As binary geological media,soil-rock mixtures(SRMs)exhibit a distinct gradational composition,leading to their unique mechanical behaviors.To appraise the stability of SRM slopes,it is essential to determine equivalen...As binary geological media,soil-rock mixtures(SRMs)exhibit a distinct gradational composition,leading to their unique mechanical behaviors.To appraise the stability of SRM slopes,it is essential to determine equivalent parameters of SRMs,which are typically obtained through experimental and numerical methods.In contrasted to other numerical methods,the numerical manifold method(NMM)is more effective in addressing SRM problems.This is because the high-precision regular mathematical meshes in NMM can be used without aligning with the soil-rock interfaces and boundaries of SRMs.In the current research,the equivalent strength parameters of SRMs,i.e.the equivalent cohesion ce and internal friction angleϕ_(e),are determined using NMM.Initially,an NMM triaxial numerical model is established and validated based on triaxial experiments.Subsequently,the soil and rock parameters are derived through parameter inversion.Moreover,the impacts of rock content,size,shape and rock blocks'major-axis orientation on ce andϕ_(e) of SRMs are thoroughly examined using the NMM triaxial numerical model.Additionally,a fitting function is proposed to linkϕ_(e) to the rock content and size of SRMs.When other influencing factors are fixed,the above fitting model leads to the following conclusions:(1)the predictedϕ_(e) of SRMs increase with the increase of rock content;and(2)SRM samples with smaller rocks display a higher predictedϕ_(e).展开更多
In fatigue damage tolerance verification tests of aircraft structures,the simulation and loading of flight-byflight spectra require considerable time and resources.To improve the efficiency of load spectrum design and...In fatigue damage tolerance verification tests of aircraft structures,the simulation and loading of flight-byflight spectra require considerable time and resources.To improve the efficiency of load spectrum design and testing,an equivalent constant-amplitude spectrum design method for flight-by-flight spectra is proposed based on the equivalence of crack growth behavior.By combining the Paris crack growth model with the Walker stress ratio correction,the equivalent stress amplitude is directly calculated using structural parameters and load spectrum characteristics,enabling a rapid transformation from variable-amplitude spectra to constant-amplitude spectra.The original spectrum is discretized based on the load-exceedance curve,and the equivalence relationship between multilevel block spectra and constant-amplitude spectra is established.Taking a typical lower wing skin structure of a transport aircraft as an example,two equivalent spectra are designed and validated through fatigue crack growth tests on 2024-T351 center-hole plate specimens.The experimental results show that the fatigue life deviation between the equivalent spectra and the original flight-by-flight spectrum is within 10%,demonstrating the effectiveness of the proposed method.Moreover,the equivalent spectrum constructed under the condition of invariant mean flight stress exhibits higher equivalence accuracy.The influence of spectral shape on the equivalent stress amplitude is further analyzed,revealing that the equivalent stress amplitude increases with the spectrum shape coefficient.The proposed method provides a useful reference for load spectrum design in aircraft structural damage tolerance verification tests.展开更多
An identification method using Allan variance and equivalent theorem is proposed to identify non-stationary sensor errors mixed out of different simple noises. This method firstly derives the discrete Allan variances ...An identification method using Allan variance and equivalent theorem is proposed to identify non-stationary sensor errors mixed out of different simple noises. This method firstly derives the discrete Allan variances of all component noises inherent in noise sources in terms of their different equations; then the variances are used to estimate the parameters of all component noise models; finally, the original errors are represented by the sum of the non-stationary component noise model and the equivalent m...展开更多
By using the properties of w-distances and Gerstewitz＇s functions, we first give a vectorial Takahashi＇s nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland＇s variatio...By using the properties of w-distances and Gerstewitz＇s functions, we first give a vectorial Takahashi＇s nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland＇s variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristfs fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland＇s variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346（2008）, 9-16] are weakened or even completely relieved.展开更多
The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate...The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.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
