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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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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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TABULAR TECHNIQUES FOR OR-COINCIDENCE LOGIC 被引量:12
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作者 Wang Pengjun Chen Xiexiong 《Journal of Electronics(China)》 2006年第2期269-273,共5页
The map folding method for the conversion between Boolean expression and COC expansions is analyzed. Based on it, the tabular techniques are proposed for the conversion between Boolean expression and COC expansion and... The map folding method for the conversion between Boolean expression and COC expansions is analyzed. Based on it, the tabular techniques are proposed for the conversion between Boolean expression and COC expansion and for the derivation of GOC expansions with fixed polarities. The Fast Tabular Technique (FTT) for the conversion from the Boolean expression to the GOC expansion with the required polarity is also proposed. The simulative result shows this FTT is faster than others in references because of its inherent parallelism. 展开更多
关键词 Tabular technique or-coincidence logic Fixed polarity or-coincidence expansion
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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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(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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On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras
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作者 ZHU Hua ZHAO Jian-bin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第2期274-292,共19页
A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-L... A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements. 展开更多
关键词 DERIVATION Boolean element Lattice implication algebra(LIA) 2-dimension linguistic lattice implication algebra(2DL-LIA) 2-dimension fuzzy linguistic information
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