A modified OMP method for multi-orbit three dimensional ISAR imaging of the space target

The conventional two dimensional(2D)inverse synthetic aperture radar(ISAR)imaging fails to provide the targets'three dimensional(3D)information.In this paper,a 3D ISAR imaging method for the space target is proposed based on mutliorbit observation data and an improved orthogonal matching pursuit(OMP)algorithm.Firstly,the 3D scattered field data is converted into a set of 2D matrix by stacking slices of the 3D data along the elevation direction dimension.Then,an improved OMP algorithm is applied to recover the space target's amplitude information via the 2D matrix data.Finally,scattering centers can be reconstructed with specific three dimensional locations.Numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed 3D imaging method.

WORMHOLE AND THE DIMENSIONALITY OF SPACETIME IN EINSTEIN-GAUGE THEORIES

The wormhole effect is discussed in the d-dimensional Einstein-Yang-Mills theory.We show that the peak of the probability function leads to the explanation of the spontaneous compactification down to a four-dimensional spacetime and vanishing four-dimensional cosmological constant,i.e.,the observable spacetime must be four-dimensional and flat.

Multi-dimensional ambiguity function for subarray-based space-time coding radar

Space-time coding radar has been recently proposed and investigated.It is a radar framework which can perform transmit beamforming at the receiver.However,the range resolution decreases when the number of the transmit element increases.A subarray-based space-time coding(sub-STC)radar is explored to alleviate the range resolution reduction.For the proposed radar configuration,an identical waveform is transmitted and it introduces a small time offset in different subarrays.The multidimensional ambiguity function of sub-STC radar is defined by considering resolutions in multiple domains including the range,Doppler,angle and probing direction.Analyses on properties of the multi-dimensional ambiguity function of the sub-STC radar with regard to the spatial coverage,resolution performance and low sidelobes are also given.Results reveal that the range resolution and low sidelobes performance are improved with the proposed approach.

Special Relativity in Three-Dimensional Space-Time Frames

In Newton’s classical physics, space and time are treated as absolute quantities. Space and time are treated as independent quantities and can be discussed sepa-rately. With his theory of relativity, Einstein proved that space and time are de-pendent and must be treated inseparably. Minkowski adopted a four-dimensional space-time frame and indirectly revealed the dependency of space and time by adding a constraint for an event interval. Since space and time are inseparable, a three-dimensional space-time frame can be constructed by embedding time into space to directly show the interdependency of space and time. The formula for time dilation, length contraction, and the Lorenz transformation can be derived from graphs utilizing this new frame. The proposed three-dimensional space-time frame is an alternate frame that can be used to describe motions of objects, and it may improve teaching and learning Special Relativity and provide additional insights into space and time.

Four-Dimensional Mathematics Creates the Super Universe

In the common theory of the Universe, the redshift of the light wavelength from distant stars indicates the speed of the star. In this study, the model of the Universe is the surface volume of the four-dimensional sphere, and the shape of the Universe results in the most of the redshift of light wavelength. Therefore, there is no dark energy accelerating the Universe. The surface of the four-dimensional sphere is a volume, and this volume is a good model for the Universe. The surface volume of the four-dimensional sphere has been explained by a model of four-dimensional cube, within which the forming of surface volume can be easily shown. The model of four-dimensional cube containing six side cubes is ingenious for explaining the structure of the four-dimensional Universe, but it is not enough because the four-dimensional cube has not six side cubes, but eight side cubes. Therefore, in this study a better method has been created to construct the four-dimensional cube. Our three-dimensional Universe is the surface of the four-dimensional sphere Universe. The volume of our three-dimensional Universe is finite, and beneath it is the infinite volume four-dimensional Super Universe. Two important basic formulae have been derived: The surface volume of the four-dimensional sphere is π3R3 in which R is the radius of the sphere, and the fourth-power volume of the four-dimensional sphere is 1/4 π3R4. The volume of the Universe has been calculated π3R3 = 62 × 1030 ly3. Time as the fourth dimension of the space takes effect only near the speed of light, and therefore it has been ignored in this study.

Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment

We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.

Quasi-real time inversion method of three-dimensional epicenter coordinate, trigger time, and magnitude based on CORS

This study explores the quasi-real time inversion principle and precision estimation of three-dimensional coordinates of the epicenter, trigger time and magnitude of earthquakes with the aim to improve traditional methods, which are flawed due to missing information or distortion in the seismograph records. The epicenter, trigger time and magnitude from the Lushan earthquake are inverted and analyzed based on high-frequency GNSS data. The inversion results achieved a high precision, which are consistent with the data published by the China Earthquake Administration. Moreover, it has been proven that the inversion method has good theoretical value and excellent application prospects.

Analyzing crude oils from the Junggar Basin(NW China) using comprehensive two-dimensional gas chromatography coupled with time-of-flight mass spectrometry(GC×GC-TOFMS)

As a new technology of analyzing crude oils, comprehensive two-dimensional gas chromatography cou- pled with time-of-flight mass spectrometry （GCxGC- TOFMS） has received much research attention. Here we present a case study in the Junggar Basin of NW China. Results show that the hydrocarbons, including saturates and aromatics, were all well-separated without large co- elution, which cannot be realized by conventional one-dimensional GC-MS. The GC×GC technique is especially effective for analyzing aromatics and low-to-middle- molecular-weight hydrocarbons, such as diamondoids. The geochemical characteristics of crude oils in the study area were investigated through geochemical parameters extracted by GC×GC-TOFMS, improving upon the understanding obtained by GC-MS. Thus, the work here represents a new successful application of GC×GC- TOFMS, showing its broad usefulness in petroleum geochemistry.

The Loeb Space of Denumerable Infinite Dimensional Probability Product Measure Spaces

Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.

Three-dimensional numerical modeling of gravity anomalies based on Poisson equation in spacewavenumber mixed domain

In gravity-anomaly-based prospecting, the computational and memory requirements for practical numerical modeling are potentially enormous. Achieving an efficient and precise inversion for gravity anomaly imaging over large-scale and complex terrain requires additional methods. To this end, we have proposed a new topography-capable By performing a two-dimensional Fourier transform in the horizontal directions, threedimensional partial differential equations in the spatial domain were transformed into a group of independent, one-dimensional differential equations engaged with different wave numbers. These independent differential equations are highly parallel across different wave numbers. differential equations with different wave numbers, and the efficiency of solving fixedbandwidth linear equations was further improved by a chasing method. In a synthetic test, a prism model was used to verify the accuracy and reliability of the proposed algorithm by comparing the numerical solution with the analytical solution. We studied the computational precision and efficiency with and without topography using different Fourier transform methods. The results showed that the Guass-FFT method has higher numerical precision, while the standard FFT method is superior, in terms of computation time, for inversion and quantitative interpretation under complicated terrain.

Guaranteed Cost Consensus for High-dimensional Multi-agent Systems With Time-varying Delays

Guaranteed cost consensus analysis and design problems for high-dimensional multi-agent systems with time varying delays are investigated. The idea of guaranteed cost con trol is introduced into consensus problems for high-dimensiona multi-agent systems with time-varying delays, where a cos function is defined based on state errors among neighboring agents and control inputs of all the agents. By the state space decomposition approach and the linear matrix inequality(LMI)sufficient conditions for guaranteed cost consensus and consensu alization are given. Moreover, a guaranteed cost upper bound o the cost function is determined. It should be mentioned that these LMI criteria are dependent on the change rate of time delays and the maximum time delay, the guaranteed cost upper bound is only dependent on the maximum time delay but independen of the Laplacian matrix. Finally, numerical simulations are given to demonstrate theoretical results.