The current artificial bone is unable to accurately replicate the inhomogeneity and anisotropy of human cancellous bone.To address this issue,we proposed a personalized approach based on clinical CT images to design m...The current artificial bone is unable to accurately replicate the inhomogeneity and anisotropy of human cancellous bone.To address this issue,we proposed a personalized approach based on clinical CT images to design mechanical equivalent porous structures for artificial femoral heads.Firstly,supported by Micro and clinical CT scans of 21 bone specimens,the anisotropic mechanical parameters of human cancellous bone in the femoral head were characterized using clinical CT values(Hounsfield unit).After that,the equivalent porous structure of cancellous bone was designed based on the gyroid surface,the influence of its degree of anisotropy and volume fraction on the macroscopic mechanical parameters was investigated by finite element analysis.Furthermore,a mapping relationship between CT values and the porous structure was established by jointly solving the mechanical parameters of the porous structure and human cancellous bone,allowing the design of personalized gradient porous structures based on clinical CT images.Finally,to verify the mechanical equivalence,implant press-in tests were conducted on 3D-printed artificial femoral heads and human femoral heads,the influence of the porous structure’s cell size in bone-implant interaction problems was also explored.Results showed that the minimum deviations of press-in stiffness(<15%)and peak load(<5%)both occurred when the cell size was 20%to 30%of the implant diameter.In conclusion,the designed porous structure can replicate the human cancellous bone-implant interaction at a high level,indicating its effectiveness in optimizing the mechanical performance of 3D-printed artificial femoral head.展开更多
The equivalent source(ES)method in the spherical coordinate system has been widely applied to processing,reduction,field modeling,and geophysical and geological interpretation of satellite magnetic anomaly data.Howeve...The equivalent source(ES)method in the spherical coordinate system has been widely applied to processing,reduction,field modeling,and geophysical and geological interpretation of satellite magnetic anomaly data.However,the inversion for the ES model suffers from nonuniqueness and instability,which remain unresolved.To mitigate these issues,we introduce both the minimum and flattest models into the model objective function as an alternative regularization approach in the spherical ES method.We first present the methods,then analyze the accuracy of forward calculation and test the proposed ES method in this study by using synthetic data.The experimental results from simulation data indicate that our proposed regularization effectively suppresses the Backus effect and mitigates inversion instability in the low-latitude region.Finally,we apply the proposed method to magnetic anomaly data from China Seismo-Electromagnetic Satellite-1(CSES-1)and Macao Science Satellite-1(MSS-1)magnetic measurements over Africa by constructing an ES model of the large-scale lithospheric magnetic field.Compared with existing global lithospheric magnetic field models,our ES model demonstrates good consistency at high altitudes and predicts more stable fields at low altitudes.Furthermore,we derive the reduction to the pole(RTP)magnetic anomaly fields and the apparent susceptibility contrast distribution based on the ES model.The latter correlates well with the regional tectonic framework in Africa and surroundings.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
The penetration of ogival-nosed projectiles into ship plates represents a complex impact dynamics issue essential for analyzing structural failuremechanisms.Although stiffenedplates are vital in ship construction,fews...The penetration of ogival-nosed projectiles into ship plates represents a complex impact dynamics issue essential for analyzing structural failuremechanisms.Although stiffenedplates are vital in ship construction,fewstudies have addressed the issue of model equivalence under penetration loading.This study employs numerical simulation to validate an experiment with an ogival-nosed projectile penetrating a Q345 steel plate.Four equivalent stiffened plate methods are proposed based on the area,flexural modulus,moment of inertia,and thickness.The results indicate that thickness equivalence(DM4)is unsuitable for penetration-loaded stiffened plates,except under low-speed,nonpenetrating through impacts,and yields less accuracy than DM1/DM3.DM1,DM2,and DM3 each perform optimally with specific velocity ranges:DM1 at very low(critical)and high velocities,DM3 at low velocities,and DM2 at high speeds.Furthermore,in penetration scenarios,T-shaped stiffeners can be replacedwith rectangular ones,as both exhibit similar failure behaviors and deflection trends,simplifying the design while preserving key structural characteristics.These findings provide valuable insights into the design of protective ship structures.