Software defect prediction aims to use measurement data of code and historical defects to predict potential problems,optimize testing resources and defect management.However,current methods face challenges:(1)Coarse-g...Software defect prediction aims to use measurement data of code and historical defects to predict potential problems,optimize testing resources and defect management.However,current methods face challenges:(1)Coarse-grained file level detection cannot accurately locate specific defects.(2)Fine-grained line-level defect prediction methods rely solely on local information of a single line of code,failing to deeply analyze the semantic context of the code line and ignoring the heuristic impact of line-level context on the code line,making it difficult to capture the interaction between global and local information.Therefore,this paper proposes a telecontext-enhanced recursive interactive attention fusion method for line-level defect prediction(TRIA-LineDP).Firstly,using a bidirectional hierarchical attention network to extract semantic features and contextual information from the original code lines as the basis.Then,the extracted contextual information is forwarded to the telecontext capture module to aggregate the global context,thereby enhancing the understanding of broader code dynamics.Finally,a recursive interaction model is used to simulate the interaction between code lines and line-level context,passing information layer by layer to enhance local and global information exchange,thereby achieving accurate defect localization.Experimental results from within-project defect prediction(WPDP)and cross-project defect prediction(CPDP)conducted on nine different projects(encompassing a total of 32 versions)demonstrated that,within the same project,the proposed methods will respectively recall at top 20%of lines of code(Recall@Top20%LOC)and effort at top 20%recall(Effort@Top20%Recall)has increased by 11%–52%and 23%–77%.In different projects,improvements of 9%–60%and 18%–77%have been achieved,which are superior to existing advanced methods and have good detection performance.展开更多
Aeromagnetic compensation is one of the key issues in high-precision geomagnetic fl ight carrier navigation, directly determining the accuracy and reliability of real-time magnetic measurement data. The accurate model...Aeromagnetic compensation is one of the key issues in high-precision geomagnetic fl ight carrier navigation, directly determining the accuracy and reliability of real-time magnetic measurement data. The accurate modeling and compensation of interference magnetic measurements on carriers are of great signifi cance for the construction of reference and real-time maps for geomagnetic navigation. Current research on aeromagnetic compensation algorithms mainly focuses on accurately modeling interference magnetic fields from model- and data-driven perspectives based on measured aeromagnetic data. Challenges in obtaining aeromagnetic data and low information complexity adversely aff ect the generalization performance of a constructed model. To address these issues, a recursive least square algorithm based on elastic weight consolidation is proposed, which eff ectively suppresses the occurrence of catastrophic forgetting by controlling the direction of parameter updates. Experimental verifi cation with publicly available aeromagnetic datasets shows that the proposed algorithm can eff ectively circumvent historical information loss caused by interference magnetic field models during parameter updates and improve the stability, robustness, and accuracy of interference magnetic fi eld models.展开更多
For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observat...For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observation models,and this further degrades filtering accuracy and consistency.Given the flaws of nonlinear iteration,this work incorporates a recursive strategy into generalized M-estimation rather than the iterative strategy.The proposed algorithm extends nonlinear recursion to nonlinear systems using the statistical linear regression method.The recursion allows for the gradual release of observation information and consequently enables the update to proceed along the nonlinear direction.Considering the correlated state and observation noise induced by recursions,a separately reweighting strategy is adopted to build a robust nonlinear system.Analogous to the nonlinear recursion,a robust nonlinear recursive update strategy is proposed,where the associated covariances and the observation noise statistics are updated recursively to ensure the consistency of observation noise statistics,thereby completing the nonlinear solution of the robust system.Compared with the iterative update strategies under non-Gaussian observation noise,the recursive update strategy can facilitate the estimator to achieve higher filtering accuracy,stronger robustness,and better consistency.Therefore,the proposed strategy is more suitable for the robust nonlinear filtering framework.展开更多
Aim To determine the measured profile of a wheel in railway vehicle.Methods So- called piecewise curve-fitting method of the third derivative continuity is employed . Results The formulas of the piecewise curve fittin...Aim To determine the measured profile of a wheel in railway vehicle.Methods So- called piecewise curve-fitting method of the third derivative continuity is employed . Results The formulas of the piecewise curve fitting method were derived the curve-fitting profile of a wheel looks very fine and its first to third derivatives are also smooth.Conclusion The new piecewise curve fitting method is fine enough to fit the measured profile data of a wheel for the purpose of vehicle system dynamic analysis.展开更多
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
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.
Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The gov- erning equations of the mot...Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The gov- erning equations of the motion, when a Lagrangian approach with the present curve-fitting method is applied, can be transformed into an easily solvable form of the system of nonlinear ordinary dif- ferential equations. The applicability of Bezier curves, B-spline, and Lagrange interpolating polyno- mials is investigated. Local Lagrange interpolating polynomials with a shift operator are proposed as the best selection for applications, since it provides superior system characteristics with minimum computing time, compared to other methods. In addition, the Gauss quadrature formula with local refinement strategy has been developed for an accurate prediction of the induced velocity computed with the line integration of the Biot-Savart law. Rotary-wing problems including a vortex ring problem are analyzed to show the efficiency, accuracy, and flexibility in the applications of the pro- posed method.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
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
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 Lapla...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.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
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 ...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.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
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
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
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
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
基金supported by National Natural Science Foundation of China(no.62376240).
