Exponential Expansiveness and Complete Admissibility For Evolution Families

Connections between uniform exponential expansiveness and complete admissibility of the pair are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.     

Double-Network Heparin Dynamic Hydrogels: Dynagels as Anti-bacterial 3D Cell Culture Scaffolds

Double cross-linked dynamic hydrogels, dynagels, have been prepared through reversible imine bonds and supramolecular interactions, which showed good pH responsiveness, injectability, self-healing property and biocompatibility. With the further encapsulation of heparin, the obtained hydrogels exhibited good anti-bacterial activity and promotion effects for 3D cell culture.     

Identically conserved currents and their charges

We examine, at a classical level, the features that distinguish dynamically conserved currents from identically conserved ones. Then we prove that, in four spacetime dimensions, the quantum charges corresponding to identically conserved currents always annihilate the vacuum state. We illustrate our discussion with several examples.     

Exponential dichotomies of evolution operators in Banach spaces

This paper considers three dichotomy concepts (exponential dichotomy, uniform exponential dichotomy and strong exponential dichotomy) in the general context of non-invertible evolution operators in Banach spaces. Connections between these concepts are illustrated. Using the notion of Green function, we give necessary conditions and sufficient ones for strong exponential dichotomy. Some illustrative examples are presented to prove that the converse of some implication type theorems are not valid.     

Numerical solution of the steady incompressible Navier—Stokes equations for the flow past a sphere by a multigrid defect correction technique

A nested non-linear multigrid algorithm is developed to solve the Navier–Stokes equations which describe the steady incompressible flow past a sphere. The vorticity–streamfunction formulation of the Navier–Stokes equations is chosen. The continuous operators are discretized by an upwind finite difference scheme. Several algorithms are tested as smoothing steps. The multigrid method itself provides only a first-order-accurate solution. To obtain at least second-order accuracy, a defect correction iteration is used as outer iteration. Results are reported for Re = 50, 100, 400 and 1000.     

A Ca2+‐, Mg2+‐, and Zn2+‐Based Dendritic Contractile Nanodevice with Two pH‐Dependent Motional Functions

A contractile dendritic motional device is reported where metal ions with biological importance—Ca²⁺ (the main regulatory and signaling species of the natural muscles), Mg²⁺, and Zn²⁺—initiate two kinds of motional functions. The first motional function is the metal‐ion‐induced contraction of a linear strand into a Z‐shaped dinuclear complex, and the second one is the change of the height of Z‐shaped complexes via transmetalation. By means of the pH‐dependent counterligand tren, the two motional features of the machine can depend on alternate additions of acid and base. An optical response is associated with the conversion of the linear form (which is yellow) into the metalated Z‐shaped one (which is red).     

Determination of four acidic nonsteroidal anti‐inflammatory drugs in wastewater samples by dispersive liquid–liquid microextraction based on solidification of floating organic droplet and high‐performance liquid chromatography

A simple, environmentally friendly, and sensitive dispersive liquid–liquid microextraction based on solidification of floating organic droplet for the extraction of four acidic nonsteroidal anti‐inflammatory drugs (ketoprofen, naproxen, ibuprofen, and diclofenac) from wastewater samples subsequent by high‐performance liquid chromatography analysis was developed. The influence of extraction parameters such as pH, the effect of solution ionic strength, type of extraction solvent, disperser solvent, and extraction solvent volume were studied. High enrichment factors (283–302) were obtained through the developed method. The method provides good linearity (r > 0.999) in a concentration range of 1–100 μg/L, good intra‐ and inter‐day precision (relative standard deviation < 7%) and low limits of quantification. The relative recoveries of the selected compounds were situated over 80% both in synthetic and real water samples. The developed method has been successfully applied for the analysis of the selected compounds in wastewater samples.     

Surface plasmon polariton assisted optical pulling force

We demonstrate both analytically and numerically the existence of optical pulling forces acting on particles located near plasmonic interfaces. Two main factors contribute to the appearance of this negative recoil force. The interference between the incident and reflected waves induces a rotating dipole with an asymmetric scattering pattern, while the directional excitation of surface plasmon polaritons (SPPs) enhances the linear momentum of scattered light. The strongly asymmetric SPP excitation is determined by spin–orbit coupling of the rotating dipole and surface plasmon polariton. As a result of the total momentum conservation, the force acting on the particle points in a direction opposite to the incident wave propagation. We derive analytical expressions for the force acting on dipolar particles placed in the proximity of plasmonic surfaces. Analytical expressions for this pulling force are derived within the dipole approximation and are in excellent agreement with results of electromagnetic numerical calculations. The forces acting on larger particles are analyzed numerically, beyond the dipole approximation.

     

The Structure of Multiplicative Tilings of the Real Line

Journal of Fourier Analysis and Applications - Suppose $$\Omega , A \subseteq \mathbb {R}\backslash {\left\{ {0}\right\} }$$ are two sets, both of mixed sign, that $$\Omega $$ is Lebesgue...