Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the...Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.展开更多
In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order qua...In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.展开更多
The invariant subspace method is used to construct the explicit solution of a nonlinear evolution equation. The second-order nonlinear differential operators that possess invariant subspaces of submaximal dimension ar...The invariant subspace method is used to construct the explicit solution of a nonlinear evolution equation. The second-order nonlinear differential operators that possess invariant subspaces of submaximal dimension are described. There are second-order nonlinear differential operators, including cubic operators and quadratic operators, which preserve an invariant subspace of submaximal dimension. A full. description, of the second-order cubic operators with constant coefficients admitting a four-dimensional invariant subspace is given. It is shown that the maximal dimension of invaxiant subspaces preserved by a second-order cubic operator is four. Several examples are given for the construction of the exact solutions to nonlinear evolution equations with cubic nonlinearities. These solutions blow up in a finite展开更多
In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol Sψ（z） on Nφ has at least m non-trivial minimal reducing subspaces, where m is the dimension of H^2（Гω）⊙φ（ω）H^2（Гω...In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol Sψ（z） on Nφ has at least m non-trivial minimal reducing subspaces, where m is the dimension of H^2（Гω）⊙φ（ω）H^2（Гω）. Moreover, the restriction of Sψ（z） on any of these minimal reducing subspaces is unitary equivalent to the Bergman shift Mz.展开更多
For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in additi...For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in addition are index 1 invariant subspaces of , with nonzero intersection, we show that . Furthermore, using the index function, we provide an example where for some , holds .展开更多
This survey presents the brief history and recent development on commutants and reducing subspaces of multiplication operators on both the Hardy space and the Bergman space, and von Neumann algebras generated by multi...This survey presents the brief history and recent development on commutants and reducing subspaces of multiplication operators on both the Hardy space and the Bergman space, and von Neumann algebras generated by multiplication operators on the Bergman space.展开更多
Dual-polarization(dual-pol)radar variables provide information about the quantity,type,size,and water content of hydrometeors.Assimilating these dual-pol radar variables into numerical weather prediction models can en...Dual-polarization(dual-pol)radar variables provide information about the quantity,type,size,and water content of hydrometeors.Assimilating these dual-pol radar variables into numerical weather prediction models can enhance forecast accuracy.Observation operators are essential for radar data assimilation.This study focuses on applying a realistic dual-pol radar observation operator to more accurately calculate dual-pol radar variables.Previously reported dual-pol radar observation operators tended to overestimate radar variables near 0℃ in convective precipitation and simulate unrealistic dual-pol radar variables in subfreezing regions.To address this,the improved operator(KNU dual-pol radar observation operator;K-DROP)limits the distribution of mixed-phase hydrometeors,which have both solid and liquid properties,in areas with strong updrafts and downdrafts,improving the overestimation of radar variables near the melting layer.Additionally,by applying the observed snow axis ratio during winter to K-DROP,the issue of differential reflectivity(Z_(DR))being calculated as a constant value in subfreezing regions has been improved.By incorporating the observed maximum radius of hydrometeors into K-DROP,the overestimation of reflectivity(Z_(H))in subfreezing regions,the overestimation of Z_(DR)in warm regions,and the underestimation of specific differential phase(K_(DP))in subfreezing regions and overestimation in warm regions,are improved.Compared to previous operators,the enhanced version reported in the present work produces more realistic dual-pol radar variables.展开更多
In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and...In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.展开更多
