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.

The Optimal Matching Parameter of Half Discrete Hilbert Type Multiple Integral Inequalities with Non-Homogeneous Kernels and Applications

By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered.

Two new discrete integrable systems

In this paper,we focus on the construction of new（1＋1）-dimensional discrete integrable systems according to a subalgebra of loop algebra A 1.By designing two new（1＋1）-dimensional discrete spectral problems,two new discrete integrable systems are obtained,namely,a 2-field lattice hierarchy and a 3-field lattice hierarchy.When deriving the two new discrete integrable systems,we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy.Moreover,we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity.

Discrete integrable couplings associated with modified Korteweg-de Vries lattice and two hierarchies of discrete soliton equations

A direct way to construct integrable couplings for discrete systems is presented by use of two semi-direct sum Lie algebras. As their applications, the discrete integrable couplings associated with modified Korteweg-de Vries （m-KdV） lattice and two hierarchies of discrete soliton equations are developed. It is also indicated that the study of integrable couplings using semi-direct sums of Lie algebras is an important step towards the complete classification of integrable couplings.

Symmetries and variational calculation of discrete Hamiltonian systems

We present a numerical simulation method of Noether and Lie symmetries for discrete Hamiltonian systems. The Noether and Lie symmetries for the systems are proposed by investigating the invariance properties of discrete Lagrangian in phase space. The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show that the difference discrete variational method preserves the exactness and the invariant quantity.

Symbolic Computation of Extended Jacobian Elliptic Function Algorithm for Nonlinear Differential-Different Equations

The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.

Lattice soliton equation hierarchy and associated properties

As a new subject, soliton theory is shown to be an effective tool for describing and explaining nonlinear phenomena in nonlinear optics, super conductivity, plasma physics, magnetic fluid, etc. Thus, the study of soliton equations has always been one of the most prominent events in the field of nonlinear science during the past few years. Moreover, it is important to seek the lattice soliton equation and study its properties. In this study, firstly, we derive a discrete integrable system by using the Tu model. Then, some properties of the obtained equation hierarchies are discussed.

Optimal predication of double-star position/SINS based on discrete integration

Aiming at Double-Star positioning system's shortcomings of delayed position information and easy exposition of the user as well as the error increase of the SINS with the accumulation of time, the integration of Double-Star positioning system and the SINS is one of the developing directions for an integrated navigation system. This paper puts forward an optimal predication method of Double-Star/SINS integrated system based on discrete integration, which can make use of the delayed position information of Double-Star positioning system to optimally predicate the integrated system, and then corrects the SINS. The experimental results show that this method can increase the user's concealment under the condition of assuring the system's accuracy.

Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product

It is shown that the Kronecker product can be applied to constructing new discrete integrable couplingsystem of soliton equation hierarchy in this paper.A direct application to the fractional cubic Volterra lattice spectralproblem leads to a novel integrable coupling system of soliton equation hierarchy.It is also indicated that the study ofdiscrete integrable couplings by using the Kronecker product is an efficient and straightforward method.This methodcan be used generally.

Discrete AKNS-D Hierarchy

In this paper, we consider the discrete AKNS-D hierarchy, make the construction of the hierarchy, prove the bilinear identity and give the construction of the τ-functions of this hierarchy.

Discrete Generalizations of Some N-Independent-Variable Integral Inequalities of Langenhop-Gollwitzer Type

We establish some new n-independent-variable discrete inequalities which are analo- gous to some Langenhop-Gollwitzer type integral inequalities obtained by the present author in J. Math.Anal.Appl.,109(1985),171-181.An application to hyperbolic summary-difference equations in n variables is also sketched.

Solitons and quasi-Grammians of the generalized lattice Heisenberg magnet model

In this paper,we study the discrete Darboux and standard binary Darboux transformation for the generalized lattice Heisenberg magnet model.We calculate the quasi-Grammian solutions by the iteration of standard binary Darboux transformation.Furthermore,we derive the explicit matrix solutions for the binary Darboux matrix and then reduce them to the elementary Darboux matrix and plot the dynamics of solutions.

Conservation laws of some lattice equations

We derive infinitely many conservation laws for some multi- dimensionally consistent lattice equations from their Lax pairs. These lattice equations are the Nijhoff-Quispel-Capel equation, lattice Boussinesq equation, lattice nonlinear SchrSdinger equation, modified lattice Boussinesq equation, Hietarinta＇s Boussinesq-type equations, Schwarzian lattice Boussinesq equation, and Toda-modified lattice Boussinesq equation.

