A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

Non-Recursive Base Conversion Using a Deterministic Markov Process

We prove that non-recursive base conversion can always be implemented by using a deterministic Markov process. Our paper discusses the pros and cons of recursive and non-recursive methods, in general. And we include a comparison between non-recursion and a deterministic Markov process, proving that the Markov process is twice as efficient.

Diagonally loaded SMI algorithm based on inverse matrix recursion

The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.

Fuzzy Shape Control Based on El man Dynamic Recursion Network Prediction Model

In the strip rolling process, shape control system possesses the characteristics of nonlinearity, strong coupling, time delay and time variation. Based on self adapting Elman dynamic recursion network prediction model, the fuzzy control method was used to control the shape on four-high cold mill. The simulation results showed that the system can be applied to real time on line control of the shape.

THE RECURSION OPERATOR FOR A CONSTRAINED CKP HIERARCHY

This paper gives a recursion operator for a 1-constrained CKP hierarchy, and by the recursion operator it proves that the 1-constrained CKP hierarchy can be reduced to the mKdV hierarchy under condition q = r.

Dark Sharma-Tasso-Olver Equations and Their Recursion Operators

A complete scalar classification for dark Sharma-Tasso-Olver＇s（STO＇s） equations is derived by requiring the existence of higher order differential polynomial symmetries. There are some free parameters for every class of dark STO systems, thus some special equations including symmetry equation and dual symmetry equation are obtained by selecting a free parameter. Furthermore, the recursion operators of STO equation and dark STO systems are constructed by a direct assumption method.

Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary

We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary,which has not been solved before because the Green＇s function technique and the Laplacian matrix approach are invalid in this case.Looking for the exact solutions of resistance is important but difficult in the case of the arbitrary boundary since the boundary is a wall or trap which affects the behavior of a finite network.In this paper,we give a general resistance formula that is composed of a single summation by using the recursion-transform method.Meanwhile,several interesting results are derived by the general formula.Further,the current distribution is given explicitly as a byproduct of the method.

Recursion Least Square Method to Study the Fault Diagnosis and Its Model of Hydraulic Equipment

In this paper establishing model of the fault diagnosis of hydraulic equipment isdescribed in details. It also studies the advantage of the recursion least square method. When theLSM is used in compuring the fault of hydraulic equipment, not only does it save the computerCPU-time and memory, but it also has a high computation speed and,makes it easy to identifythe estimation parameters.

NONLOCAL SYMMETRIES AND NONLOCAL RECURSION OPERATORS

An expose about covering method on differential equations was given. The general formulae to determine nonlocal symmetries were derived which are analogous to the prolongation formulae of generalized symmetries. In addition., a new definition of nonlocal recursion operators was proposed, which gave a satisfactory explaination in covering theory for the integro-differential recursion operators.

Recursion-transform method and potential formulae of the m×n cobweb and fan networks

In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.

A GENERALIZATION OF RECURSION OPERATORSOFDIFFERENTIAL EQUATIONS

Most important recursion operators of differential equations are integro-differential operators. One often runs into difficulties in trying to obtain a full hierarchy of symmetries. The lack of precision sometimes leads to bogus symmetries. In this paper, a generalization of recursion operators is given, which eliminates the problem. Several examples are also given to demonstrate the generalization and the significance of the generalization is shown simultaneously.

On the Use of the Initial Values of Recursions

In this paper we make a study of the use of the iniiai values of a recursion skilfully, so that the count for finding a solution of any recursion will be more simplified. Finally, we give out the "moving forth prineiple" of initial values of a recursion.

用Recursion方法计算晶格声子谱

用Recursion方法计算了体心、面心、金刚石结构晶体的声子谱。计算结果表明了这种方法计算复杂晶格结构谱密度的有效性。 这一工作也为用Recursion方法处理复杂结构无序体系问题提供了准备。

Recursion Operators of Two Supersymmetric Equations

From Lax representations,recursion operators for the supersymmetric KdV and the supersymmetric Kaup-Kupershimdt (SKK) equations are proposed explicitly.Under some special conditions,the recursion operator of the supersymmetric Sawada-Kotera equation can be recovered by the one of the SKK equation.

