Arrhythmias are a frequently occurring phenomenon in clinical practice,but how to accurately dis-tinguish subtle rhythm abnormalities remains an ongoing difficulty faced by the entire research community when conductin...Arrhythmias are a frequently occurring phenomenon in clinical practice,but how to accurately dis-tinguish subtle rhythm abnormalities remains an ongoing difficulty faced by the entire research community when conducting ECG-based studies.From a review of existing studies,two main factors appear to contribute to this problem:the uneven distribution of arrhythmia classes and the limited expressiveness of features learned by current models.To overcome these limitations,this study proposes a dual-path multimodal framework,termed DM-EHC(Dual-Path Multimodal ECG Heartbeat Classifier),for ECG-based heartbeat classification.The proposed framework links 1D ECG temporal features with 2D time–frequency features.By setting up the dual paths described above,the model can process more dimensions of feature information.The MIT-BIH arrhythmia database was selected as the baseline dataset for the experiments.Experimental results show that the proposed method outperforms single modalities and performs better for certain specific types of arrhythmias.The model achieved mean precision,recall,and F1 score of 95.14%,92.26%,and 93.65%,respectively.These results indicate that the framework is robust and has potential value in automated arrhythmia classification.展开更多
We study how can an angular momentum coherent state |τ> keeps its form-invariant during time evolution governed by the Hamiltonian H = f(t)J++ f^*(t)J-+ g(t)Jz. We discuss this topic in the context of boson realiz...We study how can an angular momentum coherent state |τ> keeps its form-invariant during time evolution governed by the Hamiltonian H = f(t)J++ f^*(t)J-+ g(t)Jz. We discuss this topic in the context of boson realization of |τ>. By employing the entangled state representation |ζ> and deriving a new binomial theorem involving two-subscript Hermite polynomials, we derive the wave function <ζ|τ>, which turns out to be a single-subscript Hermite polynomial. Based on this result the maintenance of angular momentum coherent state during time evolution is examined, and the value of τ(t) is totally determined by the parameters involved in the Hamiltonian.展开更多
In this paper,we shall exploit the Freud method in the Classical operator approximation theory to im- prove known quantitative estimalions with an emphasis on Calculah' on the generic constants.
This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.
Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalizat...Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalization of this method to the complex fractional Fourier transformation case is also possible.展开更多
Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner...Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner-product space,which avoids introducing the generating function and Taylor series expansion.The proof is also extended to any finite-dimensional inner-product space.展开更多
In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we ...In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we study the representation problems of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces,obtain the algebraic representation continued equalities(l^(0)({X_(i)}))^(*)=^(A)(c00^(0)({X_(i)}))^(*)=Ac00({X_(i)^(*)}),(l^(0)(X))^(*)=^(A)(c0^(0)(X))^(*)=^(A)(c00^(0)(X))^(*)=^(A)C00(X^(0)),and the topological representation((c00^(0)({X_(i)}))^(*),sw^(*))=c00^(0)({X_(i)^(*)}),where sw^(*)is the sequen-tial weak star topology.For the sequences of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.展开更多
In a preceding letter （2007 Opt. Lett. 32 554） we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem ...In a preceding letter （2007 Opt. Lett. 32 554） we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.展开更多
By applying the Fourier slice theorem, Sθ（λ） =∫^∞-∞Pθ（t）e^-iλt=F（λcosθ,λsinθ）,where Pθ（t） is a projection of f（x,p）=^∞∫∫-∞F（u,v）e^i（uz＋up） dudv along lines of constant, to the Wigner ...By applying the Fourier slice theorem, Sθ（λ） =∫^∞-∞Pθ（t）e^-iλt=F（λcosθ,λsinθ）,where Pθ（t） is a projection of f（x,p）=^∞∫∫-∞F（u,v）e^i（uz＋up） dudv along lines of constant, to the Wigner operator we are naturally led to a projection operator （pure state）, which results in a new complete representation. The Weyl orderimg formalism of the Wigner operator is used in the derivation.展开更多
The author obtains an algebraic version of the main result from his previous paper 'A characterization of Riesz spaces which are Riesz isomorphic to C(X) for some completely regular space X', and also studies...The author obtains an algebraic version of the main result from his previous paper 'A characterization of Riesz spaces which are Riesz isomorphic to C(X) for some completely regular space X', and also studies the relations among some conditions used therein.展开更多
