In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems a...In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained.展开更多
This paper is concerned with the oscillation of nonlinear partial difference equations with continuous variables and the corresponding dual equations. Several sufficientconditions are obtained for the oscillation of t...This paper is concerned with the oscillation of nonlinear partial difference equations with continuous variables and the corresponding dual equations. Several sufficientconditions are obtained for the oscillation of these equations.展开更多
This paper is concerned with a class of partial difference equations with variable coefficients. Explicit growth bounds are found for their solutions. These bounds provide information on the existence of exponentially...This paper is concerned with a class of partial difference equations with variable coefficients. Explicit growth bounds are found for their solutions. These bounds provide information on the existence of exponentially bounded solutions.展开更多
This paper focuses on linear-quadratic(LQ)optimal control for a class of systems governed by first-order hyperbolic partial differential equations(PDEs).Different from most of the previous works,an approach of discret...This paper focuses on linear-quadratic(LQ)optimal control for a class of systems governed by first-order hyperbolic partial differential equations(PDEs).Different from most of the previous works,an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems.The contributions of this paper consist of the following aspects:(1)The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method.(2)A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed.Meanwhile,the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations(FBPDEs).(3)The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented.It is shown that the proposed results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case,but also support the existing operator results and give a more convenient form of computation.展开更多
The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are establi...The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.展开更多
A key problem in gravity dam design is providing enough stability to prevent slide, and the difficulty increases if there are several weak structural planes in the dam foundation. Overload and material weakening were ...A key problem in gravity dam design is providing enough stability to prevent slide, and the difficulty increases if there are several weak structural planes in the dam foundation. Overload and material weakening were taken into account, and a .finite difference strength reserve method with partial safety factors based on the reliability method was developed and used to study the anti-slide stability of a concrete gravity dam on a complicated foundation with multiple slide planes. Possible slide paths were obtained, and the stability of the foundation with possible failure planes was evaluated through analysis of the stress distribution characteristics. The results reveal the mechanism and process of sliding due to weak structural planes and their deformations, and provide a reference for anti-slide stability analysis of gravity dams in complicated geological conditions.展开更多
Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric di...Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric difference sets(and partial geometric difference families) correspond to new infinite families of directed strongly regular graphs. We also discuss some of the links between partially balanced designs, 2-adesigns(which were recently coined by Cunsheng Ding in "Codes from Difference Sets"(2015)), and partial geometric designs, and make an investigation into when a 2-adesign is a partial geometric design.展开更多
Rapid and sensitive recognition of herbal pieces according to different concocted processing is crucial to quality control and pharmaceutical effect. Near-infrared （NIR） and mid-infrared （MIR） technology combined ...Rapid and sensitive recognition of herbal pieces according to different concocted processing is crucial to quality control and pharmaceutical effect. Near-infrared （NIR） and mid-infrared （MIR） technology combined with supervised pattern recognition based on partial least-squares discriminant analysis （PLSDA） was attempted to classify and recognize six different concocted processing pieces of 600 Areca catechu L. samples and the influence of fingerprint information preprocessing methods on recognition performance was also investigated in this work. Recognition rates of 99.24%, 100% and 99.49% for original fingerprint, multiple scatter correct （MSC） fingerprint and second derivative （2nd derivative） fingerprint of NIR spectra were achieved by PLSDA models, respectively. Meanwhile, a perfect recognition rate of 100% was obtained for the above three fingerprint models of MIR spectra. In conclusion, PLSDA can rapidly and effectively extract otherness of fingerprint information from NIR and MIR spectra to identify different concocted herbal pieces ofA. catechu.展开更多
