We prove that the set of homotopy classes of the paths in a topological ring is a ring object (called ring groupoid). Using this concept we show that the ring structure of a topological ring lifts to a simply connected covering space.

The purpose of this note is to use covering space theory to construct new examples of buildings. On the level of Coxeter systems, this contsruction was described previously in Davis [4]. It goes as follows. Start with a Coxeter system (W ′, S). Change some m(s, t)’s in its Coxeter matrix from integers ≥ 2 to the symbol ∞ . This defines a new Coxeter system (W, S). Suppose C′ is a building of ty...

This article contains a new argument which proves vanishing of the first cohomology for negative vector bundles over a complex projective variety if the rank of the bundle is smaller than the dimension of the base. Similar argument is applied to the construction of holomorphic functions on the universal covering of the complex projective variety .

This paper describes certain properties of the fundamental group of the shrinking wedge of circles. Covering space theory is an inadequate tool since the shrinking wedge of circles is not semi-locally simply connected. We conclude with the fact that the shrinking wedge of circles is not homotopy equivalent to the wedge product of a countable number of circles.

Let η be a line bundle on a smooth curve X with η^2=0 such that π_η, the double covering induced by η is an etale morphism. Assume also that X_η be the Prym-canonical model of X associated to K_X.η and Q is a rank 4 quadric containing X_η. After stablishing the projective normality of the prym-canonical models of curves X with Clifford index 2, we obtain in this paper a sufficient condition for...

In image steganography, a pixel can carry secret bits by choosing adding/subtracting one to/from the gray value. This kind of “ 1 steganography” can hide a longer message than simple LSB embedding. We propose a double-layered embedding method for implementing “ 1 steganography,” in which binary covering codes and wet paper codes are used to hide messages in the LSB plane and the second LSB plan...

We study the interaction of two scattering channels for a simple geometric model consisting in double covering plane with branch points, equipped Euclidean metric. show that are open sense arXiv:1202.0333 and this property is stable under suitable perturbations

In continuous-time dynamical systems, a periodic orbit becomes a fixed point on a certain Poincaré section. The eigenvalues of the Jacobian matrix at this fixed point determine the local stability and type of bifurcation of the periodic orbit. Analogously, a 2-torus quasi-periodic orbit becomes an invariant closed curve (ICC) on a Poincaré section. The Lyapunov exponents corresponding to the ei...

The decomposition numbers of the Rudvalis sporadic simple group and of its double covering group modulo 3 are completely determined. The results were obtained using the computer algebra system MOC developed by Jansen, Lux, Parker, and the author, but the proofs are given in conventional form and can be verified by hand with the ordinary character table.

murmur of decreasing intensity. His ventricular septal defect, previously demonstrated angiocardiographically, could not be found at autopsy; it is presumed to have closed by fusion of its muscular rims with subsequent covering by endocardial proliferation. The second patient, with a double-outlet right ventricle, demonstrated progressive left ventricular enlargement and congestive failure desp...