In global navigation satellite system denial environment,cross-view geo-localization based on image retrieval presents an exceedingly critical visual localization solution for Unmanned Aerial Vehicle(UAV)systems.The e...In global navigation satellite system denial environment,cross-view geo-localization based on image retrieval presents an exceedingly critical visual localization solution for Unmanned Aerial Vehicle(UAV)systems.The essence of cross-view geo-localization resides in matching images containing the same geographical targets from disparate platforms,such as UAV-view and satellite-view images.However,images of the same geographical targets may suffer from occlusions and geometric distortions due to variations in the capturing platform,view,and timing.The existing methods predominantly extract features by segmenting feature maps,which overlook the holistic semantic distribution and structural information of objects,resulting in loss of image information.To address these challenges,dilated neighborhood attention Transformer is employed as the feature extraction backbone,and Multi-feature representations based on Multi-scale Hierarchical Contextual Aggregation(MMHCA)is proposed.In the proposed MMHCA method,the multiscale hierarchical contextual aggregation method is utilized to extract contextual information from local to global across various granularity levels,establishing feature associations of contextual information with global and local information in the image.Subsequently,the multi-feature representations method is utilized to obtain rich discriminative feature information,bolstering the robustness of model in scenarios characterized by positional shifts,varying distances,and scale ambiguities.Comprehensive experiments conducted on the extensively utilized University-1652 and SUES-200 benchmarks indicate that the MMHCA method surpasses the existing techniques.showing outstanding results in UAV localization and navigation.展开更多
Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglo...Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglotz type equations for nonholonomic systems are established.Then,the Noether symmetries are studied,and the conserved quantities are obtained.The results are extended to nonholonomic canonical systems,and the Herglotz type canonical equations and the Noether theorems are obtained.Two examples are provided to demonstrate the validity of the methods and results.展开更多
Let F_(1)be the virtual field consisting of one element and(Q,I)a string pair.In this paper,we study the representations of string pairs over the virtual field F_(1).It is proved that an indecomposable F_(1)-represent...Let F_(1)be the virtual field consisting of one element and(Q,I)a string pair.In this paper,we study the representations of string pairs over the virtual field F_(1).It is proved that an indecomposable F_(1)-representation is either a string representation or a band representation by using the coefficient quivers.It is worth noting that for a given band and a positive integer,there exists a unique band representation up to isomorphism.展开更多
Artificial intelligence(AI)researchers and cheminformatics specialists strive to identify effective drug precursors while optimizing costs and accelerating development processes.Digital molecular representation plays ...Artificial intelligence(AI)researchers and cheminformatics specialists strive to identify effective drug precursors while optimizing costs and accelerating development processes.Digital molecular representation plays a crucial role in achieving this objective by making molecules machine-readable,thereby enhancing the accuracy of molecular prediction tasks and facilitating evidence-based decision making.This study presents a comprehensive review of small molecular representations and AI-driven drug discovery downstream tasks utilizing these representations.The research methodology begins with the compilation of small molecule databases,followed by an analysis of fundamental molecular representations and the models that learn these representations from initial forms,capturing patterns and salient features across extensive chemical spaces.The study then examines various drug discovery downstream tasks,including drug-target interaction(DTI)prediction,drug-target affinity(DTA)prediction,drug property(DP)prediction,and drug generation,all based on learned representations.The analysis concludes by highlighting challenges and opportunities associated with machine learning(ML)methods for molecular representation and improving downstream task performance.Additionally,the representation of small molecules and AI-based downstream tasks demonstrates significant potential in identifying traditional Chinese medicine(TCM)medicinal substances and facilitating TCM target discovery.展开更多
In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequen...In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights.展开更多
Quantum software development utilizes quantum phenomena such as superposition and entanglement to address problems that are challenging for classical systems.However,it must also adhere to critical quantum constraints...Quantum software development utilizes quantum phenomena such as superposition and entanglement to address problems that are challenging for classical systems.However,it must also adhere to critical quantum constraints,notably the no-cloning theorem,which prohibits the exact duplication of unknown quantum states and has profound implications for cryptography,secure communication,and error correction.While existing quantum circuit representations implicitly honor such constraints,they lack formal mechanisms for early-stage verification in software design.Addressing this constraint at the design phase is essential to ensure the