Trace Formulae of Characteristic Polynomial and Cayley-HamUton's Theorem, and Applications to Chiral Perturbation Theory and General Relativity

By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and we further obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace formulae of the Cayley-Hamilton＇s theorem with all coefficients explicitly given. This implies a byproduct, a complete expression for the determinant of any finite-dimensional matrix in terms of the traces of its successive powers. And we discuss some of their applications to ehiral perturbation theory and general relativity.

Modeling of Surface Tension and Viscosity for Non-electrolyte Systems by Means of the Equation of State for Square-well Chain Fluids with Variable Interaction Range

The equation of state(EOS)for square-well chain fluid with variable range(SWCF-VR) developed in our previous work based on statistical mechanical theory for chemical association is employed for the correlations of surface tension and viscosity of common fluids and ionic liquids(ILs).A model of surface tension for multi-component mixtures is presented by combining the SWCF-VR EOS and the scaled particle theory and used to produce the surface tension of binary and ternary mixtures.The predicted surface tensions are in excellent agreement with the experimental data with an overall average absolute relative deviation(AAD)of 0.36%.A method for the calculation of dynamic viscosity of common fluids and ILs at high pressure is presented by combining Eyring’s rate theory of viscosity and the SWCF-VR EOS.The calculated viscosities are in good agreement with the experimental data with the overall AAD of 1.44% for 14 fluids in 84 cases.The salient feature is that the molecular parameters used in these models are self-consistent and can be applied to calculate different thermodynamic properties such as pVT,vapor-liquid equilibrium,caloric properties,surface tension,and viscosity.

A Model of Federated Evidence Fusion for Real-time Urban Traffic State Estimation

In order to make full use of heterogeneous multi-sensor data to serve urban intelligent transportation systems, a real-time urban traffic state fusion model was proposed, named federated evidence fusion model. The model improves conventional D-S evidence theory in temporal domain, such that it can satisfy the requirement of real-time processing and utilize traffic detection information more efficaciously. The model frame and computational procedures are given. In addition, a generalized reliability weight matrix of evidence is also presented to increase the accuracy of estimation. After that, a simulation test is presented to explain the advantage of the proposed method in comparison with conventional D-S evidence theory. Besides, the validity of the model is proven by the use of the data of loop detectors and GPS probe vehicles collected from an urban link in Shanghai. Results of the experiment show that the proposed approach can well embody and track traffic state at character level in real-time conditions.

Implementation of ternary Shor's algorithm based on vibrational states of an ion in anharmonic potential

It is widely believed that Shor＇s factoring algorithm provides a driving force to boost the quantum computing research.However, a serious obstacle to its binary implementation is the large number of quantum gates. Non-binary quantum computing is an efficient way to reduce the required number of elemental gates. Here, we propose optimization schemes for Shor＇s algorithm implementation and take a ternary version for factorizing 21 as an example. The optimized factorization is achieved by a two-qutrit quantum circuit, which consists of only two single qutrit gates and one ternary controlled-NOT gate. This two-qutrit quantum circuit is then encoded into the nine lower vibrational states of an ion trapped in a weakly anharmonic potential. Optimal control theory（OCT） is employed to derive the manipulation electric field for transferring the encoded states. The ternary Shor＇s algorithm can be implemented in one single step. Numerical simulation results show that the accuracy of the state transformations is about 0.9919.

La Shalle＇s invariant-set-theory based asymptotic synchronization of duffing system with unknown parameters

A novel La Shalle＇s invariant set theory （LSIST） based adaptive asymptotic synchronization （LSISAAS） method is proposed to asymptotically synchronize Duffing system with unknown parameters which also are considered as system states. The LSISASS strategy depends on the only information, i.e. one state of the master system. According to the LSIST, the LSISASS method can asymptotically synchronize fully the states of the master system and the unknown system parameters as well. Simulation results also validate that the LSISAAS approach can obtain asymptotic synchronization.

Reduction of Dimerization Tendency Due to the Decrease in Hybridization Index by Inclusion of 4s and 4p Semicore States as Valence States in Mo_(n)(n=2-18)Clusters:A First-Principles Study

Owing to the unique structural,electronic,and physico-chemical properties,molybdenum clusters are expected to play an important role in future nanotechnologies.However,their ground states are still under debate.In this study,the crystal structure analysis by particle swarm optimization(CALYPSO)approach is used for the global minimum search,which is followed by first-principles calculations,to detect an obvious dimerization tendency in Mo_(n)(n=2-18)clusters when the 4s and 4p semicore states are not regarded as the valence states.Further,the clusters with even number of atoms are usually magic clusters with high stability.However,after including the4 s and 4 p electrons as valence electrons,the dimerization tendency exhibits a drastic reduction because the average hybridization indices H_(sp),H_(sd),and H_(pd) are reduced significantly.Overall,this work reports new ground states of Mo_(n)(n=11,14,15)clusters and proves that semicore states are essential for Mo_(n) clusters.

