Let F (z) = z − H(z) with o(H(z)) ≥ 2 be a formal map from Cn to Cn and G(z) the formal inverse of F (z). In this paper, we give two recurrent formulas for the formal inverse G(z). The first formula not only provides an efficient method for the calculation of G(z), but also reduces the inversion problem to a Cauchy problem of a partial differential equation. The second one is differential free ...

Assume G is a group definable in a model M of a stable theory T . We prove that the semigroup SG(M) of complete G-types over M is an inverse limit of some semigroups type-definable in M eq. We prove that the maximal subgroups of SG(M) are inverse limits of some definable quotients of subgroups of G. We consider the powers of types in the semigroup SG(M) and prove that in a way every type in SG(...

Let V be a variety of not necessarily associative algebras, and A an inverse limit of nilpotent algebras Ai ∈V, such that some finitely generated subalgebra S ⊆A is dense in A under the inverse limit of the discrete topologies on the Ai. A sufficient condition on V is obtained for all algebra homomorphisms from A to finite-dimensional algebras B to be continuous; in other words, for the kernels...

Human cannabinoid type 1 (CB1) G-protein coupled receptor is a potential therapeutic target for obesity. The previously predicted and experimentally validated ensemble of ligand-free conformations of CB1 [Scott, C. E. et al. Protein Sci. 2013 , 22 , 101 - 113 ; Ahn, K. H. et al. Proteins 2013 , 81 , 1304 - 1317] are used here to predict the binding sites for known CB1-selective inverse agonists...

The purpose of this paper is to introduce a new generalized inverse, called DMP inverse, associated with a square complex matrix using its Drazin and Moore-Penrose inverses. DMP inverse extends the notion of core inverse, introduced by O.M. Baksalary and G. Trenkler for matrices of index at most 1 in [Core inverse of matrices, Linear and Multilinear Algebra, 2010, 681–697] to matrices of an arb...

Fly lobula plate tangential cells are known to perform wide-field motion integration. It is assumed that the shape of these neurons, and in particular the shape of the subclass of VS cells, is responsible for this type of computation. We employed an inverse approach to investigate the morphology-function relationship underlying wide-field motion integration in VS cells. In the inverse approach ...

Given a group G of permutations of a finite n-element set Xn and a transformation f of Xn, the G-closure 〈f : G〉 of f is the semigroup generated by all the conjugates of f by permutations in G. A semigroup S of transformations of Xn is G-normal if GS = G, where GS consists of all the permutations h of Xn such that h−1fh ∈ S for all f ∈ S. We may assume that Xn is a chain and we let POIn be the ...

A monoid M is an extension of a submonoid T by a group G if there is a morphism from M onto G such that T is the inverse image of the identity of G. Our first main theorem gives descriptions of such extensions in terms of groups acting on categories. The theory developed is also used to obtain a second main theorem which answers the following question. Given a monoid M and a submonoid T , under...

We characterize the fundamental group of a locally finite graph G with ends, by embedding it canonically as a subgroup in the inverse limit of the free groups π1(G ′) with G′ ⊆ G finite. As an intermediate step, we characterize π1(|G|) combinatorially as a group of infinite words.

These informal notes are concerned with the broad themes of harmonic analysis of groups and their representations. We shall follow somewhat the view of a classical analyst, with interest in various norms in particular. At the same time we shall try to notice some algebraic aspects, which includes using fields other than the complex numbers. Let G be a group. Thus G is a set with a distinguished...