Dear Editor,This letter deals with the distributed recursive set-membership filtering(DRSMF)issue for state-saturated systems under encryption-decryption mechanism.To guarantee the data security,the encryption-decrypt...Dear Editor,This letter deals with the distributed recursive set-membership filtering(DRSMF)issue for state-saturated systems under encryption-decryption mechanism.To guarantee the data security,the encryption-decryption mechanism is considered in the signal transmission process.Specifically,a novel DRSMF scheme is developed such that,for both state saturation and encryption-decryption mechanism,the filtering error(FE)is limited to the ellipsoid domain.Then,the filtering error constraint matrix(FECM)is computed and a desirable filter gain is derived by minimizing the FECM.Besides,the bound-edness evaluation of the FECM is provided.展开更多
Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternati...Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.展开更多
In this paper, we provide an aggregate function homotopy interior point method to solve a class of Brouwer fixed-point problems. Compared with the homotopy method (proposed by Yu and Lin, Appl. Math. Comput., 74(199...In this paper, we provide an aggregate function homotopy interior point method to solve a class of Brouwer fixed-point problems. Compared with the homotopy method (proposed by Yu and Lin, Appl. Math. Comput., 74(1996), 65), the main adavantages of this method are as foUows: on the one hand, it can solve the Brouwer fixed-point problems in a broader class of nonconvex subsets Ω in R^n (in this paper, we let Ω={x∈ R^n : gi(x) ≤0, i= 1,... , m}); on the other hand, it can also deal with the subsets Ω with larger amount of constraints more effectively.展开更多
In this paper, we modify the homotopy method (proposed by Yu and Lin, Appl. Math. Comput., 74(1996), 65) and hence make the modified method be able to solve Brouwer fixed-point problems in a broader class of nonco...In this paper, we modify the homotopy method (proposed by Yu and Lin, Appl. Math. Comput., 74(1996), 65) and hence make the modified method be able to solve Brouwer fixed-point problems in a broader class of nonconvex subsets in Rn. In addition, a simple example is given to show the effectiveness of the modified method.展开更多
Nowadays, increased information capacity and transmission processes make information security a difficult problem. As a result, most researchers employ encryption and decryption algorithms to enhance information secur...Nowadays, increased information capacity and transmission processes make information security a difficult problem. As a result, most researchers employ encryption and decryption algorithms to enhance information security domains. As it progresses, new encryption methods are being used for information security. In this paper, a hybrid encryption algorithm that combines the honey encryption algorithm and an advanced DNA encoding scheme in key generation is presented. Deoxyribonucleic Acid (DNA) achieves maximal protection and powerful security with high capacity and low modification rate, it is currently being investigated as a potential carrier for information security. Honey Encryption (HE) is an important encryption method for security systems and can strongly prevent brute force attacks. However, the traditional honeyword encryption has a message space limitation problem in the message distribution process. Therefore, we use an improved honey encryption algorithm in our proposed system. By combining the benefits of the DNA-based encoding algorithm with the improved Honey encryption algorithm, a new hybrid method is created in the proposed system. In this paper, five different lookup tables are created in the DNA encoding scheme in key generation. The improved Honey encryption algorithm based on the DNA encoding scheme in key generation is discussed in detail. The passwords are generated as the keys by using the DNA methods based on five different lookup tables, and the disease names are the input messages that are encoded by using the honey encryption process. This hybrid method can reduce the storage overhead problem in the DNA method by applying the five different lookup tables and can reduce time complexity in the existing honey encryption process.展开更多
We study a special type of Boussinesq equations{δtu+u・∇u+∇P=νtα△u+θe2,δt+u・∇θ=κ△θ,∇・u=0with time-dependent viscosity coefficients,termed as tα-type Boussinesq equations.By skillfully combinin...We study a special type of Boussinesq equations{δtu+u・∇u+∇P=νtα△u+θe2,δt+u・∇θ=κ△θ,∇・u=0with time-dependent viscosity coefficients,termed as tα-type Boussinesq equations.By skillfully combining Schauder's fixed-point theorem with integrating factor techniques under the parameter constraint 0<α<1,we establish the existence and uniqueness of classical solutions for H3initial data.The analytical framework developed in this work provides a self-contained methodology with independent theoretical value.展开更多
Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of ...Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.展开更多
Under uncertain environment, it is very difficult to measure the entropy of quantum information system, because there is no effective method to model the randomness. First, different from the traditional classic uncer...Under uncertain environment, it is very difficult to measure the entropy of quantum information system, because there is no effective method to model the randomness. First, different from the traditional classic uncertainty, a quantum uncertain model is proposed to simulate a quantum information system under uncertain environment, and to simplify the entropy measurement of quantum information system. Second, different from the classic random seed under uncertain environment which is often called as pseudo-random number, here the quantum random is employed to provide us a true random model for the entropy of quantum information system. Third, the complex interaction and entangling activity of uncertain factors of quantum information is modeled as quantum binary instead of classic binary, which can help us to evaluate the entropy of uncertain environment, to analyze the entropy divergence in quantum information system. This work presents a non-classic risk factor measurement for quantum information system and a helpful entropy measurement.展开更多
This paper observes approaches to algebraic analysis of GOST 28147-89 encryption algorithm (also known as simply GOST), which is the basis of most secure information systems in Russia. The general idea of algebraic an...This paper observes approaches to algebraic analysis of GOST 28147-89 encryption algorithm (also known as simply GOST), which is the basis of most secure information systems in Russia. The general idea of algebraic analysis is based on the representation of initial encryption algorithm as a system of multivariate quadratic equations, which define relations between a secret key and a cipher text. Extended linearization method is evaluated as a method for solving the nonlinear sys- tem of equations.展开更多
基金supported by the National Natural Science Foundation of China(12471416,12171124,12301567)the Heilongjiang Provincial Natural Science Foundation of China(PL2024F015)+2 种基金the Postdoctoral Science Foundation of Heilongjiang Province of China(LBH-Z22199)the Fundamental Research Foun-dation for Universities of Heilongjiang Province of China(2022-KYYWF-0141)the Alexander von Humboldt Foundation of Germany.
