Dear Editor, The time-dependent algebraic Riccati equation(TDARE) problem is applied to many optimal control industrial applications. It is susceptible to interference from measurement noises in the virtual environmen...Dear Editor, The time-dependent algebraic Riccati equation(TDARE) problem is applied to many optimal control industrial applications. It is susceptible to interference from measurement noises in the virtual environment, which current methods cannot effectively address. A normbased adaptive coefficient zeroing neural network(NACZNN) model to solve the TDARE problem is proposed.展开更多
As an inorganic chemical,magnesium iodide has a significant crystalline structure.It is a complex and multifunctional substance that has the potential to be used in a wide range of medical advancements.Molecular graph...As an inorganic chemical,magnesium iodide has a significant crystalline structure.It is a complex and multifunctional substance that has the potential to be used in a wide range of medical advancements.Molecular graph theory,on the other hand,provides a sufficient and cost-effective method of investigating chemical structures and networks.M-polynomial is a relatively new method for studying chemical networks and structures in molecular graph theory.It displays numerical descriptors in algebraic form and highlights molecular features in the form of a polynomial function.We present a polynomials display of magnesium iodide structure and calculate several M-polynomials in this paper,particularly the M-polynomials of the augmented Zagreb index,inverse sum index,hyper Zagreb index and for the symmetric division index.展开更多
How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linea...How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms.We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system.Through the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly determined.In each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very fast.Several numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM).展开更多
Solving Algebraic Problems with Geometry Diagrams(APGDs)poses a significant challenge in artificial intelligence due to the complex and diverse geometric relations among geometric objects.Problems typically involve bo...Solving Algebraic Problems with Geometry Diagrams(APGDs)poses a significant challenge in artificial intelligence due to the complex and diverse geometric relations among geometric objects.Problems typically involve both textual descriptions and geometry diagrams,requiring a joint understanding of these modalities.Although considerable progress has been made in solving math word problems,research on solving APGDs still cannot discover implicit geometry knowledge for solving APGDs,which limits their ability to effectively solve problems.In this study,a systematic and modular three-phase scheme is proposed to design an algorithm for solving APGDs that involve textual and diagrammatic information.The three-phase scheme begins with the application of the statetransformer paradigm,modeling the problem-solving process and effectively representing the intermediate states and transformations during the process.Next,a generalized APGD-solving approach is introduced to effectively extract geometric knowledge from the problem’s textual descriptions and diagrams.Finally,a specific algorithm is designed focusing on diagram understanding,which utilizes the vectorized syntax-semantics model to extract basic geometric relations from the diagram.A method for generating derived relations,which are essential for solving APGDs,is also introduced.Experiments on real-world datasets,including geometry calculation problems and shaded area problems,demonstrate that the proposed diagram understanding method significantly improves problem-solving accuracy compared to methods relying solely on simple diagram parsing.展开更多
SKINNY-64-64 is a lightweight block cipher with a 64-bit block length and key length,and it is mainly used on the Internet of Things(IoT).Currently,faults can be injected into cryptographic devices by attackers in a v...SKINNY-64-64 is a lightweight block cipher with a 64-bit block length and key length,and it is mainly used on the Internet of Things(IoT).Currently,faults can be injected into cryptographic devices by attackers in a variety of ways,but it is still difficult to achieve a precisely located fault attacks at a low cost,whereas a Hardware Trojan(HT)can realize this.Temperature,as a physical quantity incidental to the operation of a cryptographic device,is easily overlooked.In this paper,a temperature-triggered HT(THT)is designed,which,when activated,causes a specific bit of the intermediate state of the SKINNY-64-64 to be flipped.Further,in this paper,a THT-based algebraic fault analysis(THT-AFA)method is proposed.To demonstrate the effectiveness of the method,experiments on algebraic fault analysis(AFA)and THT-AFA have been carried out on SKINNY-64-64.In the THT-AFA for SKINNY-64-64,it is only required to activate the THT 3 times to obtain the master key with a 100%success rate,and the average time for the attack is 64.57 s.However,when performing AFA on this cipher,we provide a relation-ship between the number of different faults and the residual entropy of the key.In comparison,our proposed THT-AFA method has better performance in terms of attack efficiency.To the best of our knowledge,this is the first HT attack on SKINNY-64-64.展开更多
Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bound...Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .展开更多
