In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit ...In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.展开更多
Viral infections play a crucial role in marine biogeochemical cycles,by regulating bacterial mortality and mediating nutrient and carbon fluxes.However,despite of their ecological significance,existing climate change ...Viral infections play a crucial role in marine biogeochemical cycles,by regulating bacterial mortality and mediating nutrient and carbon fluxes.However,despite of their ecological significance,existing climate change models generally fail to incorporate virus-mediated ecological processes due to the current limited understanding of marine viral dynamics under global warming.While numerous studies have explored the effect of warming for viral decay and production,how temperature regulates the total abundance of marine viruses remains unclear.In this study,we conducted year-round measurements of viral production and decay rates in Qingdao's coastal waters,with additional experimental warming treatments.The result showed that under in-situ temperature,the viral decay and production rate displayed distinct seasonal variations.With the exception of summer,elevated temperature stimulated both viral decay rate and production rate,and further improved the net viral production rate.While in summer,the net viral production rate turned negative,implying divergent threshold viral decay and viral production rate on warming.Our study deepens the understanding of the effect of global warming on marine viruses and provides scientific data for climate change models.展开更多
A novel aperiodically intermittent impulse control(AIIC)method is proposed to investigate the exponential synchronization in mean square(ESMS)of a class of impulsive stochastic infinite-dimensional systems with Poisso...A novel aperiodically intermittent impulse control(AIIC)method is proposed to investigate the exponential synchronization in mean square(ESMS)of a class of impulsive stochastic infinite-dimensional systems with Poisson jumps(ISIDSP).The AIIC control strategy inherits the flexibility of aperiodically intermittent control,including the variable control period,adjustable control interval length,and the discretization of impulsive control.In addition,this article introduces a novel mild Itô's formula.By leveraging semigroup theory,the contraction mapping principle,and graph theory,along with constructing the Lyapunov function,the criterion for the existence and uniqueness of a mild solution of ISIDSP is thereby established.Furthermore,the mean-square exponential synchronization problem of the above systems is resolved,and the constraints within the mild solution domain are alleviated.These criteria clarify the impact of control parameters,control intervals and network topology on ESMS.The theoretical results are subsequently applied to a class of neural networks with reaction-diffusion processes,and the validity of the results is verified using numerical simulations.展开更多
A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance con...A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance condition.We obtain the well-posedness using nonlinear semigroup theory arguments.Moreover,the exponential stability result of the solution is shown by using the energy method to produce a suitable Lyapunov function.展开更多
Making full use of the operator ordering method and the integration within ordered products,we obtain the analytical evolution law of a general quadratic state in the amplitude decay channel,and find that it is determ...Making full use of the operator ordering method and the integration within ordered products,we obtain the analytical evolution law of a general quadratic state in the amplitude decay channel,and find that it is determined not only by the decay rate of the amplitude decay channel but also by the coefficients of the initial quadratic state.Further,the quantum statistical properties of the initial quadratic state for amplitude decay are investigated via its average photon number and photon-counting distribution,and its Wigner distribution function evolution is discussed in detail.展开更多