The growing use of lithium-ion batteries in electric transportation and grid-scale storage systems has intensified the need for accurate and highly generalizable state-of-health(SOH)estimation.Conventional approaches ...The growing use of lithium-ion batteries in electric transportation and grid-scale storage systems has intensified the need for accurate and highly generalizable state-of-health(SOH)estimation.Conventional approaches often suffer from reduced accuracy under dynamically uncertain state-of-charge(SOC)operating ranges and heterogeneous aging stresses.This study presents a unified SOH estimation framework that integrates physics-informed modeling,subspace identification,and Transformer-based learning.A reduced-order model is derived from simplified electrochemical dynamics,providing an interpretable and computationally efficient representation of battery behavior.Subspace identification across a wide SOC and SOH range yields degradation-sensitive features,which the Transformer uses to capture long-range aging dynamics via multi-head self-attention.Experiments on LiFePO4 cells under joint-cell training show consistently accurate SOH estimation,with a maximum error of 1.39%,demonstrating the framework’s effectiveness in decoupling SOC and SOH effects.In cross-cell validation,where training and validation are performed on different cells,the model maintains a maximum error of 2.06%,confirming strong generalization to unseen aging trajectories.Comparative experiments on LiFePO_(4)and public LiCoO_(2)datasets confirm the framework’s cross-chemistry applicability.By extracting low-dimensional,physically interpretable features via subspace identification,the framework significantly reduces training cost while maintaining high SOH estimation accuracy,outperforming conventional data-driven models lacking physical guidance.展开更多
Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted...Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).展开更多
Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in oper...Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in operator workloads and significantly increase the complexity of scheduling.To address this challenge,this study investigates the Aircraft Pulsating Assembly Line Scheduling Problem(APALSP)under skilled operator allocation,with the objective of minimizing assembly completion time.A mathematical model considering skilled operator allocation is developed,and a Q-Learning improved Particle Swarm Optimization algorithm(QLPSO)is proposed.In the algorithm design,a reverse scheduling strategy is adopted to effectively manage large-scale precedence constraints.Moreover,a reverse sequence encoding method is introduced to generate operation sequences,while a time decoding mechanism is employed to determine completion times.The problem is further reformulated as a Markov Decision Process(MDP)with explicitly defined state and action spaces.Within QLPSO,the Q-learning mechanism adaptively adjusts inertia weights and learning factors,thereby achieving a balance between exploration capability and convergence performance.To validate the effectiveness of the proposed approach,extensive computational experiments are conducted on benchmark instances of different scales,including small,medium,large,and ultra-large cases.The results demonstrate that QLPSO consistently delivers stable and high-quality solutions across all scenarios.In ultra-large-scale instances,it improves the best solution by 25.2%compared with the Genetic Algorithm(GA)and enhances the average solution by 16.9%over the Q-learning algorithm,showing clear advantages over the comparative methods.These findings not only confirm the effectiveness of the proposed algorithm but also provide valuable theoretical references and practical guidance for the intelligent scheduling optimization of aircraft pulsating assembly lines.展开更多
It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and t...It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.展开更多
When D: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">...When D: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">ξ</span></span></em><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em><em><span style="white-space:nowrap;"></span></em><em></em></span> </span>is a linear differential operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D<sub>1</sub>: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">ξ</span> </span></em></span></span>such that <span style="white-space:nowrap;">D<span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">ξ</span></span></em></span>=<span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em></span></span> implies <span style="white-space:nowrap;">D<sub>1</sub><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em></span>=0</span>. When D is involutive, the procedure provides successive first order involutive operators D1, ..., D<sub>n</sub>, when the ground manifold has dimension <em>n</em>, a result first found by M. Janet as early as in 1920, in a footnote. However, the link between this “Janet sequence” and the “Spencer sequence” first found by the author of this paper in 1978 is still not acknowledged. Conversely, when D<sub>1</sub> is given, a more difficult “inverse problem” is to look for an operator D: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><em><span style="white-space:nowrap;">ξ</span></em></em><span style="white-space:nowrap;">→</span><em><em><span