Why Krogdahl’s Flat Space-Time Cosmology Is Superior to General Relativity

This paper briefly discusses existing problems with the theory of general relativity despite remarkable accuracy in most of its applications. The primary focus is on existing problems in the field of cosmology, particularly those pertaining to expectations of global cosmic space-time curvature in the absence of observational proof. The discussion centers on Krogdahl’s recent Lorentz-invariant flat space-time cosmology and its superiority to general relativity with respect to accounting for global cosmic space-time flatness and dark energy observations. The “cosmological constant problem” is briefly addressed as a problem for general relativity with respect to particle physics and quantum field theory. Finally, two very specific validation predictions in favor of Krogdahl’s flat space-time cosmology are made with respect to ongoing studies, including the dark energy survey (DES).

Circular Scale of Time as a Guide of the Schrödinger’s Perturbation Theory

The paper is a kind of a review which considers an investigation of the scale of time suggested by an application of the Schrödinger perturbation method, especially when the perturbation of a non-degenerate quantum state is examined. In fact the method was applied in numerous cases—also by Schrödinger himself—without any use of the notion of time. Simultaneously, because of the development of computers, their use in solving the perturbation problems gradually decreased. However, the point of importance in the paper became the time. We demonstrate that collisions of a quantum system with the perturbation potential can be arranged along a circular scale of time whose properties provide us precisely with the energy terms obtained by the Schrödinger perturbation theory. This validity of results is checked till the perturbation order N = 7.

Einstein’s General Relativity and Pure Gravity in a Cosserat and De Sitter-Witten Spacetime Setting as the Explanation of Dark Energy and Cosmic Accelerated Expansion

Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 killing vector fields corresponding to Witten’s five Branes model in eleven dimensional M-theory we reason that 504 of the 528 are essentially the components of the relevant killing-Yano tensor. In turn this tensor is related to hidden symmetries and torsional coupled stresses of the Cosserat micro-polar space as well as the Einstein-Cartan connection. Proceeding in this way the dark energy density is found to be that of Einstein’s maximal energy mc2 where m is the mass and c is the speed of light multiplied with a Lorentz factor equal to the ratio of the 504 killing-Yano tensor and the 528 states maximally symmetric space. Thus we have E (dark) = mc2 (504/528) = mc2 (21/22) which is about 95.5% of the total maximal energy density in astounding agreement with COBE, WMAP and Planck cosmological measurements as well as the type 1a supernova analysis. Finally theory and results are validated via a related theory based on the degrees of freedom of pure gravity, the theory of nonlocal elasticity as well as ‘t Hooft-Veltman renormalization method.

Origin of Magnetic Fields of Stellar Objects in the Universe Based on the 5D Projection Theory

