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
In this paper,we study the basic p-harmonic forms on the complete foliated Riemannian manifolds.By using the method in[1],we show that if the basic mean curvature form is bounded and co-closed,and the transversal curv...In this paper,we study the basic p-harmonic forms on the complete foliated Riemannian manifolds.By using the method in[1],we show that if the basic mean curvature form is bounded and co-closed,and the transversal curvature operator is nonnegative and positive at least one point,then we obtain a vanishing theorem for L^(p)-integrably p-harmonic r-forms.展开更多
In this paper,we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean C2-smooth surface in the Heisenberg gro...In this paper,we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean C2-smooth surface in the Heisenberg group away from characteristic points and signed geodesic curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for Euclidean C2-smooth curves on surfaces.We get Gauss-Bonnet theorems associated to two kinds of Schouten-Van Kampen affine connections in the Heisenberg group.展开更多
In this paper,we prove some Liouville-type theorems for the stationary magnetomicropolar fluids under suitable conditions in three space dimensions.We first prove that the solutions are trivial under the assumption of...In this paper,we prove some Liouville-type theorems for the stationary magnetomicropolar fluids under suitable conditions in three space dimensions.We first prove that the solutions are trivial under the assumption of certain growth conditions for the mean oscillations of the potentials.And then we show similar results assuming that the solutions are contained in L^(p)(R^(3))with p∈[2,9/2).Finally,we show the same result for lower values of p∈[1,9/4)with the further assumption that the solutions vanish at infinity.展开更多
In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some ...In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.展开更多
This article improves and advances the results achieved by Vishal and Naveen,leveraging the use of Lebesgue integrable functions.Going beyond,we investigate fixed point theorems associated with a concept introduced by...This article improves and advances the results achieved by Vishal and Naveen,leveraging the use of Lebesgue integrable functions.Going beyond,we investigate fixed point theorems associated with a concept introduced by Ovidiu Popescu.Our research not only bolsters the theoretical framework but also unveils practical applications in the domain of Lebesgue integrals as in Example 3.6.Furthermore,our contribution enhances the understanding of fixed point theorems in metric spaces and introduces novel perspectives in the study of generalizedα-Geraghty contractive mappings on Lebesgue integrals.展开更多
This paper applies Gödel’s Incompleteness Theorems to the evolution and development of human social systems.Although Gödel’s Incompleteness Theorems originated in the field of mathematics,their influence h...This paper applies Gödel’s Incompleteness Theorems to the evolution and development of human social systems.Although Gödel’s Incompleteness Theorems originated in the field of mathematics,their influence has long extended beyond mathematics,making an impact on philosophy,systems science,and the humanities and social sciences.The paper analyzes the autonomy and completeness of human social systems,arguing that evolving human societies are generally self-consistent.However,if the completeness of a human social system is compromised,the system either maintains self-consistency,ceases to evolve forward,enters a death spiral,and eventually decays and disintegrates.Or the system addresses the completeness issue,enters a state of non-self-consistency,introduces new axioms,becomes self-governing again,and enters a new form.From the sociological perspective,this is articulated as social revolution-the system continues to evolve forward;the absence of social revolution-the system does not evolve forward(Jin,1988).展开更多
In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold ...In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold andδ>1(n-1)p2/4n[p-1+(p-1)2kp],we prove a vanishing theorem for p-harmonicℓ-forms.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 Steiner-Lehmus equal bisectors theorem originated in the mid 19th century.Despite its age,it would have been accessible to Euclid and his contemporaries.The theorem remains evergreen,with new proofs continuing to ...The Steiner-Lehmus equal bisectors theorem originated in the mid 19th century.Despite its age,it would have been accessible to Euclid and his contemporaries.The theorem remains evergreen,with new proofs continuing to appear steadily.The theorem has fostered discussion about the nature of proof itself,direct and indirect.Here we continue the momentum by providing a trigonometric proof,relatively short,based on an analytic estimate that leverages algebraic trigonometric identities.Many proofs of the theorem exist in the literature.Some of these contain key ideas that already appeared in C.L.Lehmus’1850 proofs,not always with citation.In the aim of increasing awareness of and making more accessible Lehmus’proofs,we provide an annotated translation.We conclude with remarks on different proofs and relations among them.展开更多
In this paper,we study Liouville theorem for the 3D stationary Q-tensor system of liquid crystal in Lorentz and Morrey spaces.Under some additional hypotheses,stated in terms of Lorentz and Morrey spaces,using energy ...In this paper,we study Liouville theorem for the 3D stationary Q-tensor system of liquid crystal in Lorentz and Morrey spaces.Under some additional hypotheses,stated in terms of Lorentz and Morrey spaces,using energy estimation,we obtain that the trivial solution u=Q=0 is the unique solution.Our theorems correspond to improvements of some recent results and contain some known results as particular cases.展开更多
In this paper,we obtain a vector bundle valued mixed hard Lefschetz theorem.The argument is mainly based on the works of Tien-Cuong Dinh and Viet-Anh Nguyen.