correctness and reliability of quantum software.This paper presents a formal metamodeling framework using UML-style notation and and Object Constraint Language(OCL)to systematically capture and enforce the no-cloning theorem within quantum software models.The proposed metamodel formalizes key quantum concepts—such as entanglement and teleportation—and encodes enforceable invariants that reflect core quantum mechanical laws.The framework’s effectiveness is validated by analyzing two critical edge cases—conditional copying with CNOT gates and quantum teleportation—through instance model evaluations.These cases demonstrate that the metamodel can capture nuanced scenarios that are often mistaken as violations of the no-cloning theorem but are proven compliant under formal analysis.Thus,these serve as constructive validations that demonstrate the metamodel’s expressiveness and correctness in representing operations that may appear to challenge the no-cloning theorem but,upon rigorous analysis,are shown to comply with it.The approach supports early detection of conceptual design errors,promoting correctness prior to implementation.The framework’s extensibility is also demonstrated by modeling projective measurement,further reinforcing its applicability to broader quantum software engineering tasks.By integrating the rigor of metamodeling with fundamental quantum mechanical principles,this work provides a structured,model-driven approach that enables traditional software engineers to address quantum computing challenges.It offers practical insights into embedding quantum correctness at the modeling level and advances the development of reliable,error-resilient quantum software systems.展开更多
We propose the scaling rule of Morse oscillator,based on this rule and by virtue of the Her-mann-Feymann theorem,we respectively obtain the distribution of potential and kinetic ener-gy of the Morse Hamiltonian.Also,w...We propose the scaling rule of Morse oscillator,based on this rule and by virtue of the Her-mann-Feymann theorem,we respectively obtain the distribution of potential and kinetic ener-gy of the Morse Hamiltonian.Also,we derive the exact upper limit of physical energy level.Further,we derive some recursive relations for energy matrix elements of the potential and other similar operators in the context of Morse oscillator theory.展开更多
The purpose of this article is to depart from the conventional belief that John Donne,a vibrant 17th-century writer,is a full-blown metaphysical poet as widely claimed while also acknowledging the poetic ingenuity of ...The purpose of this article is to depart from the conventional belief that John Donne,a vibrant 17th-century writer,is a full-blown metaphysical poet as widely claimed while also acknowledging the poetic ingenuity of John Donne.While Donne’s poetry is rich in matter and manner,and his poems are caked in wit,intellectual superiority,and apt exploration of telling themes,dressing him fully in borrowed robes seems a stretch.Some of Donne’s poems,without a shred of doubt,contain flavors of metaphysical poetry,but the term“metaphysical”seems to be unsuitable for poems such as“A Valediction:Forbidding Mourning”.展开更多
Establishing and maintaining protected areas is a pivotal strategy for attaining the post-2020 biodiversity target. The conservation objectives of protected areas have shifted from a narrow emphasis on biodiversity to...Establishing and maintaining protected areas is a pivotal strategy for attaining the post-2020 biodiversity target. The conservation objectives of protected areas have shifted from a narrow emphasis on biodiversity to encompass broader considerations such as ecosystem stability, community resilience to climate change, and enhancement of human well-being. Given these multifaceted objectives, it is imperative to judiciously allocate resources to effectively conserve biodiversity by identifying strategically significant areas for conservation, particularly for mountainous areas. In this study, we evaluated the representativeness of the protected area network in the Qin ling Mountains concerning species diversity, ecosystem services, climate stability and ecological stability. The results indicate that some of the ecological indicators are spatially correlated with topographic gradient effects. The conservation priority areas predominantly lie in the northern foothills, the southeastern, and southwestern parts of the Qinling Mountain with areas concentrated at altitudes between 1,500-2,000 m and slopes between 40°-50° as hotspots. The conservation priority areas identified through the framework of inclusive conservation optimization account for 22.9 % of the Qinling Mountain. Existing protected areas comprise only 6.1 % of the Qinling Mountain and 13.18 % of the conservation priority areas. This will play an important role in achiev ing sustainable development in the region and in meeting the post-2020 biodiversity target. The framework can advance the different objectives of achieving a quadruple win and can also be extended to other regions.展开更多
基金supported by the Innovative Human Resource Development for Local Intel-lectualization program through the Institute of Information&Communications Technology Planning&Evaluation(IITP)grant funded by the Korea government(MSIT)(No.IITP-2026-2020-0-01741)the research fund of Hanyang University(HY-2025-1110).
