Soil nonlinear behavior displays noticeable effects on the site seismic response.This study proposes a new functional expression of the skeleton curve to replace the hyperbolic skeleton curve.By integrating shear modu...Soil nonlinear behavior displays noticeable effects on the site seismic response.This study proposes a new functional expression of the skeleton curve to replace the hyperbolic skeleton curve.By integrating shear modulus and combining the dynamic skeleton curve and the damping degradation coefficient,the constitutive equation of the logarithmic dynamic skeleton can be obtained,which considers the damping effect in a soil dynamics problem.Based on the finite difference method and the multi-transmitting boundary condition,a 1D site seismic response analysis program called Soilresp1D has been developed herein and used to analyze the time-domain seismic response in three types of sites.At the same time,this study also provides numerical simulation results based on the hyperbolic constitutive model and the equivalent linear method.The results verify the rationality of the new soil dynamic constitutive model.It can analyze the mucky soil site nonlinear seismic response,reflecting the deformation characteristics and damping effect of the silty soil.The hysteresis loop area is more extensive,and the residual strain is evident.展开更多
Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation.Essentially,for quantum systems prepared in pure states,it is difficult to...Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation.Essentially,for quantum systems prepared in pure states,it is difficult to differentiate between quantum entanglement and quantum correlation.Nonetheless,this indistinguishability is no longer holds for mixed states.To contribute to a better understanding of this differentiation,we have explored a simple model for both generating and measuring these quantum correlations.Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities,coupled through the photon hopping process.this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes.The key ingredient in analyzing quantum correlation in this system is the global covariance matrix.It forms the basis for computing two essential metrics:the logarithmic negativity(E_(N)^(m))and the Gaussian interferometric power(P_(G)^(m)).These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations,respectively.Our study reveals that the Gaussian interferometric power(P_(G)^(m))proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system,particularly in scenarios featuring resilient photon hopping.展开更多
In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of nor...In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).展开更多
In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality...In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.展开更多
The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the ...The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.展开更多
This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utiliz...This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.展开更多
In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the glob...In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data.展开更多
In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the node degree and the average path length of China aviation network in 1988,1994,2001...In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the node degree and the average path length of China aviation network in 1988,1994,2001,2008 and 2015 was studied.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network.On the basis of the statistical data,the node average path length of China aviation network in 1988,1994,2001,2008 and 2015 was calculated.Through regression analysis,it was found that the node degree had a logarithmic relationship with the average length of node path,and the two parameters of the logarithmic relationship had linear evolutionary trace.Key word:China aviation network,complex network,node degree,average length of node path,logarithmic relationship,evolutionary trace.展开更多
This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the correspon...This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).展开更多
In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the average degree and the average path length of edge vertices of China aviation netwo...In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the average degree and the average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 was studied.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network.On the basis of the statistical data,the average degree and average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Through regression analysis,it was found that the average degree had a logarithmic relationship with the average path length of edge vertices and the two parameters of the logarithmic relationship had linear evolutionary trace.展开更多
The Palu MW7.4 earthquake occurred on September 28, 2018, with the epicenter at 119.86°, 0.72°. The severe shaking caused severe damage in Central Sulawesi, especially in Palu. We conducted a postseismic def...The Palu MW7.4 earthquake occurred on September 28, 2018, with the epicenter at 119.86°, 0.72°. The severe shaking caused severe damage in Central Sulawesi, especially in Palu. We conducted a postseismic deformation study to determine the deformation pattern and reduce future earthquakes’ impact.Interferometric Synthetic Aperture Radar(In SAR) data were processed using Li CSBAS to get the time series. The time series data were fitted to exponential and logarithmic functions to determine the mechanism of postseismic deformation. The exponential model identified the influence of the viscoelastic mechanism, and the logarithm identified the afterslip mechanism. The Palu earthquake was fitted to logarithmic and exponential, but the logarithmic was more significant than an exponential function.Afterslip mechanism predominates, and viscoelastic mechanisms play a minor role in this postseismic deformation.展开更多