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 high cost and low efficiency of full-scale vehicle experiments and numerical simulations limit the efficient development of armored vehicle occupant protection systems.The floor-occupant-seat local simulation mode...The high cost and low efficiency of full-scale vehicle experiments and numerical simulations limit the efficient development of armored vehicle occupant protection systems.The floor-occupant-seat local simulation model provides an alternative solution for quickly evaluating the performance of occupant protection systems.However,the error and rationality of the loading of the thin-walled floor in the local model cannot be ignored.This study proposed an equivalent loading method for the local model,which includes two parts:the dimensionality reduction method for acceleration matrix and the joint optimization framework for equivalent node coordinates.In the dimensionality reduction method,the dimension of the acceleration matrix was reduced based on the improved kernel principal component analysis(KPCA),and a dynamic variable bandwidth was introduced to address the limitation of failing to effectively measure the similarity between acceleration data in conventional KPCA.In addition,a least squares problem with forced displacement constraints was constructed to solve the correction matrix,thereby achieving the scale restoration process of the principal component acceleration matrix.The joint optimization framework for coordinates consists of the error assessment of response time histories(EARTH)and Bayesian optimization.In this framework,the local loading error of the equivalent acceleration matrix is taken as the Bayesian optimization objective,which is quantified and scored by EARTH.The expected improvement acquisition function was used to select the new set of the equivalent acceleration node coordinates for the self-updating optimization of the observation dataset and Gaussian process surrogate model.We reduced the dimension of the acceleration matrix from 2256 to 7,while retaining 91%of the information features.The comprehensive error score of occupant's lower limb response in the local model increased from 58.5%to 80.4%.The proposed equivalent loading method provides a solution for the rapid and reliable development of occupant protection systems.展开更多
One of the core works of analyzing Electrochemical Impedance Spectroscopy(EIS)data is to select an appropriate equivalent circuit model to quantify the parameters of the electrochemical reaction process.However,this p...One of the core works of analyzing Electrochemical Impedance Spectroscopy(EIS)data is to select an appropriate equivalent circuit model to quantify the parameters of the electrochemical reaction process.However,this process often relies on human experience and judgment,which will introduce subjectivity and error.In this paper,an intelligent approach is proposed for matching EIS data to their equivalent circuits based on the Random Forest algorithm.It can automatically select the most suitable equivalent circuit model based on the characteristics and patterns of EIS data.Addressing the typical scenario of metal corrosion,an atmospheric corrosion EIS dataset of low-carbon steel is constructed in this paper,which includes five different corrosion scenarios.This dataset was used to validate and evaluate the pro-posed method in this paper.The contributions of this paper can be summarized in three aspects:(1)This paper proposes a method for selecting equivalent circuit models for EIS data based on the Random Forest algorithm.(2)Using authentic EIS data collected from metal atmospheric corrosion,the paper es-tablishes a dataset encompassing five categories of metal corrosion scenarios.(3)The superiority of the proposed method is validated through the utilization of the established authentic EIS dataset.The ex-periment results demonstrate that,in terms of equivalent circuit matching,this method surpasses other machine learning algorithms in both precision and robustness.Furthermore,it shows strong applicability in the analysis of EIS data.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
Maximize the resource utilization efficiency and guarantee the quality of service(QoS)of users by selecting the network are the key issues for heterogeneous network operators,but the resources occupied by users in dif...Maximize the resource utilization efficiency and guarantee the quality of service(QoS)of users by selecting the network are the key issues for heterogeneous network operators,but the resources occupied by users in different networks cannot be compared directly.This paper proposes a network selection algorithm for heterogeneous network.Firstly,the concept of equivalent bandwidth is proposed,through which the actual resources occupied by users with certain QoS requirements in different networks can be compared directly.Then the concept of network applicability is defined to express the abilities of networks to support different services.The proposed network selection algorithm first evaluates whether the network has enough equivalent bandwidth required by the user and then prioritizes network with poor applicability to avoid the situation that there are still residual resources in entire network,but advanced services can not be admitted.The simulation results show that the proposed algorithm obtained better performance than the baselines in terms of reducing call blocking probability and improving network resource utilization efficiency.展开更多