The damage evolution of polycrystalline Al with helium(He)bubbles under strongly decaying shock waves is studied by molecular dynamics simulations.A new damage region is observed near the loading side of the sample,an...The damage evolution of polycrystalline Al with helium(He)bubbles under strongly decaying shock waves is studied by molecular dynamics simulations.A new damage region is observed near the loading side of the sample,and the evolution characteristics and underlying mechanisms are elucidated.The development of damage in the new damage region begins after complete unloading of the incident shock wave and is further enhanced when the tensile stress arrives later.The damage evolution is completely controlled by the expansion-merging of He bubbles,without nucleation–growth of voids.This new damage region can be divided into two sections,each of which exhibits a unique dominant mechanism.The damage in the section closer to the loading side is due to the reverse velocity gradient formed after complete unloading of the incident shock wave,depending on the rate of decrease and the amplitude of the initial peak pressure.A high initial peak pressure that can lead to melting of material near the loading side is a necessary condition for the formation of the new damage region,since a significant reverse velocity gradient can only be established if melting occurs.The dominant mechanism in the section distant from the loading side is the action of tensile stress,associated with the profile of the incident shock wave upon reaching the free surface,which determines the material phase near the free surface.Moreover,the presence of He bubbles is another critical factor for formation of the new damage region,which does not occur in pure Al samples.展开更多
In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potentia...In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0） 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0） 〈 0.展开更多
To investigate decay law of acoustic emission and microseismic activities caused by disturbances associated with multilevel loading and mining blast,a new exponential decay(ED)law was proposed.The results show that th...To investigate decay law of acoustic emission and microseismic activities caused by disturbances associated with multilevel loading and mining blast,a new exponential decay(ED)law was proposed.The results show that the micro-fracture activity decay law after multistage stress loading and blasting disturbance conforms to the ED model,in which the sum of A and n represents the number of initial micro-fracture events,and n represents the level of background micro-fracture events.The ED model can describe the number of initial micro-fracture events with a deviation less than 10%.The ED model outperforms the traditional aftershock models in describing the micro-fracture event decay law in the three cases considered.The ED model can provide a reference for selecting the blasting interval in mines,which is of great significance to maintain the stability of the surrounding rock and ensure safe production in metal mines.展开更多
The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, fo...The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.展开更多
The rigid-plastic assumption has greatly simplified the theoretical analysis of dynamic plastic response of structures.Within this framework,a common tool is the modal technique using approximate independent yield cri...The rigid-plastic assumption has greatly simplified the theoretical analysis of dynamic plastic response of structures.Within this framework,a common tool is the modal technique using approximate independent yield criteria,which leads to upper-and lower-bound solutions,but usually with poor accuracy.In this paper,by utilizing the membrane factor method(MFM),the large-deflection dynamic plastic response of square plates subjected to exponentially decaying pulse loading is analyzed by taking both the transient response phase and the exact yield criterion into account.Based on the combination of saturation analysis(SA)and MFM,the complete solutions and regressive formulae of saturated deflection and saturated impulse are obtained.As the dynamic behavior of plates under rectangular pulse loading serves as a benchmark of pulse-equivalent techniques,the large plastic deformation of square plates under short-duration rectangular pulse is also analyzed in detail.Moreover,by comparing the SA results of pulse-loaded square plates with different boundary conditions,it is found that the saturated deflection and saturated impulse of the fully clamped and simply supported square plates both increase linearly with the pulse amplitude,and the slopes are approximately the same,so the conversion between the SA quantities of plates with different boundary conditions can be easily achieved.展开更多
We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably sm...We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably small.Note that although the system degenerates near vacuum,there is no need to require compatibility conditions for the initial data via time-weighted techniques.展开更多