style="white-space:nowrap;">η</span></em><em></em><em></em> </em><em></em></span> </span>having the generating CC <span style="white-space:nowrap;">D<sub>1</sub><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em></span><em></em>=0</span>. If this is possible, that is when the differential module defined by D<sub>1</sub> is torsion-free, one shall say that the operator D<sub>1</sub> is parametrized by D and there is no relation in general between D and D<sub>2</sub>. The parametrization is said to be “minimum” if the differential module defined by D has a vanishing differential rank and is thus a torsion module. The solution of this problem, first found by the author of this paper in 1995, is still not acknowledged. As for the applications of the “differential double duality” theory to standard equations of physics (<em>Cauchy</em> and Maxwell equations can be parametrized while <em>Einstein</em> equations cannot), we do not know other references. When <span style="font-size:10.0pt;font-family:;" "="">erator in arbitrary dimension</span>=1 as in control theory, the fact that controllability is a “built in” property of a control system, amounting to the existence of a parametrization and thus not depending on the choice of inputs and outputs, even with variable coefficients, is still not acknowledged by engineers. The parametrization of the <em>Cauchy</em> stress operator in arbitrary dimension <em>n</em> has nevertheless attracted, “separately” and without any general “guiding line”, many famous scientists (G.B. Airy in 1863 for <em>n </em>= 2, J.C. Maxwell in 1863, G. Morera and E. Beltrami in 1892 for <em style="white-space:normal;">n </em><span style="white-space:normal;">= 3</span> , A. Einstein in 1915 for <em style="white-space:normal;">n </em><span style="white-space:normal;">= 4</span> ). The aim of this paper is to solve the minimum parametrization problem in arbitrary dimension and to apply it through effective methods that could even be achieved by using computer algebra. Meanwhile, we prove that all these works are using the <em>Einstein</em> operator which is self-adjoint and not the <em>Ricci</em> operator, a fact showing that the <em>Einstein</em> operator, which cannot be parametrized, has already been exhibited by Beltrami more than 20 years before <em>Einstein</em>. As a byproduct, they are all based on the same confusion between the so-called <em>div</em> operator induced from the <em>Bianchi </em>operator D<sub>2</sub> and the <em>Cauchy</em> operator which is the formal adjoint of the Killing operator D parametrizing the Riemann operator D<sub>1</sub> for an arbitrary <em>n</em>. We prove that this purely mathematical result deeply questions the origin and existence of gravitational waves. We also present the similar motivating situation met in the study of contact structures when <em>n</em> = 3. Like the Michelson and Morley experiment, it is thus an open historical problem to know whether <em>Einstein</em> was aware of these previous works or not, but the comparison needs no comment.展开更多
The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(...The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.展开更多
Existing multi-view deep subspace clustering methods aim to learn a unified representation from multi-view data,while the learned representation is difficult to maintain the underlying structure hidden in the origin s...Existing multi-view deep subspace clustering methods aim to learn a unified representation from multi-view data,while the learned representation is difficult to maintain the underlying structure hidden in the origin samples,especially the high-order neighbor relationship between samples.To overcome the above challenges,this paper proposes a novel multi-order neighborhood fusion based multi-view deep subspace clustering model.We creatively integrate the multi-order proximity graph structures of different views into the self-expressive layer by a multi-order neighborhood fusion module.By this design,the multi-order Laplacian matrix supervises the learning of the view-consistent self-representation affinity matrix;then,we can obtain an optimal global affinity matrix where each connected node belongs to one cluster.In addition,the discriminative constraint between views is designed to further improve the clustering performance.A range of experiments on six public datasets demonstrates that the method performs better than other advanced multi-view clustering methods.The code is available at https://github.com/songzuolong/MNF-MDSC(accessed on 25 December 2024).展开更多
