On doubly warped product Finsler manifolds

In this paper, we introduce horizontal and vertical warped product Finsler manifolds. We prove that every C-reducible or proper Berwaldian doubly warped product Finsler manifold is Riemannian. Then, we find the relation between Riemannian curvatures of doubly warped product Finsler manifold and its components, and consider the cases that this manifold is flat or has scalar flag curvature. We define the doubly warped Sasaki-Matsumoto metric for warped product manifolds and find a condition under which the horizontal and vertical tangent bundles are totally geodesic. We obtain some conditions under which a foliated manifold reduces to a Reinhart manifold. Finally, we study an almost complex structure on the tangent bundle of a doubly warped product Finsler manifold.     

Some curvature properties of Cartan spaces with mth root metrics

In this paper, we define some non-Riemannian curvature properties for Cartan spaces. We consider a Cartan space with the mth root metric. We prove that every mth root Cartan space of isotropic Landsberg curvature, or isotropic mean Landsberg curvature, or isotropic mean Berwald curvature reduces to a Landsberg, weakly Landsberg, and weakly Berwald spaces, respectively. Then we show that the mth root Cartan space of almost vanishing H-curvature satisfies H?=?0.     

Invariant Manifold Approach for the Stabilization of Nonholonomic Chained Systems: Application to a Mobile Robot

In this paper it is shown that a class ofn-dimensional nonholonomic chained systems can bestabilized using the invariant manifold approach. First, we derive aninvariant manifold for this class of systems and we show that, once onit, all the closed-loop trajectories tend to the origin under a linearsmooth time-invariant state feedback. Thereafter, it is shown that thismanifold can be made attractive by means of a discontinuoustime-invariant state feedback. Finally, a mobile robot is taken as anexample demonstrating the effectiveness of our study.     

Weakly Douglas Finsler metrics

Periodica Mathematica Hungarica - In this paper, we define a weaker notion of Douglas metrics, namely weakly Douglas metrics. A Finsler metric satisfies a projectively invariant equation...     

Quantum signal transmission through a single-qubit chain

A system of a two-level atom of an impurity (qubit) inserted into a periodic chain coupled to the continuum is studied with the use of the effective non-Hermitian Hamiltonian. Exact solutions are derived for the quasistationary eigenstates, their complex energies, and transport properties. Due to the presence of the qubit, two long-lived states corresponding to the ground and excited states of the qubit emerge outside the Bloch energy band. These states remain essentially localized at the qubit even in the limit of sufficiently strong coupling between the chain and the environment when the super-radiant states are formed. The transmission through the chain is studied as a function of the continuum coupling strength and the chain-qubit coupling; the perfect resonance transmission takes place through isolated resonances at weak and strong continuum coupling, while the transmission is lowered in the intermediate regime.     

Improve Corrosion Resistance of Zircaloy by Copper–Graphene Nanocomposite Coatings

In this study, the corrosion behavior of Zircaloy was investigated in the presence and absence of copper–graphene nanocomposites coating. The coating was prepared employing Hummers’ and electrochemical reduction methods. The morphology of copper–graphene nanocomposites coating was studied using scanning electron microscopy (SEM). Corrosion behavior was investigated employing dynamic polarization and electrochemical impedance spectroscopy (EIS) tests in a solution containing lithium hydroxide (LiOH), boric acid (H₃BO₃), and deionized water. The results showed that corrosion resistance of Zircaloy increased with introduction of copper–graphene nanocomposites coatings. The lowest corrosion rate was attained in the Zircaloy with copper–graphene nanocomposites coating (corrosion rate: 0.040 mm/year). An approximately 20 times decrease in the corrosion rate was observed in the Zircaloy with copper–graphene nanocomposites coating when compared to the un-coated Zircaloy (corrosion rate: 0.831 mm/year).

     

A New Approach for Error Rate Analysis of Wide-Band DSSS-CDMA System with Imperfect Synchronization Under Jamming Attacks

Most of the researches on error rate analysis of direct sequence spread spectrum (DSSS-CDMA) systems assume that the synchronization is perfect. However, in practice, the synchronization is often imperfect due to various effects of channel parameters such as noise and fading. The degree of imperfection further increases due to jamming attacks. The present study, therefore, derives new expressions to compute the probability of error in DSSS-CDMA systems under imperfect synchronisation. It is assumed that the channel is wideband and is subjected to various jamming attacks. A new parameter, called as probability of successful synchronization, was introduced which includes the effects of both the probability of false alarm and detection under fast and slow jammers. Monte Carlo simulations were conducted in MATLAB to establish the validity of the derived mathematical expressions.

     

On locally dually flat (α, β)-metrics with isotropic S-curvature

In this paper, we consider locally dually flat (??, ??)-metrics with isotropic S-curvature and find some necessary and sufficient conditions under which these metrics reduce to locally Minkowskian metrics.