Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using t...Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.展开更多
The sets of Minkowski algebraic sum and geometric difference are considered. The purpose of the research in this paper is to apply the properties of Minkowski sum and geometric difference to fractional differential ga...The sets of Minkowski algebraic sum and geometric difference are considered. The purpose of the research in this paper is to apply the properties of Minkowski sum and geometric difference to fractional differential games. This paper investigates the geometric properties of the Minkowski algebraic sum and the geometric difference of sets. Various examples are considered that calculate the geometric differences of sets. The results of the research are presented and proved as a theorem. At the end of the article, the results were applied to fractional differential games.展开更多
We find a lower bound for the essential norm of the difference of two composition operators acting on H 2(BN ) or As2 (BN ) (s 1). This result plays an important role in proving a necessary and sufficient condit...We find a lower bound for the essential norm of the difference of two composition operators acting on H 2(BN ) or As2 (BN ) (s 1). This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005.展开更多
In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf(z) be a nonconstant entire function of ...In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf(z) be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f(z), f(z+c), and △n cf(z) share 0 CM, then f(z+c)≡Af(z), where A(≠0) is a complex constant. Moreover, let a(z), b(z)( O) ∈ S(f) be periodic entire functions with period c and if f(z) - a(z), f(z + c) - a(z), △cn f(z) - b(z) share 0 CM, then f(z + c) ≡ f(z).展开更多
In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar ([17]) defined the Euler spaces of m-th order difference sequences e r 0 (△ ( m ) ), e r c (△ (...In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar ([17]) defined the Euler spaces of m-th order difference sequences e r 0 (△ ( m ) ), e r c (△ ( m ) ) and e r ∞ (△ ( m ) ) and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.展开更多
Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are...Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.展开更多
In this paper, some sufficient and necessary conditions are established for the oscillatory of solutions for nonlinear functional difference equations, which extend and improve some corresponding results obtained and ...In this paper, some sufficient and necessary conditions are established for the oscillatory of solutions for nonlinear functional difference equations, which extend and improve some corresponding results obtained and are discrete analogues of the corresponding results for the continuous version.展开更多
In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green fun...In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.展开更多
This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave fo...This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.展开更多
Highly accurate spatial discretization is essentially required to perform numerical climate and weather prediction. The difference between the differential and the finite-difference operator is however a primitive err...Highly accurate spatial discretization is essentially required to perform numerical climate and weather prediction. The difference between the differential and the finite-difference operator is however a primitive error source in the numerics. This paper presents an optimization of centered finite-difference operator based on the principle of constrained cost function, which can reduce the truncation error to minimum. In the optimization point of view, such optimal operator is in fact an attempt to minimize spatial truncation er-rors in atmospheric modeling, in a simple way and indeed a quite innovative way to implement Variational Continuous Assimilation (VCA) technique. Furthermore, the optimizing difference operator is consciously designed to be meshing-independent, so that it can be used for most Arakawa-mesh configurations, such as un-staggered (Arakawa-A) or com-monly staggered (Arakawa-B, Arakawa-C, Arakawa-D) mesh. But for the calibration purpose, the pro-posed operator is implemented on an un-staggered mesh in which the truncation oscillation is mostly ex-cited, and it thus makes a severe and indeed a benchmark test for the proposed optimal scheme. Both theo-retical investigation and practical modeling indicate that the aforementioned numerical noise can be significantly eliminated.展开更多
In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014(2014), Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G (u, v; A) over the sequence space e1....In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014(2014), Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G (u, v; A) over the sequence space e1. The product operator G (u, v; △) over l1 is defined by (G(u,v;△)x)k=^k∑i=0ukvi(xi- xi-1) with xk = 0 for all k 〈 0, where x = (xk)∈e1,and u and v axe either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G (u, v; △) on the sequence space gl.展开更多
