Including Space-Time in the Extended Group Cl3* of Relativistic Form-Invariance

The inclusion of space-time in the extended group of relativistic form-invariance, Cl3*, is specified as the inclusion of the whole space-time manifold in this multiplicative Lie group. First physical results presented here are: the geometric origin of the time arrow, a better understanding of the non-simultaneity in optics and a mainly geometric origin for the universe expansion, and its recent acceleration.

TRANSLATION-INVARIANT BASED ADAPTIVE THRESHOLD DENOISING FOR IMPACT SIGNAL

A translation-invariant based adaptive threshold denoising method formechanical impact signal is proposed. Compared with traditional wavelet denoising methods, itsuppresses pseudo-Gibbs phenomena in the neighborhood of signal discontinuities. To remedy thedrawbacks of conventional threshold functions, a new improved threshold function is introduced. Itpossesses more advantages than others. Moreover, based on utilizing characteristics of signal, aadaptive threshold selection procedure for impact signal is proposed. It is data-driven andlevel-dependent, therefore, it is more rational than other threshold estimation methods. Theproposed method is compared to alternative existing methods, and its superiority is revealed bysimulation and real data examples.

Translation invariant tensor product states in a finite lattice system

We show that the matrix （or more generally tensor） product states in a finite translation invariant system can be accurately constructed from a same set of local matrices （or tensors） that are determined from an infinite lattice system in one or higher dimensions. This provides an efficient approach for studying translation invariant tensor product states in finite lattice systems. Two methods are introduced to determine the size-independent local tensors.

A Note on Unification of Translational Shape Invariant Potential and Scaling Shape Invariant Potential

This article puts forward a general shape invariant potential, which includes the translational shape invariant potential and scaling shape invariant potential as two particular cases, and derives the set of linear differential equations for obtaining general solutions of the generalized shape invariance condition.

Scale Invariant Theory of Gravitation in Einstein-Rosen Space-Time

In this paper, we have studied the perfect fluid distribution in the scale invariant theory of gravitation, when the space-time described by Einstein-Rosen metric with a time dependent gauge function. The cosmological equations for this space-time with gauge function are solved and some physical properties of the model are studied.

Generation and classification of the translational shape-invariant potentials based on the analytical transfer matrix method

For the conventional translational shape-invariant potentials （TSIPs）, it has demonstrated that the phase contribution devoted by the scattered subwaves in the analytical transfer matrix quantization condition is integrable and independent of n. Based on this fact we propose a novel strategy to generate the whole set of conventional TSIPs and classify them into three types. The generating functions are given explicitly and the Morse potential is taken as an example to illustrate this strategy.

Comparison of MRI Under-Sampling Techniques for Compressed Sensing with Translation Invariant Wavelets Using FastTestCS: A Flexible Simulation Tool

A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to perform exceedingly well in CS by reducing repetitive line pattern image artifacts that may be observed when using orthogonal wavelets. To further establish its validity as a good sparsifying transform, the TIWT is comprehensively investigated and compared with Total Variation (TV), using six under-sampling patterns through simulation. Both trajectory and random mask based under-sampling of MRI data are reconstructed to demonstrate a comprehensive coverage of tests. Notably, the TIWT in CS reconstruction performs well for all varieties of under-sampling patterns tested, even for cases where TV does not improve the mean squared error. This improved Image Quality (IQ) gives confidence in applying this transform to more CS applications which will contribute to an even greater speed-up of a CS MRI scan. High vs low resolution time of flight MRI CS re-constructions are also analyzed showing how partial Fourier acquisitions must be carefully addressed in CS to prevent loss of IQ. In the spirit of reproducible research, novel software is introduced here as FastTestCS. It is a helpful tool to quickly develop and perform tests with many CS customizations. Easy integration and testing for the TIWT and TV minimization are exemplified. Simulations of 3D MRI datasets are shown to be efficiently distributed as a scalable solution for large studies. Comparisons in reconstruction computation time are made between the Wavelab toolbox and Gnu Scientific Library in FastTestCS that show a significant time savings factor of 60×. The addition of FastTestCS is proven to be a fast, flexible, portable and reproducible simulation aid for CS research.

