The title compound, C42H48O6, was obtained via formyl-ation of 25,26,27,28-tetra-propoxycalix[4]arene with dichloro-methyl methyl ether and tin tetra-chloride. It adopts a pinched cone conformation, which leads to an open cavity. The two opposite aromatic rings bearing formyl groups are almost parallel, making a dihedral angle of 29.1 (2)°. The other pair of opposite rings are close to being pe...

We describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Let K/F be a finite separable field extension and let x, y ∈ K. When is F [x, y] = F [αx+ βy] for s...

Let K be the Lie superalgebra of contact vector fields on the supersymmetric line R. We compute the action of K on the modules of differential and pseudodifferential operators between spaces of tensor densities, in terms of their conformal symbols. As applications we deduce the geometric subsymbols, 1-cohomology, and various uniserial subquotients of these modules. We also outline the computati...

It is shown that each almost maximal valuation ring R, such that every indecomposable injective R-module is countably generated, satisfies the following condition (C): each fp-injective R-module is locally injective. The converse holds if R is a domain. Moreover, it is proved that a valuation ring R that satisfies this condition (C) is almost maximal. The converse holds if Spec(R) is countable....

1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Definition of the Witt Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3. Proof of the Existence of the Witt Rings . . . . . . . . ....

The title compound, C(14)H(16), is built up from three five-membered rings. Two of the five-membered rings display an envelope conformation and the third one is almost planar (r.m.s. deviation = 0.014 Å).

If for any maximal right ideal P of B and a ∈ N(B) ,aB/ aP is almost N-injective, then ring said to be generalized N-injective. In this article, we present some significant findings that are known N-injective rings demonstrate they hold rings. At the same time, study case in which every S.S.Right B-module

Cirrate octopods are considered to resemble the ancestor of all octopuses. Cirrates inhabit deep ocean and characterized by presence fins, a cartilaginous inner shell single row suckers alternating with pairs cirri thus comprising uniserial biserial cirri. The objective this contribution is improve taxonomy Opisthoteuthis bruuni from southeastern Pacific Ocean suggest new hypothesis cirrate phy...