Recently,Choe-Koo-Wang(J Funct Anal,2020,278)demonstrated the rigid phenomenon:The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC),implies that each difference...Recently,Choe-Koo-Wang(J Funct Anal,2020,278)demonstrated the rigid phenomenon:The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC),implies that each difference is compact on the weighted Bergman space in the unit disk.Motivated by the subtle connection of composition operator theory on the weighted Bergman spaces,Korenblum spaces and bounded holomorphic function spaces,we first explore the rigid phenomenon which also holds on the Korenblum space over the unit ball.Furthermore,we discuss which difference of composition operators is compact when the compact combination of composition operators does not satisfy the condition(CNC)on Korenblum spaces and bounded holomorphic function spaces over the unit ball setting.展开更多
In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,...In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,n/n-a)bound of M_(α)is at worst 2^(n-a).The weak type(1,n/n-a)bound of M_(α)can be estimated more directly and easily in this method,which is different from the usual ways.展开更多
Explicit asymptotic properties of the integrated density of states N(λ)with respect to the spectrum for the random Schrödinger operator H^(ω)=(-△)^(α/2)+V^(ω)are established,whereα∈(0,2]and V^(ω)(X)=∑_(I...Explicit asymptotic properties of the integrated density of states N(λ)with respect to the spectrum for the random Schrödinger operator H^(ω)=(-△)^(α/2)+V^(ω)are established,whereα∈(0,2]and V^(ω)(X)=∑_(I∈Z^(d))ξ(i)(ω)W(x-i)is a random potential term generated by a sequence of independent and identically distributed random variables{ξ(i)}_(i)∈Z^(d)and a non-negative measurable function W(x).In particular,the exact order of asymptotic properties of N(λ)depends on the decay properties of the reference function W(x)and the spectrum properties of the first Dirichlet eigenvalue of(-△)^(α/2).展开更多
In the present paper,the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined.It has shown that the new operators are the Gamma transform of the Jakimovsk...In the present paper,the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined.It has shown that the new operators are the Gamma transform of the Jakimovski-Leviatan operators.The degree of approximation is given by the modulus of continuity.It has been stressed that,there are other operators having the same error estimation with the operators,arising from the Sz´asz-Durrmeyer operators.Then the degree of global approximation is obtained in a special Lipschitz type function space.Further,a Voronovskaja type asymptotic formula and Gr¨uss-Voronovskaja type theorem are given.The approximation with these operators is visualized with the help of error tables and graphical examples.展开更多
文摘Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.
基金supported by the National Natural Science Foundation of China(Grant No.11371293)the Civil Military Integration Research Foundation of Shaanxi Province,China(Grant No.13JMR13)+2 种基金the Natural Science Foundation of Shaanxi Province,China(Grant No.14JK1246)the Mathematical Discipline Foundation of Shaanxi Province,China(Grant No.14SXZD015)the Basic Research Project Foundation of Weinan City,China(Grant No.2013JCYJ-4)
文摘In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.
基金Project supported by the National Natural Science Foundation of China(Grant No.10926082)the Natural Science Foundation of Anhui Province of China(Grant No.KJ2010A128)the Fund for Youth of Anhui Normal University,China(Grant No.2009xqn55)
文摘The invariant subspace method is used to construct the explicit solution of a nonlinear evolution equation. The second-order nonlinear differential operators that possess invariant subspaces of submaximal dimension are described. There are second-order nonlinear differential operators, including cubic operators and quadratic operators, which preserve an invariant subspace of submaximal dimension. A full. description, of the second-order cubic operators with constant coefficients admitting a four-dimensional invariant subspace is given. It is shown that the maximal dimension of invaxiant subspaces preserved by a second-order cubic operator is four. Several examples are given for the construction of the exact solutions to nonlinear evolution equations with cubic nonlinearities. These solutions blow up in a finite
文摘In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol Sψ（z） on Nφ has at least m non-trivial minimal reducing subspaces, where m is the dimension of H^2（Гω）⊙φ（ω）H^2（Гω）. Moreover, the restriction of Sψ（z） on any of these minimal reducing subspaces is unitary equivalent to the Bergman shift Mz.
文摘For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in addition are index 1 invariant subspaces of , with nonzero intersection, we show that . Furthermore, using the index function, we provide an example where for some , holds .
文摘This survey presents the brief history and recent development on commutants and reducing subspaces of multiplication operators on both the Hardy space and the Bergman space, and von Neumann algebras generated by multiplication operators on the Bergman space.
基金supported by the National Research Foundation(NRF)funded by the Korean government(MSIT)(Grant Nos.2022R1A2C1012361,2022R1A6A3A 13073165 and RS-2025-02242970).
