We continue the study of hidden Z2 symmetries of the four-point ˆ sl(2)k KnizhnikZamolodchikov equation iniciated in [1]. Here, we focus our attention on the four-point correlation function in those cases where one spectral flowed state of the sector ω = 1 is involved. We give a formula that shows how this observable can be expressed in terms of the four-point function of non spectral flowed st...

Dynamical conditions for the loss of validity of numerical chaotic solutions of physical systems are already understood. However, the fundamental questions of “how good” and “for how long” the solutions are valid remained unanswered. This work answers these questions by establishing scaling laws for the shadowing distance and for the shadowing time in terms of physically meaningful quantities t...

We calculate the rotation of the inertial frame within an almost flat cylindrical region surrounded by a pulse of non-axially-symmetric gravitational waves that rotate about the axis of our cylindrical polar coordinates. Our spacetime has only one Killing vector. It is along the z-axis and hypersurface orthogonal. We solve the Einstein equations to first order in the wave amplitude and superpos...

The benefits of hybrid electric vehicles have been recognized by the US Army and other military services. As a consequence, hybrid vehicles are being considered as future combat and tactical platforms. In order to achieve this objective, a number of integration challenges need to be overcome for every component system within the vehicle. Energy storage is one of the major systems of concern in ...

We investigate the dynamics of growth models in terms of dynamical system theory. We analyse some forms of knowledge and its influence on economic growth. We assume that the rate of change of knowledge depends on both the rate of change of physical and human capital. First, we study model with constant savings. The model with optimised behaviour of households is also considered. We show that th...

We consider solutions of Burgers’ equation with linear or quadratic external potential and stationary random initial conditions of Ornstein–Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on spaces of the form R× SU(3)/H, with H equals either SU(2)×U(1) or U(1)×U(1). For the corresponding quiver gauge theory we derive the equations of motion and construct some specific solutions for the Higgs fields using different gauge groups. Specifically we choose the gauge groups U(6) and U(8) for the space R×CP 2 as w...

Interval-flow networks are a special class of network models that can include minimum-flow requirements on some or all active arcs in a feasible solution. While this extension expresses constraints often encountered in practice, the resulting NP-hard problems are challenging to solve by standard means. This work describes a heuristic that explores adjacent extreme-point solutions to quickly fin...

Smartphones have been identified as most promising future devices for an Augmented Reality (AR) mass market. However, their use puts considerable constraints on the design and composition of AR applications. The key problem is to find a registration mechanism for accurate six degree of freedom (6DOF) self-localization with respect to the environment. Approaches based on Computer Vision (CV) hav...

We study pathwise entropy solutions for scalar conservation laws with inhomogeneous fluxes and quasilinear multiplicative rough path dependence. This extends the previous work of Lions, Perthame and Souganidis who considered spatially independent and inhomogeneous fluxes with multiple paths and a single driving singular path respectively. The approach is motivated by the theory of stochastic vi...