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Improving Performance of Computer Algebra Systems
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作者 Kostas Zotos Irena Atanassova 《Journal of Software Engineering and Applications》 2023年第10期521-529,共9页
Computer Algebra Systems have been extensively used in higher education. The reasons are many e.g., visualize mathematical problems, correlate real-world problems on a conceptual level, are flexible, simple to use, ac... Computer Algebra Systems have been extensively used in higher education. The reasons are many e.g., visualize mathematical problems, correlate real-world problems on a conceptual level, are flexible, simple to use, accessible from anywhere, etc. However, there is still room for improvement. Computer algebra system (CAS) optimization is the set of best practices and techniques to keep the CAS running optimally. Best practices are related to how to carry out a mathematical task or configure your system. In this paper, we are going to examine these techniques. The documentation sheets of CASs are the source of data that we used to compare them and examine their characteristics. The research results reveal that there are many tips that we can follow to accelerate performance. 展开更多
关键词 Mathematical Software Computer algebra systems CAS Improving Performance CAS Performance CAS Optimization MATLAB MAPLE MATHEMATICA
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Meshing analysis of toroidal drive by computer algebra system 被引量:1
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作者 张春丽 徐晓俊 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2000年第1期82-85,共4页
Presents the meshing analysis based on the Computer Algebra System to make it easier to deduce complex formulas while the expression of more complicated surface equations are visualized, by which, the contact line, me... Presents the meshing analysis based on the Computer Algebra System to make it easier to deduce complex formulas while the expression of more complicated surface equations are visualized, by which, the contact line, meshing bordlines and undercut bordlines of toroidal drive are deduced, and the results obtained are consistent with the results discussed in literature [1] , and concludes that the absolute value of the induced normal curvature is usually smaller (less than 0.12, for example), and it increases as parameters φ 2, V and R increase, decreases as parameter r increases, and hardly varies with W 2, and the variation with a, i 21  is not definite. 展开更多
关键词 MESHING THEORY TOROIDAL DRIVE COMPUTER algebra system.
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A Unified Algebraic Dynamical Solution to General Two-Photon Algebra Systems
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作者 YING Zu-jian WANG Shun-jin 《Chinese Physics Letters》 SCIE CAS CSCD 1999年第12期861-863,共3页
We use squeezing and displacement operators and apply algebraic dynamics to develop a unified solution of general time-dependent two-photon algebra systems. A set of orthogonal-and-normalized solutions are derived wit... We use squeezing and displacement operators and apply algebraic dynamics to develop a unified solution of general time-dependent two-photon algebra systems. A set of orthogonal-and-normalized solutions are derived with the ground state being the conventional squeezed state. Landau system is given as an example. 展开更多
关键词 state OPERATORS algebra
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Groupoid Approach to Ergodic Dynamical System of Commutative von Neumann Algebra
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作者 Nicholas O. Okeke Murphy E. Egwe 《Advances in Pure Mathematics》 2024年第3期167-184,共18页
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
关键词 Measure Groupoid Groupoid Equivalence Ergodic Action Convolution algebra von Neumann algebra Generalized Space
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THE BSE PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS
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作者 Fatemeh ABTAHI Ali REJALI Farshad SAYAF 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1945-1954,共10页
In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the ... In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the BSE property then A has so.We also establish the converse of this result,whenever X is discrete and A has the BSE-norm property.Furthermore,we prove the same result for the BSE property of type I.Finally,we prove that C0(X,A)has the BSE-norm property if and only if A has so. 展开更多
关键词 BSE algebras BSE-function BSE norm multiplier algebra SEMISIMPLE without order
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Root Systems Lie Algebras
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作者 Amor Hasić Fatih Destović 《Advances in Linear Algebra & Matrix Theory》 2023年第1期1-20,共20页
A root system is any collection of vectors that has properties that satisfy the roots of a semi simple Lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclide... A root system is any collection of vectors that has properties that satisfy the roots of a semi simple Lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclidean vector space that possesses some remarkable symmetries and completely defines the Lie algebra of g. The purpose of this paper is to show the essentiality of the root system on the Lie algebra. In addition, the paper will mention the connection between the root system and Ways chambers. In addition, we will show Dynkin diagrams, which are an integral part of the root system. 展开更多
关键词 Lie algebras Root systems Ways Chambers Dynkin Diagrams
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Distributed Minimum-Energy Containment Control of Continuous-Time Multi-Agent Systems by Inverse Optimal Control