Beginning with a 5D homogeneous universe [1], we have provided a plausible explanation of the self-rotation phenomenon of stellar objects previously with illustration of large number of star samples [2], via a 5D-4D projection. The origin of such rotation is the balance of the angular momenta of stars and that of positive and negative charged e-trino pairs, within a 3D ⊗1D?void of the stellar object, the existence of which is based on conservation/parity laws in physics if one starts with homogeneous 5D universe. While the in-phase e-trino pairs are proposed to be responsible for the generation of angular momentum, the anti-phase but oppositely charge pairs necessarily produce currents. In the 5D to 4D projection, one space variable in the 5D manifold was compacted to zero in most other 5D theories (including theories of Kaluza-Klein and Einstein [3] [4]). We have demonstrated, using the Fermat’s Last Theorem [5], that for validity of gauge invariance at the 4D-5D boundary, the 4th space variable in the 5D manifold is mapped into two current rings at both magnetic poles as required by Perelman entropy mapping;these loops are the origin of the dipolar magnetic field. One conclusion we draw is that there is no gravitational singularity, and hence no black holes in the universe, a result strongly supported by the recent discovery of many stars with masses well greater than 100 solar mass [6] [7] [8], without trace of phenomena observed (such as strong gamma and X ray emissions), which are supposed to be associated with black holes. We analyze the properties of such loop currents on the 4D-5D boundary, where Maxwell equations are valid. We derive explicit expressions for the dipolar fields over the whole temperature range. We then compare our prediction with measured surface magnetic fields of many stars. Since there is coupling in distribution between the in-phase and anti-phase pairs of e-trinos, the generated mag-netic field is directly related to the angular momentum, leading to the result that the magnetic field can be expressible in terms of only the mechanical variables (mass M, radius R, rotation period P)of a star, as if Maxwell equations are “hidden”. An explanation for the occurrence of this “un-expected result” is provided in Section (7.6). Therefore we provide satisfactory answers to a number of “mysteries” of magnetism in astrophysics such as the “Magnetic Bode’s Relation/Law” [9] and the experimental finding that B-P graph in the log-log plot is linear. Moreover, we have developed a new method for studying the relations among the data (M, R, P) during stellar evolution. Ten groups of stellar objects, effectively over 2000 samples are used in various parts of the analysis. We also explain the emergence of huge magnetic field in very old stars like White Dwarfs in terms of formation of 2D Semion state on stellar surface and release of magnetic flux as magnetic storms upon changing the 2D state back to 3D structure. Moreover, we provide an explanation, on the ground of the 5D theory, for the detection of extremely weak fields in Venus and Mars and the asymmetric distribution of magnetic field on the Martian surface. We predict the equatorial fields B of the newly discovered Trappist-1 star and the 6 nearest planets. The log B?−?log P graph for the 6 planets is linear and they satisfy the Magnetic Bode’s relation. Based on the above analysis, we have discovered several new laws of stellar magnetism, which are summarized in Section (7.6).

基于密度泛函理论的S掺杂碳载体负载Pt催化剂对氧还原反应的影响

采用密度泛函方法对比研究了Pt/C催化剂中碳载体掺S前后对氧还原反应(ORR)的影响。从电荷分布、态密度及d带中心等性质出发,分析了金属-载体间相互作用,研究了ORR各物种在催化剂上的吸附并计算了ORR过电势。结果表明:S掺杂使得碳载体表面发生了电子转移,S上的电子转移到邻近的C原子上,负载Pt纳米颗粒后,Pt金属上的电子转移给了碳载体;Pt在S掺杂碳载体上的吸附更强,形成了Pt—C键和Pt—S键,Pt纳米颗粒的分散度和稳定性得到了提升;掺S使得催化剂d带中心下降,对ORR各中间体的吸附减弱,ORR过电势降低,表明掺S能提高催化剂的催化活性。

基于层次分析法与改进D-S理论的阀水冷系统状态评估

为了及时评估保障换流阀可靠运行的阀水冷系统运行状态,首先,分析了换流站阀水冷系统整体构成,选取主要历史数据和实时数据构建了评估指标体系,通过三角形函数和半梯形函数以及专家调查法确定各个指标的隶属度;其次,基于层次分析法确定各个评估指标权重,改进D-S理论建立阀水冷系统运行状态评估模型;最后,通过采集实际工程阀水冷系统主要指标数据对模型进行了验证,并以阀水冷系统滤芯清洗前后数据为例对评估结果进行了对比。结果表明,所建模型能够对阀水冷系统运行状态做出准确识别和评估,有利于运维人员及时掌控阀水冷系统运行状态,保障其可靠运行。

基于熵权灰色关联和D-S证据理论的疲劳驾驶险态辨识

为解决驾驶员疲劳驾驶险态辨识的复杂不确定性问题,提出了一种疲劳驾驶行为状态辨识方法。该方法基于熵权灰色关联和Dempster-Shafer(D-S)证据理论,兼顾处理了不同指标的综合性与标识目标的不确定性。利用熵权理论计算指标权重,运用灰色关联分析法,确定各指标的不确定信度,构建不同目标的Mass函数;基于D-S证据理论的Dempster证据合成法则,融合Mass函数,实现驾驶员疲劳驾驶行为险态辨识;运用面部视频的专家评价判断方法检验辨识方法。试验结果表明:该方法在高速工况下识别精度达91.25%。因而,与基于单传感器的检测方法相比,有效提高了驾驶行为辨识的准确性、可靠性。

基于D-S证据融合的相控阵雷达状态识别

在D-S证据理论融合方法的基础上,在分析了相控阵雷达状态和信号波形,提出了利用特征函数识别相控阵雷达状态的方法。并用典型相控阵雷达参数进行了仿真实验,实验结果表明,这种方法具有较高的识别概率。

基于Lyapunov方法T-S模糊系统的H_∞控制

针对Takagi-Sugeno(T-S)模糊系统,研究了H∞状态反馈控制器的设计问题.利用Lyapunov稳定性理论,采用线性矩阵不等式(LM I)技术,以矩阵不等式和线性矩阵不等式(LM Is)的形式给出2个新的确保T-S模糊系统存在H∞状态反馈控制器的充分条件.已有的结果没有考虑各个子系统之间的联系,致使所得的条件过于保守,而所提出的方法充分考虑了每个模糊子系统之间的联系,所得到的条件具有更大的宽松性.数值算例说明了该方法的有效性.

