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 covarian...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.展开更多
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...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.展开更多
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 nonline...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.展开更多
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.
It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy.The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of ...It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy.The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived.展开更多
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...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.展开更多
Recursion by herbivores is the repeated use of the same site or plants. Recursion by wild animals is rarely investigated but may be ubiquitous. Optimal foraging theory predicts site recursion as a function of the qual...Recursion by herbivores is the repeated use of the same site or plants. Recursion by wild animals is rarely investigated but may be ubiquitous. Optimal foraging theory predicts site recursion as a function of the quality of the site, extent of its last use, and time since its last use because these influence site resource status and recovery. We used GPS collars, behaviour and site sampling to investigate recursion to foraging sites for two elephant Elephas maximus borneensis herds in the Lower Kinabatangan Wildlife Sanctuary, Borneo, over a 12 month period. Recursion occurred to 48 out of 87 foraging sites and was most common within 48 hours or between 151-250 days, indicating two different types ofrecursion. Recursion was more likely to occur if the site had previously been occupied for longer. Moreover, the time spent at a site at recursion was the same as the time spent at the site on the first occasion. The number of days that had passed between the first visit and recursion was also positively correlated with how much time was spent at the site at recursion. Habitat type also influenced the intensity of site-use, with more time spent at recursion within riverine/open grass areas along forest margins compared to other habitat types. Recursion is a common behaviour used by the elephants and its pattern suggests it may be a foraging strategy for revisiting areas of greater value. The qualities of recursion sites might usefully be incorporated into landscape management strategies for elephant conservation in the area [Current Zoology 60 （4）： 551-559, 2014].展开更多
The AFLT states|PY1,Y2has reflection symmetry,Sn|PY1,Y2=|PY2,Y2,nb=2P,where S is the screening charge.AFLT state can be constructed using this reflect symmetry.We propose a recursion formula for this construction.The ...The AFLT states|PY1,Y2has reflection symmetry,Sn|PY1,Y2=|PY2,Y2,nb=2P,where S is the screening charge.AFLT state can be constructed using this reflect symmetry.We propose a recursion formula for this construction.The recursion formula is factorized completely.展开更多
The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work...The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work,the hidden Virasoro structure in the CS model is much explored.In particular,we found that the Virasoro singular vectors form a skew hierarchy in the CS model.Literally,skew is analogous to coset,but here specifically refer to the operation on the Young tableaux.In fact,based on the construction of the Virasoro singular vectors,this hierarchical structure can be used to give a complete construction of the CS states,i.e.the Jack symmetric functions,recursively.The construction is given both in operator formalism as well as in integral representation.This new integral representation for the Jack symmetric functions may shed some insights on the spectrum constructions for the other integrable systems.展开更多
In this article, we study the Lax pairs of -dimensional equation: the modified generalized dispersive long wave (MGDLW) equation. Based on the well-known binary Darboux transformation, we dig out the recursion formula...In this article, we study the Lax pairs of -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.展开更多
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 op...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.展开更多
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 super...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.展开更多
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 ad...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.展开更多
Though the Bǎcklund transformation on time-like surfaces with constant mean curvature surfaces in R^2,1 has been obtained, it is not easy to obtain corresponding surfaces because the procedure of solving the related ...Though the Bǎcklund transformation on time-like surfaces with constant mean curvature surfaces in R^2,1 has been obtained, it is not easy to obtain corresponding surfaces because the procedure of solving the related integrable system cannot be avoided when the Bǎcklund transformation is used, For sake of this, in this article, some special work is done to reform the Bǎcklund transformation to a recursion formula, by which we can construct time-like surfaces with constant mean curvature form known ones just by quadrature procedure.展开更多
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 lea...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.展开更多
In this paper, a further investigation for the number of Derangements and Bell numbers is performed, and some new recursion formulae for the number of Derangements and Bell numbers are established by applying the gene...In this paper, a further investigation for the number of Derangements and Bell numbers is performed, and some new recursion formulae for the number of Derangements and Bell numbers are established by applying the generating function methods and Pade approximation techniques. Illustrative special cases of the main results are also presented.展开更多
Based on the corresponding theorem between dispersionless KP （dKP） hierarchy and h-dependent KP （hKP） hierarchy, a general formal representation of the recursion operators for dKP hierarchy under n-reduction is gi...Based on the corresponding theorem between dispersionless KP （dKP） hierarchy and h-dependent KP （hKP） hierarchy, a general formal representation of the recursion operators for dKP hierarchy under n-reduction is given in a systematical way from the corresponding hKP hierarchy. To illustrate this method, the recursion operators for dKP hierarchy under 2-reduction and 3-reduction are calculated in detail.展开更多
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 applicabili...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%.展开更多
In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compu...In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values.展开更多
文摘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.
基金ItemSponsored by Provincial Natural Science Foundation of Hebei Province of China (E2004000206)
文摘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.
基金Supported by the National Natural Science Foundation of China(62262031)Science and Technology Key Project of Education Department of Jiangxi Province(GJJ2200302,GJJ210307)the Graduate Innovative Special Fund Projects of Jiangxi Province(YJS2022064)
文摘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.
基金NSFC (10671187 10971109)the Program for NCET (NECT-08-0515)
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11271210 and 11201451Anhui Province Natural Science Foundation under Grant No.1608085MA04
文摘It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy.The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived.
文摘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.
文摘Recursion by herbivores is the repeated use of the same site or plants. Recursion by wild animals is rarely investigated but may be ubiquitous. Optimal foraging theory predicts site recursion as a function of the quality of the site, extent of its last use, and time since its last use because these influence site resource status and recovery. We used GPS collars, behaviour and site sampling to investigate recursion to foraging sites for two elephant Elephas maximus borneensis herds in the Lower Kinabatangan Wildlife Sanctuary, Borneo, over a 12 month period. Recursion occurred to 48 out of 87 foraging sites and was most common within 48 hours or between 151-250 days, indicating two different types ofrecursion. Recursion was more likely to occur if the site had previously been occupied for longer. Moreover, the time spent at a site at recursion was the same as the time spent at the site on the first occasion. The number of days that had passed between the first visit and recursion was also positively correlated with how much time was spent at the site at recursion. Habitat type also influenced the intensity of site-use, with more time spent at recursion within riverine/open grass areas along forest margins compared to other habitat types. Recursion is a common behaviour used by the elephants and its pattern suggests it may be a foraging strategy for revisiting areas of greater value. The qualities of recursion sites might usefully be incorporated into landscape management strategies for elephant conservation in the area [Current Zoology 60 （4）： 551-559, 2014].
基金Supported by Program "Frontier Topics in Mathematical Physics"(KJCX3-SYW-S03)National Natural Science Foundation of China under Grant No.11035008
文摘The AFLT states|PY1,Y2has reflection symmetry,Sn|PY1,Y2=|PY2,Y2,nb=2P,where S is the screening charge.AFLT state can be constructed using this reflect symmetry.We propose a recursion formula for this construction.The recursion formula is factorized completely.
基金Supported by the Chinese Academy of Sciences Program "Frontier Topics in Mathematical Physics" (KJCX3-SYW-S03)Supported Partially by the National Natural Science Foundation of China under Grant No.11035008
文摘The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work,the hidden Virasoro structure in the CS model is much explored.In particular,we found that the Virasoro singular vectors form a skew hierarchy in the CS model.Literally,skew is analogous to coset,but here specifically refer to the operation on the Young tableaux.In fact,based on the construction of the Virasoro singular vectors,this hierarchical structure can be used to give a complete construction of the CS states,i.e.the Jack symmetric functions,recursively.The construction is given both in operator formalism as well as in integral representation.This new integral representation for the Jack symmetric functions may shed some insights on the spectrum constructions for the other integrable systems.
基金The project supported by National Natural Science Foundation of China under Grant No.10101025
文摘In this article, we study the Lax pairs of -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.
文摘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.
基金Supported by Zhejiang Provincial Natural Science Foundations of China under Grant No.Y6090592National Natural Science Foundation of China under Grant Nos.10735030 and 11041003+1 种基金Ningbo Natural Science Foundation under Grant Nos.2009B21003,2010A610103 and 2009B21003K.C.Wong Magna Fund in Ningbo University
文摘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.
文摘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.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10571149, 10571165, and 10101025 We are grateful to Sha Nan-Shi and Zhang Wen-Jing, who are both students in Department of Statistics and Finance, University of Science and Technology of China, for their valuable and creative ideas in stimulating discussions as well as conscientious work of computing.
文摘Though the Bǎcklund transformation on time-like surfaces with constant mean curvature surfaces in R^2,1 has been obtained, it is not easy to obtain corresponding surfaces because the procedure of solving the related integrable system cannot be avoided when the Bǎcklund transformation is used, For sake of this, in this article, some special work is done to reform the Bǎcklund transformation to a recursion formula, by which we can construct time-like surfaces with constant mean curvature form known ones just by quadrature procedure.
文摘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.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1132605011071194)the Foundation for Fostering Talents in Kunming University of Science and Technology(Grant No.KKSY201307047)
文摘In this paper, a further investigation for the number of Derangements and Bell numbers is performed, and some new recursion formulae for the number of Derangements and Bell numbers are established by applying the generating function methods and Pade approximation techniques. Illustrative special cases of the main results are also presented.
基金Supported by the Natural Science Foundation of China under Grant No.10971109
文摘Based on the corresponding theorem between dispersionless KP （dKP） hierarchy and h-dependent KP （hKP） hierarchy, a general formal representation of the recursion operators for dKP hierarchy under n-reduction is given in a systematical way from the corresponding hKP hierarchy. To illustrate this method, the recursion operators for dKP hierarchy under 2-reduction and 3-reduction are calculated in detail.
文摘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%.
文摘In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values.