This paper proceeds the papers [3] [4], we make use of the idea of the variable ,number operators and some concepts and conclusions of the shifting operators serieswith variable coefficients in the operational field o...This paper proceeds the papers [3] [4], we make use of the idea of the variable ,number operators and some concepts and conclusions of the shifting operators serieswith variable coefficients in the operational field of Mikusinski, it is devoted to thesolution of the general three-order linear difference equation with variable,coefficients,and it is also devoted to the better solution .formula for the some special three-orderlinear difference equations with variable coefficients, in addition, we try to provide theidea and method for realizing solution of the more than three-order linear differenceequation with variable coefficients.展开更多
Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of...Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th(1<p<2)moments.Moreover,the complete convergence and strong law of large numbers are established under some mild conditions.An application to multivariate simple linear regression model is also provided.展开更多
For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation r...For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L 2 norm are derived to determine the error, in the approximate solution.展开更多
Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are ob...Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are obtained.展开更多
The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ...The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ability of the discrete forms expressing to the element functions was talked about. In discrete operator difference method, the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not. According to this point, discrete operator difference method is a method with good performance.展开更多
This paper presents a simple method of forming sum and difference patterns with adaptivenulls. The effects on the sidelobe level and the pointing null of difference pattern by adaptive null areanalyzed. The result tha...This paper presents a simple method of forming sum and difference patterns with adaptivenulls. The effects on the sidelobe level and the pointing null of difference pattern by adaptive null areanalyzed. The result that the increment value of the envelope of the sidelobe level under the effect ofa null is less than l.6dB is proved. The formula about shift value of the pointing null which is thefunction of the jammer direction and array parameters is given in the paper.展开更多
In the present paper, a new difference matrix via difference operator D is introduced. Let x = (xk) be a sequence of real numbers, then the difference operatorD is defined by D(x)n =∑kn=0(-1)k(n-kn)xk,where ...In the present paper, a new difference matrix via difference operator D is introduced. Let x = (xk) be a sequence of real numbers, then the difference operatorD is defined by D(x)n =∑kn=0(-1)k(n-kn)xk,where n = 0,1,2,3,.... Several interestingproperties of the new operator D are discussed.展开更多
In this paper, we investigate a two electronic level system with vibrational modes coupled to a Brownian oscillator bath. The difference frequency generation (DFG) signals and sum frequency generation (SFG) signal...In this paper, we investigate a two electronic level system with vibrational modes coupled to a Brownian oscillator bath. The difference frequency generation (DFG) signals and sum frequency generation (SFG) signals are calculated. It is shown that, for the same model, the SFG signals are more sensitive than the DFG signals to the changes of the vibrational modes of the electronic two-level system. Because the SFG conversion efficiency can be improved by using the time-delay method, the findings in this paper predict that the SFG spectrum may probe the changes of the microstructure more effectively.展开更多
In this study, we use analytical methods and Sylvester inertia theorem to research a class of second order difference operators with indefinite weights and coupled boundary conditions. The eigenvalue problem with sign...In this study, we use analytical methods and Sylvester inertia theorem to research a class of second order difference operators with indefinite weights and coupled boundary conditions. The eigenvalue problem with sign-changing weight has lasted a long time. The number of eigenvalues and the number of sign changes of the corresponding eigenfunctions of discrete equations under different boundary conditions are mainly studied. For the discrete Sturm-Liouville problems, similar conclusions about the properties of eigenvalues and the number of sign changes of the corresponding eigenfunctions are obtained under different boundary conditions, such as periodic boundary conditions, antiperiodic boundary conditions and separated boundary conditions etc. The purpose of this paper is to extend the similar conclusion to the coupled boundary conditions, which is of great significance to the perfection of the theory of the discrete Sturm-Liouville problems. We came to the following conclusions: first, the eigenvalues of the problem are real and single, the number of the positive eigenvalues is equal to the number of positive elements in the weight function, and the number of negative eigenvalues is equal to the number of negative elements in the weight function. Second, under some conditions, we obtain the sign change of the eigenfunction corresponding to the j-th positive/negative eigenvalue.展开更多
基金This work was financially supported by the Key Science and Technology Project of Longmen Laboratory(No.LMYLKT-001)Innovation and Entrepreneurship Training Program for College Students of Henan Province(No.202310464050)。
文摘Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.