In this paper,we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimens...In this paper,we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces.展开更多
this paper,we study Liouville theorem for 3D steady Q-tensor system of liquid crystal in mixed Lorentz spaces.We obtain u=0,Q=0 on the conditions that μ∈L^(p,∞x_(1)L^(q,∞x_(2)L^(r,∞x_(3)(R^(4)∩H^(1)(R^(3),Q∈H^(...this paper,we study Liouville theorem for 3D steady Q-tensor system of liquid crystal in mixed Lorentz spaces.We obtain u=0,Q=0 on the conditions that μ∈L^(p,∞x_(1)L^(q,∞x_(2)L^(r,∞x_(3)(R^(4)∩H^(1)(R^(3),Q∈H^(2)(R^(3),p,q,r∈(3,∞],and 1/p+1/q+1/r≥2/3, which extends some known results.展开更多
Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuz...Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.展开更多
Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were appli...Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.展开更多
This paper gives several fundamental theorems for the stability, uniform stability, asymptotic stability and uniform asymptotic stability. Those theorems allow the derivative of Lyapunov functions to be positive on ce...This paper gives several fundamental theorems for the stability, uniform stability, asymptotic stability and uniform asymptotic stability. Those theorems allow the derivative of Lyapunov functions to be positive on certain sets,relax the restriction about the rate of change of state variable in a system to be bounded in Marachkov's theorem and extend the related results in [4—7].展开更多
The conceptions of theorems, laws and corollaries of hydrology were put forward. Combining with hydrology practice, several theo- rems, laws as well as corollaries of hydrology were summarized. The study provided some...The conceptions of theorems, laws and corollaries of hydrology were put forward. Combining with hydrology practice, several theo- rems, laws as well as corollaries of hydrology were summarized. The study provided some references for accelerating the development of hydrology theory in these aspects and promoting the improvement of its production technology.展开更多
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.
基金supported by Guangzhou Science and Technology Program(202102021174)Guangdong Basic and Applied Basic Research Foundation(2023A1515012121).The second author was supported by the Natural Science Foundation of Jiangsu Province(BK20230900)+1 种基金the Fundamental Research Funds for the Central Universities(30924010838)Both authors are partially supported by NSF in China(12141104).
文摘In this paper,we study the basic p-harmonic forms on the complete foliated Riemannian manifolds.By using the method in[1],we show that if the basic mean curvature form is bounded and co-closed,and the transversal curvature operator is nonnegative and positive at least one point,then we obtain a vanishing theorem for L^(p)-integrably p-harmonic r-forms.
文摘In this paper,we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean C2-smooth surface in the Heisenberg group away from characteristic points and signed geodesic curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for Euclidean C2-smooth curves on surfaces.We get Gauss-Bonnet theorems associated to two kinds of Schouten-Van Kampen affine connections in the Heisenberg group.
基金supported by Inha University Research Grant and National Research Foundation of Korea Grant funded by the Korean Government(RS-2023-00212227)supported by National Research Foundation of Korea Grant funded by the Korean Government(NRF-2020R1C1C1A01006521)。
文摘In this paper,we prove some Liouville-type theorems for the stationary magnetomicropolar fluids under suitable conditions in three space dimensions.We first prove that the solutions are trivial under the assumption of certain growth conditions for the mean oscillations of the potentials.And then we show similar results assuming that the solutions are contained in L^(p)(R^(3))with p∈[2,9/2).Finally,we show the same result for lower values of p∈[1,9/4)with the further assumption that the solutions vanish at infinity.
基金Supported in part by the National Social Science Foundation of China(19BTJ020)。
文摘In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.
