RECURRENT NEURAL NETWORK MODEL BASED ON PROJECTIVE OPERATOR AND ITS APPLICATION TO OPTIMIZATION PROBLEMS

The recurrent neural network （RNN） model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN.

Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.

SINGULAR INTEGRAL EQUATIONS WITHCOMPLEX TRANSLATIONS

In this paper, a class of singular integral equations with complex translations is discussed. By using the Plemelj projection method the authors reduce them to the boundary value problem of analytic functions in A(+)(H) over cap(0) with upper translation and the boundary value problem of analytic functions in A-(H) over cap(0) with lower translation, which are solved here.

Arnoldi Projection Fractional Tikhonov for Large Scale Ill-Posed Problems

It is well known that Tikhonov regularization in standard form may determine approximate solutions that are too smooth for ill-posed problems,so fractional Tikhonov methods have been introduced to remedy this shortcoming.And Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining apartial Arnoldi decomposition of the given matrix.In this paper,we propose a new method to compute an approximate solution of large scale linear discrete ill-posed problems which applies projection fractional Tikhonov regularization in Krylov subspace via Arnoldi process.The projection fractional Tikhonov regularization combines the fractional matrices and orthogonal projection operators.A suitable value of the regularization parameter is determined by the discrepancy principle.Numerical examples with application to image restoration are carried out to examine that the performance of the method.

Non-Markovian dynamics of a qubit in a reservoir: different solutions of non-Markovian master equation

We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.

ERROR ESTIMATE FOR INFLUENCE OF MODEL REDUCTION OF NONLINEAR DISSIPATIVE AUTONOMOUS DYNAMICAL SYSTEM ON LONG-TERM BEHAVIOURS

From viewpoint of nonlinear dynamics, the model reduction and its influence on the long-term behaviours of a class of nonlinear dissipative autonomous dynamical system with higher dimension are investigated theoretically under some assumptions. The system is analyzed in the state space with an introduction of a distance definition which can be used to describe the distance between the full system and the reduced system, and the solution of the full system is then projected onto the complete space spanned by the eigenvectors of the linear operator of the governing equations. As a result, the influence of mode series truncation on the long-term behaviours and the error estimate are derived, showing that the error is dependent on the first products of frequencies and damping ratios in the subspace spanned by the eigenvectors with higher modal damping. Furthermore, the fundamental understanding for the topological change of the solution due to the application of different model reduction is interpreted in a mathematically precise way, using the qualitative theory of nonlinear dynamics.

Non-Markovian dynamics of two non-coupled qubits interacting with two separate reservoirs with different spectral densities

The dynamics of two non-coupled qubits independently interacting with their reservoirs is solved by the time convolutionless projection operator method. We study two-qubit quantum correlation dynamics for two different types of spectral densities, which are a Lorentzian distribution and an Ohmic spectral density with a Lorentzian–Drude cutoff function. For two qubits initially prepared in the initial Bell state, quantum discord can keep longer time and reach larger values in nonMarkovian reservoirs for the first spectral distribution or by reducing the cutoff frequency for the second case. For the initial Bell-like state, the dynamic behaviors of quantum discord and entanglement are compared. The results show that a long time of quantum correlation can be obtained by adjusting some parameters in experiment and further confirm that the discord can capture quantum correlation in addition to entanglement.

The Second-Order Differential Equation System with the Feedback Controls for Solving Convex Programming

In this paper, we establish the second-order differential equation system with the feedback controls for solving the problem of convex programming. Using Lagrange function and projection operator, the equivalent operator equations for the convex programming problems under the certain conditions are obtained. Then a second-order differential equation system with the feedback controls is constructed on the basis of operator equation. We prove that any accumulation point of the trajectory of the second-order differential equation system with the feedback controls is a solution to the convex programming problem. In the end, two examples using this differential equation system are solved. The numerical results are reported to verify the effectiveness of the second-order differential equation system with the feedback controls for solving the convex programming problem.

Research on Safety Risk Assessment Method for Large Scale Field Operation Project

By applying man-machine-environment system engineering theory, safety risks on large scale field operation project have been evaluated in this article. The factors concerning with the man, machine and environment in system were proposed separately. The value for lowest indexs was determined by decision-making of expert group. The weights were calculated based on AHP, and then safety risk assessment in different layers was made. The results show that the assessment method is reasonable, and it is significant for large scale field operation project safety managerment.

Risk Management and Operation Strategies of Chinese Overseas Risk Exploration Projects

Currently,the investment of oil and gas industry is still facing an unfavorable environment,in which,instable factors,such as financial crisis,terrorist,religious conflicts and rigorous environmental regulations,keep mucking up the business all around the world.Meanwhile,China’s rapid energy consumption growth boosted by a booming economy has put the country to rely heavily on exported oil.It is therefore extremely urgent to expand and diversify petroleum supply channel in consideration of the country’s energy security.As the world’s economy has been slowly recovering from the slump and

West-East Gas Project Operational This Year

China’s massive project to transfer natural gas from the Tarim Basin of Xinjiang Uygur autonomous region all the way to the coastal metropolis of Shanghai in the east will go into commercial operation on Dec. 30, according to the National Development and Reform Commission (NDRC).

The Connection Between the Metric and Generalized Projection Operators in Banach Spaces

In this paper we study the connection between the metric projection operator PK ： B →K, where B is a reflexive Banach space with dual space B^＊ and K is a non-empty closed convex subset of B, and the generalized projection operators ∏K ： B → K and πK ： B^＊ → K. We also present some results in non-reflexive Banach spaces.

