The improved cross-correlation algorithm for the strain demodulation of Vernier-effect-based optical fiber sensor(VE-OFS)is proposed in this article.The algorithm identifies the most similar spectrum to the measured o...The improved cross-correlation algorithm for the strain demodulation of Vernier-effect-based optical fiber sensor(VE-OFS)is proposed in this article.The algorithm identifies the most similar spectrum to the measured one from the database of the collected spectra by employing the cross-correlation operation,subsequently deriving the predicted value via weighted calculation.As the algorithm uses the complete information in the measured raw spectrum,more accurate results and larger measurement range can be obtained.Additionally,the improved cross-correlation algorithm also has the potential to improve the measurement speed compared to current standards due to the possibility for the collection using low sampling rate.This work presents an important algorithm towards a simpler,faster way to improve the demodulation performance of VE-OFS.展开更多
This paper introduced the concept of generalized quasidiagonal extension of C^(*)-algebras and gave some basic properties.We show that the extension algebra preserves quasidiagonality and finitary in generalized quasi...This paper introduced the concept of generalized quasidiagonal extension of C^(*)-algebras and gave some basic properties.We show that the extension algebra preserves quasidiagonality and finitary in generalized quasidiagonal extension.We give also an example of generalized quasidiagonal extension,which is not quasidiagonal extension.展开更多
Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_...Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_(N-1)by adding anew vertexνconnecting k vertices of K_(N-1).A graph G withχ(G)=k+1 is called edge-critical if G contains an edge e such thatχ(G-e)=k.A considerable amount of research has been conducted by previous scholars on Ramsey numbers ofgraphs.In this study,we show that for an edge-critical graph G with x(G)=k+1,when k≥2,1≥2,and n is sufficiently large,R(G,K_(1)+nK_(t))=knt+1 and r,(G,K_(1)+nK_(t))=(k-1)nt+1.展开更多
A dominating induced matching(DIM)of G is an induced matching that dominates every edge of G.In this note,we completely determine the number of DIMs in the generalized Petersen graph P(n,k).We prove that if P(n,k)is a...A dominating induced matching(DIM)of G is an induced matching that dominates every edge of G.In this note,we completely determine the number of DIMs in the generalized Petersen graph P(n,k).We prove that if P(n,k)is a generalized Petersen graph with n=0(mod 5)and k=2,3(mod 5),then E(P(n,k))can be partitioned into five DIMs.Meanwhile,in the left cases k=0,1,4(mod 5),we build some counterexamples to show that there exist some P(n,k)'s which are DIM-free.展开更多
The liquid cooling system(LCS)of fuel cells is challenged by significant time delays,model uncertainties,pump and fan coupling,and frequent disturbances,leading to overshoot and control oscillations that degrade tempe...The liquid cooling system(LCS)of fuel cells is challenged by significant time delays,model uncertainties,pump and fan coupling,and frequent disturbances,leading to overshoot and control oscillations that degrade temperature regulation performance.To address these challenges,we propose a composite control scheme combining fuzzy logic and a variable-gain generalized supertwisting algorithm(VG-GSTA).Firstly,a one-dimensional(1D)fuzzy logic controler(FLC)for the pump ensures stable coolant flow,while a two-dimensional(2D)FLC for the fan regulates the stack temperature near the reference value.The VG-GSTA is then introduced to eliminate steady-state errors,offering resistance to disturbances and minimizing control oscillations.The equilibrium optimizer is used to fine-tune VG-GSTA parameters.Co-simulation verifies the effectiveness of our method,demonstrating its advantages in terms of disturbance immunity,overshoot suppression,tracking accuracy and response speed.展开更多
Detecting coupling pattern between elements in a complex system is a basic task in data-driven analysis. The trajectory for each specific element is a cooperative result of its intrinsic dynamic, its couplings with ot...Detecting coupling pattern between elements in a complex system is a basic task in data-driven analysis. The trajectory for each specific element is a cooperative result of its intrinsic dynamic, its couplings with other elements, and the environment. It is subsequently composed of many components, only some of which take part in the couplings. In this paper we present a framework to detect the component correlation pattern. Firstly, the interested trajectories are decomposed into components by using decomposing methods such as the Fourier expansion and the Wavelet transformation. Secondly, the cross-correlations between the components are calculated, resulting into a component cross-correlation matrix(network).Finally, the dominant structure in the network is identified to characterize the coupling pattern in the system. Several deterministic dynamical models turn out to be characterized with rich structures such as the clustering of the components. The pattern of correlation between respiratory(RESP) and ECG signals is composed of five sub-clusters that are mainly formed by the components in ECG signal. Interestingly, only 7 components from RESP(scattered in four sub-clusters) take part in the realization of coupling between the two signals.展开更多