An explicit form of the elastic strain-energy function for direction-dependent large elastic strain behaviors of soft fiber-reinforced composites is first presented based upon a decoupled approach for simulating compl...An explicit form of the elastic strain-energy function for direction-dependent large elastic strain behaviors of soft fiber-reinforced composites is first presented based upon a decoupled approach for simulating complex nonlinear coupling effects.From this form,the exact closed-form solutions are then obtained for the uniaxial tension responses in the fiber and cross-fiber directions.With such exact solutions,the issue of simultaneously simulating strongly coupling nonlinear responses in the fiber and cross-fiber directions may be reduced to the issue of separately treating each decoupled uniaxial stress-strain response,thus bypassing usual complexities and uncertainties involved in identifying a large number of strongly coupled adjustable parameters.The numerical examples given are in good agreement with the experimental data for large strain responses.展开更多
In this paper,we study a porous thermoelastic problem with microtemperatures assuming parabolic higher order in time derivatives for the thermal variables.The model is derived and written as a coupled linear system.Th...In this paper,we study a porous thermoelastic problem with microtemperatures assuming parabolic higher order in time derivatives for the thermal variables.The model is derived and written as a coupled linear system.Then,a uniqueness result is proved by using the logarithmic convexity method in the case that we do not assume that the mechanical energy is positive definite.Finally,the existence of the solution is obtained by introducing an energy function and applying the theory of linear semigroups.展开更多
For anyα∈R,the logarithmic Bloch space BLαconsists of those functions f which are analytic in the unit disk D with.■In this paper,we characterize the closure of the analytic functions of bounded mean oscillation B...For anyα∈R,the logarithmic Bloch space BLαconsists of those functions f which are analytic in the unit disk D with.■In this paper,we characterize the closure of the analytic functions of bounded mean oscillation BMOA in the logarithmic Bloch space BLαfor allα∈R.展开更多
The representative collective digital signature,which was suggested by us,is built based on combining the advantages of group digital signature and collective digital signature.This collective digital signature schema...The representative collective digital signature,which was suggested by us,is built based on combining the advantages of group digital signature and collective digital signature.This collective digital signature schema helps to create a unique digital signature that deputizes a collective of people representing different groups of signers and may also include personal signers.The advantage of the proposed collective signature is that it can be built based on most of the well-known difficult problems such as the factor analysis,the discrete logarithm and finding modulo roots of large prime numbers and the current digital signature standards of the United States and Russian Federation.In this paper,we use the discrete logarithmic problem on prime finite fields,which has been implemented in the GOST R34.10-1994 digital signature standard,to build the proposed collective signature protocols.These protocols help to create collective signatures:Guaranteed internal integrity and fixed size,independent of the number of members involved in forming the signature.The signature built in this study,consisting of 3 components(U,R,S),stores the information of all relevant signers in the U components,thus tracking the signer and against the“disclaim of liability”of the signer later is possible.The idea of hiding the signer’s public key is also applied in the proposed protocols.This makes it easy for the signing group representative to specify which members are authorized to participate in the signature creation process.展开更多
Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)an...Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)and the functional LIL for a linear additive functional of the form∫[0,R]u(t,x)dx and the nonlinear additive functionals of the form∫[0,R]g(u(t,x))dx,where g:R→R is nonrandom and Lipschitz continuous,as R→∞for fixed t>0,using the localization argument.展开更多
Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning thi...Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning this,the logarithmic hyperbolic cosine(lncosh)criterion with better robustness and convergence has drawn attention in recent studies.However,existing lncosh loss-based KAFs use the stochastic gradient descent(SGD)for optimization,which lack a trade-off between the convergence speed and accuracy.But recursion-based KAFs can provide more effective filtering performance.Therefore,a Nyström method-based robust sparse kernel recursive least lncosh loss algorithm is derived in this article.Experiments via measures and synthetic data against the non-Gaussian noise confirm the superiority with regard to the robustness,accuracy performance,and computational cost.展开更多
基金Major Program of the National Natural Science Foundation of China under Grant No.52192675 and the 111 Project of China under Grant No.D21001。
文摘Soil nonlinear behavior displays noticeable effects on the site seismic response.This study proposes a new functional expression of the skeleton curve to replace the hyperbolic skeleton curve.By integrating shear modulus and combining the dynamic skeleton curve and the damping degradation coefficient,the constitutive equation of the logarithmic dynamic skeleton can be obtained,which considers the damping effect in a soil dynamics problem.Based on the finite difference method and the multi-transmitting boundary condition,a 1D site seismic response analysis program called Soilresp1D has been developed herein and used to analyze the time-domain seismic response in three types of sites.At the same time,this study also provides numerical simulation results based on the hyperbolic constitutive model and the equivalent linear method.The results verify the rationality of the new soil dynamic constitutive model.It can analyze the mucky soil site nonlinear seismic response,reflecting the deformation characteristics and damping effect of the silty soil.The hysteresis loop area is more extensive,and the residual strain is evident.