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作者 Fei Yan Xiangbiao Liu Tao Feng 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第6期1533-1535,共3页
Dear Editor,This letter focuses on the distributed optimal containment control of continuous-time multi-agent systems(CTMASs)with respect to the minimum-energy performance index over fixed topology.To achieve this,we ... Dear Editor,This letter focuses on the distributed optimal containment control of continuous-time multi-agent systems(CTMASs)with respect to the minimum-energy performance index over fixed topology.To achieve this,we firstly investigate the optimal containment control problem using the inverse optimal control method,where all states of followers asymptotically converge to the convex hull spanned by the leaders while some quadratic performance indexes get minimized.A sufficient condition for existence of the distributed optimal containment control protocol is derived.By introducing the parametric algebraic Riccati equation(PARE),it is strictly proved that the global performance index can be used to approximate the standard minimumenergy performance index as the parameters tends to infinity.In consequence,the standard minimum-energy cooperative containment control can be solved by local steady state feedback protocols. 展开更多
关键词 optimal INFINITY algebraIC
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AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS
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作者 Safoura Rezaei ADERYANI Azam AHADI +1 位作者 Reza SAADATI Hari M.SRIVASTAVA 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期311-338,共28页
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
关键词 permuting tri-homomorphism in Banach algebra permuting tri-derivation on C*-algebra fixed point theorem Ulam-Hyers-Rassias stability aggregate special functions tri-additiveψ-functional inequality
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BANACH ALGEBRA STRUCTURE IN DERIVATIVE HARDY SPACES
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作者 ZHANG Zhao-de LIU Jun-ming 《数学杂志》 2024年第6期485-493,共9页
In this paper,we consider the algebraic structure of derivative Hardy Spaces.By using the method of[6,12,15],we get the Duhamel product forming Banach algebra in derivative Hardy Spaces,and invertibility criterion,and... In this paper,we consider the algebraic structure of derivative Hardy Spaces.By using the method of[6,12,15],we get the Duhamel product forming Banach algebra in derivative Hardy Spaces,and invertibility criterion,and describe the extended eigenvalue of the integral operator V.We generalize the results in[1,2,6,11,16]. 展开更多
关键词 Duhamel product banach algebra extended eigenvalue
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Nonadditive Skew(Anti-)commuting Maps on Operator Algebras
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作者 Zhang Ting Feng Liqin Qi Xiaofei 《数学理论与应用》 2024年第3期83-93,共11页
In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obta... In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obtain the concrete characterizations of all nonadditive skew(anti-)commuting maps on some operator algebras. 展开更多
关键词 Commuting map Skew commuting map Anti-commuting map Operator algebra
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Split-Tetraquaternion Algebra and Applications
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作者 Grégoire Lutanda Panga 《Journal of Applied Mathematics and Physics》 2024年第7期2682-2690,共9页
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
关键词 Tetraquaternion algebra Split-Tetraquaternion algebra Split Quaternion algebra Clifford algebra
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Relationship of Edge States to Anomaly and Construction of Dual Systems in Quantum Hall Systems
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作者 Paul Bracken 《Journal of Modern Physics》 2024年第6期850-863,共14页
The hierarchy of bulk actions is developed which are associated with Chern-Simons theories. The connection between the bulk and edge arising from the requirement there is a cancelation of an anomaly which arises in th... The hierarchy of bulk actions is developed which are associated with Chern-Simons theories. The connection between the bulk and edge arising from the requirement there is a cancelation of an anomaly which arises in the theory. A duality transformation is studied for the Chern-Simons example. The idea that is used has been employed to describe duality in a scalar theory. The link between the edge theory with the Chern-Simons theory in the bulk then suggests that similar transformations can be implemented in the bulk Chern-Simons theory as well. 展开更多
关键词 Quantum algebra HALL Conductivity FORMS CHIRAL FERMION
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Discussion on the Homology Theory of Lie Algebras
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作者 Lilong Kang Yu Wang Caiyu Du 《Journal of Applied Mathematics and Physics》 2024年第7期2367-2376,共10页
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
关键词 Lie algebra Differential Sequence Differential Fractional algebra COHOMOLOGY
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Quantum Computingvia Entanglement in Geometric Algebra Approach
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作者 Alexander Soiguine 《Journal of Applied Mathematics and Physics》 2024年第2期445-457,共13页
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
关键词 Geometric algebra Wave Functions ENTANGLEMENT Maxwell Equations Three-Dimensional Sphere
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The Report of Homological Algebra
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作者 Junhui Zhang 《Open Journal of Applied Sciences》 2024年第9期2749-2767,共19页
The current article intends to introduce the reader to the concept of injective and projective modules and to describe the CFT. We present a clear view to show the homological algebra and injective and projective modu... The current article intends to introduce the reader to the concept of injective and projective modules and to describe the CFT. We present a clear view to show the homological algebra and injective and projective modules. 展开更多
关键词 Homological algebra CATEGORY Projective and Injective Module
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Algebraic Structure of the Dynamical Equations of Holonomic Mechanical System in Relative Motion 被引量:2
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作者 张毅 梅凤翔 《Journal of Beijing Institute of Technology》 EI CAS 1998年第1期12-18,共7页
Aim To study an algebraic of the dynamical equations of holonomic mechanical systems in relative motion. Methods The equations of motion were presented in a contravariant algebraic form and an algebraic product was... Aim To study an algebraic of the dynamical equations of holonomic mechanical systems in relative motion. Methods The equations of motion were presented in a contravariant algebraic form and an algebraic product was determined. Results and Conclusion The equations a Lie algebraic structure if any nonpotential generalized force doesn't exist while while the equations possess a Lie-admissible algebraic structure if nonpotential generalized forces exist . 展开更多
关键词 analytical mechanics holonomic system relative motion Lie-admissible algebra
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An algorithm for identifying symmetric variables in the canonical OR-coincidence algebra system
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作者 Xiao-hua LI Ji-zhong SHEN 《Journal of Zhejiang University-Science C(Computers and Electronics)》 SCIE EI 2014年第12期1174-1182,共9页
To simplify the process for identifying 12 types of symmetric variables in the canonical OR-coincidence(COC) algebra system, we propose a new symmetry detection algorithm based on OR-NXOR expansion. By analyzing the r... To simplify the process for identifying 12 types of symmetric variables in the canonical OR-coincidence(COC) algebra system, we propose a new symmetry detection algorithm based on OR-NXOR expansion. By analyzing the relationships between the coefficient matrices of sub-functions and the order coefficient subset matrices based on OR-NXOR expansion around two arbitrary logical variables, the constraint conditions of the order coefficient subset matrices are revealed for 12 types of symmetric variables. Based on the proposed constraints, the algorithm is realized by judging the order characteristic square value matrices. The proposed method avoids the transformation process from OR-NXOR expansion to AND-OR-NOT expansion, or to AND-XOR expansion, and solves the problem of completeness in the dj-map method. The application results show that, compared with traditional methods, the new algorithm is an optimal detection method in terms of applicability of the number of logical variables, detection type, and complexity of the identification process. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. Experimental results show that the proposed algorithm is convenient and efficient. 展开更多
关键词 Symmetric variable dj-map Canonical OR-coincidence algebra system Boolean function
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Analyzing Electric Circuits with Computer Algebra
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作者 Haiduke Sarafian 《American Journal of Computational Mathematics》 2023年第1期91-98,共8页
This report shows how starting from classic electric circuits embodying commonly electric components we have reached semi-complicated circuits embodying the same components that analyzing the signal characteristics re... This report shows how starting from classic electric circuits embodying commonly electric components we have reached semi-complicated circuits embodying the same components that analyzing the signal characteristics requires a Computer Algebra System. Our approach distinguishes itself from the electrical engineers’ (EE) approach that relies on utilizing commercially available software. Our approach step-by-step shows how Kirchhoff’s rules are applied conducive to the needed circuit information. It is shown for the case at hand the characteristic information is a set of coupled differential equations and that with the help of Mathematica numeric solutions are sought. Our report paves the research road for unlimited creative similar circuits with any degree of complications. Occasionally, by tweaking the circuits we have addressed the “what if” scenarios widening the scope of the investigation. Justification of the accuracy of our analysis for the generalized circuits is cross-checked by arranging the components symmetrizing the circuit leading to an intuitively predictable reasonable result. Mathematica codes are embedded assisting the interested reader in producing and extending our results. 展开更多
关键词 Characteristics of Electric Circuits DC and AC Driven Circuits Computer algebra system MATHEMATICA
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THE GROWTH OF SOLUTIONS OF SYSTEMS OF COMPLEX NONLINEAR ALGEBRAIC DIFFERENTIAL EQUATIONS 被引量:19
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作者 高凌云 《Acta Mathematica Scientia》 SCIE CSCD 2010年第3期932-938,共7页
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
关键词 Growth order algebraic differential equations entire function
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CONVERGENCE ANALYSIS OF RUNGE-KUTTA METHODS FOR A CLASS OF RETARDED DIFFERENTIAL ALGEBRAIC SYSTEMS 被引量:4
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作者 肖飞雁 张诚坚 《Acta Mathematica Scientia》 SCIE CSCD 2010年第1期65-74,共10页
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
关键词 CONVERGENCE Runge-Kutta Methods Lagrange interpolation retarded dif-ferential algebraic systems
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