Selective excitation through tapered silica fibers of fluorescent two-photon polymerized structures

Two-photon polymerization has emerged as a powerful tool to design complex three-dimensional microstructures for applications ranging from biology to nanophotonics. To broaden the application spectrum of such microstructures, different materials have been incorporated to the polymers, aiming at specific applications. In this paper we report the fabrication of microstructures containing rhodamine 610, which display strong fluorescence upon one- and two-photon excitation. The latter increases light-penetration depth and spatial selectivity of luminescence. We also demonstrate that by using silica submicrometric wires we were able to select individual microstructures to be excited, which could be explored for designing microstructure-based optical circuits.     

Time-periodic perturbation of a Liénard equation with an unbounded homoclinic loop

We consider a quadratic Liénard equation with an unbounded homoclinic loop, which is a solution tending in forward and backward time to a non-hyperbolic equilibrium point located at infinity. Under small time-periodic perturbation, this equilibrium becomes a normally hyperbolic line of singularities at infinity. We show that the perturbed system may present homoclinic bifurcations, leading to the existence of transverse intersections between the stable and unstable manifolds of such a normally hyperbolic line of singularities. The global study concerning the infinity is performed using the Poincaré compactification in polar coordinates, from which we obtain a system defined on a set equivalent to a solid torus in R³, whose boundary plays the role of the infinity. The transversality of the manifolds is proved using the Melnikov method and implies, via the Birkhoff-Smale Theorem, a complex dynamical behaviour of the perturbed system solutions in the finite part of the phase space. Numerical simulations are performed in order to illustrate this behaviour, which could be called “the chaos arising from infinity”, since it depends on the global structure of the Liénard equation, including the points at infinity. Although applied to a particular case, the analysis presented provides a geometrical approach to study periodic perturbations of homoclinic (or heteroclinic) loops to infinity of any planar polynomial vector field.     

Warm-Start Heuristic for Stochastic Portfolio Optimization with Fixed and Proportional Transaction Costs

We consider a probabilistic portfolio optimization model including fixed and proportional transaction costs. We derive a deterministic equivalent of the probabilistic model for fat-tailed portfolio returns. We develop a method which finds provably near-optimal solutions in minimal amount of time for industry-sized (up to 2000 assets) problems. To solve the mixed-integer nonlinear programming (MINLP) deterministic formulation equivalent to the stochastic problem, we design a mathematical programming-based warm-start heuristic. The tests show the computational efficiency of the heuristic which is more than an order of magnitude faster than Cplex in finding high-quality solutions.     

Nonlinear perturbations of a ‐Laplacian equation with critical growth in

We prove the existence of solution for a class of ‐Laplacian equations where the nonlinearity has a critical growth. Here, we consider two cases: the first case involves the situation where the variable exponents are periodic functions. The second one involves the case where the variable exponents are nonperiodic perturbations.     

On the optimal control of a class of non-Newtonian fluids

We consider optimal control problems of systems governed by stationary, incompressible generalized Navier–Stokes equations with shear dependent viscosity in a two-dimensional or three-dimensional domain. We study a general class of viscosity functions with shear-thinning and shear-thickening behavior. We prove an existence result for such class of optimal control problems.     

Birth of limit cycles bifurcating from a nonsmooth center

This paper is concerned with a codimension analysis of a two-fold singularity of piecewise smooth planar vector fields, when it behaves itself like a center of smooth vector fields (also called nondegenerate Σ-center). We prove that any nondegenerate Σ-center is Σ  -equivalent to a particular normal form _Z0$Z_0$. Given a positive integer number k   we explicitly construct families of piecewise smooth vector fields emerging from _Z0$Z_0$ that have k hyperbolic limit cycles bifurcating from the nondegenerate Σ  -center of _Z0$Z_0$ (the same holds for k=∞$k=\infty$). Moreover, we also exhibit families of piecewise smooth vector fields of codimension k   emerging from _Z0$Z_0$. As a consequence we prove that _Z0$Z_0$ has infinite codimension.     

Stabilization of mixture of two rigid solids modeling temperature and porosity

In this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a mixture of two rigid solids modeling temperature and porosity. Our main result is to establish conditions which ensure the analyticity and the exponential stability of the corresponding semigroup.     

Kneading Theory: A Functorial Approach

We study the homology theory of ? - modal maps of the interval. We give another proof of the Milnor and Thurston results about zeta-functions and we give a functorial approach to kneading theory. Our results give explicit methods for computing the sequences of lap numbers ? (f ^k ) and the sequences of numbers of periodic points in an arbitrary interval [x,y]. Received: 25 February 1998 / Accepted: 15 January 1999     

Thermal and structural characterization of SrTi1-xNdxO3

Sr(Ti,Nd)O₃ was synthesized in order to evaluate the influence of the amount of neodymium on the thermal and structural properties of SrTiO₃. The synthesis was carried out using the polymeric precursor method. A small mass gain was observed for the SrTiO₃ and SrTi_0.98Nd_0.02O₃ samples accompanied by an exothermic peak in the DTA curves. Other steps at higher temperatures are assigned to the combustion of the organic material and carbonate. Elimination of defects by previous calcination of the precursors is responsible by the short and long range ordering of the perovskite. Cubic phase was obtained for undoped and doped SrTiO₃.     

Development and validation of a fast isocratic liquid chromatography method for the simultaneous determination of norfloxacin,lomefloxacin and ciprofloxacin in human plasma

A simple and fast liquid chromatographic method coupled with fluorescence detection (LC‐FD) is reported, for the first time, for the simultaneous quantification of norfloxacin (NOR), ciprofloxacin (CIP) and lomefloxacin (LOM) in human plasma, using levofloxacin as internal standard (IS). Sample preparation consists of a single‐step precipitation of plasma proteins followed by vortex‐mixing and centrifugation. Chromatographic separation was achieved within 7 min on a reversed‐phase C₁₈ column with a mobile phase consisting of 0.1% aqueous formic acid (pH = 3.0, triethylamine)–methanol (82:18, v/v) pumped isocratically at 1.2 mL/min. The detector was set at excitation/emission wavelengths of 278/450 nm. Calibration curves were linear (r² ≥ 0.994) in the range of 0.02–5.0 µg/mL, and the limit of quantification was established at 0.02 µg/mL for all analytes (NOR, CIP and LOM). The overall precision did not exceed 8.19% and accuracy was within ±10.91%. NOR, CIP and LOM were extracted from human plasma with an overall mean recovery ranged from 90.1 to 111.5%. No interferences were observed at the retention times of the analytes and IS. This novel LC‐FD method enables the reliable determination of NOR, CIP and LOM in a single chromatographic run, which may be suitable to support human pharmacokinetic‐based studies with those antimicrobial agents. Copyright © 2010 John Wiley & Sons, Ltd.