Multiplicity of closed characteristics on symmetric convex hypersurfaces in R2n\R^{2n}

Let $\Sigma$ be a compact $C^2$ hypersurface in $\R^{2n}$ bounding a convex set with non-empty interior. In this paper it is proved that there always exist at least $n$ geometrically distinct closed characteristics on $\Sigma$ if $\Sigma$ is symmetric with respect to the origin.Comment: 16 page

Developing an economic estimation system for vertical farms

The concept of vertical farming is nearly twenty years old, however, there are only a few experimental prototypes despite its many advantages compared to conventional agriculture. Significantly, financial uncertainty has been identified as the largest barrier to the realization of a ‘real’ vertical farm. Some specialists have provided ways to calculate costs and return on investment, however, most of them are superficial with calculations based on particular contextual circumstances. To move the concept forwards a reliable and flexible estimating tool, specific to this new building typology, is clearly required. A computational system, software named VFer, has therefore been developed by the authors to provide such a solution. This paper examines this highly flexible, customised system and results from several typical vertical farm configurations in three mega-cities (Shanghai, London and Washington DC) are used to elucidate the potential economic return of vertical farms

On Generalized Sub-Gaussian Canonical Processes and Their Applications

We obtain the tail probability of generalized sub-Gaussian canonical processes. It can be viewed as a variant of the Bernstein-type inequality in the i.i.d case, and we further get a tighter bound of concentration inequality through uniformly randomized techniques. A concentration inequality for general functions involving independent random variables is also derived as an extension. As for applications, we derive convergence results for principal component analysis and the Rademacher complexities method.Comment: 25page

Analysis of fatigue delamination growth for piezoelectric laminated cylindrical shell considering nonlinear contact effect

AbstractThis paper presents a nonlinear analysis model of fatigue delamination growth for piezoelectric laminated cylindrical shells with asymmetric laminations. Considering the geometric nonlinearity and the nonlinear contact effect, the nonlinear governing equations and corresponding matching conditions for the delaminated shells are established by using the movable-boundary variational principle. According to the Griffith criterion and Paris law, the energy release rate and delamination growth rate along the delamination front are determined. Then, using cyclic skip method, the delamination growth lengths are derived. In numerical examples, the effects of the voltages, stiffness factor of contact region, asymmetry of delamination and delamination length on energy rate and delamination growth length are discussed