Finding optimal finite field strengths allowing for a maximum of precision in the calculation of polarizabilities and hyperpolarizabilities

The finite field method, widely used for the calculation of static dipole polarizabilities or the first and second hyperpolarizabilities of molecules and polymers, is thoroughly explored. The application of different field strengths and the impact on the precision of the calculations were investigated. Borders could be defined and characterized, establishing a range of feasible field strengths that guarantee reliable numerical results. The quality of different types of meshes to screen the feasible region is assessed. Extrapolation schemes are presented that reduce the truncation error and allow to increase the precision of finite field calculations by one to three orders of magnitude. © 2013 Wiley Periodicals, Inc.     

A new framework for implicit restarting of the Krylov–Schur algorithm

This paper introduces a new framework for implicit restarting of the Krylov–Schur algorithm. It is shown that restarting with arbitrary polynomial filter is possible by reassigning some of the eigenvalues of the Rayleigh quotient through a rank‐one correction, implemented using only the elementary transformations (translation and similarity) of the Krylov decomposition. This framework includes the implicitly restarted Arnoldi (IRA) algorithm and the Krylov–Schur algorithm with implicit harmonic restart as special cases. Further, it reveals that the IRA algorithm can be turned into an eigenvalue assignment method. Copyright © 2014 John Wiley & Sons, Ltd.     

New q‐Hermite polynomials: characterization,operators algebra and associated coherent states

This paper addresses a construction of new q‐Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three‐term recursive relation as well as the second‐order differential equation obeyed by these new polynomials are explicitly derived. Relevant operator actions, including the eigenvalue problem of the deformed oscillator and the self‐adjointness of the related position and momentum operators, are investigated and analyzed. The associated coherent states are constructed and discussed with an explicit resolution of the induced moment problem. The phase collapse in a q‐deformed boson system is studied.     

确定性矩阵可分离压缩成像

针对可分离压缩传感使用的可分离随机正交矩阵在处理大尺度图像等高维信号感知时难度太大或成本过高的问题,引入确定性测量矩阵,提出确定性矩阵可分离压缩传感,可将如托普利兹矩阵及循环矩阵等具有确定性结构的矩阵作为可分离压缩传感的左、右可分离矩阵.该方案可以降低独立元素的数目,从而显著降低前端物理实现的难度与成本.数值模拟实验分别评估了该方法在不同采样率及不同图像尺寸下的压缩重建性能,结果表明该方法在独立元素非常少的情形下得到与原随机正交矩阵相近的重建质量,证明了其可行性.     

Research on improving the accuracy of near infrared non-invasive hemoglobin detection

To optimize the accuracy of near-infrared non-invasive hemoglobin (Hb) clinical detection, high-performance instrument and prepossessing algorithm have been investigated. A near-infrared spectrophotometric system was constructed adopting InGaAs detector array with 16 pixels and plane grating spectrometer to obtain high signal noise ratio (SNR) spectral data. In our experiment, we applied the device independently to collect spectra data from 91 volunteers’ fingertips non-invasively. Two prediction tests were conducted to verify the effects of preprocessing algorithms improving the accuracy of near-infrared Hb detection and exclude the occasionality of satisfactory results in a single trial. Our non-invasive Hb detection methods were based on partial least squares (PLS). In each test, PLS, MSC coupled with PLS, DOSC coupled with PLS, three methods for non-invasive Hb detection, were analyzed respectively. The results of two trials showed that only DOSC & PLS performed excellently in both predictive ability and stability, obviously better than other two methods. Relative RMSEP was 6.16% in predicting test 1, 6.08% in predicting test 2, almost reaching the requirements of clinical application. It indicates that our independent-developed high-performance instrument and the method DOSC coupled with PLS are promising in non-invasive Hb detection clinical application.     

Free vibration of non-uniform nanobeams using Rayleigh–Ritz method

In this article, boundary characteristic orthogonal polynomials have been implemented in the Rayleigh–Ritz method to investigate free vibration of non-uniform Euler–Bernoulli nanobeams based on nonlocal elasticity theory. Non-uniform cross section of nanobeams has been considered by taking linear as well as quadratic variations of Young's modulus and density along the space coordinate. Detailed analysis has been reported for all the possible cases of such variations. The objective of the present study is to analyze the effects of nonlocal parameter, boundary condition, length-to-diameter ratio and non-uniform parameter on the frequency parameters. It is found that clamped nanobeams are having highest frequency parameters than other types of boundary conditions for a particular set of parameters. It is also observed that frequency parameters decrease with increase in scaling effect parameter. First four deflection shapes of non-uniform nanobeams have also been incorporated. In this analysis, some of the new results in terms of boundary conditions have also been included.     

Orthogonal Cationic and Radical RAFT Polymerizations to Prepare Bottlebrush Polymers

An orthogonal combination of cationic and radical RAFT polymerizations is used to synthesize bottlebrush polymers using two distinct RAFT agents. Selective consumption of the first RAFT agent is used to control the cationic RAFT polymerization of a vinyl ether monomer bearing a secondary dormant RAFT agent, which subsequently allows side‐chain polymers to be grafted from the pendant RAFT agent by a radical‐mediated RAFT polymerization of a different monomer, thus completing the synthesis of bottlebrush polymers. The high efficiency and selectivity of the cationic and radical RAFT polymerizations allow both polymerizations to be conducted in one‐pot tandem without intermediate purification.     

Influence of the molding angle on tensile properties of FDM parts with orthogonal layering

Fused deposition molding (FDM) is one of the most widely used three‐dimensional (3D) printing technologies. This paper explores the influence of the forming angle on the tensile properties of FDM specimens. Orthogonal layering details were studied through experiments, theory, and finite element simulations. The stiffness and strength of the specimens were analyzed using the classical laminated plate theory and the Tsai–Wu failure criterion. The experimental process was simulated using finite element simulations. Results show that it is feasible to predict the stiffness and strength of FDM specimens using classical laminated plate theory and the Tsai–Wu failure criterion. A molding angle of 45° leads to specimens with maximized tensile properties. Numerical simulations show that changing the molding angle changes the internal stress and deformation fields inside samples, leading to FDM samples with different mechanical properties due to the orthogonal layers at different molding angles.     

Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.     

Electrical properties of interdigitated partially bent like shaped liquid crystalline compound

This article represents the electrical studies of an interdigitated highly skewed N(4-n-pentyloxybenzylidene) 4-n-alkylaniline (5O.16) compound. Interestingly the compound is partially bent like and unsymmetrical in alkyl chain length. Dielectric and impedance spectroscopy studies indicate the coupling between the liquid crystal and the electrical field. Studies were carried out as a function of temperature as well as frequency. Semicircular nature of the Cole–Cole plots indicates the reorientation of the molecule with the applied field. Using the experimental data and the theoretically fitted results the effective equivalent model circuit was designed. Which used to explain the behavior of the compound under the external electric effect and the influence of the electrodes with different variable represent the resistor circuit. However, the effect of the conductivity of temperature and frequency are also reported.