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
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
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
A dandelion algorithm(DA) is a recently developed intelligent optimization algorithm for function optimization problems. Many of its parameters need to be set by experience in DA,which might not be appropriate for all...A dandelion algorithm(DA) is a recently developed intelligent optimization algorithm for function optimization problems. Many of its parameters need to be set by experience in DA,which might not be appropriate for all optimization problems. A self-adapting and efficient dandelion algorithm is proposed in this work to lower the number of DA's parameters and simplify DA's structure. Only the normal sowing operator is retained;while the other operators are discarded. An adaptive seeding radius strategy is designed for the core dandelion. The results show that the proposed algorithm achieves better performance on the standard test functions with less time consumption than its competitive peers. In addition, the proposed algorithm is applied to feature selection for credit card fraud detection(CCFD), and the results indicate that it can obtain higher classification and detection performance than the-state-of-the-art methods.展开更多
目的:采用HPLC法同时检测宫瘤消胶囊(GLX)中13种成分含量,并联合化学计量学及灰色关联度分析(GRA)对GLX质量进行综合评价。方法:以Dikmatech Diamonsil Plus C18为色谱柱,乙腈-0.1%磷酸为流动相,同时测定GLX中党参炔苷、紫丁香苷、鸡矢...目的:采用HPLC法同时检测宫瘤消胶囊(GLX)中13种成分含量,并联合化学计量学及灰色关联度分析(GRA)对GLX质量进行综合评价。方法:以Dikmatech Diamonsil Plus C18为色谱柱,乙腈-0.1%磷酸为流动相,同时测定GLX中党参炔苷、紫丁香苷、鸡矢藤次苷甲酯、车叶草苷酸、车叶草苷、氧化芍药苷、芍药苷、丹皮酚、香附烯酮、圆柚酮、α-香附酮、莪术二酮和莪术醇的含量。采用化学计量学挖掘影响GLX产品质量的主要标记物。基于灰色关联度法分析不同批次GLX各指标成分数据,以相对关联度为测度,对GLX综合质量进行评价。结果:13种成分在各自范围内线性关系良好(r>0.999),平均加样回收率(n=9)在96.81%~100.19%之间(RSD<2.0%)。化学计量学分析显示莪术二酮、香附烯酮、丹皮酚、车叶草苷、党参炔苷、鸡矢藤次苷甲酯、芍药苷和氧化芍药苷是影响GLX产品质量的主要潜在标志物。灰色关联度分析相对关联度0.3302~0.6068,GLX存在一定批间差异。结论:所建立的HPLC多组分定量联合化学计量学及灰色关联度分析方法,操作便捷、结果准确、全面客观,可用于GLX质量的综合评价,为该制剂质量控制提供参考。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
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).
基金supported by the Institutional Fund Projects(IFPIP-1481-611-1443)the Key Projects of Natural Science Research in Anhui Higher Education Institutions(2022AH051909)+1 种基金the Provincial Quality Project of Colleges and Universities in Anhui Province(2022sdxx020,2022xqhz044)Bengbu University 2021 High-Level Scientific Research and Cultivation Project(2021pyxm04)。
文摘A dandelion algorithm(DA) is a recently developed intelligent optimization algorithm for function optimization problems. Many of its parameters need to be set by experience in DA,which might not be appropriate for all optimization problems. A self-adapting and efficient dandelion algorithm is proposed in this work to lower the number of DA's parameters and simplify DA's structure. Only the normal sowing operator is retained;while the other operators are discarded. An adaptive seeding radius strategy is designed for the core dandelion. The results show that the proposed algorithm achieves better performance on the standard test functions with less time consumption than its competitive peers. In addition, the proposed algorithm is applied to feature selection for credit card fraud detection(CCFD), and the results indicate that it can obtain higher classification and detection performance than the-state-of-the-art methods.
文摘目的:采用HPLC法同时检测宫瘤消胶囊(GLX)中13种成分含量,并联合化学计量学及灰色关联度分析(GRA)对GLX质量进行综合评价。方法:以Dikmatech Diamonsil Plus C18为色谱柱,乙腈-0.1%磷酸为流动相,同时测定GLX中党参炔苷、紫丁香苷、鸡矢藤次苷甲酯、车叶草苷酸、车叶草苷、氧化芍药苷、芍药苷、丹皮酚、香附烯酮、圆柚酮、α-香附酮、莪术二酮和莪术醇的含量。采用化学计量学挖掘影响GLX产品质量的主要标记物。基于灰色关联度法分析不同批次GLX各指标成分数据,以相对关联度为测度,对GLX综合质量进行评价。结果:13种成分在各自范围内线性关系良好(r>0.999),平均加样回收率(n=9)在96.81%~100.19%之间(RSD<2.0%)。化学计量学分析显示莪术二酮、香附烯酮、丹皮酚、车叶草苷、党参炔苷、鸡矢藤次苷甲酯、芍药苷和氧化芍药苷是影响GLX产品质量的主要潜在标志物。灰色关联度分析相对关联度0.3302~0.6068,GLX存在一定批间差异。结论:所建立的HPLC多组分定量联合化学计量学及灰色关联度分析方法,操作便捷、结果准确、全面客观,可用于GLX质量的综合评价,为该制剂质量控制提供参考。
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.