This paper explores the significant impact of algebraic topology on diverse real-world applications.Starting with an introduction to the historical development and essence of algebraic topology,it delves into its appl...This paper explores the significant impact of algebraic topology on diverse real-world applications.Starting with an introduction to the historical development and essence of algebraic topology,it delves into its applications in neuroscience,physics,biology,engineering,data analysis,and Geographic Information Systems(GIS).Remarkable applications incorporate the analysis of neural networks,quantum mechanics,materials science,and disaster management,showcasing its boundless significance.Despite computational challenges,this study outlines prospects,emphasizing the requirement for proficient algorithms,noise robustness,multi-scale analysis,machine learning integration,user-friendly tools,and interdisciplinary collaborations.In essence,algebraic topology provides a transformative lens for uncovering stowed-away topological structures in complex data,offering solutions to perplexing problems in science,engineering,and society,with vast potential for future exploration and innovation.展开更多
In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates th...In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates the Pauli algebra, the split-biquaternion algebra and the split-quaternion algebra, we relate these algebras to Clifford algebras and we show the emergence of the stabilized Poincaré-Heisenberg algebra from the split-tetraquaternion algebra. We list without going into details some of their applications in Physics and in Born geometry.展开更多
Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent m...Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).展开更多
The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers ...The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations...We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.展开更多
Using Nevanlinna theory of the value distribution of meromorphic functions, the author investigates the problem of the growth of solutions of two types of algebraic differential equation and obtains some results.
An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinearpartial differential equations.The key idea of this method is to introduce an auxiliary ordinary differential e...An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinearpartial differential equations.The key idea of this method is to introduce an auxiliary ordinary differential equationwhich is regarded as an extended elliptic equation and whose degree Υ is expanded to the case of r>4.The efficiency ofthe method is demonstrated by the KdV equation and the variant Boussinesq equations.The results indicate that themethod not only offers all solutions obtained by using Fu's and Fan's methods,but also some new solutions.展开更多
An improved algebraic reconstruction technique(ART) combined with tunable diode laser absorption spectroscopy(TDLAS) is presented in this paper for determining two-dimensional(2D) distribution of H2O concentrati...An improved algebraic reconstruction technique(ART) combined with tunable diode laser absorption spectroscopy(TDLAS) is presented in this paper for determining two-dimensional(2D) distribution of H2O concentration and temperature in a simulated combustion flame.This work aims to simulate the reconstruction of spectroscopic measurements by a multi-view parallel-beam scanning geometry and analyze the effects of projection rays on reconstruction accuracy.It finally proves that reconstruction quality dramatically increases with the number of projection rays increasing until more than 180 for 20 × 20 grid,and after that point,the number of projection rays has little influence on reconstruction accuracy.It is clear that the temperature reconstruction results are more accurate than the water vapor concentration obtained by the traditional concentration calculation method.In the present study an innovative way to reduce the error of concentration reconstruction and improve the reconstruction quality greatly is also proposed,and the capability of this new method is evaluated by using appropriate assessment parameters.By using this new approach,not only the concentration reconstruction accuracy is greatly improved,but also a suitable parallel-beam arrangement is put forward for high reconstruction accuracy and simplicity of experimental validation.Finally,a bimodal structure of the combustion region is assumed to demonstrate the robustness and universality of the proposed method.Numerical investigation indicates that the proposed TDLAS tomographic algorithm is capable of detecting accurate temperature and concentration profiles.This feasible formula for reconstruction research is expected to resolve several key issues in practical combustion devices.展开更多
This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. ...This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.展开更多
The algebraic structure and Poisson's integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic f...The algebraic structure and Poisson's integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson's integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson's integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.展开更多
The robust stability test of time-delay systems with interval parameters can be concluded into the robust stability of the interval quasipolynomials. It has been revealed that the robust stability of the quasipolynomi...The robust stability test of time-delay systems with interval parameters can be concluded into the robust stability of the interval quasipolynomials. It has been revealed that the robust stability of the quasipolynomials depends on that of their edge polynomials. This paper transforms the interval quasipolynomials into two-dimensional (2-D) interval polynomials (2-D s-z hybrid polynomials), proves that the robust stability of interval 2-D polynomials are sufficient for the stability of given quasipolynomials. Thus, the stability test of interval quasipolynomials can be completed in 2-D s-z domain instead of classical 1-D s domain. The 2-D s-z hybrid polynomials should have different forms under the time delay properties of given quasipolynomials. The stability test proposed by the paper constructs an edge test set from Kharitonov vertex polynomials to reduce the number of testing edge polynomials. The 2-D algebraic tests are provided for the stability test of vertex 2-D polynomials and edge 2-D polynomials family. To verify the results of the paper to be correct and valid, the simulations based on proposed results and comparison with other presented results are given.展开更多
