Stability of partial difference equations governing control gains in infinite-dimensional backstepping

We examine the stability properties of a class of LTV difference equations on an infinite-dimensional state space that arise in backstepping designs for parabolic PDEs. The nominal system matrix of the difference equation has a special structure: all of its powers have entries that are −1, 0, or 1, and all of the eigenvalues of the matrix are on the unit circle. The difference equation is driven by initial conditions, additive forcing, and a system matrix perturbation, all of which depend on problem data (for example, viscosity and reactivity in the case of a reaction–diffusion equation), and all of which go to zero as the discretization step in the backstepping design goes to zero. All of these observations, combined with the fact that the equation evolves only in a number of steps equal to the dimension of its state space, combined with the discrete Gronwall inequality, establish that the difference equation has bounded solutions. This, in turn, guarantees the existence of a state-feedback gain kernel in the backstepping control law. With this approach we greatly expand, relative to our previous results, the class of parabolic PDEs to which backstepping is applicable.     

Polyaniline nanotubes: conditions of formation

The courses of aniline oxidation with ammonium peroxydisulfate in aqueous solutions of strong (sulfuric) and in weak (acetic) acids, followed by temperature and acidity changes, are different. In solutions of sulfuric acid, granular polyaniline (PANI) was produced; in solutions of acetic acid, PANI nanotubes were obtained. The external diameter of the nanotubes was 100–300 nm, the internal cavity 20–100 nm, and the length extended to several micrometres. The morphology of PANI, granular or tubular, depends on the acidity conditions during the reaction rather than on the chemical nature of the acid. PANI nanotubes were also produced when aniline was oxidized in the absence of any acid. The bulk conductivity of PANI prepared in solutions of acetic acid was 0.08–0.27 S cm^?1, depending on the acid concentration. Protonated PANI prepared in sulfuric and acetic acids were deprotonated with ammonium hydroxide to obtain PANI bases and the ammonium salt of the protonating acid. FTIR spectroscopy showed the differences in the molecular structure of the PANI bases. Irrespective of whether the polymerization was performed in solutions of sulfuric or acetic acid, PANI had hydrogen sulfate counter‐ions only. The PANI morphology is thus not controlled by the nature of counter‐ions. The acidity of the reaction medium determines the protonation of monomer, oligomer and polymer species. The chemistry of aniline oxidation is likely to be affected especially by the protonation of an intermediate in the pernigraniline form. It is proposed that, in the course of aniline oxidation, pH‐dependent self‐assembly of aniline oligomers predetermines the final PANI morphology. Copyright © 2005 Society of Chemical Industry     

Influence of Oxygen Content on Formation of Yttrium α-SiAlON Ceramics

Low porosity α- and β-SiAION composite material was prepared when the powder mixture intended for preparation of yttrium α-SiAlON, with the formula Y_0.4Si_12–m+n Al_m+nO_nN_16–n, was attritor milled in isopropyl alcohol or contained excess oxygen (n > 0.6). The region of stability of single-phase yttrium α-SiAlON was smaller at lower temperatures. Wet milling (in isopropyl alcohol) of AIN powder was found to introduce excess oxygen into the milled powder.     

The Interplay of Lung Cancer,COVID-19, and Vaccines

Patients with cancer are more susceptible to a higher risk of coronavirus infection and its severe complications than the general population. In addition, these patients were not included in the pivotal clinical trials for COVID-19 vaccines. Therefore, considerable uncertainty remains regarding the management of cancer patients during the COVID-19 pandemic and the safety of COVID-19 vaccinations in cancer patients. In this review, we summarize the current knowledge generated from the beginning of the COVID-19 pandemic on the vulnerability of cancer patients to the coronavirus disease, as well as the effectiveness of COVID-19 vaccines in this population. We also discuss the available data on the effects of anticancer treatment with immune checkpoint inhibitors on the immune responses to SARS-CoV-2 in cancer patients. Special attention in this review will be given to patients with lung cancer, as such patients are at an increased risk for severe effects from COVID-19.     

Morphology evolution during cooling of quiescent immiscible polymer blends: matrix crystallization effect on the dispersed phase coalescence

The influence of the matrix crystallization on the coalescence of the dispersed phase particles, in quiescent immiscible polymer blends, is a topic that is scientifically addressed scarcely. The coarsening of the phase structure that is induced by the matrix crystallizing domains was studied using the well-established system comprising a polypropylene and an ethylene–propylene rubber (PP/EPR blends). This subject is of great importance as the effectiveness in the toughening of PP is directly determined by the EPR particle size. Cooling experiments were commenced for resolving the correlation among the imposed cooling conditions, the formed matrix crystalline morphology, and the coalescence of the dispersed phase particles. A confirmation of the profound effect of the PP crystallization on the coalescence of EPR particles was undoubtedly obtained. The contribution of the crystallization to the coalescence of the dispersed phase particles is largest at a finite rate of cooling. A thorough discussion regarding the observed effects, encompassing a potential rejection or an engulfing of the dispersed phase particles by the growing crystallites, was undertaken.     

Macerals in bituminous coals and the coking process: Part 1: Effect of basic coal properties on the process of thermal degradation

Bituminous coals produced in the Ostrava—Karviná coal basin show considerable variation in their maceral composition and rank. In order to explain the significance of the petrographic composition, structure and chemical parameters in coal degradation processes, a large number of coal samples was investigated. From the relationships obtained, the behaviour of macerals during these processes is discussed. It is found that isometamorphic vitrinites are characterized by a distinctive behaviour affected to a first approximation by the atomic ratios C/H and C/O. Inertinite, despite its occasional significantly higher volatile matter, does not yield an appreciable amount of fused material.     

New aspects in cationization of lignocellulose materials. VII. Modification of spruce wood meal with quarternary ammonium groups

Trimethylammonium-2-hydroxypropyl (TMAHP) derivatives of spruce wood meal (SWM) and holocellulose of this specia were prepared by the reaction of wood meal with 3-chlor-2-hydroxy-propyltrimethylammoniumchloride (CHMAC) in alkaline medium. The TMAHP samples were fractionated and yields and exchange capacity (Q) of individual fractions were compared with beech and aspen fractions obtained under the same conditions. As it is evident from ¹³C-NMR spectroscopy and GPC analysis the water soluble fraction from TMAHP–SWM consists only of lignin–saccharide degradation products. The NaOH extracts of TMAHP–SWM and TMAHP–holocellulose as well as the water-soluble fraction from TMAHP–holocellulose are polymeric materials. From TMAHP–SWM only 3.1% of alkali-soluble material could be extracted, while from TMAHP–holocellulose 15.7% of water-soluble and 7.9% of alkali-soluble materials were obtained.