This paper mainly discusses the problems of fractional variational problems and fractional diffusion problems using fractional difference and summation. Through the Euler finite difference method we get a variational ...This paper mainly discusses the problems of fractional variational problems and fractional diffusion problems using fractional difference and summation. Through the Euler finite difference method we get a variational formulation of the variation problem and the discrete solution to the time-fractional and space-fractional difference equation using separating variables method and two-side Z-transform method.展开更多
This paper is concerned with hyperbolic type delay partial difference equation and elliptic type equation where a, b,p, qi are real numbers, hi and h are nonnegative integers, a, b,p ≠ 0 and not all of qi are zero fo...This paper is concerned with hyperbolic type delay partial difference equation and elliptic type equation where a, b,p, qi are real numbers, hi and h are nonnegative integers, a, b,p ≠ 0 and not all of qi are zero for 1 ≤ i ≤ u. Sufficient and necessary conditions for all solutions of the equation mentioned above to be oscillatory are obtained.展开更多
The aim of this paper is to establish some new discrete inequalities in two independent variables which can be used as handy tools.in the theory of certain fourth order partial finite difference equations. The analys...The aim of this paper is to establish some new discrete inequalities in two independent variables which can be used as handy tools.in the theory of certain fourth order partial finite difference equations. The analysis used in the proof is elementary and the results established provide new estimates for these types of inequalities.AMS (MOS) Subject Classification (1991 ): Primary 26D15.展开更多
In a recent papers,some authors applied Nevanlinna theory to prove some results on complex difference equations reminiscent of the classical Malmquist theorem in complex differential equations. We will mainly investig...In a recent papers,some authors applied Nevanlinna theory to prove some results on complex difference equations reminiscent of the classical Malmquist theorem in complex differential equations. We will mainly investigate Malmquist theorem of a type of systems of complex partial difference equations on Cn,improvements and extensions of such results are presented in this paper.展开更多
In the study of(partial)difference sets and their generalizations in groups G,the most widely used method is to translate their definition into an equation over group ring Z[G]and to investigate this equation by apply...In the study of(partial)difference sets and their generalizations in groups G,the most widely used method is to translate their definition into an equation over group ring Z[G]and to investigate this equation by applying complex representations of G.In this paper,we investigate the existence of(partial)difference sets in a different way.We project the group ring equations in Z[G]to Z[N]where N is a quotient group of G isomorphic to the additive group of a finite field,and then use polynomials over this finite field to derive some existence conditions.展开更多
In this paper, optimal estimation for discrete-time linear time-varying systems with randomly state and measurement delays is considered. By introducing a set of binary random variables, the system is converted into t...In this paper, optimal estimation for discrete-time linear time-varying systems with randomly state and measurement delays is considered. By introducing a set of binary random variables, the system is converted into the one with both multiplicative noises and constant delays. Then, an estimator which includes the cases of smoothing and filter- ing, is derived via the projection formula, and the solution is given in terms of a partial difference Riccati equation with boundary conditions. A predictor for such systems is also presented based on the proposed filter and smoother. The ob- tained estimators have the same dimension as the original state. Conditions for existence, uniqueness, and stability of the steady-state optimal estimators are studied for time-invariant cases. In this case, the obtained estimators are very easy to implement and all calculations can be performed off line, leading to a linear time-invariant estimator.展开更多
In this paper, we consider the higher divided difference of a composite function f（g（t）） in which g（t） is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multiva...In this paper, we consider the higher divided difference of a composite function f（g（t）） in which g（t） is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multivariate Newton interpolation, we generalize the divided difference form of Faà di Bruno＇s formula with a scalar argument. Moreover, a generalized Faà di Bruno＇s formula with a vector argument is derived.展开更多
We provide a complete set of linearizability conditions for nonlinear partial difference equations defined on four points and, using them, we classify all linearizable multilinear partial difference equations defined ...We provide a complete set of linearizability conditions for nonlinear partial difference equations defined on four points and, using them, we classify all linearizable multilinear partial difference equations defined on four points up to a MSbious transformation.展开更多
In this remark,we shall show some counter examples for the main results of the recent paper 'Asymptotic Behavior of Delay 2-D Discrete Logistic Systems' (IEEE Trans.Circuits Systems,49(2002),1677-1682.)