The solution for the forward displacement analysis(FDA) of the general 6-6 Stewart mechanism(i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane) has been extensive...The solution for the forward displacement analysis(FDA) of the general 6-6 Stewart mechanism(i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane) has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra(CGA). The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Grobner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Grobner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9 × 9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.展开更多
The algebraic energy method (AEM) is applied to the study of molecular dissociation energy De for 11 heteronuclear diatomic electronic states: a^3∑+ state of NaK, X^2∑+ state of XeBr, X^2∑+ state of HgI, X^1...The algebraic energy method (AEM) is applied to the study of molecular dissociation energy De for 11 heteronuclear diatomic electronic states: a^3∑+ state of NaK, X^2∑+ state of XeBr, X^2∑+ state of HgI, X^1∑+ state of LiH, A3∏(1) state of IC1, X^1∑+ state of CsH, A(3∏1) and B0+(3∏) states of CIF, 21∏ state of KRb, X^1∑+ state of CO, and c^3∑+ state of NaK molecule. The results show that the values of De computed by using the AEM are satisfactorily accurate compared with experimental ones. The AEM can serve as an economic and useful tool to generate a reliable De within an allowed experimental error for the electronic states whose molecular dissociation energies are unavailable from the existing literature展开更多
基金supported in part by the Natural Science Foundation of Guangdong Province,China(2021A 1515011847)Postgraduate Education Innovation Project of Guangdong Ocean University(202214,202250,202251,202159,202160)+1 种基金the Special Project in Key Fields of Universities in Department of Education of Guangdong Province(2019KZDZX1036)the Key Laboratory of Digital Signal and Image Processing of Guangdong Province(2019GDDSIPL-01)。
文摘Dear Editor, The time-dependent algebraic Riccati equation(TDARE) problem is applied to many optimal control industrial applications. It is susceptible to interference from measurement noises in the virtual environment, which current methods cannot effectively address. A normbased adaptive coefficient zeroing neural network(NACZNN) model to solve the TDARE problem is proposed.
文摘As an inorganic chemical,magnesium iodide has a significant crystalline structure.It is a complex and multifunctional substance that has the potential to be used in a wide range of medical advancements.Molecular graph theory,on the other hand,provides a sufficient and cost-effective method of investigating chemical structures and networks.M-polynomial is a relatively new method for studying chemical networks and structures in molecular graph theory.It displays numerical descriptors in algebraic form and highlights molecular features in the form of a polynomial function.We present a polynomials display of magnesium iodide structure and calculate several M-polynomials in this paper,particularly the M-polynomials of the augmented Zagreb index,inverse sum index,hyper Zagreb index and for the symmetric division index.
基金support provided by the Ministry of Science and Technology,Taiwan,ROC under Contract No.MOST 110-2221-E-019-044.
文摘How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms.We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system.Through the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly determined.In each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very fast.Several numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM).
基金supported by the National Natural Science Foundation of China(No.61977029)the Fundamental Research Funds for the Central Universities,CCNU(No.3110120001).
文摘Solving Algebraic Problems with Geometry Diagrams(APGDs)poses a significant challenge in artificial intelligence due to the complex and diverse geometric relations among geometric objects.Problems typically involve both textual descriptions and geometry diagrams,requiring a joint understanding of these modalities.Although considerable progress has been made in solving math word problems,research on solving APGDs still cannot discover implicit geometry knowledge for solving APGDs,which limits their ability to effectively solve problems.In this study,a systematic and modular three-phase scheme is proposed to design an algorithm for solving APGDs that involve textual and diagrammatic information.The three-phase scheme begins with the application of the statetransformer paradigm,modeling the problem-solving process and effectively representing the intermediate states and transformations during the process.Next,a generalized APGD-solving approach is introduced to effectively extract geometric knowledge from the problem’s textual descriptions and diagrams.Finally,a specific algorithm is designed focusing on diagram understanding,which utilizes the vectorized syntax-semantics model to extract basic geometric relations from the diagram.A method for generating derived relations,which are essential for solving APGDs,is also introduced.Experiments on real-world datasets,including geometry calculation problems and shaded area problems,demonstrate that the proposed diagram understanding method significantly improves problem-solving accuracy compared to methods relying solely on simple diagram parsing.