文摘Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation.Essentially,for quantum systems prepared in pure states,it is difficult to differentiate between quantum entanglement and quantum correlation.Nonetheless,this indistinguishability is no longer holds for mixed states.To contribute to a better understanding of this differentiation,we have explored a simple model for both generating and measuring these quantum correlations.Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities,coupled through the photon hopping process.this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes.The key ingredient in analyzing quantum correlation in this system is the global covariance matrix.It forms the basis for computing two essential metrics:the logarithmic negativity(E_(N)^(m))and the Gaussian interferometric power(P_(G)^(m)).These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations,respectively.Our study reveals that the Gaussian interferometric power(P_(G)^(m))proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system,particularly in scenarios featuring resilient photon hopping.
文摘In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).
基金Supported by the NSFC(11771087,12171091 and 11831005)。
文摘In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.
基金Supported by the National Natural Science Foundation of China(11501342,12001344)。
文摘The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.
文摘This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.
文摘In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data.
文摘In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the node degree and the average path length of China aviation network in 1988,1994,2001,2008 and 2015 was studied.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network.On the basis of the statistical data,the node average path length of China aviation network in 1988,1994,2001,2008 and 2015 was calculated.Through regression analysis,it was found that the node degree had a logarithmic relationship with the average length of node path,and the two parameters of the logarithmic relationship had linear evolutionary trace.Key word:China aviation network,complex network,node degree,average length of node path,logarithmic relationship,evolutionary trace.
文摘This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).
文摘In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the average degree and the average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 was studied.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network.On the basis of the statistical data,the average degree and average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Through regression analysis,it was found that the average degree had a logarithmic relationship with the average path length of edge vertices and the two parameters of the logarithmic relationship had linear evolutionary trace.
基金partially supported by UGM’s Social Fund in the scheme of the RTA Project 2022
文摘The Palu MW7.4 earthquake occurred on September 28, 2018, with the epicenter at 119.86°, 0.72°. The severe shaking caused severe damage in Central Sulawesi, especially in Palu. We conducted a postseismic deformation study to determine the deformation pattern and reduce future earthquakes’ impact.Interferometric Synthetic Aperture Radar(In SAR) data were processed using Li CSBAS to get the time series. The time series data were fitted to exponential and logarithmic functions to determine the mechanism of postseismic deformation. The exponential model identified the influence of the viscoelastic mechanism, and the logarithm identified the afterslip mechanism. The Palu earthquake was fitted to logarithmic and exponential, but the logarithmic was more significant than an exponential function.Afterslip mechanism predominates, and viscoelastic mechanisms play a minor role in this postseismic deformation.