文摘Dual-polarization(dual-pol)radar variables provide information about the quantity,type,size,and water content of hydrometeors.Assimilating these dual-pol radar variables into numerical weather prediction models can enhance forecast accuracy.Observation operators are essential for radar data assimilation.This study focuses on applying a realistic dual-pol radar observation operator to more accurately calculate dual-pol radar variables.Previously reported dual-pol radar observation operators tended to overestimate radar variables near 0℃ in convective precipitation and simulate unrealistic dual-pol radar variables in subfreezing regions.To address this,the improved operator(KNU dual-pol radar observation operator;K-DROP)limits the distribution of mixed-phase hydrometeors,which have both solid and liquid properties,in areas with strong updrafts and downdrafts,improving the overestimation of radar variables near the melting layer.Additionally,by applying the observed snow axis ratio during winter to K-DROP,the issue of differential reflectivity(Z_(DR))being calculated as a constant value in subfreezing regions has been improved.By incorporating the observed maximum radius of hydrometeors into K-DROP,the overestimation of reflectivity(Z_(H))in subfreezing regions,the overestimation of Z_(DR)in warm regions,and the underestimation of specific differential phase(K_(DP))in subfreezing regions and overestimation in warm regions,are improved.Compared to previous operators,the enhanced version reported in the present work produces more realistic dual-pol radar variables.
文摘In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G^(*)(z)+F(z),where F(z)=∑^(N)_(i)=1 A_(i)z^(i)and G(z)=∑^(N)_(i)=1 A_(−i)z^(i),A_(i)ae culants.
基金supported by the National Natural Science Foundation of China(No.52207228)the Beijing Natural Science Foundation,China(No.3224070)the National Natural Science Foundation of China(No.52077208).
文摘The growing use of lithium-ion batteries in electric transportation and grid-scale storage systems has intensified the need for accurate and highly generalizable state-of-health(SOH)estimation.Conventional approaches often suffer from reduced accuracy under dynamically uncertain state-of-charge(SOC)operating ranges and heterogeneous aging stresses.This study presents a unified SOH estimation framework that integrates physics-informed modeling,subspace identification,and Transformer-based learning.A reduced-order model is derived from simplified electrochemical dynamics,providing an interpretable and computationally efficient representation of battery behavior.Subspace identification across a wide SOC and SOH range yields degradation-sensitive features,which the Transformer uses to capture long-range aging dynamics via multi-head self-attention.Experiments on LiFePO4 cells under joint-cell training show consistently accurate SOH estimation,with a maximum error of 1.39%,demonstrating the framework’s effectiveness in decoupling SOC and SOH effects.In cross-cell validation,where training and validation are performed on different cells,the model maintains a maximum error of 2.06%,confirming strong generalization to unseen aging trajectories.Comparative experiments on LiFePO_(4)and public LiCoO_(2)datasets confirm the framework’s cross-chemistry applicability.By extracting low-dimensional,physically interpretable features via subspace identification,the framework significantly reduces training cost while maintaining high SOH estimation accuracy,outperforming conventional data-driven models lacking physical guidance.
基金supported by the Zhejiang Province Natural Science Foundation of China(LY23A010003).
文摘Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into H^(p)(1≤q<∞).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).Finally,we obtain the essential norm of H_(μ,α)from H^(p)(0<p≤1)into H^(p)(1≤q<∞).
基金supported by the National Natural Science Foundation of China(Grant No.52475543)Natural Science Foundation of Henan(Grant No.252300421101)+1 种基金Henan Province University Science and Technology Innovation Talent Support Plan(Grant No.24HASTIT048)Science and Technology Innovation Team Project of Zhengzhou University of Light Industry(Grant No.23XNKJTD0101).
文摘Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in operator workloads and significantly increase the complexity of scheduling.To address this challenge,this study investigates the Aircraft Pulsating Assembly Line Scheduling Problem(APALSP)under skilled operator allocation,with the objective of minimizing assembly completion time.A mathematical model considering skilled operator allocation is developed,and a Q-Learning improved Particle Swarm Optimization algorithm(QLPSO)is proposed.In the algorithm design,a reverse scheduling strategy is adopted to effectively manage large-scale precedence constraints.Moreover,a reverse sequence encoding method is introduced to generate operation sequences,while a time decoding mechanism is employed to determine completion times.The problem is further reformulated as a Markov Decision Process(MDP)with explicitly defined state and action spaces.Within QLPSO,the Q-learning mechanism adaptively adjusts inertia weights and learning factors,thereby achieving a balance between exploration capability and convergence performance.To validate the effectiveness of the proposed approach,extensive computational experiments are conducted on benchmark instances of different scales,including small,medium,large,and ultra-large cases.The results demonstrate that QLPSO consistently delivers stable and high-quality solutions across all scenarios.In ultra-large-scale instances,it improves the best solution by 25.2%compared with the Genetic Algorithm(GA)and enhances the average solution by 16.9%over the Q-learning algorithm,showing clear advantages over the comparative methods.These findings not only confirm the effectiveness of the proposed algorithm but also provide valuable theoretical references and practical guidance for the intelligent scheduling optimization of aircraft pulsating assembly lines.