Continuous response of range query on steaming data provides useful information for many practical applications as well as the risk of privacy disclosure.The existing research on differential privacy streaming data pu...Continuous response of range query on steaming data provides useful information for many practical applications as well as the risk of privacy disclosure.The existing research on differential privacy streaming data publication mostly pay close attention to boosting query accuracy,but pay less attention to query efficiency,and ignore the effect of timeliness on data weight.In this paper,we propose an effective algorithm of differential privacy streaming data publication under exponential decay mode.Firstly,by introducing the Fenwick tree to divide and reorganize data items in the stream,we achieve a constant time complexity for inserting a new item and getting the prefix sum.Meanwhile,we achieve time complicity linear to the number of data item for building a tree.After that,we use the advantage of matrix mechanism to deal with relevant queries and reduce the global sensitivity.In addition,we choose proper diagonal matrix further improve the range query accuracy.Finally,considering about exponential decay,every data item is weighted by the decay factor.By putting the Fenwick tree and matrix optimization together,we present complete algorithm for differentiate private real-time streaming data publication.The experiment is designed to compare the algorithm in this paper with similar algorithms for streaming data release in exponential decay.Experimental results show that the algorithm in this paper effectively improve the query efficiency while ensuring the quality of the query.展开更多
This paper deals with the initial boundary value problem for a class of nonlinear Kirchhoff-type equations with strong dissipative and source terms in a bounded domain, where and are constants. We obtain the global ex...This paper deals with the initial boundary value problem for a class of nonlinear Kirchhoff-type equations with strong dissipative and source terms in a bounded domain, where and are constants. We obtain the global existence of solutions by constructing a stable set in and show the energy exponential decay estimate by applying a lemma of V. Komornik.展开更多
A study on the potential response of exponentially decaying polarizing current of electrode was car- ried out.The appearance of critical point of the potential-time response of exponentially decaying current was ensur...A study on the potential response of exponentially decaying polarizing current of electrode was car- ried out.The appearance of critical point of the potential-time response of exponentially decaying current was ensured from theoretical analysis,and this is the theoretical foundation of the critical point method for the measurement of corrosion current of metals.The comparison of the corrosion currents measured by the critical point and static methods for the system of 321 stainless steel in 0.5N HCI+0.5N NaCI solution at static state shows that the results agree very well.Finally.the tran- sient corrosion currents of 321 stainless steel in 0.5N HCI+0.5N NaCl solution at different strain level are listed.展开更多
In this paper,we study the initial-boundary value problem for the semilinear parabolic equations ut-△Xu=|u|p-1u,where X=(X1,X2,…,Xm)is a system of real smooth vector fields which satisfy the H?rmander’s condition,...In this paper,we study the initial-boundary value problem for the semilinear parabolic equations ut-△Xu=|u|p-1u,where X=(X1,X2,…,Xm)is a system of real smooth vector fields which satisfy the H?rmander’s condition,and△X=∑j=1m Xj2 is a finitely degenerate elliptic operator.Using potential well method,we first prove the invariance of some sets and vacuum isolating of solutions.Finally,by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy,and also we discuss the asymptotic behavior of the global solutions.展开更多
The problem facing by physicians is the fact that for most drugs there is a minimum concentration below which the drug is ineffective, and a maximum concentration above which the drug is dangerous. Thus, this paper di...The problem facing by physicians is the fact that for most drugs there is a minimum concentration below which the drug is ineffective, and a maximum concentration above which the drug is dangerous. Thus, this paper discusses the effective medicine dosage and its concentration in bloodstream of a patient. For analysis of dose concentration and mathematical mo- delling of minimum and maximum concentration of a drug administered intravenously, the EDM (Exponential Decay Model) and GSF (Geometric Series and its Formula) are the powerful mathematical tools. In the present research study, these two mathematical tools were used to predict the dose concentration of a drug in bloodstream of a patient.展开更多
Blue photoluminescence is observed in aged porous silicon samples anodized under Ar^(+)488 nm laser illumination.No samples have been undergone any heating treatment process.Both nanosecond and microsecond decay of bl...Blue photoluminescence is observed in aged porous silicon samples anodized under Ar^(+)488 nm laser illumination.No samples have been undergone any heating treatment process.Both nanosecond and microsecond decay of blue photoluminescence have been measured.Samples show a good monoexponential microsecond decay with lifetimes of about 5.3μs.Photoluminescence excitation spectra of blue and red Photoluminescence indicate there is a large Stokes shift(about 800-900meV)in the excitation spectra of red photoluminescence while no this marked Stokes shift in that of blue photoluminescence.The possible origin of the photoluminescence is discussed based on the experimental results.展开更多
