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.

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.

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。

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.

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.

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%.

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.

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.

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.

Nonlinear Program Construction and Verification Method Based on Partition Recursion and Morgan's Refinement Rules

The traditional program refinement strategy cannot be refined to an executable program,and there are issues such as low verification reliability and automation.To solve the above problems,this paper proposes a nonlinear program construction and verification method based on partition recursion and Morgan’s refinement rules.First,we use recursive definition technique to characterize the initial specification.The specification is then transformed into GCL(Guarded Command Language)programs using loop invariant derivation and Morgan’s refinement rules.Furthermore,VCG(Verification Condition Generator)is used in the GCL program to generate the verification condition automatically.The Isabelle theorem prover then validates the GCL program’s correctness.Finally,the GCL code generates a C++executable program automatically via the conversion system.The effectiveness of this method is demonstrated using binary tree preorder traversal program construction and verification as an example.This method addresses the problem that the construction process’s loop invariant is difficult to obtain and the refinement process is insufficiently detailed.At the same time,the method improves verification process automation and reduces the manual verification workload.

Optical recursional binormal optical visco Landau-Lifshitz electromagnetic optical density

In this manuscript,we study a new version of the optical recursional binormal microbeam model for a flexible binormal microscale beam in terms of a binormal normalized operator.Also,we give new explanations for the optical recursional visco Landau-Lifshitz binormal electromagnetic binormal microscale beam.Finally,we obtain an optical application for the normalized visco Landau-Lifshitz electromagnetic binormal optimistic density with an optical binormal resonator.

Distributed Dynamic Load in Structural Dynamics by the Impulse-Based Force Estimation Algorithm

This paper proposes a novel approach for identifying distributed dynamic loads in the time domain.Using polynomial andmodal analysis,the load is transformed intomodal space for coefficient identification.This allows the distributed dynamic load with a two-dimensional form in terms of time and space to be simultaneously identified in the form of modal force,thereby achieving dimensionality reduction.The Impulse-based Force Estimation Algorithm is proposed to identify dynamic loads in the time domain.Firstly,the algorithm establishes a recursion scheme based on convolution integral,enabling it to identify loads with a long history and rapidly changing forms over time.Secondly,the algorithm introduces moving mean and polynomial fitting to detrend,enhancing its applicability in load estimation.The aforementioned methodology successfully accomplishes the reconstruction of distributed,instead of centralized,dynamic loads on the continuum in the time domain by utilizing acceleration response.To validate the effectiveness of the method,computational and experimental verification were conducted.

Recursion Relations for the Constrained Multi-component KP Hierarchy

In this paper, we define a new constrained multi-component KP （cMKP） hierarchy which contains the constrained KP （cKP） hierarchy as a special case. We derive the recursion operator of the constrained multi-component KP hierarchy. As a special example, we also give the recursion operator of the constrained two-component KP hierarchy.

Topological Recursion Relations from Pixton Relations

We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher genera. As an application, some results about reconstruction of Gromov–Witten invariants can be derived.

An introduction to on-shell recursion relations

This article provides an introduction to on-shell recursion relations for calculations of tree-level amplitudes. Starting with the basics, such as spinor notations and color decompositions, we ex- pose analytic properties of gauge-boson amplitudes, BCFW-deformations, the large z-behavior of amplitudes, and on-shell recursion relations of gluons. We discuss further developments of on-shell recursion relations, including generalization to other quantum field theories, supersymmetric theo- ties in particular, recursion relations for off-shell currents, recursion relation with nonzero boundary contributions, bonus relations, relations for rational parts of one-loop amplitudes, recursion relations in 3D and a proof of CSW rules. Finally, we present samples of applications, including solutions of split helicity amplitudes and of Af = 4 SYM theories, consequences of consistent conditions under re- cursion relation, Kleiss-Kuijf （KK） and Bern-Carrasco-Johansson （BCJ） relations for color-ordered gluon tree amplitudes, Kawai-Lewellen-Tye （KLT） relations.

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.

Identification of time-varying system and energy-based optimization of adaptive control in seismically excited structure

The combination of structural health monitoring and vibration control is of great importance to provide components of smart structures.While synthetic algorithms have been proposed,adaptive control that is compatible with changing conditions still needs to be used,and time-varying systems are required to be simultaneously estimated with the application of adaptive control.In this research,the identification of structural time-varying dynamic characteristics and optimized simple adaptive control are integrated.First,reduced variations of physical parameters are estimated online using the multiple forgetting factor recursive least squares(MFRLS)method.Then,the energy from the structural vibration is simultaneously specified to optimize the control force with the identified parameters to be operational.Optimization is also performed based on the probability density function of the energy under the seismic excitation at any time.Finally,the optimal control force is obtained by the simple adaptive control(SAC)algorithm and energy coefficient.A numerical example and benchmark structure are employed to investigate the efficiency of the proposed approach.The simulation results revealed the effectiveness of the integrated online identification and optimal adaptive control in systems.

Control method based on DRFNN sliding mode for multifunctional flexible multistate switch

To address the low accuracy and stability when applying classical control theory in distribution networks with distributed generation,a control method involving flexible multistate switches(FMSs)is proposed in this study.This approach is based on an improved double-loop recursive fuzzy neural network(DRFNN)sliding mode,which is intended to stably achieve multiterminal power interaction and adaptive arc suppression for single-phase ground faults.First,an improved DRFNN sliding mode control(SMC)method is proposed to overcome the chattering and transient overshoot inherent in the classical SMC and reduce the reliance on a precise mathematical model of the control system.To improve the robustness of the system,an adaptive parameter-adjustment strategy for the DRFNN is designed,where its dynamic mapping capabilities are leveraged to improve the transient compensation control.Additionally,a quasi-continuous second-order sliding mode controller with a calculus-driven sliding mode surface is developed to improve the current monitoring accuracy and enhance the system stability.The stability of the proposed method and the convergence of the network parameters are verified using the Lyapunov theorem.A simulation model of the three-port FMS with its control system is constructed in MATLAB/Simulink.The simulation result confirms the feasibility and effectiveness of the proposed control strategy based on a comparative analysis.