On Generalized Douglas–Weyl(α, β)-Metrics

In this paper, we study generalized Douglas–Weyl(α, β)-metrics. Suppose that a regular(α, β)-metric F is not of Randers type. We prove that F is a generalized Douglas–Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover, by ignoring the regularity, if F is not a Berwald metric, then we find a family of almost regular Finsler metrics which is not Douglas nor Weyl. As its application, we show that generalized Douglas–Weyl square metric or Matsumoto metric with isotropic mean Berwald curvature are Berwald metrics.     

Direct determination of free methionine in soy-based infant formula

A method was developed for the direct determination of free methionine in soy-based infant formula, with analyte separation and quantitation by reversed-phase liquid chromatography (LC), and UV absorbance at 214 nm, respectively. Sample preparation required only dilution with mobile phase and syringe filtration. Using a 0.02M KH2PO4 mobile phase (pH adjusted to 2.9 with 85% o-phosphoric acid) and 0.7 mL/min flow rate, methionine eluted at approximately 8 min, and total run time was 14 min after column regeneration with acetonitrile-water. System linearity was demonstrated as peak area versus analyte concentration, ranging from 80 to 120% of the formula specification for free methionine (r > 0.999, and all residuals < 0.45%). Intermediate precision relative standard deviation values were < 1.5% for ready-to-feed and reconstituted powder samples, and recoveries ranged from 98.0 to 103.5% for inter-method comparison with an amino acid analyzer method. The limit of quantitation was 3 mg methionine/L in the "as fed" infant formula. Despite the relatively weak UV absorptivity of methionine, the 214 nm signal was sufficiently intense in the 30-65 mg/L (201-436 microM) range to afford quantitation by peak area proportionation versus a 2-point external standard calibration. This direct UV detection after reversed-phase LC separation provides a simple and accurate method for determining free methionine without derivatization.     

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.     

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.     

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).

     

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.     

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.