The departure at large times from exponential decay in the case of resonance wavefunctions is mathematically demonstrated. Then, exact, analytical solutions to the time-dependent Schr?dinger equation in one dimension ...The departure at large times from exponential decay in the case of resonance wavefunctions is mathematically demonstrated. Then, exact, analytical solutions to the time-dependent Schr?dinger equation in one dimension are developed for a time-independent potential consisting of an infinite wall and a repulsive delta function. The exact solutions are obtained by means of a superposition of time-independent solutions spanning the given Hilbert space with appropriately chosen spectral functions for which the resulting integrals can be evaluated exactly. Square-integrability and the boundary conditions are satisfied. The simplest of the obtained solutions is presented and the probability for the particle to be found inside the potential well as a function of time is calculated. The system exhibits non-exponential decay for all times;the probability decreases at large times as . Other exact solutions found exhibit power law behavior at large times. The results are generalized to all normalizable solutions to this problem. Additionally, numerical solutions are obtained using the staggered leap-frog algorithm for select potentials exhibiting the prevalence of non-exponential decay at short times.展开更多
Of concern is a viscoelastic beam modelled using the Timoshenko theory. It is well-kimwn that the system is exponentially stable if the kernel in the memory term is sub- exponential. That is, if the product of the ker...Of concern is a viscoelastic beam modelled using the Timoshenko theory. It is well-kimwn that the system is exponentially stable if the kernel in the memory term is sub- exponential. That is, if the product of the kernel with an exponential function is a summable function. In this article we address the questions： What if the kernel is tested against a different function （say Gamma） other than the exponential function？ Would there still be stability？ In the affirmative, what kind of decay rate we get？ It is proved that for a non- decreasing function ＂Gamma＂ whose ＂logarithmic derivative＂ is decreasing to zero we have a decay of order Gamma to some power and in the case it decreases to a different value than zero then the decay is exponential.展开更多
In this work,a Timoshenko system of type Ⅲ of thermoelasticity with frictional versus viscoelastic under Dirichlet-Dirichlet-Neumann boundary conditions was considered.By exploiting energy method to produce a suitabl...In this work,a Timoshenko system of type Ⅲ of thermoelasticity with frictional versus viscoelastic under Dirichlet-Dirichlet-Neumann boundary conditions was considered.By exploiting energy method to produce a suitable Lyapunov functional,we establish the global existence and exponential decay of type-Ⅲ case.展开更多
基金Supported by the Natural Science Foundation of China(12571122,12061010)。
文摘In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.
基金supported by the National Natural Science Foundation of China(No.42276108)the Young Scientists Fund of Shandong Provincial Natural Science Foundation(No.ZR2022QD052)。
文摘Viral infections play a crucial role in marine biogeochemical cycles,by regulating bacterial mortality and mediating nutrient and carbon fluxes.However,despite of their ecological significance,existing climate change models generally fail to incorporate virus-mediated ecological processes due to the current limited understanding of marine viral dynamics under global warming.While numerous studies have explored the effect of warming for viral decay and production,how temperature regulates the total abundance of marine viruses remains unclear.In this study,we conducted year-round measurements of viral production and decay rates in Qingdao's coastal waters,with additional experimental warming treatments.The result showed that under in-situ temperature,the viral decay and production rate displayed distinct seasonal variations.With the exception of summer,elevated temperature stimulated both viral decay rate and production rate,and further improved the net viral production rate.While in summer,the net viral production rate turned negative,implying divergent threshold viral decay and viral production rate on warming.Our study deepens the understanding of the effect of global warming on marine viruses and provides scientific data for climate change models.
