We are mainly concerned with the completablity of unimodular rows to an invertible matrix. We first relate this to stable range of the ring. Further, we consider rows generating an idempotent of the ring to obtain completability under special conditions. We try to obtain analogues of important theorems regarding unimodular rows in the case of these “idempotent rows”. By ring, we shall always me...

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...

A partial information algorithm for a language A computes, for some fixed m, for input words x1, . . . , xm a set of bitstrings containing χA(x1, . . . , xm). E.g., p-selective, approximable, and easily countable languages are defined by the existence of polynomial-time partial information algorithms of specific type. Self-reducible languages, for different types of self-reductions, form subcla...

In this paper, we study the class of of C3-like Finsler metrics which contains the class of semi-C-reducible Finsler metric. We find a condition on C3-like metrics under which the notions of Landsberg curvature and mean Landsberg curvature are equivalent.

Let M be a simple 3-manifold with F a component of ∂M of genus at least two. For a slope α on F , we denote by M(α) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of α on F . Suppose that α and β are two separating slopes on F such that M(α) and M(β) are reducible. Then the distance between α and β is at most 2. As a corollary, if g(F ) = 2, then there is at mos...

It is proved that if A is aregular uniform algebra on a compact Hausdorff space X in which every closed ideal is an M-ideal, then A = C(X).

Proof. Now suppose that ρp is absolutely reducible and we want to show that for any other λ ∈ Spec(E), ρλ is also absolutely reducible. Note that there exists a finite extension K over Ep such that ρp is reducible. Then there is a vector e1 in the underline space V ′ = V ⊗Ep K such that G is stable over e1. Let χ1 be the character of G acts on e1, χ2 the character G acts on V ′/K · e1. Since χi...

We recall from [10] a Gδ σ-ideal of compact subsets of 2 ω and prove that it is not Tukey reducible to the ideal I1/n = {H ⊆ ω : ∑ h∈H 1/h <∞}. This result answers a question of S. Solecki and S. Todorčević in the negative.