文摘Arrhythmias are a frequently occurring phenomenon in clinical practice,but how to accurately dis-tinguish subtle rhythm abnormalities remains an ongoing difficulty faced by the entire research community when conducting ECG-based studies.From a review of existing studies,two main factors appear to contribute to this problem:the uneven distribution of arrhythmia classes and the limited expressiveness of features learned by current models.To overcome these limitations,this study proposes a dual-path multimodal framework,termed DM-EHC(Dual-Path Multimodal ECG Heartbeat Classifier),for ECG-based heartbeat classification.The proposed framework links 1D ECG temporal features with 2D time–frequency features.By setting up the dual paths described above,the model can process more dimensions of feature information.The MIT-BIH arrhythmia database was selected as the baseline dataset for the experiments.Experimental results show that the proposed method outperforms single modalities and performs better for certain specific types of arrhythmias.The model achieved mean precision,recall,and F1 score of 95.14%,92.26%,and 93.65%,respectively.These results indicate that the framework is robust and has potential value in automated arrhythmia classification.
基金Project supported by the National Natural Science Foundation of China(Grant No.11347026)the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2016AM03 and ZR2017MA011)
文摘We study how can an angular momentum coherent state |τ> keeps its form-invariant during time evolution governed by the Hamiltonian H = f(t)J++ f^*(t)J-+ g(t)Jz. We discuss this topic in the context of boson realization of |τ>. By employing the entangled state representation |ζ> and deriving a new binomial theorem involving two-subscript Hermite polynomials, we derive the wave function <ζ|τ>, which turns out to be a single-subscript Hermite polynomial. Based on this result the maintenance of angular momentum coherent state during time evolution is examined, and the value of τ(t) is totally determined by the parameters involved in the Hamiltonian.
文摘In this paper,we shall exploit the Freud method in the Classical operator approximation theory to im- prove known quantitative estimalions with an emphasis on Calculah' on the generic constants.
基金Supported by the National Natural Science Foundation of China (No. 69803007)
文摘This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.
基金National Natural Science Foundation of China under Grant No.10775097
文摘Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalization of this method to the complex fractional Fourier transformation case is also possible.
文摘Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner-product space,which avoids introducing the generating function and Taylor series expansion.The proof is also extended to any finite-dimensional inner-product space.
基金Supported by the National Natural Science Foundation of China(Grant No.11471236)
文摘In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we study the representation problems of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces,obtain the algebraic representation continued equalities(l^(0)({X_(i)}))^(*)=^(A)(c00^(0)({X_(i)}))^(*)=Ac00({X_(i)^(*)}),(l^(0)(X))^(*)=^(A)(c0^(0)(X))^(*)=^(A)(c00^(0)(X))^(*)=^(A)C00(X^(0)),and the topological representation((c00^(0)({X_(i)}))^(*),sw^(*))=c00^(0)({X_(i)^(*)}),where sw^(*)is the sequen-tial weak star topology.For the sequences of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.
基金supported by the National Natural Science Foundation of China (Grant No. 10775097)the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ10097)
文摘In a preceding letter （2007 Opt. Lett. 32 554） we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.
基金Supported by National Natural Science Foundation of China under Grant No.10874174
文摘By applying the Fourier slice theorem, Sθ（λ） =∫^∞-∞Pθ（t）e^-iλt=F（λcosθ,λsinθ）,where Pθ（t） is a projection of f（x,p）=^∞∫∫-∞F（u,v）e^i（uz＋up） dudv along lines of constant, to the Wigner operator we are naturally led to a projection operator （pure state）, which results in a new complete representation. The Weyl orderimg formalism of the Wigner operator is used in the derivation.
文摘The author obtains an algebraic version of the main result from his previous paper 'A characterization of Riesz spaces which are Riesz isomorphic to C(X) for some completely regular space X', and also studies the relations among some conditions used therein.
