Existence of solitary travelling waves in interfacial electrohydrodynamics

The propagation of waves on the surface of a fluid layer of finite depth is considered in the presence of a normal electric field, due to parallel electrodes at arbitrary separation distance. The combined effect of electric field, gravity and surface tension is considered in the long-wavelength small-amplitude limit. Travelling wave solutions are characterised in terms of the Froude number, an electric Weber number and a Bond number and conditions for the existence of solitary waves are determined in terms of these parameters

Average case quantum lower bounds for computing the boolean mean

We study the average case approximation of the Boolean mean by quantum algorithms. We prove general query lower bounds for classes of probability measures on the set of inputs. We pay special attention to two probabilities, where we show specific query and error lower bounds and the algorithms that achieve them. We also study the worst expected error and the average expected error of quantum algorithms and show the respective query lower bounds. Our results extend the optimality of the algorithm of Brassard et al.Comment: 18 page

Planning Practices For The Protection Of Cultural Heritage: Lessons Learnt From The Greek UNESCO Sites

By the case study conducted in the Greek UNESCO sites, it was revealed that, despite the fact that most of the monuments are subjects of multiple zoning, little is accomplished for their spatial protection. This is either because zoning and planning launched by the Ministry for the Environment is absent or taking too long to get approved or because zoning deriving from the Ministry of Culture is void of spatial regulations. This means that on the one hand the Ministry for the Environment should proceed at a faster pace to the elaboration of Local Spatial Plans that are necessary especially in the case of monuments in rural settings, while on the other hand the Ministry of Culture should immediately proceed to the revision of Protection Zones A and B, so they fall into the guidelines of the new Law 3028 and they acquire spatial restrictions and regulations; a condition that can only be achieved with the collaboration among Spatial Planners and Archaeologists and among competent bodies

Poisson Yang-Baxter maps with binomial Lax matrices

A construction of multidimensional parametric Yang-Baxter maps is presented. The corresponding Lax matrices are the symplectic leaves of first degree matrix polynomials equipped with the Sklyanin bracket. These maps are symplectic with respect to the reduced symplectic structure on these leaves and provide examples of integrable mappings. An interesting family of quadrirational symplectic YB maps on $\mathbb{C}^4 \times \mathbb{C}^4$ with $3\times 3$ Lax matrices is also presented.Comment: 22 pages, 3 figure