The Quaternion Structure of Space-Time and Arrow of Time

In fundamental theories of physics, the dynamical equations all have time inversion invariance. Except for the evolution of some simple system which has realistic inverse processes, but for a slightly more complicated system, the evolution processes are irreversible. This is the problem of arrow of time, which is always warmly debated. In different point of view, we find there may have some conceptual misunderstanding in the controversy: 1) The realization of an inverse process does not mean the time of the system goes backward. 2) The principles of relativity and covariance are the constraints to physical laws, but not constraints to specific solutions. The equations must be covariant, but the solutions are not definitely symmetric. 3) Time is a global property of the universe, which is a measurement of the evolution process of the universe. The internal time of a matter system reflecting its internal evolution speed also takes this cosmic time as a unified background and standard of measurement. 4) The universe has a unified cosmic time T and a cosmic space related to this cosmic time. They are objective and absolute. 5) The eigensolution of a spinor is a critical state losing time concept, which responses the interaction of environment with some uncertainty, then the evolution process of the world is not uniquely determined. 6) The non-uniqueness of the evolution process means that the inverse process is absent. So for a world including spinors, the evolution is essentially irreversible. In this paper, according to the widely accepted principles and direct calculations of transformation, we reveal the misunderstandings in the usual controversy, and then give more natural and reasonable explanations for structure of space-time and arrow of time.

Towards Translational Invariance of Total Energywith Finite Element Methods for Kohn-Sham Equation

Numerical oscillation of the total energy can be observed when the Kohn-Sham equation is solved by real-space methods to simulate the translational move of an electronic system.Effectively remove or reduce the unphysical oscillation is crucial not only for the optimization of the geometry of the electronic structure,but also for the study of molecular dynamics.In this paper,we study such unphysical oscillation based on the numerical framework in[G.Bao,G.H.Hu,and D.Liu,An h-adaptive fi-nite element solver for the calculations of the electronic structures,Journal of Computational Physics,Volume 231,Issue 14,Pages 4967-4979,2012],and deliver some numerical methods to constrain such unphysical effect for both pseudopotential and all-electron calculations,including a stabilized cubature strategy for Hamiltonian operator,and an a posteriori error estimator of the finite element methods for Kohn-Sham equation.The numerical results demonstrate the effectiveness of our method on restraining unphysical oscillation of the total energies.

轻小型SAR卫星平飞模式设计

对于轻小型合成孔径雷达(SAR)卫星在轨使用时对重点区域多目标观测效能提升的需求,提出轻小型SAR卫星平飞模式设计方法。介绍了卫星平飞模式设计方法,提出载荷平面相控阵天线距离维大角度扫描能力设计;针对区域多目标,提出条件触发方式目标决策策略,以及星上雷达工作参数计算策略;基于建立的目标决策和任务规划模型,分别针对卫星左侧视、在侧视、平飞、左右机动侧视等4种工作模式下进行多目标观测效能评估仿真分析。结果表明:相比于卫星斜飞模式下,平飞模式目标观测效能可提升至41%;相比于卫星左右机动侧视模式下,平飞模式目标观测效能可提升至73%。因此,设计的卫星平飞模式可有效提升面向区域多目标的观测效能。

High-visibility ghost imaging with phase-controlled discrete classical light sources

We take phase modulation to create discrete phase-controlled sources and realize the super-bunching effect by a phasecorrelated method. From theoretical and numerical simulations, we find the space translation invariance of the bunching effect is a key point for the ghost imaging realization. Experimentally, we create the orderly phase-correlated discrete sources which can realize high-visibility second-order ghost imaging than the result with chaotic sources. Moreover, some factors affecting the visibility of ghost image are discussed in detail.

簸箕型流道泵站水泵振动信号消噪方法研究

为解决水泵信号振源复杂、含噪量大,难以在信号内获得有效数据的问题,研究一种基于改进平移不变量小波阈值的振动信号消噪方法。将水泵振动信号划分为信号高频区域和低频区域,选取对应合适的小波范围,在小波分解层数作用下正交变换含噪信号。利用阈值限制小波系数完成滤波,通过设定噪声标准偏差值,求得振动信号小波系数中间值,实现信号重构。将振动信号含噪部分在时域空间完成循环平移,填补信号不连续缺陷部位,平移去噪后计算振动信号平均值,得到最终消噪振动信号。仿真分析结果显示:该方法在平移不变量的辅助下,可填补信号不连续缺陷点,从噪声中恢复出原始振动信号,波形的失真较小,信号信噪比较高,鲁棒性好,可完整地保存信号的轮廓和特征。为分析簸箕型进水流道内部流态提供新思路,保证水泵整体工作可靠性。