With the miniaturization of devices and the development of modern heating technologies,the generalization of heat conduction and thermoelastic coupling has become crucial,effectively emulating the thermodynamic behavi...With the miniaturization of devices and the development of modern heating technologies,the generalization of heat conduction and thermoelastic coupling has become crucial,effectively emulating the thermodynamic behavior of materials in ultrashort time scales.Theoretically,generalized heat conductive models are considered in this work.By analogy with mechanical viscoelastic models,this paper further enriches the heat conduction models and gives their one-dimensional physical expression.Numerically,the transient thermoelastic response of the slim strip material under thermal shock is investigated by applying the proposed models.First,the analytical solution in the Laplace domain is obtained by the Laplace transform.Then,the numerical results of the transient responses are obtained by the numerical inverse Laplace transform.Finally,the transient responses of different models are analyzed and compared,and the effects of material parameters are discussed.This work not only opens up new research perspectives on generalized heat conductive and thermoelastic coupling theories,but also is expected to be beneficial for the deeper understanding of the heat wave theory.展开更多
We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functi...We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functions are derived.Furthermore,we introduce two integrable systems known as the generalized UC(GUC)hierarchy and the generalized Btype UC(GBUC)hierarchy satisfied by the generalized universal character and the generalized B-type universal character,respectively.Based on infinite sequences of complex numbers,we further establish the multiparameter generalized universal character and the multiparameter generalized B-type universal character,which have been proved to be solutions of the GUC hierarchy and the GBUC hierarchy,respectively.展开更多
Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let Π_(C):X→C denote the generalized metric projection operator introduced by Alber in[1].In this pap...Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let Π_(C):X→C denote the generalized metric projection operator introduced by Alber in[1].In this paper,we define the Gâteaux directional differentiability of Π_(C).We investigate some properties of the Gâteaux directional differentiability of Π_(C).In particular,if C is a closed ball,or a closed and convex cone(including proper closed subspaces),or a closed and convex cylinder,then,we give the exact representations of the directional derivatives of Π_(C).By comparing the results in[12]and this paper,we see the significant difference between the directional derivatives of the generalized metric projection operator Π_(C) and the Gâteaux directional derivatives of the standard metric projection operator PC.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
We use the Schrödinger–Newton equation to calculate the regularized self-energy of a particle using a regular self-gravitational and electrostatic potential derived in string T-duality.The particle mass M is no ...We use the Schrödinger–Newton equation to calculate the regularized self-energy of a particle using a regular self-gravitational and electrostatic potential derived in string T-duality.The particle mass M is no longer concentrated into a point but is diluted and described by a quantum-corrected smeared energy density resulting in corrections to the energy of the particle,which is interpreted as a regularized self-energy.We extend our results and find corrections to the relativistic particles using the Klein–Gordon,Proca and Dirac equations.An important finding is that we extract a form of the generalized uncertainty principle(GUP)from the corrected energy.This form of the GUP is shown to depend on the nature of particles;namely,for bosons(spin 0 and spin 1)we obtain a quadratic form of the GUP,while for fermions(spin 1/2)we obtain a linear form.The correlation we find between spin and GUP may offer insights for investigating quantum gravity.展开更多
We introduce a new method to study the asymptotic behavior of solutions on the basis of the continuation theory for k-set contractions.We apply this technique to show the existence of nontrivial decaying solutions to ...We introduce a new method to study the asymptotic behavior of solutions on the basis of the continuation theory for k-set contractions.We apply this technique to show the existence of nontrivial decaying solutions to the sup-linear generalized Emden-Fowler equation and the existence of asymptotically linear solutions to the sub-linear one.展开更多
