Curved Space-Time at the Planck Scale

This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the metric tensor, is considered to be made up of a dynamic lattice of extremely small, localized fields that form a perfectly elastic Lorentz symmetric space-time at the global (macroscopic) scale. This theoretical model of space-time at the Planck scale leads to a somewhat surprising result in which matter waves in curved space-time radiate thermal gravitational energy, as well as an equally intriguing relationship for the anomalous dispersion of light in a gravitational field.

ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA

In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.

Robust Space-Time Adaptive Track-Before-Detect Algorithm Based on Persymmetry and Symmetric Spectrum

Underwater monopulse space-time adaptive track-before-detect method,which combines space-time adaptive detector(STAD)and the track-before-detect algorithm based on dynamic programming(DP-TBD),denoted as STAD-DP-TBD,can effectively detect low-speed weak targets.However,due to the complexity and variability of the underwater environment,it is difficult to obtain sufficient secondary data,resulting in a serious decline in the detection and tracking performance,and leading to poor robustness of the algorithm.In this paper,based on the adaptive matched filter(AMF)test and the RAO test,underwater monopulse AMF-DP-TBD algorithm and RAO-DP-TBD algorithm which incorporate persymmetry and symmetric spectrum,denoted as PSAMF-DP-TBD and PS-RAO-DP-TBD,are proposed and compared with the AMF-DP-TBD algorithm and RAO-DP-TBD algorithm based on persymmetry array,denoted as P-AMF-DP-TBD and P-RAO-DP-TBD.The simulation results show that the four methods can work normally with sufficient secondary data and slightly insufficient secondary data,but when the secondary data is severely insufficient,the P-AMF-DP-TBD and P-RAO-DP-TBD algorithms has failed while the PSAMF-DP-TBD and PS-RAO-DP-TBD algorithms still have good detection and tracking capabilities.

Virtually coupled train set control subject to space-time separation:A distributed economic MPC approach with emergency braking configuration

The emerging virtual coupling technology aims to operate multiple train units in a Virtually Coupled Train Set(VCTS)at a minimal but safe distance.To guarantee collision avoidance,the safety distance should be calculated using the state-of-the-art space-time separation principle that separates the Emergency Braking(EB)trajectories of two successive units during the whole EB process.In this case,the minimal safety distance is usually numerically calculated without an analytic formulation.Thus,the constrained VCTS control problem is hard to address with space-time separation,which is still a gap in the existing literature.To solve this problem,we propose a Distributed Economic Model Predictive Control(DEMPC)approach with computation efficiency and theoretical guarantee.Specifically,to alleviate the computation burden,we transform implicit safety constraints into explicitly linear ones,such that the optimal control problem in DEMPC is a quadratic programming problem that can be solved efficiently.For theoretical analysis,sufficient conditions are derived to guarantee the recursive feasibility and stability of DEMPC,employing compatibility constraints,tube techniques and terminal ingredient tuning.Moreover,we extend our approach with globally optimal and distributed online EB configuration methods to shorten the minimal distance among VCTS.Finally,experimental results demonstrate the performance and advantages of the proposed approaches.

The Lifespan of Smooth Solutions to Semilinear Wave Equations in Schwarzschild Space-Time

This paper considers the Cauchy problem of the semilinear wave equations with small initial data in the Schwarzschild space-time,□_(g)u=|ut|^(P),where g denotes the Schwarzschild metric.When 1<p<2 and the initial data are supported far away from the black hole,we can prove that the lifespan of the spherically symmetric solu-tion obtains the same order as the semilinear wave equation evolving in the Minkowski space-time by introducing an auxiliary function.

Motion of Relativistic Strings on the Equatorial Plane in the Schwarzschild Space-Time

In this paper, we investigate the basic equations of the motion for relativistic strings on the equatorial plane in the Schwarzsehild space-time, discuss smooth solutions of the motion equations for closed strings, and obtain some interesting physical results.

REAL PALEY-WIENER THEOREMS FOR THE SPACE-TIME FOURIER TRANSFORM

This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.

