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.

Continuous imaging space in three-dimensional integral imaging

We report an integral imaging method with continuous imaging space. This method simultaneously reconstructs real and virtual images in the virtual mode, with a minimum gap that separates the entire imaging space into real and virtual space. Experimental results show that the gap is reduced to 45% of that in a conventional integral imaging system with the same parameters.

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

Three-dimensionally ordered macroporous cross-linked polystyrene incorporating functional group via hydrophilic spacer arm

A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene（3DOM CLPS） by hydrophilic spacer arm has been investigated.The 3DOM CLPS with pore size 865 nm was prepared by sacrifice template method.The hydrophilic spacer arm（polyethylene glycol,molecular weight is 600） was grafted to the 3DOM CLPS via nucleophilic substitution reaction.The other side of active hydroxyl can be further converted into a lot of other functional groups.In this report,the chelating ligand 2-mercaptobenzothiazole（MBZ） group was introduced on the end of the PGE chain to evidence the versatile functionalization approach.The functionalized ordered macroporous materials were characterized by FT-IR,element analyzer,SEM.The results reveal that the pores were successfully bonded with 2-mercaptobenzothiazole groups via hydrophilic spacer arms and the original morphology of ordered macroporous materials were remained after functionalization.The MBZ group density is 0.052 mmol/m^2.The functionalized 3DOM CLPS are expected to application as heavy metal ions adsorbent.

Three-Dimensional Space Interpolation of Grey / Depth Image Sequence-A New Technique of Computer Graphics Synthesis

This paper advances a three-dimensional space interpolation method of grey / depth image sequence, which breaks free from the limit of original practical photographing route. Pictures can cruise at will in space. By using space sparse sampling, great memorial capacity can be saved and reproduced scenes can be controlled. To solve time consuming and complex computations in three-dimensional interpolation algorithm, we have studied a fast and practical algorithm of scattered space lattice and that of 'Warp' algorithm with proper depth. By several simple aspects of three dimensional space interpolation, we succeed in developing some simple and practical algorithms. Some results of simulated experiments with computers have shown that the new method is absolutely feasible.

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.

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.

Numerical study on three-dimensional flow field of continuously rotating detonation in a toroidal chamber

Gaseous detonation propagating in a toroidal chamber was numerically studied for hydrogen/oxygen/nitrogen mixtures. The numerical method used is based on the three-dimensional Euler equations with detailed finiterate chemistry. The results show that the calculated streak picture is in qualitative agreement with the picture recorded by a high speed streak camera from published literature. The three-dimensional flow field induced by a continuously rotating detonation was visualized and distinctive features of the rotating detonations were clearly depicted. Owing to the unconfined character of detonation wavelet, a deficit of detonation parameters was observed. Due to the effects of wall geometries, the strength of the outside detonation front is stronger than that of the inside portion. The detonation thus propagates with a constant circular velocity. Numerical simulation also shows three-dimensional rotating detonation structures, which display specific feature of the detonation- shock combined wave. Discrete burning gas pockets are formed due to instability of the discontinuity. It is believed that the present study could give an insight into the interest- ing properties of the continuously rotating detonation, and is thus beneficial to the design of continuous detonation propulsion systems.

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.

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.

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.

Constructing Three-Dimension Space Graph for Outlier Detection Algorithms in Data Mining

Outlier detection has very important applied value in data mining literature. Different outlier detection algorithms based on distinct theories have different definitions and mining processes. The three-dimensional space graph for constructing applied algorithms and an improved GridOf algorithm were proposed in terms of analyzing the existing outlier detection algorithms from criterion and theory. Key words outlier - detection - three-dimensional space graph - data mining CLC number TP 311. 13 - TP 391 Foundation item: Supported by the National Natural Science Foundation of China (70371015)Biography: ZHANG Jing (1975-), female, Ph. D, lecturer, research direction: data mining and knowledge discovery.

Obstacle avoidance method of three-dimensional obstacle spherical cap

Focusing on obstacle avoidance in three-dimensional space for unmanned aerial vehicle(UAV), the direct obstacle avoidance method in dynamic space based on three-dimensional velocity obstacle spherical cap is proposed, which quantifies the influence of threatening obstacles through velocity obstacle spherical cap parameters. In addition, the obstacle avoidance schemes of any point on the critical curve during the multi-obstacles avoidance are given. Through prediction, the insertion point for the obstacle avoidance can be obtained and the flight path can be replanned. Taking the Pythagorean Hodograph(PH) curve trajectory re-planning as an example, the three-dimensional direct obstacle avoidance method in dynamic space is tested. Simulation results show that the proposed method can realize the online obstacle avoidance trajectory re-planning, which increases the flexibility of obstacle avoidance greatly.

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.

Almost Injective Mappings of Totally Bounded Metric Spaces into Finite Dimensional Euclidean Spaces

Let χ= be a metric space and let ε be a positive real number. Then a function f: X→Y is defined to be an ε-map if and only if for all y∈Y, the diameter of f-1(y)?is at most ε. In Theorem 10 we will give a new proof for the following well known fact: if χ is totally bounded, then for all ε there exists a finite number n and a continuous ε-map fε: X→Rn (here Rn is the usual n-dimensional Euclidean space endowed with the Euclidean metric). If ε is “small”, then fε is “almost injective”;and still exists even if χ has infinite covering dimension (in this case, n depends on ε, of course). Contrary to the known proofs, our proof technique is effective in the sense, that it allows establishing estimations for n in terms of ε and structural properties of χ.

A combined numerical model of three-dimensional tidal motion and sediment transport in tidal current and its application

A calculation scheme, which combines a horizontal upwind finite element method with vertical implicit differences, is used to establish a three-dimensional mathematical model of tidal motion and sediment transport in tidal current. Compared with those of the relative theoretical formula, the results are satisfactory. The model mentioned above has been applied to the water area of the Lianzhou Bay, Guangxi Province. On the basis of the analysis and comparison with the field data, it shows clearly that the model calculation results are reasonable.

COARSE ISOMETRIES BETWEEN FINITE DIMENSIONAL BANACH SPACES

Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f:X→Y satisfies an integral convergence condition or weak stability on a basis,then there exists a surjective linear isometry U:X→Y such that∥f(x)−Ux∥=o(∥x∥)as∥x∥→∞.This is a generalization about the result of Lindenstrauss and Szankowski on the same finite dimensional Banach spaces without the assumption of surjectivity.As a consequence,we also obtain a stability result forε-isometries which was established by Dilworth.

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.

Study on eigenvalue space of hyperchaotic canonical four-dimensional Chua's circuit

The eigenvalue space of the canonical four-dimensional Chua＇s circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parameters and the eigenvalues of the system are established, and therefore all the circuit parameters can be determined explicitly by any given set of eigenvalues. Then, the eigenvalue space of the circuit is investigated in two cases by the nonlinear elements used. According to the types of the eigenvalues, some novel hyperchaotic attractors are presented. Further, the dynamic behaviours of the circuit are studied by the bifurcation diagrams and the Lyapunov spectra of the eigenvalues.