文摘Software defect prediction aims to use measurement data of code and historical defects to predict potential problems,optimize testing resources and defect management.However,current methods face challenges:(1)Coarse-grained file level detection cannot accurately locate specific defects.(2)Fine-grained line-level defect prediction methods rely solely on local information of a single line of code,failing to deeply analyze the semantic context of the code line and ignoring the heuristic impact of line-level context on the code line,making it difficult to capture the interaction between global and local information.Therefore,this paper proposes a telecontext-enhanced recursive interactive attention fusion method for line-level defect prediction(TRIA-LineDP).Firstly,using a bidirectional hierarchical attention network to extract semantic features and contextual information from the original code lines as the basis.Then,the extracted contextual information is forwarded to the telecontext capture module to aggregate the global context,thereby enhancing the understanding of broader code dynamics.Finally,a recursive interaction model is used to simulate the interaction between code lines and line-level context,passing information layer by layer to enhance local and global information exchange,thereby achieving accurate defect localization.Experimental results from within-project defect prediction(WPDP)and cross-project defect prediction(CPDP)conducted on nine different projects(encompassing a total of 32 versions)demonstrated that,within the same project,the proposed methods will respectively recall at top 20%of lines of code(Recall@Top20%LOC)and effort at top 20%recall(Effort@Top20%Recall)has increased by 11%–52%and 23%–77%.In different projects,improvements of 9%–60%and 18%–77%have been achieved,which are superior to existing advanced methods and have good detection performance.
基金supported by the National Natural Science Foundation of China under Grant 61673017in part by the Science and Technology Department of Shaanxi Province under Grant 2024JC-YBQN-0657。
文摘Aeromagnetic compensation is one of the key issues in high-precision geomagnetic fl ight carrier navigation, directly determining the accuracy and reliability of real-time magnetic measurement data. The accurate modeling and compensation of interference magnetic measurements on carriers are of great signifi cance for the construction of reference and real-time maps for geomagnetic navigation. Current research on aeromagnetic compensation algorithms mainly focuses on accurately modeling interference magnetic fields from model- and data-driven perspectives based on measured aeromagnetic data. Challenges in obtaining aeromagnetic data and low information complexity adversely aff ect the generalization performance of a constructed model. To address these issues, a recursive least square algorithm based on elastic weight consolidation is proposed, which eff ectively suppresses the occurrence of catastrophic forgetting by controlling the direction of parameter updates. Experimental verifi cation with publicly available aeromagnetic datasets shows that the proposed algorithm can eff ectively circumvent historical information loss caused by interference magnetic field models during parameter updates and improve the stability, robustness, and accuracy of interference magnetic fi eld models.
基金co-supported by the National Natural Science Foundation of China(No.62303246,No.62103204)the China Postdoctoral Science Foundation(No.2023M731788)。
文摘For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observation models,and this further degrades filtering accuracy and consistency.Given the flaws of nonlinear iteration,this work incorporates a recursive strategy into generalized M-estimation rather than the iterative strategy.The proposed algorithm extends nonlinear recursion to nonlinear systems using the statistical linear regression method.The recursion allows for the gradual release of observation information and consequently enables the update to proceed along the nonlinear direction.Considering the correlated state and observation noise induced by recursions,a separately reweighting strategy is adopted to build a robust nonlinear system.Analogous to the nonlinear recursion,a robust nonlinear recursive update strategy is proposed,where the associated covariances and the observation noise statistics are updated recursively to ensure the consistency of observation noise statistics,thereby completing the nonlinear solution of the robust system.Compared with the iterative update strategies under non-Gaussian observation noise,the recursive update strategy can facilitate the estimator to achieve higher filtering accuracy,stronger robustness,and better consistency.Therefore,the proposed strategy is more suitable for the robust nonlinear filtering framework.
文摘Aim To determine the measured profile of a wheel in railway vehicle.Methods So- called piecewise curve-fitting method of the third derivative continuity is employed . Results The formulas of the piecewise curve fitting method were derived the curve-fitting profile of a wheel looks very fine and its first to third derivatives are also smooth.Conclusion The new piecewise curve fitting method is fine enough to fit the measured profile data of a wheel for the purpose of vehicle system dynamic analysis.
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 EDISON Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Science,ICT and Future Planning(No.2011-0020560)
文摘Applications of a novel curve-fitting technique are presented to efficiently predict the motion of the vortex filament, which is trailed from a rigid body such as wings and rotors. The gov- erning equations of the motion, when a Lagrangian approach with the present curve-fitting method is applied, can be transformed into an easily solvable form of the system of nonlinear ordinary dif- ferential equations. The applicability of Bezier curves, B-spline, and Lagrange interpolating polyno- mials is investigated. Local Lagrange interpolating polynomials with a shift operator are proposed as the best selection for applications, since it provides superior system characteristics with minimum computing time, compared to other methods. In addition, the Gauss quadrature formula with local refinement strategy has been developed for an accurate prediction of the induced velocity computed with the line integration of the Biot-Savart law. Rotary-wing problems including a vortex ring problem are analyzed to show the efficiency, accuracy, and flexibility in the applications of the pro- posed method.
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.
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.
基金Project supported by the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20161278)
文摘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.
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.
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.
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.
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.