文摘The sets of Minkowski algebraic sum and geometric difference are considered. The purpose of the research in this paper is to apply the properties of Minkowski sum and geometric difference to fractional differential games. This paper investigates the geometric properties of the Minkowski algebraic sum and the geometric difference of sets. Various examples are considered that calculate the geometric differences of sets. The results of the research are presented and proved as a theorem. At the end of the article, the results were applied to fractional differential games.
基金Supported by the National Natural Science Foundation of China (10971219)Shanghai Education Research and Innovation Project (10YZ185)Shanghai University Research Special Foundation for Outstanding Young Teachers (sjr09015)
文摘We find a lower bound for the essential norm of the difference of two composition operators acting on H 2(BN ) or As2 (BN ) (s 1). This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005.
基金supported by the Natural Science Foundation of Guangdong Province in China(2014A030313422,2016A030310106,2016A030313745)
文摘In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf(z) be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f(z), f(z+c), and △n cf(z) share 0 CM, then f(z+c)≡Af(z), where A(≠0) is a complex constant. Moreover, let a(z), b(z)( O) ∈ S(f) be periodic entire functions with period c and if f(z) - a(z), f(z + c) - a(z), △cn f(z) - b(z) share 0 CM, then f(z + c) ≡ f(z).
基金supported by the research project#144003 of the Serbian Ministry of Science, Technology and Development
文摘In the past, several authors studied spaces of m-th order difference sequences, among them, H.Polat and F.Basar ([17]) defined the Euler spaces of m-th order difference sequences e r 0 (△ ( m ) ), e r c (△ ( m ) ) and e r ∞ (△ ( m ) ) and characterized some classes of matrix transformations on them. In our paper, we add a new supplementary aspect to their research by characterizing classes of compact operators on those spaces. For that purpose, the spaces are treated as the matrix domains of a triangle in the classical sequence spaces c 0 , c and ∞ . The main tool for our characterizations is the Hausdorff measure of noncompactness.
文摘Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.
基金Supported by the Nature Science Foundation of Jining(JB10)
文摘In this paper, some sufficient and necessary conditions are established for the oscillatory of solutions for nonlinear functional difference equations, which extend and improve some corresponding results obtained and are discrete analogues of the corresponding results for the continuous version.
文摘In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.
基金supported by the National Natural Science Foundation of China(Nos.51239008 and 51279130)
文摘This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.
基金We acknowledge the anonymous reviewers for their helpful comments and criticism on an earlier manuscript.The authors are indebted to the supports from the National Natural Science Foundation of China under Grant Nos.40175025and 40028504the State key Bas
文摘Highly accurate spatial discretization is essentially required to perform numerical climate and weather prediction. The difference between the differential and the finite-difference operator is however a primitive error source in the numerics. This paper presents an optimization of centered finite-difference operator based on the principle of constrained cost function, which can reduce the truncation error to minimum. In the optimization point of view, such optimal operator is in fact an attempt to minimize spatial truncation er-rors in atmospheric modeling, in a simple way and indeed a quite innovative way to implement Variational Continuous Assimilation (VCA) technique. Furthermore, the optimizing difference operator is consciously designed to be meshing-independent, so that it can be used for most Arakawa-mesh configurations, such as un-staggered (Arakawa-A) or com-monly staggered (Arakawa-B, Arakawa-C, Arakawa-D) mesh. But for the calibration purpose, the pro-posed operator is implemented on an un-staggered mesh in which the truncation oscillation is mostly ex-cited, and it thus makes a severe and indeed a benchmark test for the proposed optimal scheme. Both theo-retical investigation and practical modeling indicate that the aforementioned numerical noise can be significantly eliminated.
