Domination in Bipartite Graphs and in Their Complements

The domatic numbers of a graph G and of its complement $\bar G$ were studied by J. E. Dunbar, T. W. Haynes and M. A. Henning. They suggested four open problems. We will solve the following ones: Characterize bipartite graphs G having $d\left( G \right) = d\left( {\bar G} \right)$ Further, we will present a partial solution to the problem: Is it true that if G is a graph satisfying $d\left( G \right) = d\left( {\bar G} \right)$ then $\gamma \left( G \right) = \gamma \left( {\bar G} \right)$ ? Finally, we prove an existence theorem concerning the total domatic number of a graph and of its complement     

Evolution equations driven by a fractional Brownian motion

In this paper we study nonlinear stochastic evolution equations in a Hilbert space driven by a cylindrical fractional Brownian motion with Hurst parameter and nuclear covariance operator. We establish the existence and uniqueness of a mild solution under some regularity and boundedness conditions on the coefficients and for some values of the parameter H. This result is applied to stochastic parabolic equation perturbed by a fractional white noise. In this case, if the coefficients are Lipschitz continuous and bounded the existence and uniqueness of a solution holds if . The proofs of our results combine techniques of fractional calculus with semigroup estimates.     

Uniform Exponential Ergodicity of Stochastic Dissipative Systems

We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in ^d with d3.     

On a problem of a. kotzig concerning factorizations of 4-regular graphs

The paper gives a solution of a problem of A. Kotzǐg. This problem concerns the 4-regular graphs G with the property that in every decomposition of G into two edge-disjoint 2-regular factors at least one factor is a Hamiltonian circuit in G.     

CP violation from five-dimensional QED

It is shown that QED in (1 + 4)-dimensional space-time, with the fifth dimension compactified on a circle, is, in general, a CP violating theory. Depending on the fermionic boundary conditions, CP violation may be either explicit (through the Scherk-Schwarz mechanism) or spontaneous (via the Hosotani mechanism). The fifth component of the gauge field acquires (at the one-loop level) a nonzero vacuum expectation value which, in the presence of two fermionic fields, leads to spontaneous CP violation when the boundary conditions are CP symmetric. Phenomenological consequences are illustrated by a calculation of the electric dipole moment for the fermionic zero modes.