基金supported by the National Natural Science Foundation of China(Nos.12072027,62103052,61603346 and 62103379)the Henan Key Laboratory of General Aviation Technology,China(No.ZHKF-230201)+3 种基金the Funding for the Open Research Project of the Rotor Aerodynamics Key Laboratory,China(No.RAL20200101)the Key Research and Development Program of Henan Province,China(Nos.241111222000 and 241111222900)the Key Science and Technology Program of Henan Province,China(No.232102220067)the Scholarship Funding from the China Scholarship Council(No.202206030079).
文摘In global navigation satellite system denial environment,cross-view geo-localization based on image retrieval presents an exceedingly critical visual localization solution for Unmanned Aerial Vehicle(UAV)systems.The essence of cross-view geo-localization resides in matching images containing the same geographical targets from disparate platforms,such as UAV-view and satellite-view images.However,images of the same geographical targets may suffer from occlusions and geometric distortions due to variations in the capturing platform,view,and timing.The existing methods predominantly extract features by segmenting feature maps,which overlook the holistic semantic distribution and structural information of objects,resulting in loss of image information.To address these challenges,dilated neighborhood attention Transformer is employed as the feature extraction backbone,and Multi-feature representations based on Multi-scale Hierarchical Contextual Aggregation(MMHCA)is proposed.In the proposed MMHCA method,the multiscale hierarchical contextual aggregation method is utilized to extract contextual information from local to global across various granularity levels,establishing feature associations of contextual information with global and local information in the image.Subsequently,the multi-feature representations method is utilized to obtain rich discriminative feature information,bolstering the robustness of model in scenarios characterized by positional shifts,varying distances,and scale ambiguities.Comprehensive experiments conducted on the extensively utilized University-1652 and SUES-200 benchmarks indicate that the MMHCA method surpasses the existing techniques.showing outstanding results in UAV localization and navigation.
基金supported by the National Natural Science Foundation of China(Grant No.12272248)the Postgraduate Research and Practice Innovation Program of Jiangsu Province of China(Grant No.KYCX23_3296).
文摘Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglotz type equations for nonholonomic systems are established.Then,the Noether symmetries are studied,and the conserved quantities are obtained.The results are extended to nonholonomic canonical systems,and the Herglotz type canonical equations and the Noether theorems are obtained.Two examples are provided to demonstrate the validity of the methods and results.
文摘Let F_(1)be the virtual field consisting of one element and(Q,I)a string pair.In this paper,we study the representations of string pairs over the virtual field F_(1).It is proved that an indecomposable F_(1)-representation is either a string representation or a band representation by using the coefficient quivers.It is worth noting that for a given band and a positive integer,there exists a unique band representation up to isomorphism.
基金supported by the Shenzhen Key Laboratory of Intelligent Bioinformatics(No.ZDSYS20220422103800001)the Shenzhen Science and Technology Program(No.JCYJ20230807140709020)+2 种基金National Natural Science Foundation of China(Nos.62402489,U22A2041,and 62373172)the China Postdoctoral Science Foundation(No.2023M743688)Guangdong Basic and Applied Basic Research Foundation(Nos.2024A1515011960 and 2023A1515110570)。
文摘Artificial intelligence(AI)researchers and cheminformatics specialists strive to identify effective drug precursors while optimizing costs and accelerating development processes.Digital molecular representation plays a crucial role in achieving this objective by making molecules machine-readable,thereby enhancing the accuracy of molecular prediction tasks and facilitating evidence-based decision making.This study presents a comprehensive review of small molecular representations and AI-driven drug discovery downstream tasks utilizing these representations.The research methodology begins with the compilation of small molecule databases,followed by an analysis of fundamental molecular representations and the models that learn these representations from initial forms,capturing patterns and salient features across extensive chemical spaces.The study then examines various drug discovery downstream tasks,including drug-target interaction(DTI)prediction,drug-target affinity(DTA)prediction,drug property(DP)prediction,and drug generation,all based on learned representations.The analysis concludes by highlighting challenges and opportunities associated with machine learning(ML)methods for molecular representation and improving downstream task performance.Additionally,the representation of small molecules and AI-based downstream tasks demonstrates significant potential in identifying traditional Chinese medicine(TCM)medicinal substances and facilitating TCM target discovery.
