A reduced basis approach to large‐scale pseudospectra computation

For studying spectral properties of a nonnormal matrix $A\in {\mathbb{C}}^{n\times n}$, information about its spectrum σ(A) alone is usually not enough. Effects of perturbations on σ(A) can be studied by computing ε‐pseudospectra, i.e. the level sets of the resolvent norm function $\mathsf{g}(z)=\Vert {(zI?A)}^{?1}{\Vert }_2$. The computation of ε‐pseudospectra requires determining the smallest singular values ${\sigma }_{\min }(zI?A)$ for all z on a portion of the complex plane. In this work, we propose a reduced basis approach to pseudospectra computation, which provides highly accurate estimates of pseudospectra in the region of interest, in particular, for pseudospectra estimates in isolated parts of the spectrum containing few eigenvalues of A. It incorporates the sampled singular vectors of zI ? A for different values of z, and implicitly exploits their smoothness properties. It provides rigorous upper and lower bounds for the pseudospectra in the region of interest. In addition, we propose a domain splitting technique for tackling numerically more challenging examples. We present a comparison of our algorithms to several existing approaches on a number of numerical examples, showing that our approach provides significant improvement in terms of computational time.     

Kinetic modeling and optimization of maceration and ultrasound-extraction of resinoid from the aerial parts of white lady’s bedstraw (Galium mollugo L.)

In this paper, extraction of resinoid from the aerial parts of white lady’s bedstraw (Galium mollugo L.) using an aqueous ethanol solution (50% by volume) was studied at different temperatures in the absence and the presence of ultrasound. This study indicated that ultrasound-assisted extraction was effective for extracting the resinoid and gave better resinoid yields at lower extraction temperature and in much shorter time than the maceration. A phenomenological model was developed for modeling the kinetics of the extraction process. The model successfully describes the two-step extraction consisting of washing followed by diffusion of extractable substances and shows that ultrasound influences only the first step. The extraction process was optimized using response surface methodology (RMS) and artificial neural network (ANN) models. For the former modeling, the second-order polynomial equation was applied, while the second one was performed by an ANN-GA combination. The high coefficient of determination and the low MRPD between the ANN prediction and the corresponding experimental data proved that modeling the extraction process in the absence and the presence of ultrasound using ANN was more accurate than RSM modeling. The optimum extraction temperature was determined to be 80 and 40 °C, respectively for the maceration and the ultrasound-assisted extraction, ensuring the highest resinoid yield of 22.0 g/100 g in 4 h and 25.1 g/100 g in 30 min, which agreed with the yields obtained experimentally for the same time (21.7 and 25.3 g/100 g, respectively).     

Fabrication of super-macroporous nanocomposites by deposition of carbon nanotubes onto polymer cryogels

Electrically conducting super-macroporous carbon nanotube/polymer cryogel nanocomposites were fabricated by a novel approach based on deposition of carbon nanotubes (CNTs) onto the inner surface of pre-formed cryogels assisted by cryogenic treatment. Stable aqueous dispersions of multi-walled and single-walled carbon nanotubes were firstly obtained by non-covalent modification of pristine nanotubes with either pyrene containing polydimethylacrylamide or poly(ethylene oxide)₂₆-b-poly(propylene oxide)₄₀-b-poly(ethylene oxide)₂₆ copolymers and, then, exploited for the preparation of nanocomposites. The mechanical and electrical properties of nanocomposite materials were measured and compared to similar materials prepared by established method. The novel approach provided super-macroporous nanocomposites with high electrical conductivity (>10^?2 S/m) at much lower nanotube content (0.12 wt.%).     

On Trigonometric Blending Interpolation and Cubature Formulae

We discuss error representations for Hermite-Lagrange trigonometric interpolation introduced in Dryanov and Petrov (Interpolation and L ₁-approximation by trigonometric polynomials and blending functions, J. Approx. Theory 164, 1049–1064 (2012)) and obtain one-sided trigonometric quadratures for approximate integration of one-dimensional integrals. Next, we study error representations of multivariate Hermite-Lagrange transfinite trigonometric interpolation and derive one-sided trigonometric blending interpolants to multivariate functions, under some restrictions. Then, we construct one-sided transfinite cubature formulae for approximate integration of multivariate integrals. We construct also cubature formulae with positive coefficients, based on line integrals and exact in a vector space of trigonometric blending functions with prescribed order.     

Near-surface ion distribution and buffer effects during electrochemical reactions

The near-surface ion distribution at the solid-liquid interface during the Hydrogen Oxidation Reaction (HOR)/Hydrogen Evolution Reaction (HER) on a rotating platinum disc electrode is demonstrated in this work. The relation between reaction rate, mass transport and the resulting surface pH-value is used to theoretically predict cyclic voltammetry behaviour using only thermodynamic and diffusion data obtained from the literature, which were confirmed by experimental measurements. The effect of buffer addition on the current signal, the surface pH and the ion distribution is quantitatively described by analytical solutions and the fragility of the surface pH during reactions that form or consume H(+) in near-neutral unbuffered solutions or poorly buffered media is highlighted. While the ideal conditions utilized in this fundamental study cannot be directly applied to real scenarios, they do provide a basic understanding of the surface pH concept for more complex heterogeneous reactions.     