文摘In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014(2014), Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G (u, v; A) over the sequence space e1. The product operator G (u, v; △) over l1 is defined by (G(u,v;△)x)k=^k∑i=0ukvi(xi- xi-1) with xk = 0 for all k 〈 0, where x = (xk)∈e1,and u and v axe either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G (u, v; △) on the sequence space gl.
文摘This paper proceeds the papers [3] [4], we make use of the idea of the variable ,number operators and some concepts and conclusions of the shifting operators serieswith variable coefficients in the operational field of Mikusinski, it is devoted to thesolution of the general three-order linear difference equation with variable,coefficients,and it is also devoted to the better solution .formula for the some special three-orderlinear difference equations with variable coefficients, in addition, we try to provide theidea and method for realizing solution of the more than three-order linear differenceequation with variable coefficients.
基金Supported by the Outstanding Youth Research Project of Anhui Colleges(Grant No.2022AH030156)。
文摘Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th(1<p<2)moments.Moreover,the complete convergence and strong law of large numbers are established under some mild conditions.An application to multivariate simple linear regression model is also provided.
基金the Major State Basic Research Program of China(19990328)NNSF of China(19871051,19972039) the Doctorate Foundation of the State Education Commission
文摘For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L 2 norm are derived to determine the error, in the approximate solution.
基金SupportedbytheNationalNaturalScienceFoundationofChina (No .10 0 710 5 8)and (No .10 0 710 19)
文摘Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are obtained.
文摘The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ability of the discrete forms expressing to the element functions was talked about. In discrete operator difference method, the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not. According to this point, discrete operator difference method is a method with good performance.
文摘This paper presents a simple method of forming sum and difference patterns with adaptivenulls. The effects on the sidelobe level and the pointing null of difference pattern by adaptive null areanalyzed. The result that the increment value of the envelope of the sidelobe level under the effect ofa null is less than l.6dB is proved. The formula about shift value of the pointing null which is thefunction of the jammer direction and array parameters is given in the paper.
文摘In the present paper, a new difference matrix via difference operator D is introduced. Let x = (xk) be a sequence of real numbers, then the difference operatorD is defined by D(x)n =∑kn=0(-1)k(n-kn)xk,where n = 0,1,2,3,.... Several interestingproperties of the new operator D are discussed.
基金Supported by the National Natural Science Foundation of China under Grant No. 61078065, Natural Science Foundation of Ningbo City under Grant No. 2008A61009, and K.C. Wong Magna Foundation in Ningbo University
文摘In this paper, we investigate a two electronic level system with vibrational modes coupled to a Brownian oscillator bath. The difference frequency generation (DFG) signals and sum frequency generation (SFG) signals are calculated. It is shown that, for the same model, the SFG signals are more sensitive than the DFG signals to the changes of the vibrational modes of the electronic two-level system. Because the SFG conversion efficiency can be improved by using the time-delay method, the findings in this paper predict that the SFG spectrum may probe the changes of the microstructure more effectively.
文摘In this study, we use analytical methods and Sylvester inertia theorem to research a class of second order difference operators with indefinite weights and coupled boundary conditions. The eigenvalue problem with sign-changing weight has lasted a long time. The number of eigenvalues and the number of sign changes of the corresponding eigenfunctions of discrete equations under different boundary conditions are mainly studied. For the discrete Sturm-Liouville problems, similar conclusions about the properties of eigenvalues and the number of sign changes of the corresponding eigenfunctions are obtained under different boundary conditions, such as periodic boundary conditions, antiperiodic boundary conditions and separated boundary conditions etc. The purpose of this paper is to extend the similar conclusion to the coupled boundary conditions, which is of great significance to the perfection of the theory of the discrete Sturm-Liouville problems. We came to the following conclusions: first, the eigenvalues of the problem are real and single, the number of the positive eigenvalues is equal to the number of positive elements in the weight function, and the number of negative eigenvalues is equal to the number of negative elements in the weight function. Second, under some conditions, we obtain the sign change of the eigenfunction corresponding to the j-th positive/negative eigenvalue.