To address the issue that traditional finite element methods cannot fully consider the semi-infinite earth strata and have lower solution accuracy,a new equivalent force model for induced deformation during oil and ga...To address the issue that traditional finite element methods cannot fully consider the semi-infinite earth strata and have lower solution accuracy,a new equivalent force model for induced deformation during oil and gas reservoir development is derived from the perspective of semi-infinite strata.A brand-new volume boundary element numerical method solution has been developed and verified and tested.The influences of internal flow and flow boundary of the reservoir on strata deformation are equivalent to the impacts on strata deformation when external forces act at the interior and boundary of the reservoir,respectively.Calculation methods for the flow equivalent force and boundary equivalent force are provided.The deformation solution at any point in the strata can be obtained through the convolution of flow equivalent forces,boundary equivalent forces and Green’s functions.After discretization,the deformation solution at any point in the strata can be obtained by multiplying the grid boundary equivalent forces,grid flow equivalent forces with their corresponding grid boundary sources and grid volume sources respectively,and then summing them up.This numerical method is termed the Volumetric Boundary Element Method(VBEM).Compared with traditional commercial simulators,VBEM fully considers the effects of reservoir flow boundaries,pore pressure gradient fields within the reservoir,and fluid mass changes within pores on formation deformation.It eliminates the need for meshing outside the reservoir,achieves significantly improved solution accuracy,and provides a new technical framework for simulating deformation induced by reservoir development.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
The high-speed winding spindle employs a flexible support system incorporating rubber O-rings.By precisely configuring the structural parameters and the number of the O-rings,the spindle can stably surpass its critica...The high-speed winding spindle employs a flexible support system incorporating rubber O-rings.By precisely configuring the structural parameters and the number of the O-rings,the spindle can stably surpass its critical speed points and maintain operational stability across the entire working speed range.However,the support stiffness and damping of rubber O-rings exhibit significant nonlinear frequency dependence.Conventional experimental methods for deriving equivalent stiffness and damping,based on the principle of the forced non-resonance method,require fabricating custom setups for each O-ring specification and conducting vibration tests at varying frequencies,resulting in low efficiency and high costs.This study proposes a hybrid simulation-experimental method for dynamic parameter identification.Firstly,the frequency-dependent dynamic parameters of a specific O-ring support system are experimentally obtained.Subsequently,a corresponding parametric finite element model is established to simulate and solve the equivalent elastic modulus and equivalent stiffness-damping coefficient of this O-ring support system.Ultimately,after iterative simulation,the simulated and experimental results achieve a 99.7%agreement.The parametric finite element model developed herein can directly simulate and inversely estimate frequency-dependent dynamic parameters for O-rings of different specifications but identical elastic modulus.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12272393 and 52130905).
文摘As binary geological media,soil-rock mixtures(SRMs)exhibit a distinct gradational composition,leading to their unique mechanical behaviors.To appraise the stability of SRM slopes,it is essential to determine equivalent parameters of SRMs,which are typically obtained through experimental and numerical methods.In contrasted to other numerical methods,the numerical manifold method(NMM)is more effective in addressing SRM problems.This is because the high-precision regular mathematical meshes in NMM can be used without aligning with the soil-rock interfaces and boundaries of SRMs.In the current research,the equivalent strength parameters of SRMs,i.e.the equivalent cohesion ce and internal friction angleϕ_(e),are determined using NMM.Initially,an NMM triaxial numerical model is established and validated based on triaxial experiments.Subsequently,the soil and rock parameters are derived through parameter inversion.Moreover,the impacts of rock content,size,shape and rock blocks'major-axis orientation on ce andϕ_(e) of SRMs are thoroughly examined using the NMM triaxial numerical model.Additionally,a fitting function is proposed to linkϕ_(e) to the rock content and size of SRMs.When other influencing factors are fixed,the above fitting model leads to the following conclusions:(1)the predictedϕ_(e) of SRMs increase with the increase of rock content;and(2)SRM samples with smaller rocks display a higher predictedϕ_(e).
基金supported by the National Natural Science Foundation of China(No.52075244).
