Non-Noether symmetries and Lutzky conservative quantities of nonholonomic nonconservative dynamical systems

Non-Noether symmetries and conservative quantities of nonholonomic nonconservative dynamical systems are investigated in this paper. Based on the relationships among motion, nonconservative forces, nonholonomic constrained forces and Lagrangian, non-Noether symmetries and Lutzky conservative quantities are presented for nonholonomic nonconservative dynamical systems. The relation between non-Noether symmetry and Noether symmetry is discussed and it is further shown that non-Noether conservative quantities can be obtained by a complete set of Noether invariants. Finally,an example is given to illustrate these results.     

Scalar Gravity and Higgs Mechanism

The role that the auxiliary scalar field φ plays in Brans–Dicke cosmology is discussed. If a constant vacuum energy is assumed to be the origin of dark energy, then the corresponding density parameter would be a quantity varying with φ; and almost all of the fundamental components of our universe can be unified into the dynamical equation for φ. As a generalization of Brans–Dicke theory, we propose a new gravity theory with a complex scalar field ϕ which is coupled to the cosmological curvature scalar. Through such a coupling, the Higgs mechanism is naturally incorporated into the evolution of the universe, and a running density of the field vacuum energy is obtained which may release the particle standard model from the rigorous cosmological constant problem in some sense. Our model predicts a running mass scale of the fundamental particles in which the gauge symmetry breaks spontaneously. The running speed of the mass scale in our case could survive all existing experiments.     

Catalysts in electro-, photo- and photoelectrocatalytic CO2 reduction reactions

Carbon dioxide (CO₂) is regarded as a main contributor to the greenhouse effect. As a potential strategy to mitigate its negative impacts, the reduction of CO₂ is environmentally critical, economically meaningful and scientifically challenging. Being both thermodynamically and kinetically unfavored, CO₂ reduction requires catalysts as a crucial component irrespective of the reaction modes, be it electrocatalytic, photoelectrocatalytic or photocatalytic. In an effort to systematically review the types of catalysts that have been studied for CO₂ reduction, we categorize them into two major groups: those being activated by external sources and those being photoexcited and activated themselves. Attention is focused on the detailed mechanisms for each group by which the reduction of CO₂ proceeds, yielding a summary of the guiding principles for catalyst designs. This review highlights the importance of mechanistic studies, which permits us to discuss our perspectives on potential directions of catalyst investigation for future catalytic CO₂ reduction research.     

An optimal double inequality between geometric and identric means

We find the greatest value p and least value q in (0,1/2) such that the double inequality G(pa+(1−p)b,pb+(1−p)a)<I(a,b)<G(qa+(1−q)b,qb+(1−q)a) holds for all a,b>0 with a≠b. Here, G(a,b), and I(a,b) denote the geometric, and identric means of two positive numbers a and b, respectively.     

Investigation of the Stability of Bi-Anode Electrochemical Hydride Generator

The stability of the self-made bi-anode electrochemical hydride generator (BAECHG) with lead and titanium wires as cathode and anode, respectively, was improved by attaching two pieces of porous epoxy resin sheets to both sides of the anode. This improved BAECHG has good generation efficiency and stability and can run continuously for several months. Additionally, it also has the advantages of lower cost and less consumption of chemicals as compared to the chemical hydride generator. Finally, this BAECHG in combination of atomic fluorescence spectrometry (AFS) was applied to the determination of arsenic (As) and antimony (Sb) in certified soil samples. It was found that the results were close to the certified values and the recoveries of As and Sb were in the range of 96.3–107.0% and 96.0–103.0%, respectively.     

基于广义正交迭代算法的立体视觉定位

提出了一种新的基于广义正交迭代算法的立体视觉定位.该算法通过提取CenSurE局部特征和相应的U-SURF描述符,采用SAD方法进行子像素立体匹配,并利用U-SURF描述符匹配进行前后帧图像特征跟踪.在RANSAC框架下对匹配点进行3D-3D运动估计获得了运动参量的初始值.由于3D-3D运动估计使3D点集间欧式距离误差最小,而3D特征点坐标受噪音影响很大,因此运动估计误差也较大.本文把广义正交迭代算法应用到立体视觉定位方法中,得到使立体相机目标空间共线性误差最小的运动估计参量,由于共线性误差比3D-3D运动估计算法中的共点误差受噪音影响更小,从而大大较少了运动估计误差.仿真实验和户外真实实验表明：本文算法获得了较高的计算准确度、鲁棒性和实时性,优于传统方法.     

Polarization properties of nonparaxial partially polarized Gaussian Schell-model beams

The polarization properties of nonparaxial partially polarized Gaussian Schell-model (PGSM) beams are studied. Based on the beam coherence-polarization matrix, the propagation formula of the degree of polarization for the nonparaxial PGSM beams is derived. The paraxial approximation is dealt with as special cases of our general results. Some conditions that limit the choice of the parameters are established. The sufficiency condition of polarization invariance in propagation for the nonparaxial PGSM beams is derived. By using the derived formulae, the propagation properties of the degree of polarization for the nonparaxial PGSM beam in free space are illustrated and analyzed with numerical examples. Some detailed comparisons of the obtained results with the paraxial results are made.     

An Infrared Image Synthesis Model Based on Infrared Physics and Heat Transfer

Most of current image synthesis models are based on optics of visible-spectrum. While simulating the illumination effect of visible light, they cannot show the infrared signature of the objects. This paper presents a synthesis model for generating realistic infrared images. We first establish a heat equilibrium equation of the object surface. Then according to it and the heat transfer inside the object and on the boundary surface of the object, we compute the temperature and radiometries of each surface patch of the object. Finally on the basis of the radiometries, each patch is drawn by Gouraud Shading. Experimental examples of the generated infrared images are presented, which illustrate the potential of our method.     

A theorem on the transcendency and its applications

A theorem on the transcendency, for a limit of a sequence of algebraic numbers, is given and used to test the transcendencies of some classes of numbers. Project supported by the National Natural Science Foundation of China and the Natural Science Foundation of Zhejiang Province.     

On the rate of convergence of conjugate Legendre—Fourier Series of function of bounded variation

This paper gives the degree of approximation of function of bounded variation by the partial sums of conjngate Legendre—Fourier Series.