An operation M∗ which constructs from a given structure M a tree-like structure whose domain consists of the finite sequences of elements of M is considered. A notion of automata running on such tree-like structures is defined. It is shown that automata of this kind characterise expressive power of monadic second-order logic (MSOL) over tree-like structures. Using this characterisation it is pr...

In the present paper, we give a necessary and sufficient condition for a Riemannian manifold (M, g) to have a reducible action of a hyperbolic analogue of the holonomy group. This condition amounts to a decomposition of (M, g) as a warped product of a special form, in analogy to the classical de Rham decomposition theorem for Riemannian manifolds. As a consequence of these results and Berger’s ...

We obtain estimates on the character of the cohomology of an S-equivariant holomorphic vector bundle over a Kähler manifold M in terms of the cohomology of the Lerman symplectic cuts and the symplectic reduction of M . In particular, we prove and extend inequalities conjectured by Wu and Zhang [12]. The proof is based on constructing a flat family of complex spaces Mt (t ∈ C) such that Mt is is...

Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standardgraded ring, $M$ be a finitely generated graded $R$-module and $J$be a homogenous ideal of $R$. In this paper we study the gradedstructure of the $i$-th local cohomology module of $M$ defined by apair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. Moreprecisely, we discuss finiteness property and vanishing of thegraded components $H^...

Attention is called to a polarization basis formed by four Jones vectors that is reducible to two basic structures. In these states the field is linearly polarized at any point, but the polarization direction changes with the angular coordinate. Very simple equations hold for the field lines of these basis vectors. The adoption of this basis is of interest for beams possessing a single vortex o...

A unique cooperative H2 activation reaction by heterobimetallic (NHC)M'-MCp(CO)2 complexes (NHC = N-heterocyclic carbene, M' = Cu or Ag, M = Fe or Ru) has been leveraged to develop a catalytic alkyne semi-hydrogenation transformation. The optimal Ag-Ru catalyst gives high selectivity for converting alkynes to E-alkenes, a rare selectivity mode for reduction reactions with H2. The transformation...

Let M be a simple 3-manifold with a toral boundary component ∂0M . If Dehn filling M along ∂0M one way produces a toroidal manifold and Dehn filling M along ∂0M another way produces a boundary-reducible manifold, then we show that the absolute value of the intersection number on ∂0M of the two filling slopes is at most two. In the special case that the boundary-reducing filling is actually a so...

let $m$ be a module over a commutative ring $r$ and let $n$ be a proper submodule of $m$. the total graph of $m$ over $r$ with respect to $n$, denoted by $t(gamma_{n}(m))$, have been introduced and studied in [2]. in this paper, a generalization of the total graph $t(gamma_{n}(m))$, denoted by $t(gamma_{n,i}(m))$ is presented, where $i$ is an ideal of $r$. it is the graph with all elements of $...

Let G be a connected reductive linear algebraic group. We use geometric methods to investigate G-completely reducible subgroups of G, giving new criteria for G-complete reducibility. We show that a subgroup of G is G-completely reducible if and only if it is strongly reductive in G; this allows us to use ideas of R.W. Richardson and Hilbert– Mumford–Kempf from geometric invariant theory. We ded...

We show that the problem of finding the family of all so called the locally reducible factors in the binary de Bruijn graph of order k is equivalent to the problem of finding all colourings of edges in the binary de Bruijn graph of order k − 1, where each vertex belongs to exactly two cycles of different colours. In this paper we define and study such colouring for the greater class of the de B...