Algebraic structure and Poisson＇s theory of mechanico-electrical systems

The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson＇s integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson＇s integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.

Downward continuation of airborne gravimetry data based on Poisson integral iteration method

The research and application of airborne gravimetry technology has become one of the hottest topics in gravity field in recent years. Downward continuation is one of the key steps in airborne gravimetry data processing, and the quality of continuation results directly influence the further application of surveying data. The Poisson integral iteration method is proposed in this paper, and the modified Poisson integral discretization formulae are also introduced in the downward continuation of airborne gravimerty data. For the test area in this paper, compared with traditional Poisson integral discretization formula, the continuation result of modified formulae is improved by 10.8 mGal, and the precision of Poisson integral iteration method is in the same amplitude as modified formulae. So the Poisson integral iteration method can reduce the discretization error of Poisson integral formula effectively. Therefore, the research achievements in this paper can be applied directly in the data processing of our country＇s airborne scalar and vector gravimetry.

ALGEBRAIC STRUCTURES AND POISSON INTEGRALS OF RELATIVISTIC DYNAMICAL EQUATIONS FOR ROTATIONALSYSTEMS

The algebraic structures of the dynamical equations for the rotational relativistic systems are studied. It is found that the dynamical equations of holonomic conservative rotational relativistic systems and the special nonholonomic rotational relativistic systems have Lie's algebraic structure, and the dynamical equations of the general holonomic rotational relativistic systems and the general nonholonomic rotational relativistic systems have Lie admitted algebraic structure. At last the Poisson integrals of the dynamical equations for the rotational relativistic systems are given.

Quantum Mechanical Correspondence of Poisson Integral Formula

In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and its induced state,i.e.the number-difference-correlated amplitude entangled state representation.

Boundedness of the Littlewood-Paley Operator,the Function g(f),on BMO(T)

Littlewood-Paley operator,the function g(f), is considered as an operator on BMO(T). It is proved that if f E BMO (T), then g(f)∈BMO (T) and there is a constant C that is independent of f such that ‖g(f)‖_* ≤C‖f‖_*. Moreover,we have got the further results.

Fast and accurate surface normal integration on non-rectangular domains

The integration of surface normals for the purpose of computing the shape of a surface in 3D space is a classic problem in computer vision. However,even nowadays it is still a challenging task to devise a method that is flexible enough to work on non-trivial computational domains with high accuracy, robustness,and computational efficiency. By uniting a classic approach for surface normal integration with modern computational techniques, we construct a solver that fulfils these requirements. Building upon the Poisson integration model, we use an iterative Krylov subspace solver as a core step in tackling the task. While such a method can be very efficient, it may only show its full potential when combined with suitable numerical preconditioning and problem-specific initialisation. We perform a thorough numerical study in order to identify an appropriate preconditioner for this purpose.To provide suitable initialisation, we compute this initial state using a recently developed fast marching integrator. Detailed numerical experiments illustrate the benefits of this novel combination. In addition, we show on real-world photometric stereo datasets that the developed numerical framework is flexible enough to tackle modern computer vision applications.

Harmonic extension of Q-type space related to logarithmic functions

This paper studies a class of Q-type spaces Q^(m)_(log,λ)(R^(n))related to logarithmic functions.We first investigate some basic properties ofQ^(m)_(log,λ)(R^(n)).Further,by the aid of Poisson integral and harmonic function spaces H^(m)_(log,λ)(R_(+)^(n+1)),the harmonic extension of Q^(m)_(log,λ)(R^(n))and the boundary value problem of H^(m)_(log,λ)(R_(+)^(n+1))are obtained.

Poisson Integrators Based on Splitting Method for Poisson Systems

We propose Poisson integrators for the numerical integration of separable Poisson systems.We analyze three situations in which Poisson systems are separated in threeways and Poisson integrators can be constructed by using the splittingmethod.Numerical results show that the Poisson integrators outperform the higher order non-Poisson integrators in terms of long-termenergy conservation and computational cost.The Poisson integrators are also shown to be more efficient than the canonicalized sympletic methods of the same order.

Equal-Time and Equal-Space Poisson Brackets of the N-Component Coupled NLS Equation

Two Poisson brackets for the N-component coupled nonlinear Schrdinger(NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation.

Lipschitz and Total-Variational Regularization for Blind Deconvolution

In[3],Chan and Wong proposed to use total variational regularization for both images and point spread functions in blind deconvolution.Their experimental results show that the detail of the restored images cannot be recovered.In this paper,we consider images in Lipschitz spaces,and propose to use Lipschitz regularization for images and total variational regularization for point spread functions in blind deconvolution.Our experimental results show that such combination of Lipschitz and total variational regularization methods can recover both images and point spread functions quite well.