From Dirac’s Aether to the Dirac Equation

In 1951, Dirac proposed a formalism for a Lorentz invariant Aether with a vacuum state that contains all possible velocity states at each space-time point. Dirac showed no explicit path from the Aether towards the Quantum Mechanics. In this paper, we demonstrate that Dirac’s proposed Aether can be described by a lattice of possible events in space-time built in the local Lorentz frame. The idealised case of single velocity state leads to the famous Dirac equation for a plane wave state and is compatible with quantum statistics. On the lattice, possible space-time events are connected by the Dirac spinors which provide the probability of observing an event. The inertial mass of a particle is shown to be equivalent to the density of possible events on the lattice. Variation of the lattice density of events modifies the metric and provides a space-time curvature leading to the Hilbert action associated with general relativity. In classical limit, the perturbation in the density of possible events of the Aether is proportional to the Newtonian gravitational potential.

Rotation Scaling and Translation Invariants of 3D Radial Shifted Legendre Moments

This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments： a 3D substituted radial shifted Legendre moments （3DSRSLMs） and a 3D weighted radial one （3DWRSLMs）. Both are centered on two types of polynomials. In the first case, a new 3D ra- dial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendremoments （3DSRSLMs/3DWRSLMs） are introduced using a spherical representation of volumetric image. 3D invariants as derived from the sug- gested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three is- sues. To confirm the proposed approach, we have resolved three issues： rotation, scaling and translation invariants. The result of experi- ments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Sim- ultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark （PSB） database for 3D image.

Binding Energy, Root Mean Square Radius and Magnetic Dipole Moment of the Triton Nucleus

The basis functions of the translation invariant shell model are used to construct the ground state nuclear wave functions of 3H. The used residual two-body interactions consist of central, tensor, spin orbit and quadratic spin orbit terms with Gaussian radial dependence. The parameters of these interactions are so chosen in such a way that they represent the long-range attraction and the short-range repulsion of the nucleon-nucleon interactions. These parameters are so chosen to reproduce good agreement between the calculated values of the binding energy, the root mean-square radius, the D-state probability, the magnetic dipole moment and the electric quadrupole moment of the deuteron nucleus. The variation method is then used to calculate the binding energy of triton by varying the oscillator parameter which exists in the nuclear wave function. The obtained nuclear wave functions are then used to calculate the root mean-square radius and the magnetic dipole moment of the triton.

A NEW INVARIANT QUANTITY OF SPECIAL RELATIVITY AND THE MINIMAL MOVING MASS SPACE-TIME REFERENCE SYSTEM

Ⅰ. PROBLEM AND RESULTS In physics, in order to describe a motion mathematically one needs a space-time reference system ∑(x, y z; t). From the mathematical point of view, any two reference systems are equivalent, one only needs a transformation between the coordinates of the two systems.

基于平移不变的小波去噪方法及应用

基于传统的小波变换去噪算法可能使信号的急剧变化部分产生人为的振荡现象 ,产生这种现象的一个直接原因是小波缺乏平移不变性。提出了基于平移不变的小波去噪方法 ,对所分析的信号进行循环平移 ,再利用软或硬门限对该信号的小波系数进行压缩 ,重构信号 ,再进行相反的循环平移 ,通过多次的平移—消噪—平移 ,平均所获得的结果 ,从而消除小波基的平移依赖性。该方法能有效地消除人为的振荡现象 ,使消噪后的信号更加光滑 ,更好地逼近真实信号。

基于平移不变小波的声发射信号去噪研究

小波阈值去噪算法在信号的奇异点处会产生Pesudo-G ibbs现象。平移不变小波去噪方法是对阈值法的改进,该方法可以有效地抑制Pesudo-G ibbs现象,而且能够减少原始信号和估计信号的均方根误差,提高信噪比。将该方法用于声发射信号的去噪处理,并与阈值法进行了比较。仿真结果表明该研究方法可以有效地去除噪声,提取声发射信号的特征信息,具有较强的工程实用性。

小波去噪的几种方法

利用小波方法去噪 ,是小波分析应用于工程实际的一个重要方面。该文介绍了几种常用的小波去噪方法 ,分别是小波分解与重构法、非线性小波变换阈值法、平移不变量法和小波变换模极大值法。将上述几种方法分别用于叠加了高斯白噪声的仿真信号的去噪处理 ,并通过对几种方法优缺点的比较 ,为小波去噪的方法选择提供了一个参考依据。