On the Similarity of Sturm–Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.     

Advection of a passive vector field by the Gaussian velocity field with finite correlations in time

Using the field theoretic renormalization group technique the model of a passive vector field advected by an incompressible turbulent flow is investigated up to the second order of the perturbation theory (two-loop approximation). The turbulent environment is given by statistical fluctuations of the velocity field that has a Gaussian distribution with zero mean and defined noise with finite correlations in time. Two-loop analysis of all possible scaling regimes in general d-dimensional space is done in the plane of exponents ? ? η, where ? characterizes the energy spectrum of the velocity field in the inertial range E ∝ k ^{1 ? 2ε}, and η is related to the correlation time at the wave number k which is scaled as k ^{?2 + η}. It is shown that the scaling regimes of the present model of vector advection have essentially different properties than the scaling regimes of the corresponding model of passively advected scalar quantity. The results demonstrate the fact that within the present model of passively advected vector field the internal tensor structure of the advected field can have nontrivial impact on the diffusion processes deep inside in the inertial interval of given turbulent flow.     

Note on the existence theory for evolution equations with pseudo-monotone operators

In this note we present a framework which allows to prove an abstract existence result for evolution equations with pseudo-monotone operators. The assumptions on the spaces and the operators can be easily verified in concrete examples.     

Hydrophobic/hydrophilic P(VDF‐TrFE)/PHEA polymer blend membranes

Polymer blend membranes have been obtained consisting of a hydrophilic and a hydrophobic polymers distributed in co‐continuous phases. In order to obtain stable membranes in aqueous environments, the hydrophilic phase is formed by a poly(hydrohyethyl acrylate), PHEA, network while the hydrophobic phase is formed by poly(vinylidene fluoride‐co‐trifluoroethylene) P(VDF‐TrFE). To obtain the composites, in a first stage, P(VDF‐TrFE) is blended with poly(ethylene oxyde) (PEO), the latter used as sacrificial porogen. P(VDF‐TrFE)/PEO blend membranes were prepared by solvent casting at 70°C followed by cooling to room temperature. Then PEO is removed from the membrane by immersion in water obtaining a P(VDF‐TrFE) porous membrane. After removing of the PEO polymer, a P(VDF‐TrFE) membrane results in which pores are collapsed. Nevertheless the pores reopen when a mixture of hydroxethyl acrylate (HEA) monomer, ethyleneglycol dimethacrylate (as crosslinker) and ethanol (as diluent) is absorbed in the membrane and subsequent polymerization yields hybrid hydrophilic/hydrophobic membranes with controlled porosity. The membranes are thus suitable for lithium‐ion battery separator membranes and/or biostable supports for cell culture in biomedical applications. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 672–679     

Modelo numérico del comportamiento histerético de uniones entre forjados reticulares y pilares de fachada

Waffle-flat-plate structures have been widely used for residential and office buildings in the South of Europe between the seventies and nineties of the last century. These buildings were designed with old seismic codes and its vulnerability needs to be evaluated to determine whether they need to be seismic retrofitted or not. This article proposes a simple model that represents the moment transfer between plate and column, for existing exterior connections loaded in the direction normal to the building façade. The model takes into account singularities of existing waffle-flat-plate structures such as the concentration of reinforcement in the direction of the joints, and the existence of punching shear reinforcement. The model consists of frame elements for the columns and shell elements for the slabs, both connected with flexural and torsion hinges. The strength of the flexural hinges is obtained by estimating the portion of longitudinal reinforcement of the plate that transfers directly the unbalanced moment to the column by flexure. The yielding deformations of the flexural and torsion hinges are estimated with simple expressions. The ductility of the flexural hinges is taken from FEMA 356, while infinite ductility is adopted for the torsional hinges in accordance with previous experimental studies. It is shown that the proposed model provides a good approximation of the experimental response of the connection under monotonically increasing lateral displacements, in terms of stiffness, strength and ductility.     

SPE and determination by FAAS of heavy metals using a new synthesized polymer resin in various water and dried vegetables samples

Firstly, poly[phenyl thiadiazole methacrylamide-co-divinylbenzene-co-2-acrylamido-2-methylpropane sulfonic acid] (PTMAAm-co-DVB-co-AMPS), a new polymer resin was synthesized. This polymer resin was characterized by elemental analyzer, X-ray diffractometer, scanning electron microscope (SEM) and IR spectrometer. The glass column packed with the synthesized polymer resin was used for solid phase extraction (SPE). At the same time, the analytes were separated and preconcentrated from various water, dried vegetables samples and standard reference material (CRM) with SPE and determined by flame atomic absorption spectrometer (FAAS). The experimental conditions of this method such as pH, flow rates of sample, flow rates of eluent, type / concentration / volume of eluent, sample volume and matrix ions were examined. The limits of detection (µg L^?1) were calculated (3s) 0.9 for Mn(II), 1.4 for Cd(II), Co(II) and Zn(II), 1.5 for Cr(III), 2.2. for Cu(II), 1.9 for Pb(II),1.5 for Ni(II) and 1.9 for Fe(III) (n = 21). The low relative standard deviation, ≤ 2% (n = 11) and preconcentration factor as 75 for analytes were obtained.     

Aluminium fractionation using cation exchange: comparison of results obtained after fractionation in the field and in the laboratory

Dissolved aluminium was fractionated in the field and the laboratory using a cation-exchange method. Although absolute differences between results obtained from field and laboratory fractionations were generally small, relative differences, expressed as the ratio between labile aluminium determined after laboratory fractionation (Al_ll) and that obtained after field fractionation (Al_lf) could be large. The differences found were not statistically significant, although this may simply reflect the spread in the results. Al_ll/Al_lf had no apparent relationship with the temperature difference between the field and the lab. Although some significant correlations were found between Al_ll/Al_lf and H⁺, no significant correlations were found with the equivalent relative difference in {H⁺} between the lab and the field; nor was any significant correlation found with dissolved organic carbon.     

Invertibility of a linear combination of two matrices and partial orderings

In this paper, we present some results relating different matrix partial orderings and the invertibility of a linear combination of EP matrices.