let $r$ be a ring and $m$ a right $r$-module with $s=end_r(m)$. a module $m$ is called semi-projective if for any epimorphism $f:mrightarrow n$, where $n$ is a submodule of $m$, and for any homomorphism $g: mrightarrow n$, there exists $h:mrightarrow m$ such that $fh=g$. in this paper, we study sgq-projective and$pi$-semi-projective modules as two generalizations of semi-projective modules. a m...

In this paper we show that if q is a power of a prime p , then the projective special linear group PSL(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group PGL(2, q) for q odd and even respectively

This paper presents a novel image space path planning method that takes mechanical constraints into consideration. The aim is to synthesize sub-goal images that can be used as reference inputs for image-based visual servoing systems. Synthesized images are constructed based on screw decompositions represented in a projective space. The projective representation allows image synthesis for threed...

We prove the arithmetic Hodge index and hard Lefschetz conjectures for the Grassmannian G = G(2, N) parametrizing lines in projective space, for the natural arithmetic Lefschetz operator defined via the Plücker embedding of G in projective space. The analysis of the Hodge index inequality involves estimates on values of certain Racah polynomials. 0. Introduction Let X be an arithmetic variety, ...

In the present investigation we link noncommutative geometry over noncommutative tori with Gabor analysis, where the first has its roots in operator algebras and the second in time-frequency analysis. We are therefore in the position to invoke modern methods of operator algebras, e.g. topological stable rank of Banach algebras, to exploit the deeper properties of Gabor frames. Furthermore, we a...

On a manifold with a projective connection we canonically assign a second order differential operator acting on the algebra of all densities to any tensor density S of fixed weight λ. In particular, this implies that on any projectively connected manifold, a ‘bracket’ (symmetric biderivation) on the algebra of functions extends canonically to the algebra of densities.