Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness

We prove a sharp estimate for the k-modulus of smoothness, modelled upon a $L^p$-Lebesgue space, of a function f in $W^k{L}^{\frac{pn}{n+kp},p}(\mathrm{\Omega })$, where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, $k,n\in \mathbb{N}$, $k<n$ and $\frac{n}{n?k}<p<+\infty$. This sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into generalized Hölder spaces defined by means of the k-modulus of smoothness. General results are illustrated with examples. In particular, we obtain a generalization of the classical Jawerth embeddings.     

Linear independence of a finite set of time-frequency shifts

This paper introduces an open conjecture in time-frequency analysis on the linear independence of a finite set of time-frequency shifts of a given L² function. Firstly, background and motivation for the conjecture are provided. Secondly, the main progress of this linear independence in the past twenty five years is reviewed. Finally, the partial results of the high dimensional case and other cases for the conjecture are briefly presented.     

Stress memory polymers

Like shape memory polymers, a novel phenomenon of stress memory was shown in which the stress of a material can respond to an external stimulus. This concept was further enlightened by a switch‐spring‐frame model that would eliminate the limitation of existing models which overlooked the stimulus responsive nature of such polymers. The discovery being reported in this article was stemmed from a real case study into shape memory polymer fibers in compression stocking for varicose veins. The breakthrough of stress memory enabled researchers to develop applications needing stimuli‐responsive forces, which can broaden the horizon of such smart polymers in emerging smart products in many multidisciplinary fields such as sensors, stress garments, and massage devices, electronic skins, and artificial muscles. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 893–898     

Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings

The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappin...     

A 3D mesh deformation technique for irregular in‐flight ice accretion

Aircraft holding around busy airports may be requested to sustain as much as 45 min of icing before landing or being diverted to another airport. In this paper, a three‐dimensional mesh deformation scheme, based on a structural frame analogy, is proposed for the numerical simulation of ice accretion during extended exposure to adverse weather conditions. The goal is to provide an approach that is robust and efficient enough to delay or altogether avoid re‐meshing while preserving (enforcing) nearly orthogonal elements at the highly distorted ice surface. Robustness is achieved by suitably modifying the axial and torsional stiffness components of the frame elements in order to handle large and irregular grid displacements typical of in‐flight icing. Computational efficiency is obtained by applying the mesh displacement to an automatically selected small subset of the entire computational domain. The methodology is validated first in the case of deformations typical of fluid‐structure interaction problems, including wing bending, a helicopter rotor in forward flight, and the twisting of a high‐lift wing configuration. The approach is then assessed for aero‐icing on two swept wings and compared against experimental measurements where available. Copyright © 2015 John Wiley & Sons, Ltd.     

Side Information Generation Scheme Based on Coefficient Matrix Improvement Model in Transform Domain Distributed Video Coding

In order to effectively improve the quality of side information in distributed video coding, we propose a side information generation scheme based on a coefficient matrix improvement model. The discrete cosine transform coefficient bands of the Wyner–Ziv frame at the encoder side are divided into entropy coding coefficient bands and distributed video coding coefficient bands, and then the coefficients of entropy coding coefficient bands are sampled, which are divided into sampled coefficients and unsampled coefficients. For sampled coefficients, an adaptive arithmetic encoder is used for lossless compression. For unsampled coefficients and the coefficients of distributed video coding coefficient bands, the low density parity check accumulate encoder is used to calculate the parity bits, which are stored in the buffer and transmitted in small amount upon decoder request. At the decoder side, the optical flow method is used to generate the initial side information, and the initial side information is improved according to the sampled coefficients by using the coefficient matrix improvement model. The experimental results demonstrate that the proposed side information generation scheme based on the coefficient matrix improvement model can effectively improve the quality of side information, and the quality of the generated side information is improved by about 0.2–0.4 dB, thereby improving the overall performance of the distributed video coding system.     

Frame‐Guided Assembly of Amphiphiles

Frame‐guided assembly, a recently discovered strategy for amphiphilic assembly, is discussed as a strategy for constructing vesicle assemblies with programmed geometries and dimensions under identical surrounding conditions. The strategy is inspired by the cytoskeletal‐membrane protein–lipid bilayer structure and shows great potential in the understanding and controlling of the amphiphilic assembly process. Both the principles and basic requirements are discussed, along with recently reported examples. The prospects and potential investigations of frame‐guided assembly are also proposed.     

Hierarchical Porous Tubular Biochar Based Sensor for Detection of Trace Lead (II)

Hierarchical porous tubular biochar (PTBC) was prepared by selectively removing lignin simply according to reverse the pyrolysis sequence of cellulose. The properties of the PTBC sample were characterized by XRD, SEM, TEM, Raman spectra, cyclic voltammetry and electrochemical impedance spectroscopy. The electrochemical performances of PTBC modified on the screen-printing electrode illustrated excellent detection of lead ions (lead (II)) in water with the linear range (0.5–120 μg/L) and the detection limit (0.02 μg/L) by in-situ bismuth film square wave anode stripping voltammetry.