In 1694,Gregory and Newton proposed the problem to determine the kissing number of a rigid material ball.This problem and its higher dimensional generalization have been studied by many mathematicians,including Minkow...In 1694,Gregory and Newton proposed the problem to determine the kissing number of a rigid material ball.This problem and its higher dimensional generalization have been studied by many mathematicians,including Minkowski,van der Waerden,Hadwiger,Swinnerton-Dyer,Watson,Levenshtein,Odlyzko,Sloane and Musin.In this paper,we introduce and study a further generalization of the kissing numbers for convex bodies and obtain some exact results,in particular for balls in dimensions three,four and eight.展开更多
To address the issue of low measurement accuracy caused by noise interference in the acquisition of low fluid flow rate signals with ultrasonic Doppler flow meters,a novel signal processing algorithm that combines ens...To address the issue of low measurement accuracy caused by noise interference in the acquisition of low fluid flow rate signals with ultrasonic Doppler flow meters,a novel signal processing algorithm that combines ensemble empirical mode decomposition(EEMD)and cross-correlation algorithm was proposed.Firstly,a fast Fourier transform(FFT)spectrum analysis was utilized to ascertain the frequency range of the signal.Secondly,data acquisition was conducted at an appropriate sampling frequency,and the acquired Doppler flow rate signal was then decomposed into a series of intrinsic mode functions(IMFs)by EEMD.Subsequently,these decomposed IMFs were recombined based on their energy entropy,and then the noise of the recombined Doppler flow rate signal was removed by cross-correlation filtering.Finally,an ideal ultrasonic Doppler flow rate signal was extracted.Simulation and experimental verification show that the proposed Doppler flow signal processing method can effectively enhance the signal-to-noise ratio(SNR)and extend the lower limit of measurement of the ultrasonic Doppler flow meter.展开更多
In this paper,we investigate the generalized quasilinear Schrödinger equation:-div(g2(u)▽u)+g(u)g'(u)|▽u|2+u=P(εx)|u|αp-2u,x∈R^(N),where N>3,g:R→R+is a C1 even function,g(0)=1,g'(s)≥0 for all s...In this paper,we investigate the generalized quasilinear Schrödinger equation:-div(g2(u)▽u)+g(u)g'(u)|▽u|2+u=P(εx)|u|αp-2u,x∈R^(N),where N>3,g:R→R+is a C1 even function,g(0)=1,g'(s)≥0 for all s≥0,g(s)=β|s|α-1+O(|s|γ-1)as s→∞for some constantsα∈[1,2],β>0,γ<αand(α-1)g(s)≥g'(s)s for all s≥0,ε>0 is a positive parameter,and p∈(2,2^(*)).We will study the impact of the nonlinearity’s coefficient P(x)on the quantity of positive solutions.展开更多
BACKGROUND Cervical spondylosis(CS)frequently co-occurs with generalized anxiety disorder(GAD),presenting a complex clinical challenge.Managing CS-related pain in patients with GAD is particularly challenging because ...BACKGROUND Cervical spondylosis(CS)frequently co-occurs with generalized anxiety disorder(GAD),presenting a complex clinical challenge.Managing CS-related pain in patients with GAD is particularly challenging because of the bidirectional relationship between pain and anxiety,necessitating integrated treatment strategies.AIM To evaluate the efficacy of electroacupuncture(EA)in treating CS-related pain and anxiety in patients with GAD.METHODS This retrospective cohort study analyzed data from 83 patients with CS-related pain and GAD who received EA treatment over 2-year period.Pain intensity was assessed using the visual analog scale,and anxiety symptoms were measured using the Hamilton Anxiety Rating Scale.Additionally,neuroinflammatory markers,including interleukin-6,tumor necrosis factor-alpha,and high-sensitivity C-reactive protein,were examined.Outcomes were evaluated at baseline,after 4 weeks,and after 8 weeks of treatment.RESULTS EA treatment significantly reduced CS-related pain(mean visual analog scale reduction:3.24±1.18;P<0.001)and improved anxiety symptoms(mean Hamilton Anxiety Rating Scale reduction:7.83±2.65;P<0.001)after 8 weeks of treatment.Neuroinflammatory markers also showed significant reductions,with interleukin-6 and tumor necrosis factor-alpha levels decreasing by 32.7%and 28.5%,respectively(P<0.01).Pain reduction was significantly correlated with improvements in anxiety symptoms(r=0.68;P<0.001)and a decrease in inflammatory markers(r=0.54;P<0.01).CONCLUSION EA demonstrates significant efficacy in reducing CS-related pain in patients with comorbid GAD,along with concurrent improvements in anxiety symptoms and neuroinflammatory profiles.These findings suggest that EA may offer a valuable integrative approach for managing this complex clinical presentation,potentially addressing both pain and anxiety through the modulation of neuroinflammatory pathways.展开更多
Fibonacci sequence,generated by summing the preceding two terms,is a classical sequence renowned for its elegant properties.In this paper,leveraging properties of generalized Fibonacci sequences and formulas for conse...Fibonacci sequence,generated by summing the preceding two terms,is a classical sequence renowned for its elegant properties.In this paper,leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of equidistant sub-sequences,we investigate the ratio of the sum of numbers along main-diagonal and sub-diagonal of odd-order grids containing generalized Fibonacci sequences.We show that this ratio is solely dependent on the order of the grid,providing a concise and splendid identity.展开更多