基金Project supported by the National Natural Science Foundation of China(Nos.12172151 and12172149)the Research Project of Introducing High-level Foreign Experts from the Ministry of Sicence and Technology of China(No.G20221990122)the Start-up Fund from Jinan University(Guangzhou)of China(No.88019062)。
文摘An explicit form of the elastic strain-energy function for direction-dependent large elastic strain behaviors of soft fiber-reinforced composites is first presented based upon a decoupled approach for simulating complex nonlinear coupling effects.From this form,the exact closed-form solutions are then obtained for the uniaxial tension responses in the fiber and cross-fiber directions.With such exact solutions,the issue of simultaneously simulating strongly coupling nonlinear responses in the fiber and cross-fiber directions may be reduced to the issue of separately treating each decoupled uniaxial stress-strain response,thus bypassing usual complexities and uncertainties involved in identifying a large number of strongly coupled adjustable parameters.The numerical examples given are in good agreement with the experimental data for large strain responses.
基金part of the project(No.PID2019-105118GB-I00),funded by the Spanish Ministry of Science,Innovation and Universities and FEDER“A way to make Europe”。
文摘In this paper,we study a porous thermoelastic problem with microtemperatures assuming parabolic higher order in time derivatives for the thermal variables.The model is derived and written as a coupled linear system.Then,a uniqueness result is proved by using the logarithmic convexity method in the case that we do not assume that the mechanical energy is positive definite.Finally,the existence of the solution is obtained by introducing an energy function and applying the theory of linear semigroups.
基金supported by the National Natural Science Foundation of China(11671357,11801508)。
文摘For anyα∈R,the logarithmic Bloch space BLαconsists of those functions f which are analytic in the unit disk D with.■In this paper,we characterize the closure of the analytic functions of bounded mean oscillation BMOA in the logarithmic Bloch space BLαfor allα∈R.
基金supported by Duy Tan University,Da Nang,Vietnam.
文摘The representative collective digital signature,which was suggested by us,is built based on combining the advantages of group digital signature and collective digital signature.This collective digital signature schema helps to create a unique digital signature that deputizes a collective of people representing different groups of signers and may also include personal signers.The advantage of the proposed collective signature is that it can be built based on most of the well-known difficult problems such as the factor analysis,the discrete logarithm and finding modulo roots of large prime numbers and the current digital signature standards of the United States and Russian Federation.In this paper,we use the discrete logarithmic problem on prime finite fields,which has been implemented in the GOST R34.10-1994 digital signature standard,to build the proposed collective signature protocols.These protocols help to create collective signatures:Guaranteed internal integrity and fixed size,independent of the number of members involved in forming the signature.The signature built in this study,consisting of 3 components(U,R,S),stores the information of all relevant signers in the U components,thus tracking the signer and against the“disclaim of liability”of the signer later is possible.The idea of hiding the signer’s public key is also applied in the proposed protocols.This makes it easy for the signing group representative to specify which members are authorized to participate in the signature creation process.
基金supported by the National Natural Science Foundation of China(11771178 and 12171198)the Science and Technology Development Program of Jilin Province(20210101467JC)+1 种基金the Science and Technology Program of Jilin Educational Department during the“13th Five-Year”Plan Period(JJKH20200951KJ)the Fundamental Research Funds for the Central Universities。
文摘Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)and the functional LIL for a linear additive functional of the form∫[0,R]u(t,x)dx and the nonlinear additive functionals of the form∫[0,R]g(u(t,x))dx,where g:R→R is nonrandom and Lipschitz continuous,as R→∞for fixed t>0,using the localization argument.
基金supported in part by the National Natural Science Foundation of China under Grants No.62027803,No.61601096,No.61971111,and No.61801089in part by the Science and Technology Program under Grants No.8091C24,No.2021JCJQJJ0949,and No.2022JCJQJJ0784in part by the Industrial Technology Development Program under Grant No.2020110C041.
文摘Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning this,the logarithmic hyperbolic cosine(lncosh)criterion with better robustness and convergence has drawn attention in recent studies.However,existing lncosh loss-based KAFs use the stochastic gradient descent(SGD)for optimization,which lack a trade-off between the convergence speed and accuracy.But recursion-based KAFs can provide more effective filtering performance.Therefore,a Nyström method-based robust sparse kernel recursive least lncosh loss algorithm is derived in this article.Experiments via measures and synthetic data against the non-Gaussian noise confirm the superiority with regard to the robustness,accuracy performance,and computational cost.