文摘In fatigue damage tolerance verification tests of aircraft structures,the simulation and loading of flight-byflight spectra require considerable time and resources.To improve the efficiency of load spectrum design and testing,an equivalent constant-amplitude spectrum design method for flight-by-flight spectra is proposed based on the equivalence of crack growth behavior.By combining the Paris crack growth model with the Walker stress ratio correction,the equivalent stress amplitude is directly calculated using structural parameters and load spectrum characteristics,enabling a rapid transformation from variable-amplitude spectra to constant-amplitude spectra.The original spectrum is discretized based on the load-exceedance curve,and the equivalence relationship between multilevel block spectra and constant-amplitude spectra is established.Taking a typical lower wing skin structure of a transport aircraft as an example,two equivalent spectra are designed and validated through fatigue crack growth tests on 2024-T351 center-hole plate specimens.The experimental results show that the fatigue life deviation between the equivalent spectra and the original flight-by-flight spectrum is within 10%,demonstrating the effectiveness of the proposed method.Moreover,the equivalent spectrum constructed under the condition of invariant mean flight stress exhibits higher equivalence accuracy.The influence of spectral shape on the equivalent stress amplitude is further analyzed,revealing that the equivalent stress amplitude increases with the spectrum shape coefficient.The proposed method provides a useful reference for load spectrum design in aircraft structural damage tolerance verification tests.
基金National Basic Research Program of China (JW132006093)
文摘An identification method using Allan variance and equivalent theorem is proposed to identify non-stationary sensor errors mixed out of different simple noises. This method firstly derives the discrete Allan variances of all component noises inherent in noise sources in terms of their different equations; then the variances are used to estimate the parameters of all component noise models; finally, the original errors are represented by the sum of the non-stationary component noise model and the equivalent m...
基金Supported by the National Natural Science Foundation of China(10871141)
文摘By using the properties of w-distances and Gerstewitz＇s functions, we first give a vectorial Takahashi＇s nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland＇s variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristfs fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland＇s variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346（2008）, 9-16] are weakened or even completely relieved.
文摘The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.
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 the National Key R&D Program of China(Grant No.2021YFC2501700).
文摘The current artificial bone is unable to accurately replicate the inhomogeneity and anisotropy of human cancellous bone.To address this issue,we proposed a personalized approach based on clinical CT images to design mechanical equivalent porous structures for artificial femoral heads.Firstly,supported by Micro and clinical CT scans of 21 bone specimens,the anisotropic mechanical parameters of human cancellous bone in the femoral head were characterized using clinical CT values(Hounsfield unit).After that,the equivalent porous structure of cancellous bone was designed based on the gyroid surface,the influence of its degree of anisotropy and volume fraction on the macroscopic mechanical parameters was investigated by finite element analysis.Furthermore,a mapping relationship between CT values and the porous structure was established by jointly solving the mechanical parameters of the porous structure and human cancellous bone,allowing the design of personalized gradient porous structures based on clinical CT images.Finally,to verify the mechanical equivalence,implant press-in tests were conducted on 3D-printed artificial femoral heads and human femoral heads,the influence of the porous structure’s cell size in bone-implant interaction problems was also explored.Results showed that the minimum deviations of press-in stiffness(<15%)and peak load(<5%)both occurred when the cell size was 20%to 30%of the implant diameter.In conclusion,the designed porous structure can replicate the human cancellous bone-implant interaction at a high level,indicating its effectiveness in optimizing the mechanical performance of 3D-printed artificial femoral head.
基金supported by the National Natural Science Foundation of China(Grant Nos.42250103 and 42174090)the Opening Fund of Key Laboratory of Geological Survey and Evaluation of Ministry of Education(Grant No.GLAB2023ZR02)the MOST Special Fund from the State Key Laboratory of Geological Processes and Mineral Resources(Grant No.MSFGPMR2022-4).
文摘The equivalent source(ES)method in the spherical coordinate system has been widely applied to processing,reduction,field modeling,and geophysical and geological interpretation of satellite magnetic anomaly data.However,the inversion for the ES model suffers from nonuniqueness and instability,which remain unresolved.To mitigate these issues,we introduce both the minimum and flattest models into the model objective function as an alternative regularization approach in the spherical ES method.We first present the methods,then analyze the accuracy of forward calculation and test the proposed ES method in this study by using synthetic data.The experimental results from simulation data indicate that our proposed regularization effectively suppresses the Backus effect and mitigates inversion instability in the low-latitude region.Finally,we apply the proposed method to magnetic anomaly data from China Seismo-Electromagnetic Satellite-1(CSES-1)and Macao Science Satellite-1(MSS-1)magnetic measurements over Africa by constructing an ES model of the large-scale lithospheric magnetic field.Compared with existing global lithospheric magnetic field models,our ES model demonstrates good consistency at high altitudes and predicts more stable fields at low altitudes.Furthermore,we derive the reduction to the pole(RTP)magnetic anomaly fields and the apparent susceptibility contrast distribution based on the ES model.The latter correlates well with the regional tectonic framework in Africa and surroundings.