As space equipment become larger in size and more flexible,generalized mechanisms are being widely used in space-deployable structures.Dynamic modeling of large-scale generalized space-deployable mechanisms is challen...As space equipment become larger in size and more flexible,generalized mechanisms are being widely used in space-deployable structures.Dynamic modeling of large-scale generalized space-deployable mechanisms is challenging owing to the coupling between the deformation of flexible links and rigid body motion.This study develops a dynamic modeling method for generalized mechanisms using the local frame of the SE(3)Lie group.The model represents both rigid and flexible links within a unified Lie group setting.The expressions for the velocities of rigid links and deformation of flexible links are derived using the Lie algebra framework.The nonuniqueness of the degrees of freedom of generalized kinematic pairs is considered,and the velocity fields of kinematic pairs in different situations are expressed.The equations of motion are derived using Hamilton’s principle.Because the velocities are expressed in the local frame,the mass matrix in the equation is constant,which yields a compact and unified expression for the dynamic equation.A Lie group generalized-αtime integration method is adopted to ensure numerical stability and efficiency in simulating multibody systems with large rotations and deformations.Two numerical examples are studied to demonstrate a formulation that reflects the motion responses under varying configurations and loading conditions.This study broadens the application of the local frame of the Lie group formulation in space mechanisms and provides a new concept for dynamic modeling of generalized mechanisms.展开更多
In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditio...In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.展开更多
The existing analytical models for umbrella arch method(UAM)based on elastic foundation beams often overlook the influence of the surrounding soil beyond the beam edges on the shear stresses acting on the beam.Consequ...The existing analytical models for umbrella arch method(UAM)based on elastic foundation beams often overlook the influence of the surrounding soil beyond the beam edges on the shear stresses acting on the beam.Consequently,such models fail to adequately reflect the continuity characteristics of soil deformation.Leveraging the Pasternak foundation-Euler beam model,this study considers the generalized shear force on the beam to account for the influence of soil outside the beam ends on the shear stress.An analytical model for the deformation and internal forces of finite-length beams subjected to arbitrary loads is derived based on the initial parameter method under various conditions.The mechanical model of the elastic foundation beam for advanced umbrella arch under typical tunnel excavation cycles is established,yielding analytical solutions for the longitudinal response of the umbrella arch.The reliability of the analytical model is verified with the existing test data.The improved model addresses anomalies in existing models,such as abnormal upward deformation in the loosened segment and maximum deflection occurring within the soil mass.Additionally,dimensionless characteristic parameters reflecting the relative stiffness between the umbrella arch structure and the foundation soil are proposed.Results indicate that the magnitude of soil characteristic parameters significantly influences the deformation and internal forces of the umbrella arch.Within common ranges of soil values,the maximum deformation and internal forces of the umbrella arch under semi-logarithmic coordinates exhibit nearly linear decay with decreasing soil characteristic parameters.The impact of tunnel excavation height on the stress of unsupported sections of the umbrella arch is minor,but it is more significant for umbrella arch buried within the soil mass.Conversely,the influence of tunnel excavation advance on the umbrella arch is opposite.展开更多
文摘The improved cross-correlation algorithm for the strain demodulation of Vernier-effect-based optical fiber sensor(VE-OFS)is proposed in this article.The algorithm identifies the most similar spectrum to the measured one from the database of the collected spectra by employing the cross-correlation operation,subsequently deriving the predicted value via weighted calculation.As the algorithm uses the complete information in the measured raw spectrum,more accurate results and larger measurement range can be obtained.Additionally,the improved cross-correlation algorithm also has the potential to improve the measurement speed compared to current standards due to the possibility for the collection using low sampling rate.This work presents an important algorithm towards a simpler,faster way to improve the demodulation performance of VE-OFS.
