Bending wave intensity in a thick beam

I.IntroductionMeasurementSofbendingwaveintensityinoneortwodimensi0na1structuresbecomequitepopularandgetavarietyofindustria1app1icati0ns.Theexistingintensitytheory['-']wasderivedbasedontheclassicaIBernou11i-Eu1ertheorywhichisanapproximatetheoryforana-lyzingstructuralvibration.Inthe1ow-frequencylimitwherebendingwavelengthsaremuchlongincomparisonwiththethicknessofthestructurealongwhichtheypr0pagate(i.e.,thinstructurcs),theuse0ftheclassica1theorywi1lresu1tinanegligiblyerro/`].Forshortwave-1ength…     

Eavesdropping on Quantum Secure Direct Communication with W State in Noisy Channel

Security of the quantum secure direct communication protocol （i.e., the C-S QSDC protocol） recently proposed by Cao and Song [Chin. Phys. Lett. 23 （2006） 290] is analyzed in the case of considerable quantum channel noise. The eavesdropping scheme is presented, which reveals that the C-S QSDC protocol is not secure if the quantum bit error rate （QBER） caused by quantum channel noise is higher than 4.17%. Our eavesdropping scheme induces about 4.17% QBER for those check qubits. However, such QBER can be hidden in the counterpart induced by the noisy quantum channel if the eavesdropper Eve replaces the original noisy channel by an ideal one. Furthermore, if the QBER induced by quantum channel noise is lower than 4.17%, then in the eavesdropping scheme Eve still can eavesdrop part of the secret messages by safely attacking a fraction of the transmitted qubits. Finally, an improvement on the C-S QSDC protocol is put forward.     

A study of properties of adaptive quadratic grids for three-dimensional near-surface field computations

Curved geometries and the corresponding near-surface fields typically require a large number of linear computational elements. High-order numerical solvers have been primarily used with low-order meshes. There is a need for curved, high-order computational elements. Typical near-surface meshes consist of hexahedral and/or prismatic elements. The present work studies the employment of quadratic meshes that are relatively coarse for field simulations. Directionally quadratic high-order elements are proposed for the near-surface field regions. The quadratic meshes are compared with the conventional low-order ones in terms of accuracy and efficiency. The cases considered include closed surface volume calculations, as well as computation of gradients of several analytic fields. A special method of adaptive local quadratic meshes is proposed and evaluated. Truncation error analysis for quadratic grids yields comparison with the conventional linear hexahedral/prismatic meshes, which are subject to typical distortions such as stretching, skewness, and torsion.     

Terpolymerization of Triisopropylsilyl Acrylate,Methyl Methacrylate,and Butyl Acrylate: Reactivity Ratio Estimation

Ternary monomer reactivity ratios of triisopropylsilyl acrylate (SiA), methyl methacrylate (MMA), and n‐butyl acrylate (BA), as common monomers in self‐polishing coatings (SPCs) binders are obtained using experimental data collected from free radical bulk polymerization at 70 °C. Different terpolymerizations at low and medium‐high conversions are performed at optimized feed compositions. Estimations are made using the error‐in‐variables model (EVM) framework, applying the recast form of the Alfrey–Goldfinger (AG) model and a direct numerical integration (DNI) approach to the collected data. Estimations from individual low and medium‐high conversion data are compared to those found with the combined data (full conversion range data). The highest certainty in point estimates are obtained with analysis of the full conversion range data. Furthermore, the reactivity ratios determined from the combined data fall between those found with analysis of individual low and medium‐high conversion data, another corroboration of reliable data collection. Reactivity ratios determined from analysis of the combined data (r_SiA/MMA = 0.4185, r_MMA/SiA = 1.3754, r_SiA/BA = 0.8739, r_BA/SiA = 0.5736, r_BA/MMA = 0.3692, r_MMA/BA = 1.7919) are used in the recast AG model to predict cumulative terpolymer composition as a function of conversion. The experimental data and model prediction show satisfactory agreement.     

Second moment of error term of mean value for binary Egyptian fractions

We study the mean square of the error term of the mean value for binary Egyptian fractions.We get an asymptotic formula under the Riemann Hypothesis.     

A class of loss functions of catenary form

The catenary form of loss function is considered in the framework of Bayesian decision theory. The mathematical tractability of this form seems to be unrecognized; it contains quadratic loss as a limiting case. For various probability distributions expressions are given for posterior analysis, and limiting properties are investigated.     

用于光谱解混的正交向量投影算法

光谱解混是高光谱技术中的关键部分,对地物成分的定量分析至关重要。线性光谱解混方法在计算端元丰度时,大多需要涉及矩阵求逆或方阵行列式的计算,导致软件实现的计算复杂度高,且硬件实现困难。同时,当端元数量增加时,算法的计算量也会随之呈指数级快速增长。论文基于传统的正交子空间投影方法,利用正交原理,提出了一种新的光谱解混方法——正交向量投影。该方法首先利用Gram-Schmidt过程计算每个端元的最终正交向量分量,并将其作为代表端元的投影向量。然后对于任意的待解混光谱向量,直接将其投影到该正交向量上。最后,计算得到投影分量的长度与正交向量的长度比,即为该正交向量所代表端元的无约束丰度。该过程避免了正交子空间投影和最小方差方法中计算复杂、实现困难的矩阵求逆运算,更便于并行计算的设计和硬件实现。通过理论的推导分析,证明了该算法与正交子空间投影和最小方差方法是完全一致的。另外,由于算法避免了矩阵相乘和求逆运算,简化了解混过程,通过对不同算法复杂度的具体分析,也证明该算法相对其他算法可以对端元数量降低一个量级。最后,在模拟数据和实际图像上分别进行实验测试,结果的分析和比较,也说明了算法的有效性。     

Optimal error estimate of the penalty finite element method for the time-dependent Navier-Stokes equations

A fully discrete penalty finite element method is presented for the two-dimensional time-dependent Navier-Stokes equations. The time discretization of the penalty Navier-Stokes equations is based on the backward Euler scheme; the spatial discretization of the time discretized penalty Navier-Stokes equations is based on a finite element space pair which satisfies some approximate assumption. An optimal error estimate of the numerical velocity and pressure is provided for the fully discrete penalty finite element method when the parameters and are sufficiently small.

     

Aliasing Error of Sampling Series in Wavelet Subspaces

Alising error arises whenever a sampling formula, valid for a prescribed space, is applied to a function in a bigger space. In this work, we estimate the aliasing error of classic and average sampling expansions in wavelet subspaces of a multiresolution analysis.     

惠斯登电桥精测电阻的方法和误差分析

本文探讨了惠斯登电桥精确测量和校准电阻的方法，并分析了内插法和代换法的系统误差。