基金Supported by the National Natural Science Foundation of China(12301101)the Guangdong Basic and Applied Basic Research Foundation(2022A1515110019 and 2020A1515110585)。
文摘In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights.
文摘Quantum software development utilizes quantum phenomena such as superposition and entanglement to address problems that are challenging for classical systems.However,it must also adhere to critical quantum constraints,notably the no-cloning theorem,which prohibits the exact duplication of unknown quantum states and has profound implications for cryptography,secure communication,and error correction.While existing quantum circuit representations implicitly honor such constraints,they lack formal mechanisms for early-stage verification in software design.Addressing this constraint at the design phase is essential to ensure the correctness and reliability of quantum software.This paper presents a formal metamodeling framework using UML-style notation and and Object Constraint Language(OCL)to systematically capture and enforce the no-cloning theorem within quantum software models.The proposed metamodel formalizes key quantum concepts—such as entanglement and teleportation—and encodes enforceable invariants that reflect core quantum mechanical laws.The framework’s effectiveness is validated by analyzing two critical edge cases—conditional copying with CNOT gates and quantum teleportation—through instance model evaluations.These cases demonstrate that the metamodel can capture nuanced scenarios that are often mistaken as violations of the no-cloning theorem but are proven compliant under formal analysis.Thus,these serve as constructive validations that demonstrate the metamodel’s expressiveness and correctness in representing operations that may appear to challenge the no-cloning theorem but,upon rigorous analysis,are shown to comply with it.The approach supports early detection of conceptual design errors,promoting correctness prior to implementation.The framework’s extensibility is also demonstrated by modeling projective measurement,further reinforcing its applicability to broader quantum software engineering tasks.By integrating the rigor of metamodeling with fundamental quantum mechanical principles,this work provides a structured,model-driven approach that enables traditional software engineers to address quantum computing challenges.It offers practical insights into embedding quantum correctness at the modeling level and advances the development of reliable,error-resilient quantum software systems.
基金supported by the National Natural Science Foundation of China(No.10874174)。
文摘We propose the scaling rule of Morse oscillator,based on this rule and by virtue of the Her-mann-Feymann theorem,we respectively obtain the distribution of potential and kinetic ener-gy of the Morse Hamiltonian.Also,we derive the exact upper limit of physical energy level.Further,we derive some recursive relations for energy matrix elements of the potential and other similar operators in the context of Morse oscillator theory.
文摘The purpose of this article is to depart from the conventional belief that John Donne,a vibrant 17th-century writer,is a full-blown metaphysical poet as widely claimed while also acknowledging the poetic ingenuity of John Donne.While Donne’s poetry is rich in matter and manner,and his poems are caked in wit,intellectual superiority,and apt exploration of telling themes,dressing him fully in borrowed robes seems a stretch.Some of Donne’s poems,without a shred of doubt,contain flavors of metaphysical poetry,but the term“metaphysical”seems to be unsuitable for poems such as“A Valediction:Forbidding Mourning”.
基金supported by the National Natural Science Foun-dation of China(Grant No.72349002).
文摘Establishing and maintaining protected areas is a pivotal strategy for attaining the post-2020 biodiversity target. The conservation objectives of protected areas have shifted from a narrow emphasis on biodiversity to encompass broader considerations such as ecosystem stability, community resilience to climate change, and enhancement of human well-being. Given these multifaceted objectives, it is imperative to judiciously allocate resources to effectively conserve biodiversity by identifying strategically significant areas for conservation, particularly for mountainous areas. In this study, we evaluated the representativeness of the protected area network in the Qin ling Mountains concerning species diversity, ecosystem services, climate stability and ecological stability. The results indicate that some of the ecological indicators are spatially correlated with topographic gradient effects. The conservation priority areas predominantly lie in the northern foothills, the southeastern, and southwestern parts of the Qinling Mountain with areas concentrated at altitudes between 1,500-2,000 m and slopes between 40°-50° as hotspots. The conservation priority areas identified through the framework of inclusive conservation optimization account for 22.9 % of the Qinling Mountain. Existing protected areas comprise only 6.1 % of the Qinling Mountain and 13.18 % of the conservation priority areas. This will play an important role in achiev ing sustainable development in the region and in meeting the post-2020 biodiversity target. The framework can advance the different objectives of achieving a quadruple win and can also be extended to other regions.
