In this article, the notions of non-abelian tensor and exterior products of two normal crossed submodules of a given crossed module of groups are introduced and some of their basic properties are established. In particular, we investigate some common properties between normal crossed modules and their tensor products, and present some bounds on the nilpotency class and solvability length of the...

In this paper, we study a special class of generalized Douglas-Weyl metrics whose Douglas curvature is constant along any Finslerian geodesic. We prove that for every Landsberg metric in this class of Finsler metrics, ? = 0 if and only if H = 0. Then we show that every Finsler metric of non-zero isotropic flag curvature in this class of metrics is a Riemannian if and only if ? = 0.

‎The object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎At first we prove that a quasi-conformally flat spacetime is Einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎Einstein's field equation with cosmological constant is covariant constant‎. ‎Next‎, ‎we prove that if the perfect flui...

The ability to make decisions and to assess po­ tential courses of action is a comer-stone of many AI applications, and usually this requires explicit information about the decision-maker's prefer­ ences. In many applications, preference elic­ itation is a serious bottleneck. The user ei­ ther does not have the time, the knowledge, or the expert support required to specify complex multi-attribu...

Two major degradations, edge displacement and comer erosion, change the appearance of bilevel images. The displacement of an edge determines stroke width, and the erosion ofa comer affects crispness. These degradations are functions of the system parameters: the point spread function (PSF) width and functional form, and the binarization threshold. Changing each of these parameters will affect a...