\mathfrak D -parallelism of normal and structure Jacobi operators for hypersurfaces in complex two-plane Grassmannians

In this paper, we give non-existence theorems for Hopf hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C }^{m+2})$ with $\mathfrak D $ -parallel normal Jacobi operator ${\bar{R}}_N$ and $\mathfrak D $ -parallel structure Jacobi operator $R_{\xi }$ if the distribution $\mathfrak D $ or $\mathfrak D ^{\bot }$ component of the Reeb vector field is invariant by the shape operator, respectively.     

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.     

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.     

Fractional derivatives: Probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.     

Fractional generalization of memristor and higher order elements

Fractional calculus generalizes integer order derivatives and integrals. Memristor systems generalize the notion of electrical elements. Both concepts were shown to model important classes of phenomena. This paper goes a step further by embedding both tools in a generalization considering complex-order objects. Two complex operators leading to real-valued results are proposed. The proposed class of models generate a broad universe of elements. Several combinations of values are tested and the corresponding dynamical behavior is analyzed.     

Theoretical analysis of aggregation in block‐copolymer films: The optical signature

We focus this work on the theoretical investigation of the block‐copolymer poly[oxyoctyleneoxy‐(2,6‐dimethoxy‐1,4phenylene‐1,2‐ethinylene‐phenanthrene‐2,4diyl) named as LaPPS19, recently proposed for optoelectronic applications. We used for that a variety of methods, from molecular mechanics to quantum semiempirical techniques (AM1, ZINDO/S‐CIS). Our results show that as expected isolated LaPPS19 chains present relevant electron localization over the phenanthrene group. We found, however, that LaPPS19 could assemble in a π‐stacked form, leading to impressive interchain interaction; the stacking induces electronic delocalization between neighbor chains and introduces new states below the phenanthrene‐related absorption; these results allowed us to associate the red‐shift of the absorption edge, seen in the experimental results, to spontaneous π‐stack aggregation of the chains. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Adsorption/Desorption Behavior of Bovine Serum Albumin and Porcine Insulin on Chemically Patterned Porous Gel Networks

Adsorption/desorption of proteins onto a biomaterial surface plays a major role on the biocompatibility of the implanted material. By modifying the biomaterial surface with specially designed functional groups one may achieve the most specific behavior of the developed material used in a biological system. Based on that, porous gel matrixes with functionalized surfaces offer unlimited possibilities to control the protein-substrate interaction behavior. In the present work, we have functionalized the surface of porous glass with several chemical groups during the synthesis of the silica matrix. The porous glass matrixes were obtained using tetraethoxysilane (TEOS)/ethanol and functionalized with 3-mercaptopropyltrimethoxysilane (MPTMS) and 3-aminopropyltriethoxysilane (APTES). In vitro tests of the kinetics of protein adsorption and desorption from the gel matrix were monitored by UV-visible spectroscopy. The bioactivity of the incorporated protein was verified by in vivo experiments with adult male rats, where they presented an acute hypoglycemic peak.     

Luminescence quantum yield determination for molecules adsorbed onto solid powdered particles.

A new methodology for the determination of the fluorescence quantum yield of dyes adsorbed onto microcrystalline cellulose is presented and applied to rhodamine 101, cresyl violet and auramine O. It is based on a previously reported method by Ruetten and Thomas (J. Phys. Chem., 1998, 102, 598-606), which is not applicable to the dyes used in the present study. It uses ground-state diffuse reflectance spectra obtained with and without filters, which prevents the luminescence of the dye from reaching the integrating sphere and the photodetector. New equations are presented here, correcting for the fluorescence emission of the dye, which depends on the detector sensitivity. Cut-on filters, which have a transmittance close to unity in the absorption region, and close to zero in the emission region, of the dye are used to obtain corrected reflectance spectra. The influence of the substrate was also taken into account. This methodology may be applied to other probes and surfaces or emissions of a different nature (i.e., phosphorescence or delayed fluorescence), and constitutes a very simple and general procedure to solve the important problem of luminescence quantum yield determination of probes adsorbed onto solid powdered surfaces.