RENORMALIZATION GROUP RECURSIONS BY VARIATIONAL CUMULANT EXPANSION APPROXIMATION

Renormalization group recursions are obtained by virtue of the variational cumulant expansion method. Good qualitative estimates are obtained for the d=2 square Ising system.

OPTIMAL SCHEME FOR SEQUENTIAL COMPUTATIONS OF F_m(z) INTEGRALS IN AB INITIO CALCULATIONS----COMBINATORY USE OF UPWARD AND DOWNWARD RECURSIONS

The quantitative rules of the transfer and variation of errors,when the Gaussian integral functions F.(z) are evaluated sequentially by recurring,have been expounded.The traditional viewpoint to negate the applicability and reliability of upward recursive formula in principle is amended.An optimal scheme of upward-and downward-joint recursions has been developed for the sequential F(z) computations.No additional accuracy is needed with the fundamental term of recursion because the absolute error of Fn(z) always decreases with the recursive approach.The scheme can be employed in modifying any of existent subprograms for Fn<z> computations.In the case of p-d-f-and g-type Gaussians,combining this method with Schaad's formulas can reduce,at least,the additive operations by a factor 40%;the multiplicative and exponential operations by a factor 60%.

A Review of the Debates on Faculty of Language——A Brief Comment of Recursion-Only Hypothesis

In the scientific study of the faculty of language,M.Hauser,N.Chomsky & T.Fitch have proposed the recursion-only hypothesis in the context of biological evolution,while R.Jackendoff & S.Pinker have put forward a strong refutation---the language-as-adaptation hypothesis.This paper briefly introduces HCF hypothesis,meanwhile examines PJ's critical comment,and finally attempts to comment on both hypothesis with a balanced view.

Carleman Linearization and Systems of Arbitrary Depth Polynomial Recursions

New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polynomial recurrences. Subsequently, the systems of depth-one polynomial recurrence relations are discussed. The corresponding transition matrix is constructed and upper triangularized. Furthermore, the powers of the transition matrix are calculated using the back substitution procedure. The explicit expression for a solution to a broad family of recurrence relations is obtained. We investigate to which recurrences the framework can be applied and construct sufficient conditions for the method to work. It is shown how introduction of auxiliary variables can be used to reduce arbitrary depth systems to the depth-one system of recurrences dealt with earlier. Finally, the limitations of the method are discussed, outlining possible directions for future research.

Recursive recurrent neural network:A novel model for manipulator control with different levels of physical constraints

Manipulators actuate joints to let end effectors to perform precise path tracking tasks.Recurrent neural network which is described by dynamic models with parallel processing capability,is a powerful tool for kinematic control of manipulators.Due to physical limitations and actuation saturation of manipulator joints,the involvement of joint constraints for kinematic control of manipulators is essential and critical.However,current existing manipulator control methods based on recurrent neural networks mainly handle with limited levels of joint angular constraints,and to the best of our knowledge,methods for kinematic control of manipulators with higher order joint constraints based on recurrent neural networks are not yet reported.In this study,for the first time,a novel recursive recurrent network model is proposed to solve the kinematic control issue for manipulators with different levels of physical constraints,and the proposed recursive recurrent neural network can be formulated as a new manifold system to ensure control solution within all of the joint constraints in different orders.The theoretical analysis shows the stability and the purposed recursive recurrent neural network and its convergence to solution.Simulation results further demonstrate the effectiveness of the proposed method in end‐effector path tracking control under different levels of joint constraints based on the Kuka manipulator system.Comparisons with other methods such as the pseudoinverse‐based method and conventional recurrent neural network method substantiate the superiority of the proposed method.

Construction of Recursion Formulas for Lax Pairs of （2＋l）-Dimensionai Equation：Modified Generalized Dispersive Long Wave Equation

In this article, we study the Lax pairs of (2+1)-dimensional equation: the modified generalized dispersive long wave (MGDLW) equation. Based on the well-known binary Darboux transformation, we dig out the recursion formulas of the first part of the Lax pairs. Then by further discussion and doing some revisional work, we make the recursion formulas fit for the second part of Lax pairs. At last, some solutions to the MGDLW equation are worked out by using the recursion formula.