A note on double lacunary statistical $$\sigma$$-convergence of fuzzy numbers

Quite recently, Sava? (Appl Math Lett 21:134–141, 2008), defined the lacunary statistical analogue for double sequence \(X=\{X_{k,l}\}\) of fuzzy numbers as follows: a double sequence \(X=\{X_{k,l}\}\) is said to be lacunary P-statistically convergent to \(X_{0}\) provided that for each \(\epsilon >0\)

$ P-\lim_{r,s}\frac{1}{h_{r,s}}\left | \{(k,l)\in I_{r,s}: d(X_{k,l },X_0)\geq \epsilon\}\right|= 0. $

In this paper we introduce and study double lacunary \(\sigma\)-statistical convergence for sequence of fuzzy numbers and also we get some inclusion theorems.

     

内建电场调控光生电荷分离效率的研究进展

光催化技术是解决现今环境污染和能源危机的重要手段之一,然而大部分催化剂的光催化效率较低,提高光生电荷的分离是提高光催化效率的一种有效方法。首先对催化剂的光催化原理进行了概述;结合近年来国内外在提高光生电荷分离效率方面取得的最新成果及进展,从内建电场的产生机理入手,综述了半导体p⁃n结、异相结、极化表面和铁电材料极化对光生电荷分离效率及光催化性能的影响;最后对内建电场在未来光催化领域的发展方向进行了展望。     

Preparation of Iron Filler-Based Photocomposites and Application in 3D Printing

The introduction of metallic fillers to polymers via the photopolymerization approach can endow the composite materials with some unique properties, but the relevant research is still scarce due to the issue of light penetration and inner filter effect. Herein, for the first time the fabrication of photocomposites based on fine iron powder (i.e., a typical kind of metallic filler) is reported in this work. The free radical polymerization of two different acrylate monomers, poly(ethylene glycol) diacrylate and trimethylolpropane triacrylate, is performed in the presence of iron filler under mild conditions (i.e., light emitting diode (LED)@405 nm irradiation at room temperature under air). And the real-time Fourier transform infrared spectroscopy reveals remarkable photopolymerization kinetics of acrylates with high final conversions and fast polymerization rates despite the increasing contents of iron filler in the composites. Interestingly, the 3D printing technique is applied to the iron filler-based composites to produce tridimensional patterns with excellent spatial resolution. This work not only paves the way for the investigation of photocomposites based on metallic fillers through photochemical methods, but also broadens the potential application prospects.     

3D Printing of Polyvinylidene Fluoride Based Piezoelectric Nanocomposites: An Overview

Recently, polyvinylidene fluoride (PVDF) based nanocomposites have attracted much attention for next-generation wearable applications such as promising piezoelectric energy harvesters (nanogenerators), energy storage devices, sensing devices, and biomedical devices due to their high flexibility, and high dielectric and piezoelectric properties. 3D printing technology, PVDF based piezoelectric nanocomposites, the studies based on 3D printing of PVDF based piezoelectric nanocomposites by inkjet printing and fused deposition modeling, and enhancements of energy harvesting and storage performance of nanocomposites by structural design are comprehensively overviewed here. An insight is provided into 3D printing techniques, structure and properties of PVDF based polymers, various nanofillers and production methods for nanocomposites, solutions to enhance β phase (crystallinity) of PVDF, and improvements of nanocomposites’ breakdown strength, discharged energy density, and piezoelectric power output by mentoring structural design.     

Matching ultrasonic transducer using two matching layers where one of them is glue

The aim of this work is to propose an original solution to the acoustic impedance mismatch between a PZT transducer and a water load. The characteristic acoustic impedance of the PZT is around 33 MRayl. Theoretically, a quarter-wave layer with characteristic acoustic impedance equal to 7 MRayl is necessary to match the transducer to water. In practice, it is difficult to find a material with this particular impedance. Two or more quarter-wave layers may also be used. The following proposed solution consists in using two matching layers where one of them is the glue. Moreover, their thicknesses are not equal to a quarter of their individual wavelength. Once the glue is taken as the first matching layer, the specific material of the second layer can easily be found. In this work, the second layer, which is also the front layer, is made of glass. The thickness of each matching layer is then calculated as a function of the characteristic acoustic impedance of the two layers. The influence of the thickness of these layers is discussed. The proposed matching configuration is analyzed and theoretical results have been carefully and successfully compared with measurements.     

The Structure of the Irreversibly Bound Adhesion Promoter-Substrate Interfacial Layer of γ-Aminopropylsilanetriol on Crystalline Si, as Measured by XPS and FTIR

The irreversibly bound interfacial layer deposited by the γ-aminopropysilanetriol adhesion promoter onto a crystalline silicon substrate, which remains even after profuse washing, was found by XPS to have resulted from the fragmentation and rearrangement of the original γ-aminopropylsilanetriol molecule. A mechanism is proposed, involving the homolytic scission of the terminal N-C bond. One of the subsequent reactions is believed to involve hydrogen loss by abstraction and the formation of a terminal vinyl group, which bonds to the substrate. Support for this mechanism is found in IR spectroscopy of this layer.     

Factors influencing the formation of elongated morphologies in immiscible polymer blends during melt processing

The morphology of the dispersed phase in immiscible polymer blends plays an important role in the determination of the final physical properties. This paper considers factors that influence the final state of deformation of the dispersed phase, and in particular, the formation of fibers and lamellae. Blends of polyethylene and nylon-6 were extruded by ribbon extrusion at different draw ratios. Prior to single-screw extrusion the materials were blended in a co-rotating twin-screw extruder, and the size of the dispersed phase was studied as a function of the viscosity ratio. As the blends are extruded into ribbons and drawn through the calender rolls, the morphology of the dispersed phase undergoes drastic transformations. The fiber formation is enhanced by increasing the draw ratio. At high draw ratios, long thin fibers are observed. Some biaxial deformation is obtained for the noncompatibilized systems when the extruded materials enter the calender with the maximum closing pressure applied to the rolls. The same effect is observed for the compatibilized systems with lower values of the viscosity ratio. As a general rule, it has been observed that the final dispersed phase deformation is diminished in interfacially compatibilized systems.     

EXPERIMENTAL STUDY ON MIXING: POWER CONSUMPTION AND DEGREE OF SUSPENSION

An experimental study on mixing, degree of suspension and power consumption in solid-liquid suspensions was done. A system similar to those found in anaerobic fermentation processes of animal manures was used, and an existing mixing equipment was adapted for the study. Power consumption and degree of suspension for both mechanical mixing and mixing by gas was determined. The influence of variables such as geometry, solids concentration, stirrer velocity, and gas velocity was studied, discussed, and compared to data from the literature. Best results were obtained for gas mixing, the power consumption being about one fourth of that required by mechanical agitation. Finally, extended correlations relating Power and Reynolds numbers for mechanical mixing and mixing by gas are proposed.     

Decentralized observers with consensus filters for distributed discrete-time linear systems

This paper presents a decentralized observer with a consensus filter for the state observation of discrete-time linear distributed systems. Each agent in the distributed system has an observer with a model of the plant that utilizes the set of locally available measurements, which may not make the full plant state detectable. This lack of detectability is overcome by utilizing a consensus filter that blends the state estimate of each agent with its neighbors’ estimates. It is proven that the state estimates of the proposed observer exponentially converge to the actual plant states under arbitrarily changing, but connected, communication and pseudo-connected sensing graph topologies. Except these connectivity properties, full knowledge of the sensing and communication graphs is not needed at the design time. As a byproduct, we obtained a result on the location of eigenvalues, i.e., the spectrum, of the Laplacian for a family of graphs with self-loops.