotie...

Given a finite group G, let ram(G) (resp. ramt(G)) denote the minimal positive integer such that G can be realized as the Galois group of an extension of Q (resp. a tamely ramified extension of Q) ramified only at ram(G) (resp. ramt(G)) finite primes. The present paper is devoted to study ram(G) and ramt(G), for some solvable groups G. More precisely, we consider the case where G is either a fi...

1. Introduction. Combining the work of many people yields a complete quasi-isometry classification of irreducible lattices in semisimple Lie groups (see [F] for an overview of these results). One of the first general results in this classification is the complete description, up to quasi-isometry, of all nonuniform lattices in semisimple Lie groups of rank 1, proved by R. Schwartz [S1]. He show...

Angell’s logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC Ferguson, and 16-valued Fine. It is that the former image surjective homomorphism from latter, i.e., an epimorphic image. Some candidate 7-valued matrices are ruled out as characteristic AC. Whether with fewer than 9 values exist remains open question. The results were obtained help MUltlog syst...

— We prove stability of the bound states for the quantum harmonic oscillator under non-resonant, time quasi-periodic perturbations by proving that the associated Floquet Hamiltonian has pure point spectrum. Résumé (Stabilité de l’oscillateur harmonique quantique sous les perturbations quasipériodiques) Nous démontrons la stabilité des états bornés de l’oscillateur harmonique sous les perturbati...

Let G be a graph. For any two distinct vertices x and y in G, denote distG(x, y) the distance in G from x and y. For u, v ∈ V (G) with distG(u, v) = 2, denote JG(u, v) = {w ∈ NG(u)∩NG(v)|N(w) ⊆ N [u]∪ N [v]}. A graph G is claw-free if it contains no induced subgraph isomorphic to K1,3. A graph G is called quasi-claw-free if JG(u, v) 6= ∅ for any u, v ∈ V (G) with distG(u, v) = 2. Kriesell’s res...

For G an almost simple simply connected algebraic group defined over a field F , Rost has shown that there exists a canonical map RG : H (F, G) → H(F, Q/Z(2)). This includes the Arason invariant for quadratic forms and Rost’s mod 3 invariant for Albert algebras as special cases. We show that RG has trivial kernel if G is quasi-split of type E6 or E7. A case-by-case analysis shows that it has tr...

In G\"odel-type Som-Raychaudhuri (SR) cosmic string spacetime background, we re-cycle the Klein-Gordon (KG) oscillators and report their correct exact solutions. We argue that mathematical collapse of KG-equation into 2-dimensional radial Schr\"odinger-like oscillator does not yield parametric characterizations one is inherited by other. The angular frequency (positive) in Schr\"odinger case re...

Let n ≥ 2 and Fn be the free group of rank n. Its automorphism group Aut(Fn) has a well-known surjective linear representation ρ : Aut(Fn) −→ Aut(Fn/F ′ n) = GLn(Z) where F ′ n denotes the commutator subgroup of Fn. By Aut (Fn) := ρ(SLn(Z)) we denote the special automorphism group of Fn. For an epimorphism π : Fn → G of Fn onto a finite group G we call Γ(G, π) := {φ ∈ Aut(Fn) | πφ = π} the stan...