Capable Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field

In this paper, we classify all capable nilpotent Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field. Moreover, the explicit structure of such Lie algebras of class 3 is given.     

Piezoelectric property improvement of polyethylene ferroelectrets using postprocessing thermal‐pressure treatment

In this work, biaxially stretched polymer foams with well‐defined cellular structures were prepared from polyethylene via blown‐film extrusion and subjected to corona charging to produce a piezoelectric response. The charging parameters were first optimized in terms of charging voltage and needle distance, as well as the gas type and pressure to investigate their effect on the piezoelectric coefficient (d₃₃). The results show that samples charged under nitrogen (N₂) at 100 kPa had better d₃₃ coefficient than those charged under ambient air or N₂ at 20 kPa. Moreover, 2 different thermal pressure treatments were imposed to obtain an optimized eye‐like cellular structure with different cell aspect ratios (AR). The results showed that when the cells were elongated in both the longitudinal and transverse directions (higher AR), higher d₃₃ coefficients were achieved. From all the samples produced, the best results were obtained for a longitudinal aspect ratio (AR‐L) of 7.1, a transversal aspect ratio (AR‐T) of 4.6, and a relative foam density of 0.52 leading to a d₃₃ coefficient of 935 pC/N. This coefficient was further increased using reverse charging and multilayered films, reaching a maximum of 2550 pC/N. This value is much higher than typical ones reported so far for any polyethylene and polypropylene ferroelectrets. These results could increase the use of polyethylene in piezoelectric applications as these materials are very attractive for the large‐scale production of electret‐based sensors and transducers due to their low cost and easy processing.     

[2]Pseudorotaxane-Based Supramolecular Optical Indicator for the Visual Detection of Cellular Cyanide Excretion

Cyanide is extremely hazardous to living organisms and the environment. Owing to its wide range of applications and high toxicity, the development of functional materials for cyanide detection and sensing is highly desirable. Host–guest complexation between bis(p-phenylene)-34-crown-10 H and N-methylacridinium salt G remarkably decreases the detection limit for cyanide anions compared with that of the guest itself. The [2]pseudorotaxane selectively recognizes the cyanide anion with high optical sensitivity as a result of the nucleophilic addition of the cyanide anion at the 9-position of G . The host–guest complexation is further incorporated into supramolecular materials for the visual detection of cyanide anions, especially the detection of cellular cyanide excretion with a detection limit of 0.6 μm . This supramolecular method provides an extremely distinct strategy for the visual detection of cyanide anions.     

Nash multiplicities and isolated points of maximum multiplicity

Let X be an algebraic variety defined over a field of characteristic zero, and let $\xi \in \underset{\_}{\mathrm{Max}}\mathrm{mult}(X)$ be a point in the closed subset of maximum multiplicity of X. We provide a criterion, given in terms of arcs, to determine whether ξ is isolated in $\underset{\_}{\mathrm{Max}}\mathrm{mult}(X)$. More precisely, we use invariants of arcs derived from the Nash multiplicity sequence to characterize when ξ is an isolated point in $\underset{\_}{\mathrm{Max}}\mathrm{mult}(X)$.     

Stability of a general adaptive immunity virus dynamics model with multistages of infected cells and two routes of infection

This paper studies an (n+4)-dimensional nonlinear virus dynamics model that characterizes the interactions of the viruses, susceptible host cells, n-stages of infected cells, B cells and cytotoxic T lymphocyte (CTL) cells. Both viral and cellular infections have been incorporated into the model. The infected-susceptible and virus-susceptible infection rates as well as the generation and removal rates of all compartments are described by general nonlinear functions. Five threshold parameters are computed, which insure the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established, which is sufficient to investigate the global dynamics of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions.