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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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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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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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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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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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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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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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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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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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Supercoherent State of the Orthosymplectic (2,1) Superalgebra
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作者 CHEN Yong-Qing SONG Xing-Chang 《Chinese Physics Letters》 SCIE CAS CSCD 2001年第7期844-846,共3页
The normalization supercoherent state of the orthosymplectic(OSP)(2,1)superalgebra is constructed and its properties are discussed in detail.The new inhomogeneous differential realizations of the OSP(2,1)superalgebras... The normalization supercoherent state of the orthosymplectic(OSP)(2,1)superalgebra is constructed and its properties are discussed in detail.The new inhomogeneous differential realizations of the OSP(2,1)superalgebras are given.It may be of use for determining new concrete structure of the quasi-exactly-solvable hamiltonian corresponding to the OSP(2,1)supersymmetric quantum system. 展开更多
关键词 COHERENT symplectic algebra
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Symplectic analysis for regulating wave propagation in a one-dimensional nonlinear graded metamaterial 被引量:3
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作者 Yunping ZHAO Xiuhui HOU +1 位作者 Kai ZHANG Zichen DENG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第5期745-758,共14页
An analytical method,called the symplectic mathematical method,is proposed to study the wave propagation in a spring-mass chain with gradient arranged local resonators and nonlinear ground springs.Combined with the li... An analytical method,called the symplectic mathematical method,is proposed to study the wave propagation in a spring-mass chain with gradient arranged local resonators and nonlinear ground springs.Combined with the linearized perturbation approach,the symplectic transform matrix for a unit cell of the weakly nonlinear graded metamaterial is derived,which only relies on the state vector.The results of the dispersion relation obtained with the symplectic mathematical method agree well with those achieved by the Bloch theory.It is shown that wider and lower frequency bandgaps are formed when the hardening nonlinearity and incident wave intensity increase.Subsequently,the displacement response and transmission performance of nonlinear graded metamaterials with finite length are studied.The dual tunable effects of nonlinearity and gradation on the wave propagation are explored under different excitation frequencies.For small excitation frequencies,the gradient parameter plays a dominant role compared with the nonlinearity.The reason is that the gradient tuning aims at the gradient arrangement of local resonators,which is limited by the critical value of the local resonator mass.In contrast,for larger excitation frequencies,the hardening nonlinearity is dominant and will contribute to the formation of a new bandgap. 展开更多
关键词 symplectic mathematical method nonlinear graded metamaterial tunable bandgap
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Some results on derivations of MV-algebras 被引量:1
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作者 WANG Jun-tao HE Peng-fei SHE Yan-hong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第1期126-143,共18页
In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations an... In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316]. 展开更多
关键词 MV-algebra DERIVATION fixed point set IDEAL Boolean algebra
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Non-Linear Effects in Optical Systems by Lie Algebra and Symplectic Mapping
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作者 Víctor M. Castañ o 《Journal of Modern Physics》 CAS 2022年第11期1314-1323,共10页
The use of signals of different frequencies determines the geometrical deviation with respect to the optical axes of a given beam. This angle can be determined by Sympletic Map (SM), a powerful and simple mathematical... The use of signals of different frequencies determines the geometrical deviation with respect to the optical axes of a given beam. This angle can be determined by Sympletic Map (SM), a powerful and simple mathematical tool for the characterization and construction of images in Geometrical Optics. The Sympletic Map constitutes a Lie Group, with an algebra associated: the Lie Algebra. In general, the SM can be expressed as an infinite series, where each term corresponds to different contributions produced by the optical devices that constitute the optical system (lenses, apertures, bandwidth cutoff, etc.). The level of correction to be performed on the image to recover the original object is clear and controllable by SM. This formalism can be extended easily to physical optics to describe diffraction and interference phenomena. 展开更多
关键词 symplectic Mapping Geometrical Optics Non-Linear Effects
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Wrinkling in graded core/shell systems using symplectic formulation
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作者 Yaqi GUO Guohua NIE 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第12期2057-2070,共14页
Wrinkles in flat graded elastic layers have been recently described as a timevarying Hamiltonian system by the energy method.Cylindrical core/shell structures can also undergo surface instabilities under the external ... Wrinkles in flat graded elastic layers have been recently described as a timevarying Hamiltonian system by the energy method.Cylindrical core/shell structures can also undergo surface instabilities under the external pressure.In this study,we show that by treating the radial direction as a pseudo-time variable,the graded core/shell system with radially decaying elastic properties can also be described within the symplectic framework.In combination with the shell buckling equation,the present paper addresses the surface wrinkling of graded core/shell structures subjected to the uniform external pressure by solving a series of ordinary differential equations with varying coefficients.Three representative gradient distributions are showcased,and the predicted critical pressure and critical wave number are verified by finite element simulations.The symplectic framework provides an efficient and accurate approach to understand the surface instability and morphological evolution in curved biological tissues and engineered structures. 展开更多
关键词 WRINKLING graded core/shell system symplectic analysis gradient distribution
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(ρ, τ, σ)-Derivations of Dendriform Algebras
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作者 Yousuf A. Alkhezi 《Applied Mathematics》 2023年第12期839-846,共8页
We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provid... We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provide all generalized derivations for complex low-dimensional dendriform algebras. 展开更多
关键词 Dendriform algebras DERIVATIONS Generalized Derivations
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Norm-Based Adaptive Coefficient ZNN for Solving the Time-Dependent Algebraic Riccati Equation
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作者 Chengze Jiang Xiuchun Xiao 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第1期298-300,共3页
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
关键词 algebraIC EQUATION OPTIMAL
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Algebraic Properties for Molecular Structure of Magnesium Iodide
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作者 Ali N.A.Koam Ali Ahmad +1 位作者 Muhammad Azeem Muhammad Kamran Siddiqui 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第5期1131-1146,共16页
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
关键词 Magnesium iodide M-polynomials algebraic properties of magnesium iodide algebraic formation of numerics of magnesium iodide
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2D Curves in Conformal Hyperquaternion Algebras H⊗2m
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作者 Grégoire Lutanda Panga 《Journal of Applied Mathematics and Physics》 2023年第10期2904-2912,共9页
The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H<sup>⊗2m</sup> in which a higher order plane curve can be described by generalizing the well-known cases of conics... The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H<sup>⊗2m</sup> in which a higher order plane curve can be described by generalizing the well-known cases of conics and cubic curves in 2D. In other words, the determination of the order of a plane curve through n points and its conformal hyperquaternion algebra H<sup>⊗2m</sup> is the object of this work. 展开更多
关键词 Clifford algebra Hyperquaternion algebra Conformal Hyperquaternion Al-gebra
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New Class of Doubt Bipolar Fuzzy Sub Measure Algebra
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作者 Shadia Majeed Noori Abd Ghafur Ahmad Shuker Mahmood Khalil 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第4期293-300,共8页
The ideas of ambiguous bipolar skepticism under algebra and closed skepticism ambiguous bipolar ideals and related features have been developed.The fuzzy measure ideal is described in terms of bipolar ambiguous measur... The ideas of ambiguous bipolar skepticism under algebra and closed skepticism ambiguous bipolar ideals and related features have been developed.The fuzzy measure ideal is described in terms of bipolar ambiguous measure algebra and bipolar skepticism,and the linkages between bipolar fuzzy measure algebra are determined.A bipolar misty ideal’s skepticism is examined.InBCW andBCL-measure algebra,homogeneous ideas and dubious pictures of fuzzy bipolar measure ideas are examined.Also,we gave the relationship between these concepts.Finally,it is given the perfect terms for an occult bipolar doubt to be a measure of ideal fuzzy bipolar closed doubt. 展开更多
关键词 Fuzzy measure algebra fuzzy measure BCW-idials BCF-ideals
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A symplectic finite element method based on Galerkin discretization for solving linear systems
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作者 Zhiping QIU Zhao WANG Bo ZHU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第8期1305-1316,共12页
We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is ... We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems. 展开更多
关键词 Galerkin finite element method linear system structural dynamic response symplectic difference scheme
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