基金Supported by NSF of Jiangsu Province(No.BK20171421)。
文摘This paper introduced the concept of generalized quasidiagonal extension of C^(*)-algebras and gave some basic properties.We show that the extension algebra preserves quasidiagonality and finitary in generalized quasidiagonal extension.We give also an example of generalized quasidiagonal extension,which is not quasidiagonal extension.
基金supported by the National Key Research and Development Program of China(2023YFA1010200,2020YFA0713100)the National Natural Science Foundation of China(12071453)the Innovation Program for Quantum Science and Technology(2021ZD0302902).
文摘Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_(N-1)by adding anew vertexνconnecting k vertices of K_(N-1).A graph G withχ(G)=k+1 is called edge-critical if G contains an edge e such thatχ(G-e)=k.A considerable amount of research has been conducted by previous scholars on Ramsey numbers ofgraphs.In this study,we show that for an edge-critical graph G with x(G)=k+1,when k≥2,1≥2,and n is sufficiently large,R(G,K_(1)+nK_(t))=knt+1 and r,(G,K_(1)+nK_(t))=(k-1)nt+1.
基金Ming Chen was supported by National Key Research and Development Program of China(No.2024YFA1013900)。
文摘A dominating induced matching(DIM)of G is an induced matching that dominates every edge of G.In this note,we completely determine the number of DIMs in the generalized Petersen graph P(n,k).We prove that if P(n,k)is a generalized Petersen graph with n=0(mod 5)and k=2,3(mod 5),then E(P(n,k))can be partitioned into five DIMs.Meanwhile,in the left cases k=0,1,4(mod 5),we build some counterexamples to show that there exist some P(n,k)'s which are DIM-free.
基金Supported by the Major Science and Technology Project of Jilin Province(20220301010GX)the International Scientific and Technological Cooperation(20240402071GH).
文摘The liquid cooling system(LCS)of fuel cells is challenged by significant time delays,model uncertainties,pump and fan coupling,and frequent disturbances,leading to overshoot and control oscillations that degrade temperature regulation performance.To address these challenges,we propose a composite control scheme combining fuzzy logic and a variable-gain generalized supertwisting algorithm(VG-GSTA).Firstly,a one-dimensional(1D)fuzzy logic controler(FLC)for the pump ensures stable coolant flow,while a two-dimensional(2D)FLC for the fan regulates the stack temperature near the reference value.The VG-GSTA is then introduced to eliminate steady-state errors,offering resistance to disturbances and minimizing control oscillations.The equilibrium optimizer is used to fine-tune VG-GSTA parameters.Co-simulation verifies the effectiveness of our method,demonstrating its advantages in terms of disturbance immunity,overshoot suppression,tracking accuracy and response speed.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11875042 and 11505114)the Shanghai Project for Construction of Top Disciplines (Grant No. USST-SYS-01)。
文摘Detecting coupling pattern between elements in a complex system is a basic task in data-driven analysis. The trajectory for each specific element is a cooperative result of its intrinsic dynamic, its couplings with other elements, and the environment. It is subsequently composed of many components, only some of which take part in the couplings. In this paper we present a framework to detect the component correlation pattern. Firstly, the interested trajectories are decomposed into components by using decomposing methods such as the Fourier expansion and the Wavelet transformation. Secondly, the cross-correlations between the components are calculated, resulting into a component cross-correlation matrix(network).Finally, the dominant structure in the network is identified to characterize the coupling pattern in the system. Several deterministic dynamical models turn out to be characterized with rich structures such as the clustering of the components. The pattern of correlation between respiratory(RESP) and ECG signals is composed of five sub-clusters that are mainly formed by the components in ECG signal. Interestingly, only 7 components from RESP(scattered in four sub-clusters) take part in the realization of coupling between the two signals.