Integrable discretization of soliton equations via bilinear method and Backlund transformation

We present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota’s bilinear method.This approach is mainly based on the compatibility between an integrable system and its B¨acklund transformation.We apply this procedure to several equations,including the extended Korteweg-deVries(Kd V)equation,the extended Kadomtsev-Petviashvili(KP)equation,the extended Boussinesq equation,the extended Sawada-Kotera(SK)equation and the extended Ito equation,and obtain their associated semidiscrete analogues.In the continuum limit,these differential-difference systems converge to their corresponding smooth equations.For these new integrable systems,their B¨acklund transformations and Lax pairs are derived.

A New Negative Discrete Hierarchy and Its N-Fold Darboux Transformation

Starting from a matrix discrete spectral problem, we derive a negative discrete hierarchy. It is shown that the hierarchy is integrable in the Liouville sense and possesses a bi-Hamiltonian structure. Furthermore, its N-fold Darboux transformation is established with the help of gauge transformation of Lax pair. As an application of the Darboux transformation, some new exact solutions for a discrete equation in the negative hierarchy are obtained.

Multi-Soliton Solutions and Integrable Discretization for a Coupled Modified Volterra Lattice Equation

In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new explicit solutions including multi-soliton and multi-positon. Furthermore, an integrable discretization of the coupled modified Volterra lattice equation is constructed.

Integrable discretizations of the Dym equation

Integrable discretizations of are proposed. N-soliton solutions for analogues of the complex and real Dym the complex and real Dym equations both semi-discrete and fully discrete equations are also presented.

A COMBINATORIAL ASPECT OF A DISCRETE-TIME SEMI-INFINITE LOTKA-VOLTERRA EQUATION

A graph is introduced,which allows of a combinatorial interpretation of a discrete-timesemi-infinite Lotka-Volterra (dLV) equation.In particular,Hankel determinants used in a determinantsolution to the dLV equation are evaluated,via the Gessel-Viennot method,in terms of non-intersectingsubgraphs.Further,the recurrence of the dLV equation describing its time-evolution is equivalentlyexpressed as a time-evolution of weight of specific subgraphs.

A DISSIPATION-PRESERVING INTEGRATOR FOR DAMPED OSCILLATORY HAMILTONIAN SYSTEMS

In this paper,based on discrete gradient,a dissipation-preserving integrator for weakly dissipative perturbations of oscillatory Hamiltonian system is established.The solution of this system is a damped nonlinear oscillator.Basically,lots of nonlinear oscillatory mechanical systems including frictional forces lend themselves to this approach.The new integrator gives a discrete analogue of the dissipation property of the original system.Meanwhile,since the integrator is based on the variation-of-constants formula for oscillatory systems,it preserves the oscillatory structure of the system.Some properties of the new integrator are derived.The convergence is analyzed for the implicit iterations based on the discrete gradient integrator,and it turns out that the convergence of the implicit iterations based on the new integrator is independent of k Mk,where M governs the main oscillation of the system and usually k Mk≫1.This significant property shows that a larger stepsize can be chosen for the new schemes than that for the traditional discrete gradient integrators when applied to the oscillatory Hamiltonian system.Numerical experiments are carried out to show the effectiveness and efficiency of the new integrator in comparison with the traditional discrete gradient methods in the scientific literature。

A tight sandstone multi-physical hydraulic fractures simulator study and its field application

During the past years,the recovery of unconventional gas formation has attracted lots of attention and achieved huge success.To produce gas from the low-permeability unconventional formations,hydraulic fracturing technology is essential and critical.In this paper,we present the development of a three-dimensional thermalhydraulic-mechanical numerical simulator for the simulation of hydraulic fracturing operations in tight sandstone reservoirs.Our simulator is based on integrated finite difference(IFD)method.In this method,the simulation domain is subdivided into sub domains and the governing equations are integrated over a sub domain with flux terms expressed as an integral over the sub domain boundary using the divergence theorem.Our simulator conducts coupled thermal-hydraulic-mechanical simulation of the initiation and extension of hydraulic fractures.It also calculates the mass/heat transport of injected hydraulic fluids as well as proppants.Our simulator is able to handle anisotropic formations with multiple layers.Our simulator has been validated by comparing with an analytical solution as well as Ribeiro and Sharma model.Our model can simulate fracture spacing effect on fracture profile when combining IFD with Discontinuous Displacement Method(DDM).