基金supported by the NSF of Henan Province(222300420397,242300421394)Xie’s research was supported by the NSFC(11571089,11871191).
文摘In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained.
基金Supported by the NSF of China(60174010)Supported by NSF of Hebei Province(102160)Supported by NS of Education Office in Heibei Province(2004123)
文摘This paper is concerned with the oscillation of nonlinear partial difference equations with continuous variables and the corresponding dual equations. Several sufficientconditions are obtained for the oscillation of these equations.
文摘This paper is concerned with a class of partial difference equations with variable coefficients. Explicit growth bounds are found for their solutions. These bounds provide information on the existence of exponentially bounded solutions.
基金supported by the National Natural Science Foundation of China under Grant Nos.61821004 and 62250056the Natural Science Foundation of Shandong Province under Grant Nos.ZR2021ZD14 and ZR2021JQ24+1 种基金Science and Technology Project of Qingdao West Coast New Area under Grant Nos.2019-32,2020-20,2020-1-4,High-level Talent Team Project of Qingdao West Coast New Area under Grant No.RCTDJC-2019-05Key Research and Development Program of Shandong Province under Grant No.2020CXGC01208.
文摘This paper focuses on linear-quadratic(LQ)optimal control for a class of systems governed by first-order hyperbolic partial differential equations(PDEs).Different from most of the previous works,an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems.The contributions of this paper consist of the following aspects:(1)The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method.(2)A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed.Meanwhile,the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations(FBPDEs).(3)The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented.It is shown that the proposed results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case,but also support the existing operator results and give a more convenient form of computation.
文摘The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.
基金supported by the Innovation Program for College Graduate of Jiangsu Province of 2007 (Grant No. CX07B_133Z)
文摘A key problem in gravity dam design is providing enough stability to prevent slide, and the difficulty increases if there are several weak structural planes in the dam foundation. Overload and material weakening were taken into account, and a .finite difference strength reserve method with partial safety factors based on the reliability method was developed and used to study the anti-slide stability of a concrete gravity dam on a complicated foundation with multiple slide planes. Possible slide paths were obtained, and the stability of the foundation with possible failure planes was evaluated through analysis of the stress distribution characteristics. The results reveal the mechanism and process of sliding due to weak structural planes and their deformations, and provide a reference for anti-slide stability analysis of gravity dams in complicated geological conditions.
文摘Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric difference sets(and partial geometric difference families) correspond to new infinite families of directed strongly regular graphs. We also discuss some of the links between partially balanced designs, 2-adesigns(which were recently coined by Cunsheng Ding in "Codes from Difference Sets"(2015)), and partial geometric designs, and make an investigation into when a 2-adesign is a partial geometric design.
基金supported by the National Natural Science Foundation of China(Nos.21205145,21276006,21036009)the Open Funds of State Key Laboratory of Chemo/Biosensing and Chemometrics of Hunan University(No.201111)+1 种基金the Special Fund for Basic Scientific Research of Central Colleges,South-Central University for Nationalities(Nos.CZZ10005 and CZQ11012)the 'Five-twelfth' National Science and Technology Support Program (No.2012BAI27B00)
文摘Rapid and sensitive recognition of herbal pieces according to different concocted processing is crucial to quality control and pharmaceutical effect. Near-infrared （NIR） and mid-infrared （MIR） technology combined with supervised pattern recognition based on partial least-squares discriminant analysis （PLSDA） was attempted to classify and recognize six different concocted processing pieces of 600 Areca catechu L. samples and the influence of fingerprint information preprocessing methods on recognition performance was also investigated in this work. Recognition rates of 99.24%, 100% and 99.49% for original fingerprint, multiple scatter correct （MSC） fingerprint and second derivative （2nd derivative） fingerprint of NIR spectra were achieved by PLSDA models, respectively. Meanwhile, a perfect recognition rate of 100% was obtained for the above three fingerprint models of MIR spectra. In conclusion, PLSDA can rapidly and effectively extract otherness of fingerprint information from NIR and MIR spectra to identify different concocted herbal pieces ofA. catechu.