基金supported in part by the National Natural Science Foundation of China(12471422,62573274,12371173)the Natural Science Foundation of Shandong Province of China(ZR2022LLZ003,ZR2024MF001)the Funding for Visiting Studies and Research by Teachers in Ordinary Undergraduate Colleges and Universities in Shandong Province。
文摘A novel aperiodically intermittent impulse control(AIIC)method is proposed to investigate the exponential synchronization in mean square(ESMS)of a class of impulsive stochastic infinite-dimensional systems with Poisson jumps(ISIDSP).The AIIC control strategy inherits the flexibility of aperiodically intermittent control,including the variable control period,adjustable control interval length,and the discretization of impulsive control.In addition,this article introduces a novel mild Itô's formula.By leveraging semigroup theory,the contraction mapping principle,and graph theory,along with constructing the Lyapunov function,the criterion for the existence and uniqueness of a mild solution of ISIDSP is thereby established.Furthermore,the mean-square exponential synchronization problem of the above systems is resolved,and the constraints within the mild solution domain are alleviated.These criteria clarify the impact of control parameters,control intervals and network topology on ESMS.The theoretical results are subsequently applied to a class of neural networks with reaction-diffusion processes,and the validity of the results is verified using numerical simulations.
文摘A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance condition.We obtain the well-posedness using nonlinear semigroup theory arguments.Moreover,the exponential stability result of the solution is shown by using the energy method to produce a suitable Lyapunov function.
文摘Making full use of the operator ordering method and the integration within ordered products,we obtain the analytical evolution law of a general quadratic state in the amplitude decay channel,and find that it is determined not only by the decay rate of the amplitude decay channel but also by the coefficients of the initial quadratic state.Further,the quantum statistical properties of the initial quadratic state for amplitude decay are investigated via its average photon number and photon-counting distribution,and its Wigner distribution function evolution is discussed in detail.
基金supported by the National Natural Science Foundation of China(Grant No.12172063).
文摘The damage evolution of polycrystalline Al with helium(He)bubbles under strongly decaying shock waves is studied by molecular dynamics simulations.A new damage region is observed near the loading side of the sample,and the evolution characteristics and underlying mechanisms are elucidated.The development of damage in the new damage region begins after complete unloading of the incident shock wave and is further enhanced when the tensile stress arrives later.The damage evolution is completely controlled by the expansion-merging of He bubbles,without nucleation–growth of voids.This new damage region can be divided into two sections,each of which exhibits a unique dominant mechanism.The damage in the section closer to the loading side is due to the reverse velocity gradient formed after complete unloading of the incident shock wave,depending on the rate of decrease and the amplitude of the initial peak pressure.A high initial peak pressure that can lead to melting of material near the loading side is a necessary condition for the formation of the new damage region,since a significant reverse velocity gradient can only be established if melting occurs.The dominant mechanism in the section distant from the loading side is the action of tensile stress,associated with the profile of the incident shock wave upon reaching the free surface,which determines the material phase near the free surface.Moreover,the presence of He bubbles is another critical factor for formation of the new damage region,which does not occur in pure Al samples.
文摘In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0） 〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0） 〈 0.
基金financial supports from the National Natural Science Foundation of China(Nos.51704056,51974059)the China Postdoctoral Science Foundation(No.2017M621152)the Fundamental Research Funds for the Central University of China(Nos.N160103006,N180115010,N2001001)。
文摘To investigate decay law of acoustic emission and microseismic activities caused by disturbances associated with multilevel loading and mining blast,a new exponential decay(ED)law was proposed.The results show that the micro-fracture activity decay law after multistage stress loading and blasting disturbance conforms to the ED model,in which the sum of A and n represents the number of initial micro-fracture events,and n represents the level of background micro-fracture events.The ED model can describe the number of initial micro-fracture events with a deviation less than 10%.The ED model outperforms the traditional aftershock models in describing the micro-fracture event decay law in the three cases considered.The ED model can provide a reference for selecting the blasting interval in mines,which is of great significance to maintain the stability of the surrounding rock and ensure safe production in metal mines.
文摘The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.
基金the support of the Wuhan University of Technology start-up fund for Distinguished Professors(No.471-40120163)the China Scholarship Council(CSC).