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.
基金supported by Natural Science Foundation of Fujian Province(2022I0019)Scientific Research Foundation for Jimei University(ZQ2024041,ZQ2024042).
文摘The penetration of ogival-nosed projectiles into ship plates represents a complex impact dynamics issue essential for analyzing structural failuremechanisms.Although stiffenedplates are vital in ship construction,fewstudies have addressed the issue of model equivalence under penetration loading.This study employs numerical simulation to validate an experiment with an ogival-nosed projectile penetrating a Q345 steel plate.Four equivalent stiffened plate methods are proposed based on the area,flexural modulus,moment of inertia,and thickness.The results indicate that thickness equivalence(DM4)is unsuitable for penetration-loaded stiffened plates,except under low-speed,nonpenetrating through impacts,and yields less accuracy than DM1/DM3.DM1,DM2,and DM3 each perform optimally with specific velocity ranges:DM1 at very low(critical)and high velocities,DM3 at low velocities,and DM2 at high speeds.Furthermore,in penetration scenarios,T-shaped stiffeners can be replacedwith rectangular ones,as both exhibit similar failure behaviors and deflection trends,simplifying the design while preserving key structural characteristics.These findings provide valuable insights into the design of protective ship structures.
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.
基金supported by the National Natural Science Foundation of China(Grant Nos.52272437 and 52272370)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX24_0635)。
文摘The high cost and low efficiency of full-scale vehicle experiments and numerical simulations limit the efficient development of armored vehicle occupant protection systems.The floor-occupant-seat local simulation model provides an alternative solution for quickly evaluating the performance of occupant protection systems.However,the error and rationality of the loading of the thin-walled floor in the local model cannot be ignored.This study proposed an equivalent loading method for the local model,which includes two parts:the dimensionality reduction method for acceleration matrix and the joint optimization framework for equivalent node coordinates.In the dimensionality reduction method,the dimension of the acceleration matrix was reduced based on the improved kernel principal component analysis(KPCA),and a dynamic variable bandwidth was introduced to address the limitation of failing to effectively measure the similarity between acceleration data in conventional KPCA.In addition,a least squares problem with forced displacement constraints was constructed to solve the correction matrix,thereby achieving the scale restoration process of the principal component acceleration matrix.The joint optimization framework for coordinates consists of the error assessment of response time histories(EARTH)and Bayesian optimization.In this framework,the local loading error of the equivalent acceleration matrix is taken as the Bayesian optimization objective,which is quantified and scored by EARTH.The expected improvement acquisition function was used to select the new set of the equivalent acceleration node coordinates for the self-updating optimization of the observation dataset and Gaussian process surrogate model.We reduced the dimension of the acceleration matrix from 2256 to 7,while retaining 91%of the information features.The comprehensive error score of occupant's lower limb response in the local model increased from 58.5%to 80.4%.The proposed equivalent loading method provides a solution for the rapid and reliable development of occupant protection systems.
基金support of the project from the National Key R&D Program of China,Research and Application of Sensing System for Cross-regional Complex Oil&Gas Pipeline Network Safe and Efficiency Operational Status Monitoring(Grant No.2022YFB3207603).
