NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS(Ⅱ)──PART 1

The study of linear and global. properties of linear dynamical systems on vector bundles appeared rather extensive already in the past.Presently we propose to study perturbations of this linear dynamics The perturbed dynamical system which we shallconsider is no longer linear.while the properties to be studied will be still global in general.Moreover.we are interested in the nonuniformly hyperbolic properties.In this paper,we set an appropriate definition for such perturbations.Though it appearssome what not quite usual yet has deeper root in standard systens of differential equations in the theory of differentiable dynamical systens The general problen is to see which property of the original given by the dynamical system is persistent when a perturbation takes place.The whole contenl of the paper is deyoted to establishinga theorem of this sort.

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS (Ⅱ)──PART 2

In the part 2, theorem 3.1 stut ed in part 1[15] is proved first. The proof is obtained via a way of changing variables to reduce the original system of differentialequations to a form concerning Standard systems of equations in the theory ofdifferentiable dynamical systems. Then by using theorem 3.1 together with thepreliminary theorem 2.l, foe main theorem of this paper announced in part 1 is proved.The definition of admissible perturbation is contained in the appendix of part 2. Themeanings of the main theorem is described in the introduction of part 1.

Mobility-Aware Adaptive Beam Tracking for Vehicles in Mm Wave Communication Networks

The millimeter wave(mm Wave)is a potential solution for high data rate communication due to its availability of large bandwidth.However,it is challenging to perform beam tracking in vehicular mm Wave communication systems due to high mobility and narrow beams.In this paper,an adaptive beam tracking algorithm is proposed to improve the network throughput performance while reducing the training signal overhead.In particular,based on the mobility prediction at base station(BS),a novel frame structure with dynamic bundled timeslot is designed.Moreover,an actor-critic reinforcement learning based algorithm is proposed to obtain the joint optimization of both beam width and the number of bundled timeslots,which makes the beam tracking adapt to the changing environment.Simulation results demonstrate that,compared with the traditional full scan and Kalman filter based beam tracking algorithms,our proposed algorithm can improve the time-averaged throughput by 11.34%and 24.86%respectively.With the newly designed frame structure,it also outperforms beam tracking with conventional frame structure,especially in scenarios with large range of vehicle speeds.

Brownian Dynamics Simulations of Rigid Polyelectrolyte Chains Grafting to Spherical Colloid

Brownian dynamics simulations are employed to explore the effects of chain stiffness and trivalent salt concentration on the conformational behavior of spherical polyelectrolyte brush. The rigid brush adopts bundle-like morphology at a wide range of trivalent salt concentration. The number variation of bundles pinned on the colloid surface shows a non-monotonic profile as a function of the chain stiffness. The radial distributions of monomers and ions and the charge ratio between condensed ions and monomers are calculated. The charge inversion is observed for the high salt concentration regardless of chain rigidity. Furthermore, the pair correlation functions of monomer-monomer and monomer-salt cation are used to elucidate the aggregated mechanism of the bundle-like structure.

Application of Connection in Molecular Dynamics

The evolution of electronic states in molecule has two origins: dynamical one produced by Schr¨odinger equation and kinematical one caused by base transformation due to nuclear motion.In current theories,the former gets analytic expression; the latter depends on heavy numerical calculation,which contains uncertainty.By using connection of fiber bundles,this paper establishes an analytic formula for the latter,and the numerical work is simplified.It shows the mathematical structure of molecule is fiber bundle.