基金supported in part by the Natural Science Foundation of Heilongjiang Province of China(Grant No.LH2022F053)in part by the Scientific and technological development project of the central government guiding local(Grant No.SBZY2021E076)+2 种基金in part by the PostdoctoralResearch Fund Project of Heilongjiang Province of China(Grant No.LBH-Q21195)in part by the Fundamental Research Funds of Heilongjiang Provincial Universities of China(Grant No.145209146)in part by the National Natural Science Foundation of China(NSFC)(Grant No.61501275).
文摘SKINNY-64-64 is a lightweight block cipher with a 64-bit block length and key length,and it is mainly used on the Internet of Things(IoT).Currently,faults can be injected into cryptographic devices by attackers in a variety of ways,but it is still difficult to achieve a precisely located fault attacks at a low cost,whereas a Hardware Trojan(HT)can realize this.Temperature,as a physical quantity incidental to the operation of a cryptographic device,is easily overlooked.In this paper,a temperature-triggered HT(THT)is designed,which,when activated,causes a specific bit of the intermediate state of the SKINNY-64-64 to be flipped.Further,in this paper,a THT-based algebraic fault analysis(THT-AFA)method is proposed.To demonstrate the effectiveness of the method,experiments on algebraic fault analysis(AFA)and THT-AFA have been carried out on SKINNY-64-64.In the THT-AFA for SKINNY-64-64,it is only required to activate the THT 3 times to obtain the master key with a 100%success rate,and the average time for the attack is 64.57 s.However,when performing AFA on this cipher,we provide a relation-ship between the number of different faults and the residual entropy of the key.In comparison,our proposed THT-AFA method has better performance in terms of attack efficiency.To the best of our knowledge,this is the first HT attack on SKINNY-64-64.
文摘Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .
文摘This paper explores the significant impact of algebraic topology on diverse real-world applications.Starting with an introduction to the historical development and essence of algebraic topology,it delves into its applications in neuroscience,physics,biology,engineering,data analysis,and Geographic Information Systems(GIS).Remarkable applications incorporate the analysis of neural networks,quantum mechanics,materials science,and disaster management,showcasing its boundless significance.Despite computational challenges,this study outlines prospects,emphasizing the requirement for proficient algorithms,noise robustness,multi-scale analysis,machine learning integration,user-friendly tools,and interdisciplinary collaborations.In essence,algebraic topology provides a transformative lens for uncovering stowed-away topological structures in complex data,offering solutions to perplexing problems in science,engineering,and society,with vast potential for future exploration and innovation.
文摘In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates the Pauli algebra, the split-biquaternion algebra and the split-quaternion algebra, we relate these algebras to Clifford algebras and we show the emergence of the stabilized Poincaré-Heisenberg algebra from the split-tetraquaternion algebra. We list without going into details some of their applications in Physics and in Born geometry.
文摘Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).
文摘The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
基金supported by the Natural Science Foundationof China (10471065)the Natural Science Foundation of Guangdong Province (N04010474)
文摘We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.
基金The project Supported by NNSF of China(19971052)
文摘Using Nevanlinna theory of the value distribution of meromorphic functions, the author investigates the problem of the growth of solutions of two types of algebraic differential equation and obtains some results.
基金National Natural Science Foundation of China under Grant No.10672053
文摘An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinearpartial differential equations.The key idea of this method is to introduce an auxiliary ordinary differential equationwhich is regarded as an extended elliptic equation and whose degree Υ is expanded to the case of r>4.The efficiency ofthe method is demonstrated by the KdV equation and the variant Boussinesq equations.The results indicate that themethod not only offers all solutions obtained by using Fu's and Fan's methods,but also some new solutions.