基于参数辨识的DTP-PMSM无传感器控制

针对双三相永磁同步电动机(DTP-PMSM)在受到外界和电机内部影响时,会出现电气参数变化和传感器精度下降的问题,提出一种带参数辨识的无传感器控制方案。该方案通过MRAS来实现电阻和电感的在线辨识,为了减小谐波的影响,将其推广到静止坐标系中,采用Popov超稳定性理论设计出新的自适应律,并使用BP神经网络来优化自适应律的增益,实现增益的在线调节,提高系统的辨识精度。此外,为进一步提高系统的鲁棒性,提出了一种基于线性扩张状态观测器和滑模控制相结合的改进锁相环,通过Lyapunove函数证明其稳定性。仿真结果表明,提出的方法能够实现对电气参数的准确辨识,提高系统控制性能。

基于正态云模型和D-S证据理论的开关柜运行状态综合评估

以高压开关柜为研究对象,提出了一种基于正态云模型和D-S证据理论的分层评估算法。通过对影响开关柜运行状态的指标进行聚类分层,运用正态云模型确定各指标与各评价等级的关联度,并利用改进的模糊算法进行第1层评估,在此基础上运用D-S证据理论对开关柜整体运行状态进行评估。采用KYN28A-12型号某开关柜的一次检测数据为例,通过实例验证证明了评估算法的有效性。该评估模型结构清晰,评价指标易于得到,为开关柜状态评估提供了一种新思路。

基于改进D-S证据理论数据融合的路段单元交通状态判别方法

为探究不同类型车辆运动特征差异对路段整体交通流状态判别的影响,解决单一数据源导致判别结果精度不高的问题,针对多种类型车辆的浮动车数据存在的显著差异,提出了基于改进D-S(Dempster-Shafer)证据理论数据融合的路段单元交通状态判别方法。通过分析不同类型车辆的浮动车数据,探究其在速度分布、交通状态划分标准及样本量等方面存在的差异;针对D-S证据理论在融合高冲突信息时的失效问题,从修正数据源基本信任分配函数与优化合成规则两方面改进D-S证据,并据此构建路段单元交通状态判别模型。经实例验证发现:基于出租车、公交车、私家车单一浮动车数据的路段单元交通状态判别准确率分别为83.58%,70.15%,61.19%,利用传统D-S证据理论融合数据的交通状态判别准确率为85.07%,改进方法判别准确率为94.03%。这表明改进方法可有效融合高度冲突的多种浮动车数据,其交通状态判别准确率高于基于单一浮动车数据或传统D-S证据理论的判别方法。

S_N2反应X_l^-+CH_3X_r→X_lCH_3+X_l^-(X_l=X_r=F,Cl,Br,I)的价键方法研究

应用最近发展的价键组态相互作用 ( VBCI)方法计算了 SN2反应 X-l +CH3 Xr→ Xl CH3 +X-r ( Xl=Xr=F,Cl,Br,I)的反应能垒和价键相关参数 .计算结果表明 ,VBCI能垒与采用分子轨道理论的 CCSD( T)方法计算的能垒相一致 .讨论了 SN2反应的反应参数 .

基于改进D-S证据理论的变压器多维信息融合及状态评估

对变压器的运行状态进行正确的评估可以极大提高供电可靠性。为提高变压器状态评估的准确性,针对传统变压器状态评估方法选取单一参数的不足,提出利用改进证据理论实现多维信息融合的变压器状态参数评估方法。该方法选取常用变压器型式试验参数指标作为在线监测指标,再对指标进行归一化处理。利用改进的D-S证据理论对状态指标进行融合,搭建变压器状态参数评估模型。改进的D-S证据理论对合成规则进行了修改,有效避免了冲突证据,该方法能够充分融合多种信息。通过实验表明,该方法使变压器状态评估的准确性得到很大提升。