Warming and depth convergence of the Arctic Intermediate Water in the Canada Basin during 1985–2006

The warming of the Arctic Intermediate Water （AIW） is studied based on the analyses of hydro- graphic observations in the Canada Basin of the Arctic Ocean during 1985-2006. It is shown that how the anomalously warm AIW spreads in the Canada Basin during the observation time through the analysis of the AIW temperature spatial distribution in different periods. The results indicate that by 2006, the entire Canada Basin has almost been covered by the warming AIW. In order to study interannual variability of the AIW in the Canada Basin, the Canada Basin is divided into five regions according to the bottom topography. From the interannual variation of AIW temperature in each region, it is shown that a cooling period follows after the warming event in upstream regions. At the Chukchi Abyssal Plain and Chukchi Plateau, upstream of the Arctic Circumpolar Boundary Current （ACBC） in the Canada Basin, the AIW temperature reached maximum and then started to fall respectively in 2000 and 2002. However, the AIW in the Canada Abyssal Plain and Beaufort Sea continues to warm monotonically until the year 2006. Furthermore, it is revealed that there is convergence of the AIW depth in the five different regions of the Canada Basin when the AIW warming occurs during observation time. The difference of AIW depth between the five regions of the Canada Basin is getting smaller and smaller, all approaching 410 m in recent years. The results show that depth convergence is related to the variation of AIW potential density in the Canada Basin.

CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

This paper is concerned with a singular limit for the one-dimensional compress- ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie （2011） [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact 1 discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie＇s convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.

HOMOGENIZATION FOR NONLINEAR SCHRODINGER EQUATIONS WITH PERIODIC NONLINEARITY AND DISSIPATION IN FRACTIONAL ORDER SPACES

We study the nonlinear SchrSdinger equation with time-oscillating nonlinearity and dissipation originated from the recent studies of Bose-Einstein condensates and optical systems which reads iψt＋△ψ＋Ф（ωt）｜ψ｜αψ＋iξ （ωt）ψ= 0. Under some conditions, we show that as ω→∞ , the solution ψω will locally converge to the solution of the averaged equation iψt＋△ψ＋Ф（ωt）｜ψ｜αψ＋iξ （ωt）ψ= 0 with the same initial condition in Lq（（0, T）, B-S/T,2） for all admissible pairs （q, r）, where T∈ （0, Tmax）. We also show that if the dissipation coefficient ξ0 large enough, then, ψω is global if w is sufficiently large and ψω converges to ψ in Lq（（0, ∞）, B-S/T,2）, for all admissible pairs （q, r）. In particular, our results hold for both subcritical and critical nonlinearities.

Superlinear Convergence of a Smooth Approximation Method for Mathematical Programs with Nonlinear Complementarity Constraints

Mathematical programs with complementarity constraints(MPCC) is an important subclass of MPEC.It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem.In this paper,we propose a new smoothing method for MPCC by using the aggregation technique.A new SQP algorithm for solving the MPCC problem is presented.At each iteration,the master direction is computed by solving a quadratic program,and the revised direction for avoiding the Maratos effect is generated by an explicit formula.As the non-degeneracy condition holds and the smoothing parameter tends to zero,the proposed SQP algorithm converges globally to an S-stationary point of the MPEC problem,its convergence rate is superlinear.Some preliminary numerical results are reported.

CONVERGENCE OF DERIVATIVES OF GENERALIZED BERNSTEIN OPERATORS

In the present paper, we obtain estimations of convergence rate derivatives of the q-Bernstein polynomials Bn （f, qn ;x） approximating to f＇ （x） as n →∞, which is a general- ization of that relating the classical case qn = 1. On the other hand, we study the conver- gence properties of derivatives of the limit q-Bernstein operators B∞（f, q;x） as q→1-.

Convergence Theorems of Mann and Ishikawa Iterative Processes with Errors for Multivalued Φ-strongly Accretive Mapping

Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160).