基金Project supported by the Guangdong Basic and Applied Basic Research Foundation of China(No.2023A1515012809)the Natural Science Foundation of Shaanxi Province of China(No.2023-JC-YB-073)the Fundamental Research Funds for the Central Universities of China(No.D5000230066)。
文摘With the miniaturization of devices and the development of modern heating technologies,the generalization of heat conduction and thermoelastic coupling has become crucial,effectively emulating the thermodynamic behavior of materials in ultrashort time scales.Theoretically,generalized heat conductive models are considered in this work.By analogy with mechanical viscoelastic models,this paper further enriches the heat conduction models and gives their one-dimensional physical expression.Numerically,the transient thermoelastic response of the slim strip material under thermal shock is investigated by applying the proposed models.First,the analytical solution in the Laplace domain is obtained by the Laplace transform.Then,the numerical results of the transient responses are obtained by the numerical inverse Laplace transform.Finally,the transient responses of different models are analyzed and compared,and the effects of material parameters are discussed.This work not only opens up new research perspectives on generalized heat conductive and thermoelastic coupling theories,but also is expected to be beneficial for the deeper understanding of the heat wave theory.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12461048 and 12061051)the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant No.2023MS01003)+2 种基金the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(Grant No.NJYT23096)the financial support from the Program of China Scholarships Council(Grant No.202306810054)for one year study at the University of Leedsthe support of Professor Ke Wu and Professor Weizhong Zhao at Capital Normal University,China。
文摘We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functions are derived.Furthermore,we introduce two integrable systems known as the generalized UC(GUC)hierarchy and the generalized Btype UC(GBUC)hierarchy satisfied by the generalized universal character and the generalized B-type universal character,respectively.Based on infinite sequences of complex numbers,we further establish the multiparameter generalized universal character and the multiparameter generalized B-type universal character,which have been proved to be solutions of the GUC hierarchy and the GBUC hierarchy,respectively.
文摘Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let Π_(C):X→C denote the generalized metric projection operator introduced by Alber in[1].In this paper,we define the Gâteaux directional differentiability of Π_(C).We investigate some properties of the Gâteaux directional differentiability of Π_(C).In particular,if C is a closed ball,or a closed and convex cone(including proper closed subspaces),or a closed and convex cylinder,then,we give the exact representations of the directional derivatives of Π_(C).By comparing the results in[12]and this paper,we see the significant difference between the directional derivatives of the generalized metric projection operator Π_(C) and the Gâteaux directional derivatives of the standard metric projection operator PC.
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We use the Schrödinger–Newton equation to calculate the regularized self-energy of a particle using a regular self-gravitational and electrostatic potential derived in string T-duality.The particle mass M is no longer concentrated into a point but is diluted and described by a quantum-corrected smeared energy density resulting in corrections to the energy of the particle,which is interpreted as a regularized self-energy.We extend our results and find corrections to the relativistic particles using the Klein–Gordon,Proca and Dirac equations.An important finding is that we extract a form of the generalized uncertainty principle(GUP)from the corrected energy.This form of the GUP is shown to depend on the nature of particles;namely,for bosons(spin 0 and spin 1)we obtain a quadratic form of the GUP,while for fermions(spin 1/2)we obtain a linear form.The correlation we find between spin and GUP may offer insights for investigating quantum gravity.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12001397,12171039)the Science&Technology Development Fund of Tianjin Education Commission for Higher Education(Grant No.2022KJ204).
文摘We introduce a new method to study the asymptotic behavior of solutions on the basis of the continuation theory for k-set contractions.We apply this technique to show the existence of nontrivial decaying solutions to the sup-linear generalized Emden-Fowler equation and the existence of asymptotically linear solutions to the sub-linear one.
基金supported by the National Natural Science Foundation of China(12226006,11921001)the Natural Key Research and Development Program of China(2018YFA0704701).