文摘One of the core works of analyzing Electrochemical Impedance Spectroscopy(EIS)data is to select an appropriate equivalent circuit model to quantify the parameters of the electrochemical reaction process.However,this process often relies on human experience and judgment,which will introduce subjectivity and error.In this paper,an intelligent approach is proposed for matching EIS data to their equivalent circuits based on the Random Forest algorithm.It can automatically select the most suitable equivalent circuit model based on the characteristics and patterns of EIS data.Addressing the typical scenario of metal corrosion,an atmospheric corrosion EIS dataset of low-carbon steel is constructed in this paper,which includes five different corrosion scenarios.This dataset was used to validate and evaluate the pro-posed method in this paper.The contributions of this paper can be summarized in three aspects:(1)This paper proposes a method for selecting equivalent circuit models for EIS data based on the Random Forest algorithm.(2)Using authentic EIS data collected from metal atmospheric corrosion,the paper es-tablishes a dataset encompassing five categories of metal corrosion scenarios.(3)The superiority of the proposed method is validated through the utilization of the established authentic EIS dataset.The ex-periment results demonstrate that,in terms of equivalent circuit matching,this method surpasses other machine learning algorithms in both precision and robustness.Furthermore,it shows strong applicability in the analysis of EIS data.
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.
文摘Maximize the resource utilization efficiency and guarantee the quality of service(QoS)of users by selecting the network are the key issues for heterogeneous network operators,but the resources occupied by users in different networks cannot be compared directly.This paper proposes a network selection algorithm for heterogeneous network.Firstly,the concept of equivalent bandwidth is proposed,through which the actual resources occupied by users with certain QoS requirements in different networks can be compared directly.Then the concept of network applicability is defined to express the abilities of networks to support different services.The proposed network selection algorithm first evaluates whether the network has enough equivalent bandwidth required by the user and then prioritizes network with poor applicability to avoid the situation that there are still residual resources in entire network,but advanced services can not be admitted.The simulation results show that the proposed algorithm obtained better performance than the baselines in terms of reducing call blocking probability and improving network resource utilization efficiency.
基金Supported by the China National Natural Science Foundation Project(52274048)Beijing Natural Science Foundation Project(3222037)。
文摘To address the issue that traditional finite element methods cannot fully consider the semi-infinite earth strata and have lower solution accuracy,a new equivalent force model for induced deformation during oil and gas reservoir development is derived from the perspective of semi-infinite strata.A brand-new volume boundary element numerical method solution has been developed and verified and tested.The influences of internal flow and flow boundary of the reservoir on strata deformation are equivalent to the impacts on strata deformation when external forces act at the interior and boundary of the reservoir,respectively.Calculation methods for the flow equivalent force and boundary equivalent force are provided.The deformation solution at any point in the strata can be obtained through the convolution of flow equivalent forces,boundary equivalent forces and Green’s functions.After discretization,the deformation solution at any point in the strata can be obtained by multiplying the grid boundary equivalent forces,grid flow equivalent forces with their corresponding grid boundary sources and grid volume sources respectively,and then summing them up.This numerical method is termed the Volumetric Boundary Element Method(VBEM).Compared with traditional commercial simulators,VBEM fully considers the effects of reservoir flow boundaries,pore pressure gradient fields within the reservoir,and fluid mass changes within pores on formation deformation.It eliminates the need for meshing outside the reservoir,achieves significantly improved solution accuracy,and provides a new technical framework for simulating deformation induced by reservoir development.
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.
基金National Key R&D Program of China(No.2017YFB1304000)Fundamental Research Funds for the Central Universities,China(No.2232023G-05-1)。
文摘The high-speed winding spindle employs a flexible support system incorporating rubber O-rings.By precisely configuring the structural parameters and the number of the O-rings,the spindle can stably surpass its critical speed points and maintain operational stability across the entire working speed range.However,the support stiffness and damping of rubber O-rings exhibit significant nonlinear frequency dependence.Conventional experimental methods for deriving equivalent stiffness and damping,based on the principle of the forced non-resonance method,require fabricating custom setups for each O-ring specification and conducting vibration tests at varying frequencies,resulting in low efficiency and high costs.This study proposes a hybrid simulation-experimental method for dynamic parameter identification.Firstly,the frequency-dependent dynamic parameters of a specific O-ring support system are experimentally obtained.Subsequently,a corresponding parametric finite element model is established to simulate and solve the equivalent elastic modulus and equivalent stiffness-damping coefficient of this O-ring support system.Ultimately,after iterative simulation,the simulated and experimental results achieve a 99.7%agreement.The parametric finite element model developed herein can directly simulate and inversely estimate frequency-dependent dynamic parameters for O-rings of different specifications but identical elastic modulus.
