In this paper we study the automorphism group of procongruence mapping class through its action on associated curve and pants complexes. Our main result is a rigidity theorem for completion complex. As an application prove that moduli stacks smooth algebraic curves satisfy weak anabelian property in setting.

We unify the Kumjian-Renault Weyl groupoid construction with Lawson-Lenz version of Exel's tight construction. do this by utilising only a weak algebraic fragment C*-algebra structure, namely its *-semigroup reduct. Fundamental properties like local compactness are also shown to remain valid in general classes *-rings.

In this work, we define the notion of an algebraic distance in algebraic cone metric spaces defined by Niknam et al. [A. Niknam, S. Shamsi Gamchi and M. Janfada, Some results on TVS-cone normed spaces and algebraic cone metric spaces, Iranian J. Math. Sci. Infor. 9 (1) (2014), 71--80] and introduce some its elementary properties. Then we prove the existence and uniqueness of fixed point for a B...

The logical and algebraic approaches are regarded as two of the dominant methodologies for the development of reactive and concurrent systems. It is well known that the logic approach is more abstract, but lacks compositionality; while the algebraic approach is inherently compositional, but lacks abstractness. However, connecting the two approaches is a major challenge in computer science, and ...

We give an overview of a number of algebraic multigrid methods targeting finite element discretization problems. The focus is on the properties of the constructed hierarchy of coarse spaces that guarantee (two-grid) convergence. In particular, a necessary condition known as “weak approximation property,” and a sufficient one, referred to as “strong approximation property,” are discussed. Their ...

The theory of compensated compactness of Murat and Tartar links the algebraic condition of rank-r convexity with the analytic condition of weak lower semicontinuity. The former is an algebraic condition and therefore it is, in principle, very easy to use. However, in applications of this theory, the need for an efficient classification of rank-r convex forms arises. In the present paper, we def...

Let G be a connected linear algebraic group over a geometric field k of cohomological dimension 2 of one of the types which were considered by Colliot-Thélène, Gille and Parimala. Basing on their results, we compute the group of classes of R-equivalence G(k)/R, the defect of weak approximation AΣ(G), the first Galois cohomology H(k,G), and the Tate–Shafarevich kernel x(k,G) (for suitable k) in ...