Novel properties of PES fabrics modified by corona discharge and colloidal TiO2 nanoparticles

The objective of this study was to highlight the potential application of the corona discharge at atmospheric pressure for the surface activation of polyester (PES) fabrics in order to improve the binding efficiency of colloidal TiO₂ nanoparticles. The obtained nanocomposite textile materials provide desirable level of UV protection, self‐cleaning properties, and photodegradation activity. The measured UV protection factor (UPF) of fabrics corresponds to UPF rating of 50+, designating the maximum UV protection. Additionally, the total photodegradation of methylene blue in aqueous solution was achieved after 24 hr of UV illumination and this capability was preserved and even improved after four repeated cycles. The results showed that the corona treated PES fabrics loaded with TiO₂ nanoparticles had considerably enhanced the overall efficiency compared to PES fabrics loaded only with TiO₂ nanoparticles. Copyright © 2009 John Wiley & Sons, Ltd.     

Biocompatible cryogels of thermosensitive polyglycidol derivatives with ultra-rapid swelling properties

Novel thermosensitive macroporous cryogels, based on various hydrophobically modified high molar mass (HMM) polyglycidol precursors, were synthesized using the UV-irradiation technique. The method involved the preparation of a semi-dilute aqueous solution of thermosensitive poly(glycidol-co-ethyl glycidyl carbamate) (PGL-Et), subsequent freezing at a moderately negative temperature (−20 °C) and irradiation with UV light. All PGL-Et cryogels had a spongy-like structure of smooth polymer walls surrounding interconnected macroscopic pores. Consequently, the cryogels exhibited temperature triggered, reversible, ultra-rapid volume phase transition (VPT) from a swollen to deswollen state within 20–25 s. The VPT temperature of the PGL-Et cryogels was strongly dependent on the degree of modification of the PGL precursors and it decreased proportionally with increased ethyl glycidyl carbamate content. The PGL-Et cryogels were used as a scaffold for skin cell (fibroblast) adhesion. Adhesion and proliferation tests indicated that the gels were good supports for cell cultivation.     

Epitaxial growth on porous GaAs substrates

We report on the electrochemical preparation of porous GaAs substrates in fluoride-iodide aqueous electrolytes for the lattice mismatched epitaxial growth from the vapor phase. The aim is to gain control over the uniformity of the pore nucleation layer and pore branching below this layer to achieve structures with a high degree of porosity and periodicity while leaving minimum damage on the substrate surface. Layers of In_xGa_1-xAs with varying In content are grown on GaAs substrates with different pore geometries and depths. Substantial differences in the surface morphology and photoluminescence efficiency of the layers grown on porous and conventional substrates are observed.     

Dimethyl‐methylphenyl copolysiloxanes by dimethylsilanolate‐initiated ring opening polymerization. Evidence for linearity of the resulting polymer structures

Recently, we reported that dimethylsilanolate‐initiated anionic ring opening polymerization of dimethylsiloxy‐ and diphenylsiloxy‐cyclic siloxanes results in polymer chain branching by dimethylsilanolate‐induced cleavage of only one Si‐C_Ar side bond in diphenylsiloxy repeat units, leading to formation of “Ph‐T‐branches”, and not extending to the cleavage of the second phenyl group. We attributed this behavior to electronic structures of the participating dimethylsiloxy‐, diphenylsiloxy and Ph‐T‐branch silicons and predicted that copolymers prepared by this synthetic route from dimethylsiloxy‐ and methylphenylsiloxy‐cyclics should not undergo branching at all but should have perfect linear chain configuration. Here, we describe results of a study of two such dimethylsilanolate‐initiated ring opening polymerizations of dimethylsiloxy‐ and methyphenylsiloxy‐cyclic tetramers and characterization of the resulting polymers by SEC‐MALS‐VIS, Mark‐Houwink‐Sakurada relationship and ²⁹Si NMR. The results obtained clearly confirmed our prediction of expected linearity of these polymer chains and also indicated that the resulting polymers were completely amorphous even at as low methylphenylsiloxy‐content as 3.9 mol %. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 1122–1129     

Fluorescent dendritic polymers and nanostructured coatings for the detection of chemical warfare agents and other analytes

Polyamidoamine (PAMAM) dendrimers of generations zero (G0) to four (G4), and a hyperbranched polyurea (HB‐PU), were functionalized with 1,5‐dansyl (1,5‐D), 2,5‐dansyl (2,5‐D), 2,6‐dansyl (2,6‐D) and nitrobenzofurazan (NBD) fluorophores that change their fluorescence emission wavelength in response to chemical environment, and the resulting dendritic polymers were characterized by MALDI‐TOF mass spectrometry, ¹H NMR, ¹³C NMR, and fluorescence spectroscopy. Fluorophore‐functionalized dendritic polymers were then reacted further with 3‐acryloxypropyldimethoxymethylsilane (AOP‐DMOMS) at various fluorophore to DMOMS substitution ratios. The resulting materials were cast onto glass slides, and cured into robust nanostructured coatings. Coatings with 50% fluorophore–50% DMOMS substitution showed the strongest fluorescence and the best physical properties. Coated coupons were tested against a wide range of analytes including the chemical warfare agent simulants dimethyl methylphosphonate (DMMP) and chloroethylethylsulfide (CEES), and the water‐methanol‐ethanol series. It was found that the ability of the coatings to distinguish between analytes decreased with increasing cross‐link density for both dendrimer and hyperbranched polymer‐based coatings. It was also found that the percent fluorophore substitution and the type of dendritic polymer carrying the fluorophore had no significant effect upon fluorescence emission wavelength, but fluorescence emission wavelength became less dependent upon solvent with increasing dendrimer generation and molecular mass. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5101–5115, 2009