文摘The rigid-plastic assumption has greatly simplified the theoretical analysis of dynamic plastic response of structures.Within this framework,a common tool is the modal technique using approximate independent yield criteria,which leads to upper-and lower-bound solutions,but usually with poor accuracy.In this paper,by utilizing the membrane factor method(MFM),the large-deflection dynamic plastic response of square plates subjected to exponentially decaying pulse loading is analyzed by taking both the transient response phase and the exact yield criterion into account.Based on the combination of saturation analysis(SA)and MFM,the complete solutions and regressive formulae of saturated deflection and saturated impulse are obtained.As the dynamic behavior of plates under rectangular pulse loading serves as a benchmark of pulse-equivalent techniques,the large plastic deformation of square plates under short-duration rectangular pulse is also analyzed in detail.Moreover,by comparing the SA results of pulse-loaded square plates with different boundary conditions,it is found that the saturated deflection and saturated impulse of the fully clamped and simply supported square plates both increase linearly with the pulse amplitude,and the slopes are approximately the same,so the conversion between the SA quantities of plates with different boundary conditions can be easily achieved.
基金supported by National Natural Science Foundation of China(11701193,11671086)Natural Science Foundation of Fujian Province(2018J05005,2017J01562)+3 种基金Program for Innovative Research Team in Science and Technology in Fujian Province University Quanzhou High-Level Talents Support Plan(2017ZT012)supported by National Natural Science Foundation of China(11901474)the Chongqing Talent Plan for Young Topnotch Talents(CQYC202005074)the Innovation Support Program for Chongqing Overseas Returnees(cx2020082).
文摘We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably small.Note that although the system degenerates near vacuum,there is no need to require compatibility conditions for the initial data via time-weighted techniques.
基金This work is supported,in part,by the National Natural Science Foundation of China under grant numbers 61300026in part,by the Natural Science Foundation of Fujian Province under grant numbers 2017J01754, 2018J01797.
文摘Continuous response of range query on steaming data provides useful information for many practical applications as well as the risk of privacy disclosure.The existing research on differential privacy streaming data publication mostly pay close attention to boosting query accuracy,but pay less attention to query efficiency,and ignore the effect of timeliness on data weight.In this paper,we propose an effective algorithm of differential privacy streaming data publication under exponential decay mode.Firstly,by introducing the Fenwick tree to divide and reorganize data items in the stream,we achieve a constant time complexity for inserting a new item and getting the prefix sum.Meanwhile,we achieve time complicity linear to the number of data item for building a tree.After that,we use the advantage of matrix mechanism to deal with relevant queries and reduce the global sensitivity.In addition,we choose proper diagonal matrix further improve the range query accuracy.Finally,considering about exponential decay,every data item is weighted by the decay factor.By putting the Fenwick tree and matrix optimization together,we present complete algorithm for differentiate private real-time streaming data publication.The experiment is designed to compare the algorithm in this paper with similar algorithms for streaming data release in exponential decay.Experimental results show that the algorithm in this paper effectively improve the query efficiency while ensuring the quality of the query.
文摘This paper deals with the initial boundary value problem for a class of nonlinear Kirchhoff-type equations with strong dissipative and source terms in a bounded domain, where and are constants. We obtain the global existence of solutions by constructing a stable set in and show the energy exponential decay estimate by applying a lemma of V. Komornik.
文摘A study on the potential response of exponentially decaying polarizing current of electrode was car- ried out.The appearance of critical point of the potential-time response of exponentially decaying current was ensured from theoretical analysis,and this is the theoretical foundation of the critical point method for the measurement of corrosion current of metals.The comparison of the corrosion currents measured by the critical point and static methods for the system of 321 stainless steel in 0.5N HCI+0.5N NaCI solution at static state shows that the results agree very well.Finally.the tran- sient corrosion currents of 321 stainless steel in 0.5N HCI+0.5N NaCl solution at different strain level are listed.