A second order finite difference-spectral method for space fractional diffusion equations

A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The stability and error estimates of the temporal semidiscrete scheme are rigorously discussed,and the convergence order of the proposed method is proved to be O(τ2+Nα-m)in L2-norm,whereτ,N,αand m are the time step size,polynomial degree,fractional derivative index and regularity of the exact solution,respectively.Numerical experiments are carried out to demonstrate the theoretical analysis.

A New Sequential Systems of Linear Equations Algorithm of Feasible Descent for Inequality Constrained Optimization

Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations （SSLE） algorithm generating feasible iterates is proposed for solving nonlinear optimization problems with inequality constraints. In this paper, we introduce a new technique for constructing the system of linear equations, which recurs to a perturbation for the gradients of the constraint functions. At each iteration of the new algorithm, a feasible descent direction is obtained by solving only one system of linear equations without doing convex combination. To ensure the global convergence and avoid the Maratos effect, the algorithm needs to solve two additional reduced systems of linear equations with the same coefficient matrix after finite iterations. The proposed algorithm is proved to be globally and superlinearly convergent under some mild conditions. What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improving direction is obtained easily and the computation cost of generating a new iterate is reduced. Finally, a preliminary implementation has been tested.

Convergence performance comparisons of PID, MRAC, and PID ＋ MRAC hybrid controller

This study proposes a hybrid controller by combining a proportional-integral-derivative （PID） control and a model reference adaptive control （MRAC）, which named as PID ＋ MRAC controller. The convergence performances of the PID control, MRAC, and hybrid PID ＋ MRAC are also compared. Through the simulation in Matlab, the results show that the convergence speed and performance of the MRAC and the PID ＋MRAC controller are better than those of the PID controller. In addition, the convergence performance of the hybrid control is better than that of the MRAC control.

A NONMONOTONE TRUST REGION TECHNIQUEFOR UNCONSTRAINED OPTIMIZAfIONPROBLEMS

Trust region methods with nonmonotone technique for unconstrained opti-mization problems are presented and analyzed. The convergence results are demonstratedfor the proposed algorithms even if the conditions are mild.

Global and Local Convergence of a New Affine Scaling Trust Region Algorithm for Linearly Constrained Optimization

Chen and Zhang [Sci. China, Set. A, 45, 1390-1397 （2002）] introduced an affine scaling trust region algorithm for linearly constrained optimization and analyzed its global convergence. In this paper, we derive a new affine scaling trust region algorithm with dwindling filter for linearly constrained optimization. Different from Chen and Zhang＇s work, the trial points generated by the new algorithm axe accepted if they improve the objective function or improve the first order necessary optimality conditions. Under mild conditions, we discuss both the global and local convergence of the new algorithm. Preliminary numerical results are reported.

INEXACT TWO-GRID METHODS FOR EIGENVALUE PROBLEMS

We discuss the inexact two-grid methods for solving eigenvalue problems, including both partial differential and integral equations. Instead of solving the linear system exactly in both traditional two-grid and accelerated two-grid method, we point out that it is enough to apply an inexact solver to the fine grid problems, which will cut down the computational cost. Different stopping criteria for both methods are developed for keeping the optimality of the resulting solution. Numerical examples are provided to verify our theoretical analyses.

A Homogeneous Smoothing-type Algorithm for Symmetric Cone Linear Programs

In this paper, we investigate a smoothing-type algorithm for solving the symmetric cone linear program （（SCLP） for short） by making use of an augmented system of its optimality conditions. The algorithm only needs to solve one system of linear equations and to perform one line search at each iteration. It is proved that the algorithm is globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, the algorithm may correctly detect solvability of （SCLP）. Furthermore, if （SCLP） has a solution, then the algorithm will generate a solution of （SCLP）, and if the problem is strongly infeasible, the algorithm will correctly detect infeasibility of （SCLP）.

