We study projective dimension, a graph parameter (denoted by pd(G) for a graph G), introduced by Pudlák and Rödl [13], who showed that proving lower bounds for pd(Gf ) for bipartite graphs Gf associated with a Boolean function f imply size lower bounds for branching programs computing f . Despite several attempts [13, 17], proving super-linear lower bounds for projective dimension of explicit f...

In this paper, we study the relation between m-strongly Gorenstein projective (resp. injective) modules and n-strongly Gorenstein projective (resp. injective) modules whenever m 6= n, and the homological behavior of n-strongly Gorenstein projective (resp. injective) modules. We introduce the notion of n-strongly Gorenstein flat modules. Then we study the homological behavior of n-strongly Goren...

In this paper, we study a particular case of Gorenstein projective, injective, and flat modules, which we call, respectively, strongly Gorenstein projective, injective, and flat modules. These last three classes of modules give us a new characterization of the first modules, and confirm that there is an analogy between the notion of “Gorenstein projective, injective, and flat modules”and the no...

Quadratically parametrized maps from a real projective space to a complex projective space are constructed as projections of the Veronese embedding. A classification theorem relates equivalence classes of projections to real congruence classes of complex symmetric matrix pencils. The images of some low-dimensional cases include certain quartic curves in the Riemann sphere, models of the real pr...

This paper presents a dependencyconstrained hierarchical machine translation model that uses Moses open-source toolkit for rule extraction and decoding. Experiments are carried out for the German-English language pair in both directions for projective and non-projective dependencies. We examine effects on SCFG size and automatic evaluation results when constraints are applied with respect to pr...

The Haagerup norm ‖ · ‖h on the tensor product A ⊗ B of two C∗-algebras A and B is shown to be Banach space equivalent to either the Banach space projective norm ‖ · ‖γ or the operator space projective norm ‖ · ‖∧ if and only if either A or B is finite dimensional or A and B are infinite dimensional and subhomogeneous. The Banach space projective norm and the operator space projective norm are ...

— We show that the connected sum of two copies of real projective 3-space does not admit a real projective structure. This is the first known example of a connected 3-manifold without a real projective structure.

We describe a construction of fuzzy spaces which approximate projective toric varieties. The construction uses the canonical embedding of such varieties into a complex projective space: The algebra of fuzzy functions on a toric variety is obtained by a restriction of the fuzzy algebra of functions on the complex projective space appearing in the embedding. We give several explicit examples for ...

Problem statement: Algebraic K-theory of projective modules over commutative rings were introduced by Bass and central simple superalgebras, supercommutative super-rings were introduced by many researchers such as Knus, Racine and Zelmanov. In this research, we classified the projective supermodules over (torsion free) supercommutative super-rings and through out this study we forced our selves...

The camera mapping can be seen in two ways. The classic approach is to emphasize the projective nature of the camera. But also the re-projective nature can be taken into account: Every point in the image plane determines a viewing ray. Both mappings can be described by the same set of parameters. In fact the re-projective camera mapping can be seen as the inversion of the projective camera mapp...