Generic Profit Singularities in Time-Averaged Optimization for Cyclic Processes in Polydynamical Systems

We consider the optimization problem of maximizing the time-averaged profit for the motion of a smooth polydynamical system on the circle in the presence of a smooth profit density. If the problem depends on a k-dimensional parameter, then the optimal averaged profit is a function of the parameter. It is known from [4] that an optimal motion can always be selected among stationary strategies and a special type of periodic motions called level cycles. We present a classification of all generic singularities of the optimal averaged profit if k?≤?2 and the maximum is provided by level cycles.     

On the hyperbolic order

We define the hyperbolic order of any locally injective holomorphic function between arbitrary hyperbolic domains of the complex plane and study the relation between the hyperbolic order and the Schwarzian derivative for locally injective holomorphic functions from the unit disk into itself.     

Simple HPLC‐UV for the quantification of a new leishmanicidal candidate (E)‐1‐4(trifluoromethyl) benzylidene)‐5‐(2‐4‐dichlorozoyl) carbonylhydrazine (LASSBio‐1736) in rat plasma for pharmacokinetics assessment

In this study, a sensitive HPLC‐UV assay was developed and validated for the determination of LASSBio‐1736 in rat plasma with sodium diclofenac as internal standard (IS). Liquid–liquid extraction using acetonitrile was employed to extract LASSBio‐1736 and IS from 100 μL of plasma previously basified with NaOH 0.1 M. Chromatographic separation was carried on Waters Spherisorb^®S5 ODS2 C₁₈ column (150 × 4.6 mm, 5 μm) using an isocratic mobile phase composed by water with triethylamine 0.3% (pH 4), methanol and acetonitrile grade (45:15:40, v/v/v) at a flow rate of 1 mL/min. Both LASSBio‐1736 and IS were eluted at 4.2 and 5 min, respectively, with a total run time of 8 min only. The lower limit of quantification was 0.2 μg/mL and linearity between 0.2 and 4 μg/mL was obtained, with an R² > 0.99. The accuracy of the method was >90.5%. The relative standard deviations intra and interday were <6.19 and <7.83%, respectively. The method showed the sensitivity, linearity, precision, accuracy and selectivity required to quantify LASSBio‐1736 in preclinical pharmacokinetic studies according to the criteria established by the US Food and Drug Administration and European Medicines Agency. Copyright © 2016 John Wiley & Sons, Ltd.     

Nested Cantor sets

We give sufficient conditions for two Cantor sets of the line to be nested for a positive set of translation parameters. This problem occurs in diophantine approximations. It also occurs as a toy model of the parameter selection for non-uniformly hyperbolic attractors of the plane. For natural Cantors sets, we show that this condition is optimal.     

Charge dynamics,Majorana condition and the topology of the interacting electromagnetic field

In previous works [1, 2], the 2-dimensional charge transport with parallel (in plane) magnetic field was considered from the theoretical point of view showing explicitly that the specific form of the emergent equation enforces the respective field solution to fulfil the Majorana condition. In this paper we review, explain and analyze these important results in the context of the generated physical effects, namely, the quantum ring as spin filter, the quantum Hall effect and a new one of pure topological origin (as the described by the Aharonov–Casher theorems). The link with supersymmetrical models is briefly discussed.