The He–McKellar–Wilkens effect for spin-1 particles on non-commutative space

By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topological HMW phase on NC space where the additional terms related to the space-space non-commutativity are given explicitly.

Characteristic Functions over C*-Probability Spaces

Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.

Motion of a Nonrelativistic Quantum Particle in Non-commutative Phase Space

The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the modified equations of motion. Next, using novel transformations, we solve the equation of motion and report the exact analytical solutions.

Sequential Approximation of Functions in Sobolev Spaces Using Random Samples

We present an iterative algorithm for approximating an unknown function sequentially using random samples of the function values and gradients. This is an extension of the recently developed sequential approximation (SA) method, which approximates a target function using samples of function values only. The current paper extends the development of the SA methods to the Sobolev space and allows the use of gradient information naturally. The algorithm is easy to implement, as it requires only vector operations and does not involve any matrices. We present tight error bound of the algorithm, and derive an optimal sampling probability measure that results in fastest error convergence. Numerical examples are provided to verify the theoretical error analysis and the effectiveness of the proposed SA algorithm.

Characterization of Type p Banach Spaces by the Weak Law of Large Numbers

For weighted sums of the form?j=1kn anj Xnj\sum{_{j=1}^{k_(n)}}a_({nj})X_({nj})where{a_(nj),1?j?k_(n)↑∞,n?1}is a real constant array and{X_(aj),1≤j≤k n,n≥1}is a rowwise independent,zero mean,random element array in a real separable Banach space of typep,we establishL r convergence theorem and a general weak law of large numbers respectively,conversely,we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.

Study of Nonlinear Earthquake Flow Functions and Their Application to the Space Increased Probability of Strong Earthquake (SIP)

The definition and abnormality discriminatory criteria of earthquake flow function are introduced in this paper based on the algorithm of Space Increased Probability (SIP). Nine earthquake flow functions were defined by the method. The retrospect test that applied the SIP algorithm with the nonlinear earthquake flow function to 7 earthquakes, which occurred from 1975 to 1989 in Eastern China, with a magnitude of 6 or greater depicted that 6 of the 7 strong earthquakes (86%) were located in the SIP areas, and the SIP covers about 32% of the total research time-space domain. These suggest that the R-value, an effective scale for earthquake forecast, is 54% and may imply that the nonlinear earthquake flow function introduced in this paper can be applied to the intermediate-term earthquake forecast research.

Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space

The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.

基于state-space-split法的滞回非线性系统随机动力响应分析

采用SSS(state-space-split)法,建立了引入Bouc-Wen滞回模型的杜芬非线性系统在高斯白噪声激励下的概率密度函数(PDF)的近似求解方法,分析了其随机动力响应变化规律。首先,将Bouc-Wen滞回模型引入杜芬非线性系统,分别考虑非线性系统中的几何非线性和材料非线性对动力响应的影响。随后,对该模型进行了等效线性化(EQL)处理,基于等效线性化法结果,介绍了SSS法的简化方法和计算原理,并通过该方法求解了三维FPK方程的近似联合概率密度函数。最后,将该方法应用于三个案例和一个工程实例,通过求解其概率密度函数分布及动力可靠度验证了提出方法的适用性、可行性和优越性。

Probability Density Function Method for Observing Reconstructed Attractor Structure

Probability density function (PDF) method is proposed for analysing the structure of the reconstructed attractor in computing the correlation dimensions of RR intervals of ten normal old men. PDF contains important information about the spatial distribution of the phase points in the reconstructed attractor. To the best of our knowledge, it is the first time that the PDF method is put forward for the analysis of the reconstructed attractor structure. Numerical simulations demonstrate that the cardiac systems of healthy old men are about 6-6.5 dimensional complex dynamical systems. It is found that PDF is not symmetrically distributed when time delay is small, while PDF satisfies Gaussian distribution when time delay is big enough. A cluster effect mechanism is presented to explain this phenomenon. By studying the shape of PDFs, that the roles played by time delay are more important than embedding dimension in the reconstruction is clearly indicated. Results have demonstrated that the PDF method represents a promising numerical approach for the observation of the reconstructed attractor structure and may provide more information and new diagnostic potential of the analyzed cardiac system.

A New Version of Unified Field Theory—Stochastic Quantum Space Theory on Particle Physics and Cosmology

Stochastic Quantum Space (SQS) theory is a new version of unified field theory based on three fundamental postulations: Gaussian Probability Postulation, Prime Numbers Postulation, Vacuon Postulation. It build a framework with theoretical results agree with many experimental data well. For more information, please refer to the PDF.

PROBABILISTIC NORM OF LINEAR OPERATORS ON PN SPACE

In this paper, the new definition of probabilistic norm of linear operators on a PN space is given. In virtue of this, the boundedness of linear operators is described and the completeness of the PN space composed of all bounded linear operators is showed.

A Carrier Synchronization Algorithm for AutonomousRadio Receiver in Deep Space

The carrier synchronization algorithm of the autonomous radio for deep space is studied.When the signal modulation is unknown,this paper improves the existing universal carrier synchronization loop for multiple modulations,expands the frequency tracking range of the loop,proposes a Tong detection-based M-ary Phase Shift Keying(M-PSK)signal locking detection algorithm to rapidly and effectively determine whether the current phase discrimination mode matches the modulation mode,so as to independently choose whether to switch the phase discrimination mode.Through theoretical analysis and comparison,it is described that the total detection probability of the algorithm proposed in this paper is significantly higher than the probability of single lock detection.Simulation results show that the algorithm has high detection probabiUty and low computational complexity at a low signal to noise ratio.