Real-time Three-dimensional Echocardiographic Assessment of Left Ventricular Remodeling Index in Patients with Hypertensive Heart Disease and Coronary Artery Disease

Left ventricular remodeling index （LVRI） was assessed in patients with hypertensive heart disease （HHD） and coronary artery disease （CAD） by real-time three-dimensional echocardiography （RT3DE）. RT3DE data of 18 patients with HHD, 20 patients with CAD and 22 normal controis （NC） were acquired. Left ventricular end-diastolic volume （EDV） and left ventricular end-diastolic epicardial volume （EDVepi） were detected by RT3DE and two-dimensional echocardiography Simpson biplane method （2DE）. LVRI （left ventricular mass/EDV） was calculated and compared. The results showed that LVRI measurements detected by RT3DE and 2DE showed significant differences inter-groups （P〈0.01）. There was no significant difference in NC group （P〉0.05）, but significant difference in HHD and CAD intra-group （P〈0.05）. There was good positive correlations between LVRI detected by RT3DE and 2DE in NC and HHD groups （t=0.69, P〈0.01; r=0.68, P〈0.01）, but no significant correlation in CAD group （r=0.30, P〉0.05）. It was concluded that LVRI derived from RT3DE as a new index for evaluating left ventricular remodeling can provide more superiority to LVRI derived from 2DE.

Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space II: Special Relativity

The diagrammatic approach to the collision problems in Newtonian mechanics is useful. We show in this article that the same technique can be applied to the case of the special relativity. The two circles play an important role in Newtonian mechanics, while in the special relativity, we need one circle and one ellipse. The circle shows the collision in the center-of-mass system. And the ellipse shows the collision in the laboratory system. These two figures give all information on two dimensional elastic collisions in the special relativity.

Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space I: Newtonian Mechanics

We present the usefulness of the diagrammatic approach for analyzing two dimensional elastic collision in momentum space. In the mechanics course, we have two major purposes of studying the collision problems. One is that we have to obtain velocities of the two particles after the collision from initial velocities by using conservation laws of momentum and energy. The other is that we have to study two ways of looking collisions, i.e. laboratory system and center-of-mass system. For those two major purposes, we propose the diagrammatic technique. We draw two circles. One is for the center-of-mass system and the other is for the laboratory system. Drawing these two circles accomplish two major purposes. This diagrammatic technique can help us understand the collision problems quantitatively and qualitatively.

Evaluation of Atrial Septal Defect Using Real-time Three-dimensional Echocardiography:Comparison with Surgical Findings

The present study evaluated the application of three dimensional echocardigraphy （3DE） in the diagnosis of atrial septal defect （ASD） and the measurement of its size by 3DE and compared the size with surgical findings. Two-dimensional and real-time three dimensional echocardiography （RT3DE） was performed in 26 patients with atrial septal defect, and the echocardiographic data were compared with the surgical findings. Significant correlation was found between defect diameter by RT3DE and that measured during surgery （r=0.77, P〈0.001）. The defect area changed significantly during cardiac cycle. Percentage change in defect size during cardiac cycle ranged from 6%-70%. Our study showed that the size and morphology of atrial septal defect obtained with RT3DE correlate well with surgical findings. Therefore, RT3DE is a feasible and accurate non-invasive imaging tool for assessment of atrial septal size and dynamic changes.

Variable dimensional state space based global path planning for mobile robot

A variable dimensional state space（VDSS） has been proposed to improve the re-planning time when the robotic systems operate in large unknown environments.VDSS is constructed by uniforming lattice state space and grid state space.In VDSS,the lattice state space is only used to construct search space in the local area which is a small circle area near the robot,and grid state space elsewhere.We have tested VDSS with up to 80 indoor and outdoor maps in simulation and on segbot robot platform.Through the simulation and segbot robot experiments,it shows that exploring on VDSS is significantly faster than exploring on lattice state space by Anytime Dynamic A＊（AD＊） planner and VDSS is feasible to be used on robotic systems.