基金supported by the NSFC(12301115)the Natural Science Foundation of Huzhou(2023YZ11,2024YZ37)the second author was supported by the NSFC(12071437).
文摘It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.
文摘When D: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">ξ</span></span></em><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em><em><span style="white-space:nowrap;"></span></em><em></em></span> </span>is a linear differential operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D<sub>1</sub>: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em><span style="white-space:nowrap;"><span style="white-space:nowrap;">→</span></span><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">ξ</span> </span></em></span></span>such that <span style="white-space:nowrap;">D<span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">ξ</span></span></em></span>=<span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em></span></span> implies <span style="white-space:nowrap;">D<sub>1</sub><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em></span>=0</span>. When D is involutive, the procedure provides successive first order involutive operators D1, ..., D<sub>n</sub>, when the ground manifold has dimension <em>n</em>, a result first found by M. Janet as early as in 1920, in a footnote. However, the link between this “Janet sequence” and the “Spencer sequence” first found by the author of this paper in 1978 is still not acknowledged. Conversely, when D<sub>1</sub> is given, a more difficult “inverse problem” is to look for an operator D: <span style="white-space:nowrap;"><span style="white-space:nowrap;"><em><em><span style="white-space:nowrap;">ξ</span></em></em><span style="white-space:nowrap;">→</span><em><em><span style="white-space:nowrap;">η</span></em><em></em><em></em> </em><em></em></span> </span>having the generating CC <span style="white-space:nowrap;">D<sub>1</sub><span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;">η</span></span></em></span><em></em>=0</span>. If this is possible, that is when the differential module defined by D<sub>1</sub> is torsion-free, one shall say that the operator D<sub>1</sub> is parametrized by D and there is no relation in general between D and D<sub>2</sub>. The parametrization is said to be “minimum” if the differential module defined by D has a vanishing differential rank and is thus a torsion module. The solution of this problem, first found by the author of this paper in 1995, is still not acknowledged. As for the applications of the “differential double duality” theory to standard equations of physics (<em>Cauchy</em> and Maxwell equations can be parametrized while <em>Einstein</em> equations cannot), we do not know other references. When <span style="font-size:10.0pt;font-family:;" "="">erator in arbitrary dimension</span>=1 as in control theory, the fact that controllability is a “built in” property of a control system, amounting to the existence of a parametrization and thus not depending on the choice of inputs and outputs, even with variable coefficients, is still not acknowledged by engineers. The parametrization of the <em>Cauchy</em> stress operator in arbitrary dimension <em>n</em> has nevertheless attracted, “separately” and without any general “guiding line”, many famous scientists (G.B. Airy in 1863 for <em>n </em>= 2, J.C. Maxwell in 1863, G. Morera and E. Beltrami in 1892 for <em style="white-space:normal;">n </em><span style="white-space:normal;">= 3</span> , A. Einstein in 1915 for <em style="white-space:normal;">n </em><span style="white-space:normal;">= 4</span> ). The aim of this paper is to solve the minimum parametrization problem in arbitrary dimension and to apply it through effective methods that could even be achieved by using computer algebra. Meanwhile, we prove that all these works are using the <em>Einstein</em> operator which is self-adjoint and not the <em>Ricci</em> operator, a fact showing that the <em>Einstein</em> operator, which cannot be parametrized, has already been exhibited by Beltrami more than 20 years before <em>Einstein</em>. As a byproduct, they are all based on the same confusion between the so-called <em>div</em> operator induced from the <em>Bianchi </em>operator D<sub>2</sub> and the <em>Cauchy</em> operator which is the formal adjoint of the Killing operator D parametrizing the Riemann operator D<sub>1</sub> for an arbitrary <em>n</em>. We prove that this purely mathematical result deeply questions the origin and existence of gravitational waves. We also present the similar motivating situation met in the study of contact structures when <em>n</em> = 3. Like the Michelson and Morley experiment, it is thus an open historical problem to know whether <em>Einstein</em> was aware of these previous works or not, but the comparison needs no comment.