文摘This article improves and advances the results achieved by Vishal and Naveen,leveraging the use of Lebesgue integrable functions.Going beyond,we investigate fixed point theorems associated with a concept introduced by Ovidiu Popescu.Our research not only bolsters the theoretical framework but also unveils practical applications in the domain of Lebesgue integrals as in Example 3.6.Furthermore,our contribution enhances the understanding of fixed point theorems in metric spaces and introduces novel perspectives in the study of generalizedα-Geraghty contractive mappings on Lebesgue integrals.
文摘This paper applies Gödel’s Incompleteness Theorems to the evolution and development of human social systems.Although Gödel’s Incompleteness Theorems originated in the field of mathematics,their influence has long extended beyond mathematics,making an impact on philosophy,systems science,and the humanities and social sciences.The paper analyzes the autonomy and completeness of human social systems,arguing that evolving human societies are generally self-consistent.However,if the completeness of a human social system is compromised,the system either maintains self-consistency,ceases to evolve forward,enters a death spiral,and eventually decays and disintegrates.Or the system addresses the completeness issue,enters a state of non-self-consistency,introduces new axioms,becomes self-governing again,and enters a new form.From the sociological perspective,this is articulated as social revolution-the system continues to evolve forward;the absence of social revolution-the system does not evolve forward(Jin,1988).
文摘In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold andδ>1(n-1)p2/4n[p-1+(p-1)2kp],we prove a vanishing theorem for p-harmonicℓ-forms.
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 Steiner-Lehmus equal bisectors theorem originated in the mid 19th century.Despite its age,it would have been accessible to Euclid and his contemporaries.The theorem remains evergreen,with new proofs continuing to appear steadily.The theorem has fostered discussion about the nature of proof itself,direct and indirect.Here we continue the momentum by providing a trigonometric proof,relatively short,based on an analytic estimate that leverages algebraic trigonometric identities.Many proofs of the theorem exist in the literature.Some of these contain key ideas that already appeared in C.L.Lehmus’1850 proofs,not always with citation.In the aim of increasing awareness of and making more accessible Lehmus’proofs,we provide an annotated translation.We conclude with remarks on different proofs and relations among them.
基金Supported by National Natural Science Foundation of China(11871305,11901346).
文摘In this paper,we study Liouville theorem for the 3D stationary Q-tensor system of liquid crystal in Lorentz and Morrey spaces.Under some additional hypotheses,stated in terms of Lorentz and Morrey spaces,using energy estimation,we obtain that the trivial solution u=Q=0 is the unique solution.Our theorems correspond to improvements of some recent results and contain some known results as particular cases.
基金supported by the National key R and D Program of China 2020YFA0713100the NSFC(12141104,12371062 and 12431004).
文摘In this paper,we obtain a vector bundle valued mixed hard Lefschetz theorem.The argument is mainly based on the works of Tien-Cuong Dinh and Viet-Anh Nguyen.
基金Supported by National Natural Science Foundation of China(Grant No.11771070).
文摘In this paper,we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces.
基金Supported by the National Natural Science Foundation of China(11871305)。
文摘this paper,we study Liouville theorem for 3D steady Q-tensor system of liquid crystal in mixed Lorentz spaces.We obtain u=0,Q=0 on the conditions that μ∈L^(p,∞x_(1)L^(q,∞x_(2)L^(r,∞x_(3)(R^(4)∩H^(1)(R^(3),Q∈H^(2)(R^(3),p,q,r∈(3,∞],and 1/p+1/q+1/r≥2/3, which extends some known results.
基金Supported by the Aeronautical Science Foundation(20115868009)the Open Project Program of Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education in Xiangtan University(2011ICIP04)+1 种基金the Program of 211 Innovation Engineering on Information in Xiamen University(2009-2011)the College Students Innovation Training Plan of Xianmen University~~
文摘Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.
文摘Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.
文摘This paper gives several fundamental theorems for the stability, uniform stability, asymptotic stability and uniform asymptotic stability. Those theorems allow the derivative of Lyapunov functions to be positive on certain sets,relax the restriction about the rate of change of state variable in a system to be bounded in Marachkov's theorem and extend the related results in [4—7].
文摘The conceptions of theorems, laws and corollaries of hydrology were put forward. Combining with hydrology practice, several theo- rems, laws as well as corollaries of hydrology were summarized. The study provided some references for accelerating the development of hydrology theory in these aspects and promoting the improvement of its production technology.
