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     

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.     

On Some Properties of $c$-Frames

In this paper we discuss about $c$-frames, namely continuous frames. Since, $c$-frames are generalizations of discrete frames, we generalize some results of discrete frames to continuous version. We explain some results about relations of projections in Hilbert spaces and $c$-frames to characterize these frames. Also, we will specify (precisely) the synthesis and frame operators of Bochner integrable $c$-frames. Finally, we classify Hilbert-Schmidt operators by $c$-frames and express some new identities for Parseval $c$-frames.     

Norm Retrievable Frames and Their Perturbation in Finite Dimensional Complex Hilbert Spaces

In this article, we study the property of norm retrievability of spanning vectors in a finite dimensional complex Hilbert space ?. Using the set of zero trace operators on ? and two sets of self-adjoint operators on ? denoted by 𝒮^1,0 and 𝒮^1,1, we present some equivalent conditions to the norm retrievable frames in ?. We will also show that the property of norm retrievability for n-dimensional complex Hilbert space ? with n≠2 is stable under enough small perturbation of the frame set only for phase retrievable frames.     

A Complete Solution to the Existence of ‐Cycle Frames of Type

The existence problem of a ‐cycle frame of type is now solved for any quadruple .     

A detailed insight into the optimization of plate and frame heat exchanger design by comparing old and new generation metaheuristics algorithms

The voluminous utilization and application of plate and frame heat exchangers (PFHE) in many industries has accelerated the consumer and designer both to optimize exchanger total cost. Over the last few years, several old and new generation algorithms were employed and exploited to optimize PFHE cost. This study explores the application and performance of three new-generation algorithms Big Bang-Big Crunch (BBBC), Grey Wolf Optimizer (GWO), and Water Evaporation Optimization (WEO) in designing optimally PFHE. Besides, this study also compares the performance of three well-established old generations algorithms namely genetic algorithm (genetics and natural selection), particle swarm optimization (animals behaviour), and differential evolution (population-based) with the above three new algorithms in the optimization of PFHE.Seven design factors are chosen for PFHE optimization: exchanger length on hot and cold sides, height and thickness of fin, length of the fin-strip, fin frequency, and the number of hot side layers. The applicability of the suggested algorithms is assessed using a case study based on published research. Though DE performs the best in this study of design optimization concerning total cost and computational time, the three new-generation meta-heuristic algorithms BBBC, GWO, and WEO also provide the novel scope of application in heat exchanger design optimization and successfully finding the cost of the heat exchanger. According to this study, capital costs increase by 19.5% for BBBC, 24% for GWO, and 7.6% for GWO, but operational costs fall by 9.5% for BBBC and GWO when compared to the best performing algorithm (DE). On the other hand, WEO shows an increase of 32.6% in operational costs. Aside from that, a full analysis of the computing time for each algorithm is also provided. The DE has the quickest run time of 0.09 ?s, while the PSO takes the longest at 33.97 ?s. The rest of the algorithms have nearly identical values. As a result, a good comparison is established in this study, offering an excellent platform for designers and customers to make selections. Additionally, the three new generations algorithms mentioned here were not used earlier for optimization of PFHE and the comparative study illustrates that each of them possesses eat potential for cost optimization and also solving other complex problems.