基金Supported by Sichuan Science and Technology Program (No.2022ZYD0010)。
文摘The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.
基金supported by the National Key R&D Program of China(2023YFC3304600).
文摘Existing multi-view deep subspace clustering methods aim to learn a unified representation from multi-view data,while the learned representation is difficult to maintain the underlying structure hidden in the origin samples,especially the high-order neighbor relationship between samples.To overcome the above challenges,this paper proposes a novel multi-order neighborhood fusion based multi-view deep subspace clustering model.We creatively integrate the multi-order proximity graph structures of different views into the self-expressive layer by a multi-order neighborhood fusion module.By this design,the multi-order Laplacian matrix supervises the learning of the view-consistent self-representation affinity matrix;then,we can obtain an optimal global affinity matrix where each connected node belongs to one cluster.In addition,the discriminative constraint between views is designed to further improve the clustering performance.A range of experiments on six public datasets demonstrates that the method performs better than other advanced multi-view clustering methods.The code is available at https://github.com/songzuolong/MNF-MDSC(accessed on 25 December 2024).
基金supported by National Science Foundations of China(Grant No.11771340,12171373).
文摘Recently,Choe-Koo-Wang(J Funct Anal,2020,278)demonstrated the rigid phenomenon:The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC),implies that each difference is compact on the weighted Bergman space in the unit disk.Motivated by the subtle connection of composition operator theory on the weighted Bergman spaces,Korenblum spaces and bounded holomorphic function spaces,we first explore the rigid phenomenon which also holds on the Korenblum space over the unit ball.Furthermore,we discuss which difference of composition operators is compact when the compact combination of composition operators does not satisfy the condition(CNC)on Korenblum spaces and bounded holomorphic function spaces over the unit ball setting.
基金Supported by by Natural Science Foundation of Henan(202300410184 and242300421387)。
文摘In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,n/n-a)bound of M_(α)is at worst 2^(n-a).The weak type(1,n/n-a)bound of M_(α)can be estimated more directly and easily in this method,which is different from the usual ways.
基金supported by the National Natural Science Foundation of China(12071076)the Scientific Research Start-up Foundation of Fujian University of Technology(GY-Z23238)the Program for Education and Scientific Research of Young and Middle-Aged Teachers in Fujian Province(JAT191128,JT180818)。
文摘Explicit asymptotic properties of the integrated density of states N(λ)with respect to the spectrum for the random Schrödinger operator H^(ω)=(-△)^(α/2)+V^(ω)are established,whereα∈(0,2]and V^(ω)(X)=∑_(I∈Z^(d))ξ(i)(ω)W(x-i)is a random potential term generated by a sequence of independent and identically distributed random variables{ξ(i)}_(i)∈Z^(d)and a non-negative measurable function W(x).In particular,the exact order of asymptotic properties of N(λ)depends on the decay properties of the reference function W(x)and the spectrum properties of the first Dirichlet eigenvalue of(-△)^(α/2).
基金Supported by Fujian Provincial Natural Science Foundation of China(2024J01792)。
文摘In the present paper,the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined.It has shown that the new operators are the Gamma transform of the Jakimovski-Leviatan operators.The degree of approximation is given by the modulus of continuity.It has been stressed that,there are other operators having the same error estimation with the operators,arising from the Sz´asz-Durrmeyer operators.Then the degree of global approximation is obtained in a special Lipschitz type function space.Further,a Voronovskaja type asymptotic formula and Gr¨uss-Voronovskaja type theorem are given.The approximation with these operators is visualized with the help of error tables and graphical examples.