Some Applications of Projection Operators in Wavelets

By rewriting the projection operator P0 in wavelets in another formula,we obtain a characterization of dim JV0（x）where V0 is a Γ-shift-invariant subspace of L2（Rn）derived from a dual wavelet basis and prove that there does not exist a wavelet function ψ ∈ L2（R）such that （?）has compact support and ∪k∈ZZ（supp■+4πk）=R up to a zero subset of R.

Decomposition of Molecular Motions into Translational, Rotational, and Intramolecular Parts by a Projection Operator Technique

The motion of the atoms in a molecule may be described as a superposition of translational motion of the molecular center-of-mass,rotational motion about the principal molecular axes,and an intramolecular motion that may be associated with vibrations and librations as well as molecular conformational changes.We have constructed projection operators that use the atomic coordinates and velocities at any two times,t=0 and a later time t,to determine the molecular center-of-mass,rotational,and intramolecular motions in a molecular dynamics simulation.This model-independent technique facilitates characterization of the atomic motions within a system of complex molecules and is important for the interpretation of experiments that rely on time correlation functions of atomic and molecular positions and velocities.The application of the projection operator technique is illustrated for the inelastic neutron scattering functions and for the translational and rotational velocity autocorrelation functions.

SUPERAPPROXIMATION PROPERTIES OF THE INTERPOLATION OPERATOR OF PROJECTION TYPE AND APPLICATIONS

Presents information on a study which analyzed superapproximation properties for the interpolation operator of projection type on two-dimensional domain. Discussion on the interpolation operator of projection type and its superapproximation properties; Superconvergence of Ritz projection; Proof and applications of the superconveregence of Ritz-Volterra projection.

Distributed accelerated primal-dual neurodynamic approaches for resource allocation problem

This paper investigates two distributed accelerated primal-dual neurodynamic approaches over undirected connected graphs for resource allocation problems(RAP)where the objective functions are generally convex.With the help of projection operators,a primal-dual framework,and Nesterov's accelerated method,we first design a distributed accelerated primal-dual projection neurodynamic approach(DAPDP),and its convergence rate of the primal-dual gap is O(1/(t^(2)))by selecting appropriate parameters and initial values.Then,when the local closed convex sets are convex inequalities which have no closed-form solutions of their projection operators,we further propose a distributed accelerated penalty primal-dual neurodynamic approach(DAPPD)on the strength of the penalty method,primal-dual framework,and Nesterov's accelerated method.Based on the above analysis,we prove that DAPPD also has a convergence rate O(1/(t^(2)))of the primal-dual gap.Compared with the distributed dynamical approaches based on the classical primal-dual framework,our proposed distributed accelerated neurodynamic approaches have faster convergence rates.Numerical simulations demonstrate that our proposed neurodynamic approaches are feasible and effective.

The hydrological effect between Jingjiang River and Dongting Lake during the initial period of Three Gorges Project operation

Based on the measured hydrological data from 1951 to 2008, the chain hydrological effect between Jingjiang River and Dongting Lake is analyzed by comparative method after the Three Gorges Project operation. The result indicates that 1） the scouring amount in Jing- jiang River made up 78.9% of the total from Yichang to Chenglingji, and its average scouring intensity was higher than the latter; 2） the water and sand diversion rates at the three outlets of the Jingjiang River were reduced by 2.33% and 2.78% separately; 3） the proportion of multi-year average runoff and sediment through the three outlets in the total into the Dongting Lake decreased by 7.7% and 24.4% respectively; 4） in Dongting Lake, the speed of sediment accumulation was lowered by 26.7%, in flood season, the runoff amount was 20.2% less than the multi-year average value, leading to seasonal scarcity of water year by year. The former prolonged the lake life, while the latter induced droughts in summer and fall in successive years, shortage of drinking and industrial water, shipping insecurity, as well as ecological problems such as decrease of birds and quick increase of Microtus fortis; 5） The multi-year average values of sediment and flood transporting capacity at the lake outlet were respec- tively increased by 26.6% and 3.7%, the adapt to the new change of the river-lake embankments were protected effectively. Then, to relation, some suggestions were put forward, such as optimizing further operation program of the Three Gorges Reservoir, reexamining the idea of river and lake regulation, and maintaining connection of the river and the lake.

DOMAIN DECOMPOSITION WITH NONMATCHING GRIDS FOR EXTERIOR TRANSMISSION PROBLEMS VIA FEM AND DTN MAPPING

In this paper, we are concerned with a non-overlapping domain decomposition method （DDM） for exterior transmission problems in the plane. Based on the natural boundary integral operator, we combine the DDM with a Dirichlet-to-Neumann （DtN） mapping and provide the numerical analysis with nonmatching grids. The weak continuity of the approximation solutions on the interface is imposed by a dual basis multiplier. We show that this multiplier space can generate optimal error estimate and obtain the corresponding rate of convergence. Finally, several numerical examples confirm the theoretical results.

Decomposition and Approximation of Multivariate Functions on the Cube

In this paper, we present a decomposition method of multivariate functions. This method shows that any multivariate function f on [0, 1]d is a finite sum of the form ∑jФjψj, where each Фj can be extended to a smooth periodic function, each ψj is an algebraic polynomial, and each Фjψj is a product of separated variable type and its smoothness is same as f. Since any smooth periodic function can be approximated well by trigonometric polynomials, using our decomposition method, we find that any smooth multivariate function on [0, 1]d can be approximated well by a combination of algebraic polynomials and trigonometric polynomials. Meanwhile, we give a precise estimate of the approximation error.