In a recent paper it has been established that over an Artinian ring R all two-dimensional polynomial automorphisms having Jacobian determinant one are tame if R is a Q-algebra. This is a generalization of the famous Jung-Van der Kulk Theorem, which deals with the case that R is a field (of any characteristic). Here we will show that for tameness over an Artinian ring, the Q-algebra assumption ...

We define an invariant β(M) of a finite volume hyperbolic 3manifoldM in the Bloch group B(C) and show it is determined by the simplex parameters of any degree one ideal triangulation of M . We show β(M) lies in a subgroup of B(C) of finite Q-rank determined by the invariant trace field of M . Moreover, the Chern-Simons invariant of M is determined modulo rationals by β(M). This leads to a simpl...

Let S be topological semigroup, we consider an appropriate semigroup compacti cation b S of S. In this paper we study the connection between subgroups of a maximal group in a minimal left ideal of b S, which arise as equivalence classes of some closed left congruence, and the minimal ow characterized by the left congruence. A particular topology is de ned on a maximal group and it is shown that...

Cancer treatment failure, drug resistance, or metastatic recurrence are thought to be caused mainly by the existence of a very small number of cancer stem cells (CSCs). The characteristics of this subgroup of cells include self-renewal, tumorigenesis, multiple differentiation and high invasiveness, metastasis, and drug resistance potential. Many studies have demonstrated that CSCs play importan...

Let A be a local commutative principal ideal ring. We study the double coset space of GLn(A) with respect to the subgroup of upper triangular matrices. Geometrically, these cosets describe the relative position of two full flags of free primitive submodules of A. We introduce some invariants of the double cosets. If k is the length of the ring, we determine for which of the pairs (n, k) the dou...

Background:One of the main reasons for extraction of endodontically treated teeth is vertical root fracture (VRF). Some factors such as root canal treatment are involved in vertical root fracture because of their potential to weaken the tooth structure. Therefore, this study aimed to investigate the effect of combining different obturation materials and rotary systems on the fr...

Let $G$ be a group and $H$ a subgroup of $G$‎. ‎ $H$ is said to have semi-$Pi$-property in $G$ if there is a subgroup $T$ of $G$ such that $G=HT$ and $Hcap T$ has $Pi$-property in $T$‎. ‎In this paper‎, ‎investigating on semi-$Pi$-property of subgroups‎, ‎we shall obtain some new description of finite groups‎.

1. The main theorems revisited We now state in more detail the main theorems of class field theory. However, we need two more preliminary definitions: Definition 1.1. Given an extension L/K of number fields, and a fractional ideal I of L, we define the fractional ideal N L/K (I) of K as follows: write I = i q ei i , let p i = q i ∩ O K , and let N L/K (I) = i p eifi i. Definition 1.2. Let σ : K...

For every hyperbolic group, we construct an ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant which implies that several Measure Equivalence and Orbit Equivalence rigidity results established in [26] hold for all non-elementary hyperbolic groups and their non-elementary subgroups. For any subgroup Γ o...