In this paper we give a criterion for a left Gorenstein algebra to be AS-regular. Let A be a left Gorenstein algebra such that the trivial module Ak admits a finitely generated minimal free resolution. Then A is AS-regular if and only if its left Gorenstein index is equal to− inf{i |ExtA A (k, k)i = 0}. Furthermore, A is Koszul AS-regular if and only if its left Gorenstein index is depthAA = − ...

in this paper we establish a characterization of abelian compact hausdorff semigroups with unique idempotent and ideal retraction property. we also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal withrespect to these properties.

We prove some formulas relating Cauchy-Riemann operators defined on hypercomplex subspaces of an alternative *-algebra to a differential operator associated with the concept slice-regularity and spherical Dirac operator. These results in particular allow introduce definition locally slice-regular function open path for local slice analysis. Since factor corresponding Laplacian operators, proven...

Considering the Euclidean Jordan algebra of the real symmetric matrices endowed with the Jordan product and the inner product given by the usual trace of matrices, we construct an alternating Schur series with an element of the Jordan frame associated to the adjacency matrix of a strongly regular graph. From this series we establish necessary conditions for the existence of strongly regular gra...

In the present work the properties of Cartan subalgebras and their connection with regular elements in finite dimensional Lie algebras are extended to the case of Leibniz algebras. It is shown that Cartan subalgebras and regular elements of a Leibniz algebra correspond to Cartan subalgebras and regular elements of a Lie algebra by a natural homomorphism. Conjugacy of Cartan subalgebras of Leibn...

The minimum backward Fréchet distance (MBFD) problem is a natural optimization problem for the weak Fréchet distance, a variant of the well-known Fréchet distance. In this problem, a threshold ε and two polygonal curves, T1 and T2, are given. The objective is to find a pair of walks on T1 and T2, which minimizes the union of the portions of backward movements while the distance between the movi...

We propose an improved fast local level set method for the inverse problem of gravimetry by developing two novel algorithms: one is of linear complexity designed for computing the Frechet derivative of the nonlinear domain inverse problem, and the other is designed for carrying out numerical continuation rapidly so as to obtain fictitious full measurement data from partial measurement. Since th...

We remark that the result presented here can be proved more simply using the closed graph theorem. However we believe that our results can be used to prove a more interesting result. Details to follow in a later paper. One of the remarkable features of the space of holomorphic functions (in either one or several variables) is that the standard Frechet space topologies— say, for example, the L o...

Quantum bialgebras derivable from Uq(sl2) which contain idempotents and von Neumann regular Cartan-like generators are introduced and investigated. Various types of antipodes (invertible and von Neumann regular) on these bialgebras are constructed, which leads to a Hopf algebra structure and a von Neumann-Hopf algebra structure, respectively. For them, explicit forms of some particular R-matric...

We identify the Bethe algebra of the Gaudin model associated to gl N acting on a suitable representation with the center of the rational Cherednik algebra and with the algebra of regular functions on the Calogero-Moser space.