HIGH ORDER FINITE DIFFERENCE/SPECTRAL METHODS TO A WATER WAVE MODEL WITH NONLOCAL VISCOSITY

In this paper,efficient numerical scheme is proposed for solving the water wave model with nonlocal viscous term that describe the propagation of surface water wave.By using the Caputo fractional derivative definition to approximate the nonlocal fractional operator,finite difference method in time and spectral method in space are constructed for the considered model.The proposed method employs known 5/2 order scheme for fractional derivative and a mixed linearization for the nonlinear term.The analysis shows that the proposed numerical scheme is unconditionally stable and error estimates are provided to predict that the second order backward differentiation plus 5/2 order scheme converges with order 2 in time,and spectral accuracy in space.Several numerical results are provided to verify the efficiency and accuracy of our theoretical claims.Finally,the decay rate of solutions are investigated.

NONPARAMETRIC IDENTIFICATION OF MISO HAMMERSTEIN SYSTEM FROM STRUCTURED DATA

The problem of nonparametric identification of a multivariate nonlinearity in a D-input Hammer- stein system is examined. It is demonstrated that if the input measurements are structured, in the sense that there exists some hidden relation between them, i.e. if they are distributed on some （unknown） d-dimensional space M in IRD, d 〈 D, then the system nonlinearity can be recovered at points on M with the convergence rate O（n-1/（2＋d）） dependent on d. This rate is thus faster than the generic rate O（n-1/（2＋D）） achieved by typical nonparametric algorithms and controlled solely by the number of inputs D.

Iterative Algorithm with Mixed Errors for Solving a New System of Generalized Nonlinear Variational-Like Inclusions and Fixed Point Problems in Banach Spaces

A new system of generalized nonlinear variational-like inclusions involving A- maximal m-relaxed η-accretive （so-called, （A, η）-accretive in [36]） mappings in q-uniformly smooth Banach spaces is introduced, and then, by using the resolvent operator technique associated with A-maximal m-relaxed ~/-accretive mappings due to Lan et al., the exis- tence and uniqueness of a solution to the aforementioned system is established. Applying two nearly uniformly Lipschitzian mappings 81 and 82 and using the resolvent operator technique associated with A-maximal m-relaxed ~？-accretive mappings, we shall construct a new perturbed N-step iterative algorithm with mixed errors for finding an element of the set of the fixed points of the nearly uniformly Lipschitzian mapping Q = （S1, S2） which is the unique solution of the aforesaid system. We also prove the convergence and stability of the iterative sequence generated by the suggested perturbed iterative algorithm under some suitable conditions, The results presented in this paper extend and improve some known results in the literature.

Half thresholding eigenvalue algorithm for semidefinite matrix completion

The semidefinite matrix completion(SMC) problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, SMC problem and S1/2relaxation model share a unique solution. Then we prove that the global optimal solutions of S1/2regularization model are fixed points of a symmetric matrix half thresholding operator. We give an iterative scheme for solving S1/2regularization model and state convergence analysis of the iterative sequence.Through the optimal regularization parameter setting together with truncation techniques, we develop an HTE algorithm for S1/2regularization model, and numerical experiments confirm the efficiency and robustness of the proposed algorithm.

Two-Sided Empirical Bayes Test for the Exponential Family with Contaminated Data

In this study, the two-sided Empirical Bayes test （EBT） rules for the parameter of continuous one-parameter exponential family with contaminated data （errors in variables） are constructed by a deconvolution kernel method. The asymptotically optimal uniformly over a class of prior distributions and uniform rates of convergence, which depends on two types of the error distribu- tions for the proposed EBT rules, are obtained under suitable con- ditions. Finally, an example about the main results of this paper is given.

On a Linear Combination Operator of Neumann-Bessel Series

In this paper we construct a new operator Hn,r（N,B） （f; z） by means of the partial sums S（N,S） （f; z） of Neumann-Bessel series. The operator converges uniformly to any fixed continuous function f（z） on the unit circle ｜ z ｜= 1 and has the best approximation order for f（z） on ｜ z ｜= 1.

WEAK AND STRONG CONVERGENCE THEOREMS FOR SPLIT GENERALIZED MIXED EQUILIBRIUM PROBLEM

The purpose of this paper is to introduce a split generalized mixed equi- librium problem （SGMEP） and consider some iterative sequences to find a solution of the generalized mixed equilibrium problem such that its image un- der a given bounded linear operator is a solution of another generalized mixed equilibrium problem. We obtain some weak and strong convergence theorems.