Real-time Three-Dimensional Color Doppler Flow Imaging： An Improved Technique for Quantitative Analysis of Aortic Regurgitation

The recently introduced real-time three-dimensional color Doppler flow imaging （RT-3D CDFI） technique provides a quick and accurate calculation of regurgitant jet volume （RJV） and fraction. In order to evaluate RT-3D CDFI in the noninvasive assessment of aortic RJV and regurgitant jet fraction （RJF） in patients with isolated aortic regurgitation, real-time three-dimensional echocardiographic studies were performed on 23 patients with isolated aortic regurgitation to obtain LV end-diastolic volumes （LVEDV）, end-systolic volumes （LVESV） and RJV, and then RJF could be calculated. The regurgitant volume （RV） and regurgitant fraction （RF） calculated by two-dimensional pulsed Doppler （2D-PD） method served as reference values. The results showed that aortic RJV measured by the RT-3D CDFI method showed a good correlation with the 2D-PD measurements （r= 0.93, Y=0.89X＋ 3.9, SEE= 8.6 mL, P〈0.001 ）; the mean （SD） difference between the two methods was - 1.5 （9.8） mL. % RJF estimated by the RT-3D CDFI method was also correlated well with the values obtained by the 2D-PD method （r=0.88, Y=0.71X＋ 14.8, SEE= 6.4 %, P〈0. 001）; the mean （SD） difference between the two methods was -1.2 （7.9） %. It was suggested that the newly developed RT-3D CDFI technique was feasible in the majority of patients. In patients with eccentric aortic regurgitation, this new modality provides additional information to that obtained from the two-dimensional examination, which overcomes the inherent limitations of two-dimensional echocardiography by depicting the full extent of the jet trajectory. In addition, the RT-3D CDFI method is quick and accurate in calculating RJV and RJF.

Evaluation of Right Ventricular Volume and Systolic Function by Real-time Three-dimensional Echocardiography

The optimal plane for measurement of the right ventricular (RV) volumes by real-time three-dimensional echocardiography (RT3DE) was determined and the feasibility and accuracy of RT3DE in studying RV systolic function was assessed. RV “Full volume” images were acquired by RT3DE in 22 healthy subjects. RV end-diastolic volumes (RVEDV) and end-systolic volumes (RVESV) were outlined using apical biplane, 4-plane, 8-plane, 16-plane offline separately. RVSV and RVEF were calculated. Meanwhile tricuspid annual systolic excursion (TASE) was measured by M-mode echo. LVSV was outlined by 2-D echo according to the biplane Simpson's rule. The results showed: (1) There was a good correlation between RVSV measured from series planes and LVSV from 2-D echo (r=0.73; r=0.69; r=0.63; r=0.66, P<0.25—0.0025); (2) There were significant differences between RVEDV in biplane and those in 4-, 8-, 16-plane (P<0.001). There was also difference between RV volume in 4-plane and that in 8-plane (P<0.05), but there was no significant difference between RV volume in 8-plane and that in 16-plane (P>0.05); (3) Inter-observers and intro-observers variability analysis showed that there were close agreements and relations for RV volumes (r=0.986, P<0.001; r=0.93, P<0.001); (4) There was a significantly positive correlation of TASE to RVSV and RVEF from RT3DE (r=0.83; r=0.90). So RV volume measures with RT3DE are rapid, accurate and reproducible. In view of RV's complex shape, apical 8-plane method is better in clinical use. It may allow early detection of RV systolic function.

Risk Assessment of Coal Mine Water Hazard Based on Three-Dimensional Model of Geology and Underground Space

Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coal production.It is showed by statistics that 60%of mine accidents are affected by groundwater,which not only result in the production losses,casualties and a variety of

Splitting Based Scheme for Three-dimensional MHD with Dual Time Stepping

A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avoid the occurrence of negative pressure in the reconstructed profiles and its updated value,a positivity preserving method is provided.Furthermore,the MHD equations are solved at each physical time step by advancing in pseudo time.The use of dual time stepping is beneficial in the computation since the use of dual time stepping allows the physical time step not to be limited by the corresponding values in the smallest cell and to be selected based on the numerical accuracy criterion.This newly established hybrid scheme combined with positivity preserving method and dual time technique has demonstrated the accurateness and robustness through numerical experiments of benchmark problems such as the 2D Orszag-Tang vortex problem and the3 D shock-cloud interaction problem.