Determination of organophosphate esters in air samples by dynamic sonication-assisted solvent extraction coupled on-line with large-volume injection gas chromatography utilizing a programmed-temperature vaporizer

An on-line method for the determination of airborne organophosphate esters based on dynamic sonication-assisted solvent extraction and large-volume injection (LVI) gas chromatography with nitrogen-phosphorous detection is introduced. The LVI is performed with a programmed-temperature vaporizer. The entire extracted fraction of 800 microl (hexane-methyl-tert.-butyl ether, 7:3, v/v) is introduced directly into the GC system without any clean-up step following extraction. The extraction and analysis step were completed in less than 15 min. The limit of detection of the investigated organophosphate esters was established to be in the range of 5-32 pg/filter. The correlation coefficients (r2) were investigated in the linear range study of the entire system and established to be approximately 0.9900 for all the investigated organophosphates esters. Applications of the method was demonstrated with the extraction of air samples collected onto glass fiber filters from different indoor environments. Six organophosphate esters were found at the levels 0.4-138 ng/m3.     

Immunomodulatory Properties of Masticadienonic Acid and 3α-Hydroxy Masticadienoic Acid in Dendritic Cells

Dendritic cells are antigen-presenting cells, which identify and process pathogens to subsequently activate specific T lymphocytes. To regulate the immune responses, DCs have to mature by the recognition of TLR ligands, TNFα or IFNγ. These ligands have been used as adjuvants to activate DCs in situ or in vitro, with toxic effects. It has been shown that some molecules affect the immune system, e.g., Masticadienonic acid (MDA) and 3α-hydroxy masticadienoic acid (3α-OH MDA) triterpenes naturally occurring in several medicinal plants, since they activate the nitric oxide synthase in macrophages and induce T lymphocyte proliferation. The DCs maturation induced by MDA or 3a-OH MDA was determined by incubating these cells with MDA or 3α-OH MDA, and their phenotype was afterwards analyzed. The results showed that only 3α-OH MDA was able to induce DCs maturation. When mice with melanoma were inoculated with DCs/3α-OH MDA, a decreased tumor growth rate was observed along with an extended cell death area within tumors compared to mice treated with DCs incubated with MDA. In conclusion, it is proposed that 3α-OH MDA may be an immunostimulant molecule. Conversely, it is proposed that MDA may be a molecule with anti-inflammatory properties.     

Lead-free ferroelectric BaTiO3 doped-(Na0.5Bi0.5)TiO3 thin films processed by pulsed laser deposition technique

The difficulties in synthesizing phase pure BaTiO₃ doped-(Na_0.5Bi_0.5)TiO₃ are known. In this work, we reporting the optimized pulsed laser deposition (PLD) conditions for obtaining pure phase 0.92(Na_0.5Bi_0.5)TiO₃-0.08BaTiO₃, (BNT-BT_0.08), thin films. Dielectric, ferroelectric and piezoelectric properties of BNT-BT_0.08, thin films deposited by PLD on Pt/TiO₂/SiO₂/Si substrates are investigated in this paper. Perovskite structure of BNT-BT_0.08 thin films with random orientation of nanocrystallites has been obtained by deposition at 600 °C. The relative dielectric constant and loss tangent at 100 kHz, of BNT-BT_0.08 thin film with 530 nm thickness, were 820 and 0.13, respectively. Ferroelectric hysteresis measurements indicated a remnant polarization value of 22 μC/cm² and a coercive field of 120 kV/cm. The piezoresponse force microscopy (PFM) data showed that most of the grains seem to be constituted of single ferroelectric domain. The as-deposited BNT-BT_0.08 thin film is ferroelectric at the nanoscale level and piezoelectric.     

Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a ₀ + a ₁ x ₁ + . . . + a _n x _n subject to certain constraints to solve the problem of minimizing a rational function of the form (a ₀ + a ₁ x ₁ + . . . + a _n x _n )/(b ₀ + b ₁ x ₁ + . . . + b _n x _n ) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo’s result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo’s result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an α-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an α-approximation (1/α-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others.     

$${\mathbb{Z}_2\mathbb{Z}_4}$$-linear codes: rank and kernel

A code C{{\mathcal C}} is \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C{{\mathcal C}} by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). The corresponding binary codes of \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-additive codes under an extended Gray map are called \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes. In this paper, the invariants for \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the rank and dimension of the kernel, are studied. Specifically, given the algebraic parameters of \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the possible values of these two invariants, giving lower and upper bounds, are established. For each possible rank r between these bounds, the construction of a \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with dimension of the kernel k is given. Finally, the bounds on the rank, once the kernel dimension is fixed, are established and the construction of a \mathbbZ₂\mathbbZ₄{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code for each possible pair (r, k) is given.     

On Elliptic Extensions in the Disk

Given two arbitrary functions f ⁽⁰⁾, f ⁽¹⁾ on the boundary of the unit disk D in \({\mathbb R}^2\), it is shown that there exists a second order uniformly elliptic operator L and a function v in L ^p , with L ^p second derivatives (1?p?Lv?=?0 a.e. in D and with v?=?f ⁽⁰⁾ and \(\frac{ \partial v}{\partial n} = f^{(1)}\) on \(\partial{D}\). A similar extension property was proved in Cavazzoni (2003) for any pair of functions f ⁽⁰⁾, f ⁽¹⁾ that are analytic; a result is obtained under weaker regularity assumptions, e.g. with \(\frac{\partial f^{(0)}}{\partial \theta}\) and f ⁽¹⁾ Hölder continuous with exponent \(\eta > \frac{1}{2}\).     

Cubic spline functions and initial value problems

A numerical process is presented which provides a cubic spline function approximation for the solution of initial value problems in ordinary differential equations. With interpolate cubic spline functions we can achieveO(h ⁴) convergence.     

Topological invariants in the study of a chaotic food chain system

The study of ecological systems has generated deep interest in exploring the complexity of chaotic food chains. The role of chaos in ecosystems is not entirely understood. One approach to have a better comprehension of ecological chaos is by analyzing it in mathematical models of basic food chains. In this article it is considered a classical chaotic food chain model from the literature. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of kneading sequences associated with one-dimensional maps that reproduce significant aspects of the model dynamics. The topological entropy allows us to distinguish different chaotic states in some realistic system parameter region. Another numerical invariant is introduced in order to characterize isentropic dynamics. Studying a set of maps with the same topological entropy, we exhibit numerical results about the relation between the second topological invariant and each of the control parameters in consideration. This work provides an illustration of how our understanding of ecological models can be enhanced by the theory of symbolic dynamics.     

Influence of steady background gradients on the accuracy of molecular diffusion anisotropy measurements

Spatial susceptibility variations of body components lead to local gradients of the static magnetic field. Effects of such background gradients on fractional diffusion anisotropy (FA) measurements on whole-body magnetic resonance units operating at 1.5, 3.0 and 7.0 T were analyzed theoretically and experimentally. Analytical expressions were derived for the cases of diffusion occurring in isotropic media and in tissues with cylindrical symmetry (e.g., white matter tracts or skeletal musculature). Typical magnitudes of background gradient strengths were estimated from in vivo and in vitro measurements with B0 field mapping sequences. Additionally, numerical simulations of magnetic field distributions and resulting field gradients were performed considering tissue-air interfaces in simplified geometrical arrangements. For media with isotropic diffusion, both measurements and analytical calculations showed increasing FA inaccuracy with stronger coupling between diffusion-encoding and background gradients. For cylindrical symmetry, FA values were estimated for a standard diffusion tensor imaging protocol in a realistic scenario. At 1 mm distance from a water-air interface, susceptibility-related background gradients amount to approximately 9 mT/m at 7 T and lead to a relative error of the measured FA of up to 48%. The error in the anisotropy assessment rises considerably with increasing field strength and must be taken into account especially for experimental and clinical studies on modern high-field systems.