摘要Dear Editor,This letter deals with the distributed recursive set-membership filtering(DRSMF)issue for state-saturated systems under encryption-decryption mechanism.To guarantee the data security,the encryption-decryption mechanism is considered in the signal transmission process.Specifically,a novel DRSMF scheme is developed such that,for both state saturation and encryption-decryption mechanism,the filtering error(FE)is limited to the ellipsoid domain.Then,the filtering error constraint matrix(FECM)is computed and a desirable filter gain is derived by minimizing the FECM.Besides,the bound-edness evaluation of the FECM is provided.
基金Research was supported by the NSFC Grant 11872210Research was supported by the NSFC Grant 11872210 and Grant No.MCMS-I-0120G01+1 种基金Research supported in part by the AFOSR Grant FA9550-20-1-0055NSF Grant DMS-2010107.
摘要Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.
摘要In this paper, we provide an aggregate function homotopy interior point method to solve a class of Brouwer fixed-point problems. Compared with the homotopy method (proposed by Yu and Lin, Appl. Math. Comput., 74(1996), 65), the main adavantages of this method are as foUows: on the one hand, it can solve the Brouwer fixed-point problems in a broader class of nonconvex subsets Ω in R^n (in this paper, we let Ω={x∈ R^n : gi(x) ≤0, i= 1,... , m}); on the other hand, it can also deal with the subsets Ω with larger amount of constraints more effectively.
摘要In this paper, we modify the homotopy method (proposed by Yu and Lin, Appl. Math. Comput., 74(1996), 65) and hence make the modified method be able to solve Brouwer fixed-point problems in a broader class of nonconvex subsets in Rn. In addition, a simple example is given to show the effectiveness of the modified method.
摘要Nowadays, increased information capacity and transmission processes make information security a difficult problem. As a result, most researchers employ encryption and decryption algorithms to enhance information security domains. As it progresses, new encryption methods are being used for information security. In this paper, a hybrid encryption algorithm that combines the honey encryption algorithm and an advanced DNA encoding scheme in key generation is presented. Deoxyribonucleic Acid (DNA) achieves maximal protection and powerful security with high capacity and low modification rate, it is currently being investigated as a potential carrier for information security. Honey Encryption (HE) is an important encryption method for security systems and can strongly prevent brute force attacks. However, the traditional honeyword encryption has a message space limitation problem in the message distribution process. Therefore, we use an improved honey encryption algorithm in our proposed system. By combining the benefits of the DNA-based encoding algorithm with the improved Honey encryption algorithm, a new hybrid method is created in the proposed system. In this paper, five different lookup tables are created in the DNA encoding scheme in key generation. The improved Honey encryption algorithm based on the DNA encoding scheme in key generation is discussed in detail. The passwords are generated as the keys by using the DNA methods based on five different lookup tables, and the disease names are the input messages that are encoded by using the honey encryption process. This hybrid method can reduce the storage overhead problem in the DNA method by applying the five different lookup tables and can reduce time complexity in the existing honey encryption process.
基金Supported by the Natural Science Foundation of Hunan Province(Grant No.2023JJ0007)the National Natural Science Foundation of China(Grant No.12001064)+1 种基金the Research Project on Teaching Reform in Colleges and Universities of Hunan Province(Grant No.HNJG-2021-0462)the National First-class Offline Undergraduate Course Complex Variable Functions and Integral Transformations and Major Scientific and Technological Innovation Platform Project of Hunan Province(Grant No.2024JC1003)。
摘要We study a special type of Boussinesq equations{δtu+u・∇u+∇P=νtα△u+θe2,δt+u・∇θ=κ△θ,∇・u=0with time-dependent viscosity coefficients,termed as tα-type Boussinesq equations.By skillfully combining Schauder's fixed-point theorem with integrating factor techniques under the parameter constraint 0<α<1,we establish the existence and uniqueness of classical solutions for H3initial data.The analytical framework developed in this work provides a self-contained methodology with independent theoretical value.
摘要Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.
摘要Under uncertain environment, it is very difficult to measure the entropy of quantum information system, because there is no effective method to model the randomness. First, different from the traditional classic uncertainty, a quantum uncertain model is proposed to simulate a quantum information system under uncertain environment, and to simplify the entropy measurement of quantum information system. Second, different from the classic random seed under uncertain environment which is often called as pseudo-random number, here the quantum random is employed to provide us a true random model for the entropy of quantum information system. Third, the complex interaction and entangling activity of uncertain factors of quantum information is modeled as quantum binary instead of classic binary, which can help us to evaluate the entropy of uncertain environment, to analyze the entropy divergence in quantum information system. This work presents a non-classic risk factor measurement for quantum information system and a helpful entropy measurement.
摘要This paper observes approaches to algebraic analysis of GOST 28147-89 encryption algorithm (also known as simply GOST), which is the basis of most secure information systems in Russia. The general idea of algebraic analysis is based on the representation of initial encryption algorithm as a system of multivariate quadratic equations, which define relations between a secret key and a cipher text. Extended linearization method is evaluated as a method for solving the nonlinear sys- tem of equations.