Space-time correlations of passive scalar in Kraichnan model

We consider the two-point,two-time(space-time)correlation of passive scalar R(r,τ)in the Kraichnan model under the assumption of homogeneity and isotropy.Using the fine-gird PDF method,we find that R(r,τ)satisfies a diffusion equation with constant diffusion coefficient determined by velocity variance and molecular diffusion.Itssolution can be expressed in terms of the two-point,one time correlation of passive scalar,i.e.,R(r,0).Moreover,the decorrelation o R(k,τ),which is the Fourier transform of R(r,τ),is determined byR(k,0)and a diffusion kernal.

Coulomb Force, Charge, and Electric Properties under Collision Space-Time

We have recently published a series of papers on a theory we call collision space-time, that seems to unify gravity and quantum mechanics. In this theory, mass and energy are redefined. We have not so far demonstrated how to make it compatible with electric properties such as charge and the Coulomb force. The aim of this paper is to show how electric properties can be reformulated to make it consistent with collision space-time. It is shown that we need to incorporate the Planck scale into the electric constants to do so. This is also fully possible from a practical point of view, as it has recently been shown how to measure the Planck length independent of other constants and without the need for dimensional analysis.

对高维Schwarzschild-de Sitter黑洞视界处Fermions量子隧穿辐射率的修正

根据Lorentz-breaking理论对弦量场作用量进行修正并应用变分原理得到了高维Schwarzschild-de Sitter黑洞时空中的费米子动力学方程。通过对此动力学方程的研究得到了高维Schwarzschild-de Sitter黑洞事件视界处和宇宙视界处的量子隧穿率的修正形式,从而研究了此黑洞事件视界处和宇宙视界处的修正形式的Hawking温度和Bekenstein-Hawking熵的新的表达式。在得到研究结果的基础之上,文中最后还对研究方法和结论进行了讨论。

Local Stability to the Einstein-Euler System in Schwarzschild Space-time

We study the Schwarzschild spacetime solutions to the Einstein-Euler equations.In our analysis,we aim to show local stability under small perturbations.To resolve this problem,we use the Nash-Moser(-Hamilton)theorem.The work was originally developed for the nonrelativistic Euler-Poisson equations.

Revised Newtonian Formula of Gravity and Equation of Cosmology in Flat Space-Time Transformed from Schwarzschild Solution

By transforming the geodesic equation of the Schwarzschild solution of the Einstein’s equation of gravity field to flat space-time for description, the revised Newtonian formula of gravity is obtained. The formula can also describe the motion of object with mass in gravity field such as the perihelion precession of the Mercury. The space-time singularity in the Einstein’s theory of gravity becomes the original point r = 0 in the Newtonian formula of gravity. The singularity problem of gravity in curved space-time is eliminated thoroughly. When the formula is used to describe the expansive universe, the revised Friedmann equation of cosmology is obtained. Based on it, the high red-shift of Ia supernova can be explained well. We do not need the hypotheses of the universe accelerating expansion and dark energy again. It is also unnecessary for us to assume that non-baryon dark material is 5 - 6 times more than normal baryon material in the universe if they really exist. The problem of the universal age can also be solved well. The theory of gravity returns to the traditional form of dynamic description and becomes normal one. The revised equation can be taken as the foundation of more rational cosmology.

Scalable transcoding for video transmission over space-time OFDM systems

A new scheme combining a scalable transcoder with space time block codes （STBC） for an orthogonal frequency division multiplexing （OFDM） system is proposed for robust video transmission in dispersive fading channels. The target application for such a scalable transcoder is to provide successful access to the pre-encoded high quality video MPEG-2 from mobile wireless terminals. In the scalable transcoder, besides outputting the MPEG-4 fine granular scalability （FGS） bitstream, both the size of video frames and the bit rate are reduced. And an array processing algorithm of layer interference suppression is used at the receiver which makes the system structure provide different levels of protection to different layers. Furthermore, by considering the important level of scalable bitstream, the different bitstreams can be given different level protection by the system structure and channel coding. With the proposed system, the concurrent large diversity gain characteristic of STBC and alleviation of the frequency-selective fading effect of OFDM can be achieved. The simulation results show that the proposed schemes integrating scalable transcoding can provide a basic quality of video transmission and outperform the conventional single layer transcoding transmitted under the random and bursty error channel conditions.