基金supported by National Natural Science Foundation of China(11631011 and 11626251)
文摘In this paper,we study the initial-boundary value problem for the semilinear parabolic equations ut-△Xu=|u|p-1u,where X=(X1,X2,…,Xm)is a system of real smooth vector fields which satisfy the H?rmander’s condition,and△X=∑j=1m Xj2 is a finitely degenerate elliptic operator.Using potential well method,we first prove the invariance of some sets and vacuum isolating of solutions.Finally,by the Galerkin method and the concavity method we show the global existence and blow-up in finite time of solutions with low initial energy or critical initial energy,and also we discuss the asymptotic behavior of the global solutions.
文摘The problem facing by physicians is the fact that for most drugs there is a minimum concentration below which the drug is ineffective, and a maximum concentration above which the drug is dangerous. Thus, this paper discusses the effective medicine dosage and its concentration in bloodstream of a patient. For analysis of dose concentration and mathematical mo- delling of minimum and maximum concentration of a drug administered intravenously, the EDM (Exponential Decay Model) and GSF (Geometric Series and its Formula) are the powerful mathematical tools. In the present research study, these two mathematical tools were used to predict the dose concentration of a drug in bloodstream of a patient.
基金Supported by the National Natural Science Foundation of China under Grant No.59372108the Laboratory of Excited State Processes,Changchun Institute of Physics,Chinese Academy of Sciences。
文摘Blue photoluminescence is observed in aged porous silicon samples anodized under Ar^(+)488 nm laser illumination.No samples have been undergone any heating treatment process.Both nanosecond and microsecond decay of blue photoluminescence have been measured.Samples show a good monoexponential microsecond decay with lifetimes of about 5.3μs.Photoluminescence excitation spectra of blue and red Photoluminescence indicate there is a large Stokes shift(about 800-900meV)in the excitation spectra of red photoluminescence while no this marked Stokes shift in that of blue photoluminescence.The possible origin of the photoluminescence is discussed based on the experimental results.
文摘The departure at large times from exponential decay in the case of resonance wavefunctions is mathematically demonstrated. Then, exact, analytical solutions to the time-dependent Schr?dinger equation in one dimension are developed for a time-independent potential consisting of an infinite wall and a repulsive delta function. The exact solutions are obtained by means of a superposition of time-independent solutions spanning the given Hilbert space with appropriately chosen spectral functions for which the resulting integrals can be evaluated exactly. Square-integrability and the boundary conditions are satisfied. The simplest of the obtained solutions is presented and the probability for the particle to be found inside the potential well as a function of time is calculated. The system exhibits non-exponential decay for all times;the probability decreases at large times as . Other exact solutions found exhibit power law behavior at large times. The results are generalized to all normalizable solutions to this problem. Additionally, numerical solutions are obtained using the staggered leap-frog algorithm for select potentials exhibiting the prevalence of non-exponential decay at short times.
基金the financial support and the facilities provided by King Fahd University of Petroleum and Minerals through project No. IN111034
文摘Of concern is a viscoelastic beam modelled using the Timoshenko theory. It is well-kimwn that the system is exponentially stable if the kernel in the memory term is sub- exponential. That is, if the product of the kernel with an exponential function is a summable function. In this article we address the questions： What if the kernel is tested against a different function （say Gamma） other than the exponential function？ Would there still be stability？ In the affirmative, what kind of decay rate we get？ It is proved that for a non- decreasing function ＂Gamma＂ whose ＂logarithmic derivative＂ is decreasing to zero we have a decay of order Gamma to some power and in the case it decreases to a different value than zero then the decay is exponential.
基金Supported by the NNSF of China with contract numbers 11671075
文摘In this work,a Timoshenko system of type Ⅲ of thermoelasticity with frictional versus viscoelastic under Dirichlet-Dirichlet-Neumann boundary conditions was considered.By exploiting energy method to produce a suitable Lyapunov functional,we establish the global existence and exponential decay of type-Ⅲ case.