基金Project supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.61205151)the National Key Scientific Instrument and Equipment Development Project of China(Grant No.2014YQ060537)the National Basic Research Program,China(Grant No.2013CB632803)
文摘An improved algebraic reconstruction technique(ART) combined with tunable diode laser absorption spectroscopy(TDLAS) is presented in this paper for determining two-dimensional(2D) distribution of H2O concentration and temperature in a simulated combustion flame.This work aims to simulate the reconstruction of spectroscopic measurements by a multi-view parallel-beam scanning geometry and analyze the effects of projection rays on reconstruction accuracy.It finally proves that reconstruction quality dramatically increases with the number of projection rays increasing until more than 180 for 20 × 20 grid,and after that point,the number of projection rays has little influence on reconstruction accuracy.It is clear that the temperature reconstruction results are more accurate than the water vapor concentration obtained by the traditional concentration calculation method.In the present study an innovative way to reduce the error of concentration reconstruction and improve the reconstruction quality greatly is also proposed,and the capability of this new method is evaluated by using appropriate assessment parameters.By using this new approach,not only the concentration reconstruction accuracy is greatly improved,but also a suitable parallel-beam arrangement is put forward for high reconstruction accuracy and simplicity of experimental validation.Finally,a bimodal structure of the combustion region is assumed to demonstrate the robustness and universality of the proposed method.Numerical investigation indicates that the proposed TDLAS tomographic algorithm is capable of detecting accurate temperature and concentration profiles.This feasible formula for reconstruction research is expected to resolve several key issues in practical combustion devices.
文摘This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.
基金Project supported by the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the National Natural Science Foundation of China (Grant Nos 10471145 and 10372053) and the Natural Science Foundation of Henan Provincial Government of China (Grant Nos 0311011400 and 0511022200).
文摘The algebraic structure and Poisson's integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson's integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson's integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.
基金This project was supported by the National Science Foundation of China (60572093).
文摘The robust stability test of time-delay systems with interval parameters can be concluded into the robust stability of the interval quasipolynomials. It has been revealed that the robust stability of the quasipolynomials depends on that of their edge polynomials. This paper transforms the interval quasipolynomials into two-dimensional (2-D) interval polynomials (2-D s-z hybrid polynomials), proves that the robust stability of interval 2-D polynomials are sufficient for the stability of given quasipolynomials. Thus, the stability test of interval quasipolynomials can be completed in 2-D s-z domain instead of classical 1-D s domain. The 2-D s-z hybrid polynomials should have different forms under the time delay properties of given quasipolynomials. The stability test proposed by the paper constructs an edge test set from Kharitonov vertex polynomials to reduce the number of testing edge polynomials. The 2-D algebraic tests are provided for the stability test of vertex 2-D polynomials and edge 2-D polynomials family. To verify the results of the paper to be correct and valid, the simulations based on proposed results and comparison with other presented results are given.
基金Supported by National Natural Science Foundation of China(Grant No.51375059)National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA040203)+1 种基金Special Fund for Agro-scientific Research in the Public Interest of China(Grant No.201313009-06)National Key Technology R&D Program of the Ministry of Science and Technology of China(Grant No.2013BAD17B06)
文摘The solution for the forward displacement analysis(FDA) of the general 6-6 Stewart mechanism(i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane) has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra(CGA). The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Grobner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Grobner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9 × 9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.
基金Project supported by the Science Foundation of China West Normal University (Grant No 05B016) and the Science Foundation of Sichuan province Educational Bureau of China (Grant No 2006A080).
文摘The algebraic energy method (AEM) is applied to the study of molecular dissociation energy De for 11 heteronuclear diatomic electronic states: a^3∑+ state of NaK, X^2∑+ state of XeBr, X^2∑+ state of HgI, X^1∑+ state of LiH, A3∏(1) state of IC1, X^1∑+ state of CsH, A(3∏1) and B0+(3∏) states of CIF, 21∏ state of KRb, X^1∑+ state of CO, and c^3∑+ state of NaK molecule. The results show that the values of De computed by using the AEM are satisfactorily accurate compared with experimental ones. The AEM can serve as an economic and useful tool to generate a reliable De within an allowed experimental error for the electronic states whose molecular dissociation energies are unavailable from the existing literature