EM-based detection scheme for differential unitary space-time modulation

The performance loss of an approximately 3 dB signal-to-noise ratio is always paid with conventional differential detection compared to the related coherent detection. A new detection scheme consisting of two steps is proposed for the differential unitary space-time modulation （DUSTM） system. In the first step, the data sequence is estimated by conventional unitary space-time demodulation （DUSTD） and differentially encoded again to produce an initial estimate of the transmitted symbol stream. In the second step, the initial estimate of the symbol stream is utilized to initialize an expectation maximization （EM）-based iterative detector. In each iteration, the most recent detected symbol stream is employed to estimate the channel, which is then used to implement coherent sequence detection to refine the symbol stream. Simulation results show that the proposed detection scheme performs much better than the conventional DUSTD after several iterations.

基于space-time的二叉树表示动态环境中的路径规划

研究具有空间和时间的三维动态环境下的机器人路径规划分析了四叉树表示二维空间的搜索算法,在此基础上,提出采space-time,用二叉树表示二维空间的方法时间信息中增加加速度利用二叉树遍历方法和算法设计一个在动态障碍物环境下进行路径规划的新算法并,,A*,,在足球机器人系统中进行仿真,实现了较好的路径规划。

Design of super-orthogonal space-time trellis codes based on trace criterion

A design of super-orthogonal space-time trellis codes （SOSTTCs） based on the trace criterion （TC） is proposed for improving the design of SOSTTCs. The shortcomings of the rank and determinant criteria based design and the advantages of the TC-based design are analyzed. The optimization principle of four factors is presented, which includes the space-time block coding （STBC） scheme, set partitioning, trellis structure, and the assignment of signal subsets and STBC schemes in the trellis. According to this principle, systematical and handcrafted design steps are given in detail. By constellation expansion, the code performance can be further improved. The code design results are given, and the new codes outperform others in the simulation.

Method of combining space-time block coding with adaptive beamforming

A method of space-time block coding （STBC） system based on adaptive beamforming of cyclostationarity signal algorithm is proposed.The method uses cyclostationarity of signals to achieve adaptive beamforming,then constructs a pair of low correlated transmit beams based on beamform estimation of multiple component signals of uplink.Using these two selected transmit beams,signals encoded by STBC are transmitted to achieve diversity gain and beamforming gain at the same time,and increase the signal to noise ratio （SNR） of downlink.With simple computation and fast convergence performance,the proposed scheme is applicable for time division multiple access （TDMA） wireless communication operated in a complex interference environment.Simulation results show that the proposed scheme has better performance than conventional STBC,and can obtain a gain of about 5 dB when the bit error ratio （BER） is 10-4.

ON MARKOV CHAINS IN SPACE-TIME RANDOM ENVIRONMENTS

In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...

On analyzing space-time distribution of evaporation duct height over the global ocean

The statistical features of the evaporation duct over the global ocean were comprehensively investigated with reanalysis data sets from the National Centers for Environmental Prediction. These data sets have time and spatial resolutions of 1 h and 0.313°x0.312°, respectively. The efficiency of the analysis was evaluated by processing weather buoy data from the Pacific Ocean and measuring propagation loss in the Yellow Sea of China. The distribution features of evaporation duct height （EDH） and the related meteorological factors for different seas were analyzed. The global EDH is generally high and demonstrates a latitudinal distribution for oceans at low latitudes. The average EDH is approximately 11 m over oceans beside the equator with a latitude of less than 20°. The reasons for the formation of the global EDH features were also analyzed for different sea areas.

Performance Evaluation of Space-Time Spreading and Orthogonal Transmit Diversity

Space-time spreading (STS) and orthogonal transmit diversity (OTD) are towtransmit diversity schemes proposed by cdma2000 standard. In this paper, performance comparisonanalysis of the two transmits diversity schemes in multipath channel under multiuser situation arecarried out. Link level simulation in forward link cdma2000 is performed in IMT-2000 channel.Performance analysis and simulation results show that the performance improvement provided STS overOTD decreases as the increase of propagation path number and decrease of the user number.