文摘In 1694,Gregory and Newton proposed the problem to determine the kissing number of a rigid material ball.This problem and its higher dimensional generalization have been studied by many mathematicians,including Minkowski,van der Waerden,Hadwiger,Swinnerton-Dyer,Watson,Levenshtein,Odlyzko,Sloane and Musin.In this paper,we introduce and study a further generalization of the kissing numbers for convex bodies and obtain some exact results,in particular for balls in dimensions three,four and eight.
基金supported by National Natural Science Foundation of China(No.61973234)Tianjin Science and Technology Plan Project(No.22YDTPJC00090)。
文摘To address the issue of low measurement accuracy caused by noise interference in the acquisition of low fluid flow rate signals with ultrasonic Doppler flow meters,a novel signal processing algorithm that combines ensemble empirical mode decomposition(EEMD)and cross-correlation algorithm was proposed.Firstly,a fast Fourier transform(FFT)spectrum analysis was utilized to ascertain the frequency range of the signal.Secondly,data acquisition was conducted at an appropriate sampling frequency,and the acquired Doppler flow rate signal was then decomposed into a series of intrinsic mode functions(IMFs)by EEMD.Subsequently,these decomposed IMFs were recombined based on their energy entropy,and then the noise of the recombined Doppler flow rate signal was removed by cross-correlation filtering.Finally,an ideal ultrasonic Doppler flow rate signal was extracted.Simulation and experimental verification show that the proposed Doppler flow signal processing method can effectively enhance the signal-to-noise ratio(SNR)and extend the lower limit of measurement of the ultrasonic Doppler flow meter.
基金supported by the NSFC(12161007)the Guangxi Natural Science(2023GXNSFAA026190)+1 种基金supported by the National Natural Science Foundation of China(12301145,12261107)the Yunnan Fundamental Research Projects(202301AU070144,202401AU070123)。
文摘In this paper,we investigate the generalized quasilinear Schrödinger equation:-div(g2(u)▽u)+g(u)g'(u)|▽u|2+u=P(εx)|u|αp-2u,x∈R^(N),where N>3,g:R→R+is a C1 even function,g(0)=1,g'(s)≥0 for all s≥0,g(s)=β|s|α-1+O(|s|γ-1)as s→∞for some constantsα∈[1,2],β>0,γ<αand(α-1)g(s)≥g'(s)s for all s≥0,ε>0 is a positive parameter,and p∈(2,2^(*)).We will study the impact of the nonlinearity’s coefficient P(x)on the quantity of positive solutions.
文摘BACKGROUND Cervical spondylosis(CS)frequently co-occurs with generalized anxiety disorder(GAD),presenting a complex clinical challenge.Managing CS-related pain in patients with GAD is particularly challenging because of the bidirectional relationship between pain and anxiety,necessitating integrated treatment strategies.AIM To evaluate the efficacy of electroacupuncture(EA)in treating CS-related pain and anxiety in patients with GAD.METHODS This retrospective cohort study analyzed data from 83 patients with CS-related pain and GAD who received EA treatment over 2-year period.Pain intensity was assessed using the visual analog scale,and anxiety symptoms were measured using the Hamilton Anxiety Rating Scale.Additionally,neuroinflammatory markers,including interleukin-6,tumor necrosis factor-alpha,and high-sensitivity C-reactive protein,were examined.Outcomes were evaluated at baseline,after 4 weeks,and after 8 weeks of treatment.RESULTS EA treatment significantly reduced CS-related pain(mean visual analog scale reduction:3.24±1.18;P<0.001)and improved anxiety symptoms(mean Hamilton Anxiety Rating Scale reduction:7.83±2.65;P<0.001)after 8 weeks of treatment.Neuroinflammatory markers also showed significant reductions,with interleukin-6 and tumor necrosis factor-alpha levels decreasing by 32.7%and 28.5%,respectively(P<0.01).Pain reduction was significantly correlated with improvements in anxiety symptoms(r=0.68;P<0.001)and a decrease in inflammatory markers(r=0.54;P<0.01).CONCLUSION EA demonstrates significant efficacy in reducing CS-related pain in patients with comorbid GAD,along with concurrent improvements in anxiety symptoms and neuroinflammatory profiles.These findings suggest that EA may offer a valuable integrative approach for managing this complex clinical presentation,potentially addressing both pain and anxiety through the modulation of neuroinflammatory pathways.