Model of constant probability event and its application in information fusion

A model of constant probability event is constructed rigorously in event space of PSCEA. It is showed that the numericalbased fusion and the algebraicbased fusion have a consistent result when the weight is regarded as a constant probability event. From the point of view of algebra, we present a novel similarity measure in product space. Based on the similarity degree, we use a similarity aggregation method to fusion experts' evaluation. We also give a numerical example to illustrate the method.

Multi-Hop Free Space Optical Communications Using Serial Decode-and-Forward Relay Transmissions

This paper investigates the performance of multi-hop Free Space Optical(FSO) communications using serial Decode-and-Forward(DF) relay transmissions.A statistical model for the optical intensity fluctuation at the receiver due to the combined effects of atmospheric turbulence-induced fading,mis alignment fading and pass-loss is presented.Under given weather and mis alignment conditions,a closed-form analytical expression for the end-to-end outage probability of serial Decode-and-Forward(DF) multi-hop FSO communications is derived.Numerical results show that the serial DF multi-hop transmission is a promising technology to enhance the performance of FSO communications.Moreover,the derived analytical expression can provide close approximations to the simulation results.

Analysis of the Impact of Large Constellations on the Space Debris Environment and Countermeasures

Large constellations have developed rapidly in recent years because of their unique advantages, but they will inevitably have a major negative impact on the space debris environment, leading to its deterioration. The key to mitigate the impact is the success rate and duration of the post-mission disposal(PMD) process. Aiming at solving this problem, this paper further studies the impact of large constellations on other space assets under different PMD strategies through simulation, and proposes corresponding strategies and suggestions for mitigation.According to One Web’s large constellation launch plan, the dangerous intersection of the large constellation with existing space assets at different stages of the constellations life cycle is calculated by simulation. Based on this, the influence of the large constellation operation on existing space assets at different times and strategies of PMD is analyzed. The conclusion shows that in the PMD stage, large constellations have the greatest impact on existing space assets;the PMD duration and number of satellites performing PMD at the same time are key factors to the degree of negative impact. The faster the PMD is, the less threat it poses to other spacecraft. More results and conclusions are still being analyzed.

A Note on the Product Borel Probability Measure

In this paper,a necessary and sufficient condition of a measure to be the product Borel probability measure on the product space of some compact metric spaces are given.

An Evolution Model of Space Debris Environment

Various types of models including engineering models and evolution models have been developed to understand space debris environment since 1960s. Evolution model, consisting of a set of supporting models such as Launch Model, Breakup Model and Atmosphere Model, can reliably predicts the evolution of space debris environment. Of these supporting models, Breakup Model is employed to describe the distribution of debris and debris cloud during a explosion or collision case which is one of the main factors affecting the amount of total space debris. An analytical orbit debris environment model referred to as the "Particles In Boxes" model has been introduced. By regarding the orbit debris as the freedom particles running in the huge volume, the sources and sinks mechanism is established. Then the PIB model is expanded to the case of multiple species in multiple tier system. Combined with breakup model, the evolution of orbit debris environment is predicted.

因素空间理论下的因果概率推理分类算法研究

机器学习方法与因果推理结合能极大地提升方法性能。为探究因果概率正逆向推理的分类效果,基于因素空间理论下的因素概率论,利用条件概率,研究正向因素概率推理原理及模型并提出正向因果概率推理分类法(forward causal probabilistic inference classification algorithm,FCPIC)和简化条件的可取度分类法;研究逆向因素概率推理原理及模型并结合贝叶斯网络提出逆向因果概率推理分类法(reverse causal probabilistic inference classification algorithm,RCPIC)。将3个分类算法与KNN(K-Nearest neighbor)和SVM(support vector machine)算法进行实例对比验证,研究结果表明:FCPIC算法、可取度分类算法和RCPIC算法简单有效、具有可行性和实用性,且可取度分类法和RCPIC算法性能优于SVM和KNN算法,FCPIC算法对实际数据预测中必要类有查全需求的情况更优。研究结论丰富了因素空间的理论研究和应用价值。

基于碰撞概率的GEO业务卫星空间安全规避策略

针对GEO业务卫星空间规避问题,提出一种基于碰撞概率优化的GEO卫星空间规避策略.建立脉冲推力控制下的位保模型,解释碰撞概率的假设条件与计算原理,针对GEO卫星对原有碰撞概率计算方法进行改进,提出了一种考虑了速度误差的碰撞概率计算方法,以脉冲速度大小为变量,以消耗速度冲量最小和碰撞概率最小为优化目标,基于非支配排序多目标遗传算法(NSGA-Ⅱ)进行多目标优化,对碰撞概率较大的问题求出其帕累托最优解.考虑GEO卫星定点保持的业务要求,得到满足其位保精度的空间规避策略,并进行仿真验证了空间规避策略的有效性.研究结果可为在轨业务卫星实现满足位保要求的空间安全规避提供思路.

基于潜在空间生成器的联邦知识蒸馏

用户的异质性对联邦学习(FL)构成了显著挑战,这可能导致全局模型偏移和收敛速度缓慢。针对此问题,提出一种结合知识蒸馏和潜在空间生成器的联邦学习方法(FedLSG)。该方法通过中央服务器学习一个搭载潜在空间生成器的生成模型,该模型能够提取并模拟不同用户端样本标签的概率分布,从而生成更加丰富和多样的伪样本来指导用户端模型的训练。这种方法旨在有效解决FL中的用户异质性问题。通过理论分析和实验验证,展示了与现有FedGen方法相比,FedLSG普遍比FedGen的测试精度高出1%左右,前20轮的通信效率优于FedGen,同时还能提供一定程度的用户隐私保护。