Decomposition of stochastic flows with automorphism of subbundles component

We show that given a $G$-structure $P$ on a differentiable manifold $M$, if the group $G(M)$ of automorphisms of $P$ is big enough, then there exists the quotient of an stochastic flows $phi_t$ by $G(M)$, in the sense that $\phi_t = \xi_t \circ \rho_t$ where $\xi_t \in G(M)$, the remainder $\rho_t$ has derivative which is vertical but transversal to the fibre of $P$. This geometrical context generalizes previous results where $M$ is a Riemannian manifold and $\phi_t$ is decomposed with an isometric component, see Liao \cite{Liao1} and Ruffino \cite{Ruffino}, which in our context corresponds to the particular case of an SO(n)-structure on $M$.Comment: To appear in Stochastics and Dynamics, 201

On the hyperbolicity of C1C^1-generic homoclinic classes

Works of Liao, Ma\~n\'e, Franks, Aoki and Hayashi characterized lack of hyperbolicity for diffeomorphisms by the existence of weak periodic orbits. In this note we announce a result which can be seen as a local version of these works: for C$^1$-generic diffeomorphism, a homoclinic class either is hyperbolic or contains a sequence of periodic orbits that have a Lyapunov exponent arbitrarily close to 0. Des travaux de Liao, Ma\~n\'e, Franks, Aoki et Hayashi ont caract\'eris\'e le manque d'hyperbolicit\'e des diff\'eomorphismes par l'existence d'orbites p\'eriodiques faibles. Dans cette note, nous annon\c{c}ons un r\'esultat qui peut \^{e}tre consid\'{e}r\'{e} comme une version locale de ces travaux: pour les diff\'{e}omorphismes C$^1$-g\'{e}n\'{e}riques, une classe homocline ou bien est hyperbolique, ou bien contient une suite d'orbites p\'{e}riodiques qui ont un exposant de Lyapunov arbitrairement proche de 0

Improving Resource Efficiency with Partial Resource Muting for Future Wireless Networks

We propose novel resource allocation algorithms that have the objective of finding a good tradeoff between resource reuse and interference avoidance in wireless networks. To this end, we first study properties of functions that relate the resource budget available to network elements to the optimal utility and to the optimal resource efficiency obtained by solving max-min utility optimization problems. From the asymptotic behavior of these functions, we obtain a transition point that indicates whether a network is operating in an efficient noise-limited regime or in an inefficient interference-limited regime for a given resource budget. For networks operating in the inefficient regime, we propose a novel partial resource muting scheme to improve the efficiency of the resource utilization. The framework is very general. It can be applied not only to the downlink of 4G networks, but also to 5G networks equipped with flexible duplex mechanisms. Numerical results show significant performance gains of the proposed scheme compared to the solution to the max-min utility optimization problem with full frequency reuse.Comment: 8 pages, 9 figures, to appear in WiMob 201

Ageing and Temperature Influence on Polarization/Depolarization Current Behaviour of Paper Immersed in Natural Ester

Transformers play an important role in providing a reliable and efficient electricity supply and are one of the most critical equipments in electric power transmission and distribution systems. The most commonly used liquid in power transformers is mineral oil due to its low price and good properties. However the performance of mineral oil starts to be limited due to environmental consideration [1]. Natural ester insulating fluid offers fire safety, environment and insulation aging advantages over mineral oil and are found to be suitable for the use in transformer insulation system [1]. However, transformer owners require to assess the status of the cellulose insulation in transformer non-destructively. Polarization/depolarization Current (PDC) measurement [2] is one of the non-destructive techniques which have been used to achieve this aim. At the present, there are few publications about the PDC behaviour of natural ester-paper insulation, though the natural ester becomes more widely used in transformers. In this paper, the influence of ageing and temperature on the PDC behaviour of the paper immersed in natural ester and mineral oil were compared. Results show PDC technique can be used to assess the aging condition of the natural-ester paper insulation. The ageing and temperature have similar influence on the PDC behaviour of the paper immersed in natural ester and in mineral oil. The depolarization current of paper immersed in natural ester is lower than that immersed in mineral oil at the same test temperature. The depolarization current of the paper immersed in natural ester and mineral oil increase with the aging time increased. Therefore, the depolarization current can be used to indicate the aging status of natural ester-paper insulation

Some Issues in a Gauge Model of Unparticles

We address in a recent gauge model of unparticles the issues that are important for consistency of a gauge theory, i.e., unitarity and Ward identity of physical amplitudes. We find that non-integrable singularities arise in physical quantities like cross section and decay rate from gauge interactions of unparticles. We also show that Ward identity is violated due to the lack of a dispersion relation for charged unparticles although the Ward-Takahashi identity for general Green functions is incorporated in the model. A previous observation that the unparticle's (with scaling dimension d) contribution to the gauge boson self-energy is a factor (2-d) of the particle's has been extended to the Green function of triple gauge bosons. This (2-d) rule may be generally true for any point Green functions of gauge bosons. This implies that the model would be trivial even as one that mimics certain dynamical effects on gauge bosons in which unparticles serve as an interpolating field.Comment: v1:16 pages, 3 figures. v2: some clarifications made and presentation improved, calculation and conclusion not modified; refs added and updated. Version to appear in EPJ