In this paper, the notion of Moore–Penrose biorthogonal systems is generalized. In [Fiedler, Moore–Penrose biorthogonal systems in Euclidean spaces, Lin. Alg. Appl. 362 (2003), pp. 137–143], transformations of generating systems of Euclidean spaces are examined in connection with the Moore-Penrose inverses of their Gram matrices. In this paper, g-inverses are used instead of the Moore–Penrose i...

This paper deals with the Weak Inverse Galois Problem, which, for a given field $k$, states that, every finite group $G$, there exists separable extension $L/k$ such that ${\rm {Aut}}(L/k)=G$. One of paper’s goals is to explain how one ca

We prove an interpolation type inequalitie between C , L∞ and L spaces and use it to establish the local Hölder continuity of the inverse of the p-Laplace operator: ‖(−∆p)(f)−(−∆p)(g)‖C1(Ω̄) ≤ C‖f−g‖ r L(Ω) , for any f and g in a bounded set in L(Ω).

Keywords--Genera l ized inverses, Recursive determination, Unified approach, Dynamic programming. 1. I N T R O D U C T I O N The recursive determination of a generalized inverse of a matr ix finds extensive applications in the fields of statistical inference [1-3], filtering theory, estimation theory [4], and system identification [5]. More recently, generalized inverses have found renewed appl...

A prospective, large library virtual screen against an activated β2-adrenergic receptor (β2AR) structure returned potent agonists to the exclusion of inverse-agonists, providing the first complement to the previous virtual screening campaigns against inverse-agonist-bound G protein coupled receptor (GPCR) structures, which predicted only inverse-agonists. In addition, two hits recapitulated the...

A simple consequence of a theorem of Franks says that whenever a continuous map, g, is homotopic to angle doubling on the circle it is semiconjugate to it. We show that when this semiconjugacy has one disconnected point inverse, then the typical point in the circle has a point inverse with uncountably many connected components. Further, in this case the topological entropy of g is strictly larg...

In this paper, new aspects of treatment comparison are brought out via the dimension reduction model of Li (1991) for general regression settings. Denote the treatment indicator by Z and the covariate by X. The model Y = g(v 0 X + Z;) is discussed in detail. Estimates of v and are obtained without assuming a functional form for g. Our method is based on the use of SIR (sliced inverse regression...

In this paper, new aspects of treatment comparison are brought out via the dimension reduction model of Li (1991) for general regression settings. Denoting the treatment indicator by Z and the covariate by X, the model Y = g(v0X + Z; ) is discussed in detail. Estimates of v and are obtained without assuming a functional form for g. Our method is based on the use of SIR (sliced inverse regressio...

Given a simple graph G with a vertex set V and a set of "requirements" {rvw \ v , w E V}, we consider a problem to find a Hamilton cycle minimizing an objective function similar to that in the optimum requirement spanning tree (ORST) problem studied by Hu. And we show that a particular Hamilton cycle C" which is explicitly definable is a solution to the problem when G is complete and { r v w } ...

We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the free groups ⇡1(G 0) with G0 ✓ G finite.