There are only finitely many locally projective regular polytopes of type {5, 3, 5}. They are covered by a locally spherical polytope whose automorphism group is J1 × J1 × L2(19), where J1 is the first Janko group, of order 175560, and L2(19) is the projective special linear group of order 3420. This polytope is minimal, in the sense that any other polytope that covers all locally projective po...

We consider the existence of blocking semiovals in nite projective planes which have intersection sizes 1; m + 1 or n + 1 with the lines of the plane, for 1 m < n. For those prime powers q 1024, in almost all cases, we are able to show that, apart from a trivial example, no such blocking semioval exists in a projective plane of order q. We are able to prove also, for general q, that if q 2 + q ...

For an unmixed bipartite graph G we consider the lattice of vertex covers LG and compute depth, projective dimension and extremal Bettinumbers of R/I(G) in terms of this lattice.

We investigate the structure of pure-syzygy modules in a pure-projective resolution of any right R-module over an associative ring R with an identity element. We show that a right R-module M is pure-projective if and only if there exists an integer n ≥ 0 and a pure-exact sequence 0 → M → Pn → · · · → P0 → M → 0 with pure-projective modules Pn, . . . , P0. As a consequence we get the following v...

Let G be a finite group. Suppose that Y is a projective algebraic variety over Z (i.e an integral scheme which is projective and flat over Spec (Z)) of relative dimension d. In this paper, we consider finite Galois covers π : X → Y with group G which are everywhere unramified, i.e “G-torsors”. Let F be a G-equivariant coherent sheaf on X. Consider the value of the right derived global section f...

A curve on a sphere, aane or projective space is called nondegenerate if its osculating frame is nondegenerate at every point. We calculate the number of connected components in the space of all closed nondegenerate curves immersed into S n ; R n or P n. In the cases of S n or R n it is equal to 4 for odd n > 3 and 6 for even n > 4 (for S 2 the answer is also 6). For projective space P n the nu...

The aim of this paper is to review thoroughly the applications ∩ -large pseudo N-injective acts in quasi-Frobenius monoid theory, and therefore, relationship with some class injectivity studied. Applications properties injective theory are proven. Also, it’s proved that subsequent parity, every union (direct sum) two a act if only under Noetherian condition for right S. Additionally, we categor...

Different versions for defining Ashtekar’s generalized connections are investigated depending on the chosen smoothness category for the paths and graphs – the label set for the projective limit. Our definition covers the analytic case as well as the case of

In this paper our focus is to study certain covering properties in topological spaces by using semi-open covers. A part of this article deals with Rothberger-type covering properties. The notions of s-Rothberger, almost s-Rothberger, star s-Rothberger, almost star s-Rothberger, strongly star s-Rothberger spaces are defined and corresponding properties are investigated.