文摘This paper mainly discusses the problems of fractional variational problems and fractional diffusion problems using fractional difference and summation. Through the Euler finite difference method we get a variational formulation of the variation problem and the discrete solution to the time-fractional and space-fractional difference equation using separating variables method and two-side Z-transform method.
文摘This paper is concerned with hyperbolic type delay partial difference equation and elliptic type equation where a, b,p, qi are real numbers, hi and h are nonnegative integers, a, b,p ≠ 0 and not all of qi are zero for 1 ≤ i ≤ u. Sufficient and necessary conditions for all solutions of the equation mentioned above to be oscillatory are obtained.
文摘The aim of this paper is to establish some new discrete inequalities in two independent variables which can be used as handy tools.in the theory of certain fourth order partial finite difference equations. The analysis used in the proof is elementary and the results established provide new estimates for these types of inequalities.AMS (MOS) Subject Classification (1991 ): Primary 26D15.
基金Supported by the National Natural Science Foundation of China(No.10471065)the Natural Science Foundation of Guangdong Province(No.04010474)
文摘In a recent papers,some authors applied Nevanlinna theory to prove some results on complex difference equations reminiscent of the classical Malmquist theorem in complex differential equations. We will mainly investigate Malmquist theorem of a type of systems of complex partial difference equations on Cn,improvements and extensions of such results are presented in this paper.
基金This work is partially supported by Natural Science Foundation of Hunan Province(No.2019JJ30030)Training Program for Excellent Young Innovators of Changsha(No.kql905052).
文摘In the study of(partial)difference sets and their generalizations in groups G,the most widely used method is to translate their definition into an equation over group ring Z[G]and to investigate this equation by applying complex representations of G.In this paper,we investigate the existence of(partial)difference sets in a different way.We project the group ring equations in Z[G]to Z[N]where N is a quotient group of G isomorphic to the additive group of a finite field,and then use polynomials over this finite field to derive some existence conditions.
基金supported by the Natural Science Foundation of Shandong Province (No. ZR2011FQ020)the National Natural Science Foundation for Distinguished YoungScholars of China (No. 60825304)the National Natural Science Foundation of China (Nos. 61104050, 61074021)
文摘In this paper, optimal estimation for discrete-time linear time-varying systems with randomly state and measurement delays is considered. By introducing a set of binary random variables, the system is converted into the one with both multiplicative noises and constant delays. Then, an estimator which includes the cases of smoothing and filter- ing, is derived via the projection formula, and the solution is given in terms of a partial difference Riccati equation with boundary conditions. A predictor for such systems is also presented based on the proposed filter and smoother. The ob- tained estimators have the same dimension as the original state. Conditions for existence, uniqueness, and stability of the steady-state optimal estimators are studied for time-invariant cases. In this case, the obtained estimators are very easy to implement and all calculations can be performed off line, leading to a linear time-invariant estimator.
基金Acknowledgments. This work was supported by the National Science Foundation of China （Grant Nos. 10471128, 10731060）.
文摘In this paper, we consider the higher divided difference of a composite function f（g（t）） in which g（t） is an s-dimensional vector. By exploiting some properties from mixed partial divided differences and multivariate Newton interpolation, we generalize the divided difference form of Faà di Bruno＇s formula with a scalar argument. Moreover, a generalized Faà di Bruno＇s formula with a vector argument is derived.
文摘We provide a complete set of linearizability conditions for nonlinear partial difference equations defined on four points and, using them, we classify all linearizable multilinear partial difference equations defined on four points up to a MSbious transformation.
文摘In this remark,we shall show some counter examples for the main results of the recent paper 'Asymptotic Behavior of Delay 2-D Discrete Logistic Systems' (IEEE Trans.Circuits Systems,49(2002),1677-1682.)