基金Supported by the National Natural Science Foundation of China(Grant No.12471298)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.23JSQ031)the Shaanxi Province College Student Innovation and Entrepreneurship Training Program(Grant Nos.S202210699481 and S202310699324X).
文摘Fibonacci sequence,generated by summing the preceding two terms,is a classical sequence renowned for its elegant properties.In this paper,leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of equidistant sub-sequences,we investigate the ratio of the sum of numbers along main-diagonal and sub-diagonal of odd-order grids containing generalized Fibonacci sequences.We show that this ratio is solely dependent on the order of the grid,providing a concise and splendid identity.
基金Supported by National Natural Science Foundation of China(Grant No.52475280)Key Laboratory Project of the Key Program of the Natural Science Basic Research Program of Shaanxi Province of China(Grant No.2025SYS-SYSZD-105)+1 种基金Natural Science Foundation of Shaanxi Province of China(Grant No.2025JC-YBQN-505)China Postdoctoral Science Foundation(Grant No.2024M752510).
文摘As space equipment become larger in size and more flexible,generalized mechanisms are being widely used in space-deployable structures.Dynamic modeling of large-scale generalized space-deployable mechanisms is challenging owing to the coupling between the deformation of flexible links and rigid body motion.This study develops a dynamic modeling method for generalized mechanisms using the local frame of the SE(3)Lie group.The model represents both rigid and flexible links within a unified Lie group setting.The expressions for the velocities of rigid links and deformation of flexible links are derived using the Lie algebra framework.The nonuniqueness of the degrees of freedom of generalized kinematic pairs is considered,and the velocity fields of kinematic pairs in different situations are expressed.The equations of motion are derived using Hamilton’s principle.Because the velocities are expressed in the local frame,the mass matrix in the equation is constant,which yields a compact and unified expression for the dynamic equation.A Lie group generalized-αtime integration method is adopted to ensure numerical stability and efficiency in simulating multibody systems with large rotations and deformations.Two numerical examples are studied to demonstrate a formulation that reflects the motion responses under varying configurations and loading conditions.This study broadens the application of the local frame of the Lie group formulation in space mechanisms and provides a new concept for dynamic modeling of generalized mechanisms.
基金supported by the National Natural Science Foundation of China(12171373)Chen's work also supported by the Fundamental Research Funds for the Central Universities of China(GK202207018).
文摘In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.
基金Projects(52008403,52378421)supported by the National Natural Science Foundation of ChinaProject(2022-Key-10)supported by the Science and Technology Research and Development Program Project of China Railway Group LimitedProject(202207)supported by the Hunan Provincial Transportation Science and Technology,China。
文摘The existing analytical models for umbrella arch method(UAM)based on elastic foundation beams often overlook the influence of the surrounding soil beyond the beam edges on the shear stresses acting on the beam.Consequently,such models fail to adequately reflect the continuity characteristics of soil deformation.Leveraging the Pasternak foundation-Euler beam model,this study considers the generalized shear force on the beam to account for the influence of soil outside the beam ends on the shear stress.An analytical model for the deformation and internal forces of finite-length beams subjected to arbitrary loads is derived based on the initial parameter method under various conditions.The mechanical model of the elastic foundation beam for advanced umbrella arch under typical tunnel excavation cycles is established,yielding analytical solutions for the longitudinal response of the umbrella arch.The reliability of the analytical model is verified with the existing test data.The improved model addresses anomalies in existing models,such as abnormal upward deformation in the loosened segment and maximum deflection occurring within the soil mass.Additionally,dimensionless characteristic parameters reflecting the relative stiffness between the umbrella arch structure and the foundation soil are proposed.Results indicate that the magnitude of soil characteristic parameters significantly influences the deformation and internal forces of the umbrella arch.Within common ranges of soil values,the maximum deformation and internal forces of the umbrella arch under semi-logarithmic coordinates exhibit nearly linear decay with decreasing soil characteristic parameters.The impact of tunnel excavation height on the stress of unsupported sections of the umbrella arch is minor,but it is more significant for umbrella arch buried within the soil mass.Conversely,the influence of tunnel excavation advance on the umbrella arch is opposite.
